The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Humans harbor a complex gut microbiota whose composition varies between different regions in the gastrointestinal (GI) tract (Zoetendal et al., 2012). It has been reported that the number of uncultured species in the gut microbiota reached 1952 (Almeida et al., 2019). Physiological changes in different areas of the small intestine and colon, including chemical and nutritional gradients and isolated host immune activity, are thought to affect the composition of bacterial communities (Donaldson et al., 2016). The gut microbiota plays a critical role in the human internal environment. It evolves with the host and performs essential physiological functions for the host, such as preventing infection from various pathogens; promoting the maturation of the immune system; participating in the regulation of the immune response, nutritional absorption and metabolism; and promoting anti-cancer functions (Foster et al., 2017; Kim et al., 2017; Macpherson et al., 2017; Li et al., 2019). The colonization of newborn microbiota begins in utero (Dunn et al., 2017). Both the delivery mode and the cessation of breastfeeding are considered to be essential for adult-like gut microbiota assembly. The microbial composition changes abruptly during the 1st year of life (La Rosa et al., 2014; Bäckhed et al., 2015).

Magnification =  Distance to Object (mm) Focal Length (mm) =  Real Object height (mm) Object height on sensor (mm) This is magnification on the sensor or film. The image must still be enlarged for viewing.1:1 macro reproduction at 1× is when these two top and bottom values are equal.Distant object size is reduced greatly, like perhaps maybe magnification of 0.001x or less.

Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Mucosal biopsy only covers a small surface area and may result in sampling deviation and inaccessibility of rare taxa if the microbial population distributes unevenly. Mucosal biopsy often contains a large amount of contaminated host DNA, which complicates metagenomic and other molecular analyses (Huse et al., 2014).

This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

FOV to focal length calculator

* feet or meters (but both same units) There are Other possible arrangements. But this next one must use Field dimension and Height converted to mm (304.8 mm per foot), because each ratio must be a dimensionless number. Magnification =  Distance to Object (mm) Focal Length (mm) =  Real Object height (mm) Object height on sensor (mm) This is magnification on the sensor or film. The image must still be enlarged for viewing.1:1 macro reproduction at 1× is when these two top and bottom values are equal.Distant object size is reduced greatly, like perhaps maybe magnification of 0.001x or less.

The lower GI tract of mammals contains diverse microbial habitats along the small intestine, cecum, and colon. Endoscopic biopsy provides a way to investigate mucosal microbiota composition in different anatomical sites of the GI tract. The mucosal microbiota is thought to be important to the host because they are in contact with intestinal-related lymphoid tissue (Heinsen et al., 2015).

Our present work focuses on the collection of intestinal fluid samples by minorly invasive methods. We also investigated an inexpensive and convenient capsule device, Intestine Microbiome Aspiration (IMBA), which aims to collect intestinal fluid samples autonomously. Without using expensive microelectromechanical system technologies, IMBA utilizes controlled-release technology equipped with a novel sampling mechanism to achieve precise and regional sampling in the intestine. Moreover, the form of capsules improves patient compliance, and sampling conditions closer to the physiological state (no need for bowel preparation) provide higher accuracy. The key of this technology is how to accurately locate and collect intestinal fluid.

The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

There is a Field of View Calculator here, but this page is about the math. There are approximations in calculations. The math is precise, but the data is less so. The required Focal length and Sensor Size are rounded specifications, losing a bit of precision. This little difference at the small sensor gets magnified in the field and scene. However, the results certainly are close enough to be very useful in any practical case. My experience is that the field is fairly accurate (at distances of at least a meter or so), assuming you actually know your parameters. Some problems are: You absolutely must know the actual correct sensor size in mm. Or the FOV calculator here can make a reasonable approximation of sensor size from the accurate Crop Factor. If not accurate, the field of view calculation will not be accurate. If you're guessing, your results will likely be troubled. Please see this summary of Issues determining Sensor Size which might help. You must know the actual correct lens focal length in mm. Zoom lens focal length is different at each and every zoom position. The image EXIF data may show focal length (but it is rounded in some degree). And of course just guessing about the field distance may be an approximation, or may not be at all accurate. Field of View calculators do NOT work for macro distances. Macro uses reproduction ration, like 1:1. Thin Lens Equation The Marked focal length of any lens is a rounded nominal number, like 50 or 60 mm. The actual can be a few percent different. Furthermore, the Marked focal length is only applicable to focus at infinity. Focal length normally increases when lens is extended forward to focus closer. Lens specs normally indicate this internal extension at closest focus distance. But internal focusing lenses can do internal tricks with focal length (some zooms and macro lenses can be shorter when up close, instead of longer). But generally speaking, focal length becomes a little longer at very close distances (2x longer at 1:1), so field of view could be a little smaller, but should be insignificant as long as magnification is greater than 0.1x, which in regular lenses is normally near their Minimum focus distance. But this calculation does not include macro distances. We are only seeking a ballpark FOV number anyway, we adjust small differences with our subject framing or cropping, but vague guesses about your distance and sensor size or focal length don't help FOV accuracy. And a fisheye lens is a different animal, wider view than this formula predicts. A regular lens is rectilinear, meaning it shows straight lines as straight lines, not curved. A fisheye is rather unconcerned about this distortion, and can show a wider view, poorly purists might say, but very wide, and very possibly interesting. Focal Length varies with zoom, and the Exif data with the image should report focal length (in coarse zoom steps, as best it can). Actual focal length could be determined by the Magnification (Wikipedia) and distance. The distance from the front nodal point to the object in the subject plane (s1), and the distance from the rear nodal point to the image plane (s2) (when focused) are related by this Thin Lens equation (Wikipedia), which the diagram and formulas below simplify. If OK with a little geometry and algebra, you can see the derivation of this classic Thin Lens Equation at the Khan Academy. In this equation, we can see that if the subject at s1 is at infinity, then 1/s1 is zero, so then s2 = f. This is the marked focal length that applies when focused at infinity. What camera lenses call the focused distance is s = s1 + s2, from subject to the sensor plane. Also if at 1:1 magnification (equal image size on both sides of lens), then s1 = s2, saying that the working macro distance in front of the lens node (extended at 1:1) is equal to the distance to the sensor image plane (both sides at 2x focal length). This makes f/stop number be 2x, which is 2 EV light loss. Those are basics. Internal focusing macro lenses can slightly reduce this light loss, but it is still near 2 EV. The Math Sensor dimension / 2focal length  =  Field dimension / 2distance This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

Funding. This study was supported by the grants (81570478, 81741075) from the National Natural Science Foundation of China and the grant (17JCYBJC24900) from Natural Science Foundation of Tianjin, and the grant (2019M651049) from Postdoctoral Science Foundation of China.

Official websites use .gov A .gov website belongs to an official government organization in the United States.

Despite considerable efforts by researchers to obtain accurate samples, the shortcomings of current sampling methods are bound to be insurmountable. It will be difficult to obtain accurate results from inaccurate samples. Feces have become the sample source of most bacterial flora studies because of their convenience and non-invasive nature, but even the microbiota content in the lower digestive tract, which is closest to feces, is significantly different from that of feces (Zmora et al., 2018). Most of the remaining sampling methods are invasive and not suitable for healthy people. Issues to be solved in future sampling methods should include reducing invasiveness, non-cross-contamination sampling at fixed points and minimizing disturbance to normal intestinal physiology.

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The Thin Lens Equations use the distance d in front of the lens node, but the lens specifications are "focused distance" (marked s in the diagram) which is to the sensor plane. Working Distance = d = S1 (distance in front of lens) Focal Length = f = S2 (distance behind lens) Focus Distance = d + f (subject distance to the sensor plane) The Thin Lens Model simplifies, and is practical and adequate for most computing, even if this model has one glass element and one central node point. Camera lenses have multiple glass elements, and are "thick lenses", much more complex, and have two node points, often called H for the field view side node, and H' for the sensor view side node. These two nodes might be designed a few inches apart, but they necessarily still see the same angle. The actual node position normally only matters to us for close macro distances, or perhaps in efforts to correct panoramic parallax. Sensor focal plane marking ϴ This front node is often a point inside the lens, perhaps crudely assumed about the middle of the lens (but it does move with zoom), but it is small and can often be ignored. Lens specifications normally instead measure field focus distance from the sensor, so you could subtract a few inches from your subject distance (to be at that node) to compute Field of View, but normally this is not significant except at extremely close focus and macro distances. It is more significant for macro distances. Example, the Nikon 105mm f/2.8 VR macro lens has specification "Minimum focus distance: 31.4 cm (1.03 feet), which is measured to the sensor plane at rear of the camera top. There's a small measuring symbol on top of the camera there, an O with a line through it (shown on this Nikon DSLR, or is often on the side of the pentaprism dome) to mark the sensor focal plane location. But at 1:1, a reliable chart of macro lens working distances says that 105 mm lens has a Working Distance (in front of lens) at 1:1, which is significantly less, 14.8 cm (5.8 inches), which differs by 16.6 mm due to the length of the lens and thickness of the camera body. SO NOTE: the terms Focal Length and lens focus distance are measured to the sensor plane, to that mark just mentioned. But Field of View and Depth of Field are computed to a node inside or near the lens. However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Sensor dimension / 2focal length  =  Field dimension / 2distance This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

by J Skrzypecki · 2023 · Cited by 1 — Spherical aberration is an imperfection of the optical system of the human eye. The role of spherical aberration of the human eye in the quality of vision ...

This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

Object height on sensor (mm)Focal length (mm)  =   Real Object size *Distance to Object * Rearrange this ratio to compute desired unknown value. Examples: Distance to Object *  =   Real Object height * × Focal Length (mm) Object height on sensor (mm) Real Object height *  =   Distance to Object * × Object height on sensor (mm) Focal Length (mm) * feet or meters (but both same units) There are Other possible arrangements. But this next one must use Field dimension and Height converted to mm (304.8 mm per foot), because each ratio must be a dimensionless number. Magnification =  Distance to Object (mm) Focal Length (mm) =  Real Object height (mm) Object height on sensor (mm) This is magnification on the sensor or film. The image must still be enlarged for viewing.1:1 macro reproduction at 1× is when these two top and bottom values are equal.Distant object size is reduced greatly, like perhaps maybe magnification of 0.001x or less.

Hikvisionfield of viewcalculator

Compared with the use of fecal samples to analyze the composition of the GI microbiota, few studies have been conducted to collect tissue samples and luminal contents to assess microbiota in different microbial niches during endoscopic procedures. More comprehensive information on the gut microbiome can be obtained by using tools (such as biopsy forceps and luminal brushes) through endoscopy. There are several common defects of sampling methods. First, endoscopy is invasive and not friendly to patients. Second, many studies have reported that the effect of bowel preparation on gut microflora is unavoidable. Then, when sampling tools go through the endoscopic channel, they may be contaminated by the content existing in the channel. Finally, because of the complex structure, endoscopy is limited to reach the distal small intestine. At present, there are several methods to obtain gut microbiota samples by endoscopy.

For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Field of viewcalculator astrophotography

The accuracy of samples has a remarkable effect on the value of studies of gut microbiota; therefore, more precise sampling methods are needed to ensure the reliability of research. The design of future optimal intestinal microbiota collection devices should accord with the following requirements. First, the devices can collect intestinal contents at a fixed point effectively and prevent the samples from cross-contamination. Second, the size of the devices must be small, which enables smooth passage through the pylorus and ileocecal valve. Then, the device is simple in structure and easy to operate, and the sampling process causes less psychological pressure and discomfort. Material used in manufacturing equipment should be non-toxic, harmless, non-teratogenic, and non-carcinogenic. Moreover, the cost of devices is also a pivotal consideration for large cohort studies. Finally, given that bowel preparation has a greater impact on the composition of gut microbiota, new technologies are best to eliminate this procedure. In view of the shortcomings of current sampling methods, the development of more accurate sampling methods is critical for future gut microbiota research. To meet these requirements, the development of swallowable devices seems to be the most feasible method. In the future, small, autonomous sampling swallowable devices will enable researchers and clinicians to study intestinal flora with specificity, localization and sensitivity. On the other hand, the spatial structure of intestinal flora is also an important component of studying the interaction between flora and host. For ethical reasons, it seems impractical to collect samples containing information on the positional relationship between the microbes and the gut. As an alternative, the establishment of human gut microbiota in gnotobiotic mice also provides us with a solution to the difficulties of sampling. Although fluorescence imaging cannot study complex microbiomes, the application of unbiased spatial macrogenomics in gnotobiotic mice will greatly promote our understanding of the spatial organization of gut microbiota.

The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

The Math Sensor dimension / 2focal length  =  Field dimension / 2distance This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

This front node is often a point inside the lens, perhaps crudely assumed about the middle of the lens (but it does move with zoom), but it is small and can often be ignored. Lens specifications normally instead measure field focus distance from the sensor, so you could subtract a few inches from your subject distance (to be at that node) to compute Field of View, but normally this is not significant except at extremely close focus and macro distances. It is more significant for macro distances. Example, the Nikon 105mm f/2.8 VR macro lens has specification "Minimum focus distance: 31.4 cm (1.03 feet), which is measured to the sensor plane at rear of the camera top. There's a small measuring symbol on top of the camera there, an O with a line through it (shown on this Nikon DSLR, or is often on the side of the pentaprism dome) to mark the sensor focal plane location. But at 1:1, a reliable chart of macro lens working distances says that 105 mm lens has a Working Distance (in front of lens) at 1:1, which is significantly less, 14.8 cm (5.8 inches), which differs by 16.6 mm due to the length of the lens and thickness of the camera body. SO NOTE: the terms Focal Length and lens focus distance are measured to the sensor plane, to that mark just mentioned. But Field of View and Depth of Field are computed to a node inside or near the lens. However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

When it is difficult to reach the distal ileum in endoscopy, surgery provides us with a way to sample the distal ileum. Methods to obtain intestinal flora at surgery include direct needle aspiration or the biopsy of mucosal samples (Bentley et al., 1972; Corrodi et al., 1978; Thadepalli et al., 1979; Lavelle et al., 2015). Since surgical sampling is not susceptible to contamination, in theory, the samples obtained from this method best represent the gut microbiota. However, the reality is that several preparations must be performed before surgery. These preparations may include fasting, mechanical bowel cleansing, and antibiotic administration, all of which can disrupt microbiota (Antonopoulos et al., 2009; Ubeda and Pamer, 2012; Ferrer et al., 2014; Zarrinpar et al., 2014; Jalanka et al., 2015). In this context, Thadepalli et al. drew duodenal, jejunal and ileal fluid from patients with abdominal trauma requiring emergency laparotomy by needle aspiration to explore microbiota of the small intestine. None of the patients underwent routine preoperative preparation; therefore, these samples obtained without interference from preoperative preparation were in the ideal condition. In addition, sampling during an operation can also circumvent the problem of small intestinal inaccessibility by using in vivo model systems (Booijink et al., 2007). Patients who undergo ileostomy can be used as an in vivo model and provide ileostomy effluent to obtain gut microbiota (Go et al., 1988; Ala Aldeen and Barer, 1989). Zoetendal et al. demonstrated that common microbial components in the samples excreted by ileostomists (individuals without a colon) could also be found in the small intestine of healthy subjects by the application of phylogenetic microarray analyses (Zoetendal et al., 2012). Compared to the colonic microbiota, the microbiota in the ileal effluent is relatively unstable and less complicated and consists of different dominating phylotypes (Booijink et al., 2010). Moreover, in vivo models can also be used to explore the effects of diet on the intestinal flora. Jonsson et al. investigated the effect of high-fiber intake on segmented filamentous bacteria by collecting human ileostomy samples (Jonsson, 2013). In addition to the above methods, Haysahi et al. obtained samples of intestinal contents from autopsy and demonstrated a gradient distribution in the number of OTUs from the proximal to the distal end of the intestine (Hayashi et al., 2005). Although the in vivo model provides convenience for sampling at any time, surgery itself results in significant alterations in the composition of gut microbiota that persist for a long time (Guyton and Alverdy, 2017). The ileostomy changes the anatomical structure of the intestine that may have an irreversible effect on the composition of the gut microbiota. Therefore, it is not clear whether the research results based on ileostomy effluent are suitable for people with normal anatomical structures. As surgery is invasive, acquiring a sample from healthy controls seems impossible. For operation and autopsy, surgical application is obviously limited. Surgery is not conducive to a comprehensive analysis of the relationship between bacterial flora and diseases in different populations.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The Thin Lens Model simplifies, and is practical and adequate for most computing, even if this model has one glass element and one central node point. Camera lenses have multiple glass elements, and are "thick lenses", much more complex, and have two node points, often called H for the field view side node, and H' for the sensor view side node. These two nodes might be designed a few inches apart, but they necessarily still see the same angle. The actual node position normally only matters to us for close macro distances, or perhaps in efforts to correct panoramic parallax. Sensor focal plane marking ϴ This front node is often a point inside the lens, perhaps crudely assumed about the middle of the lens (but it does move with zoom), but it is small and can often be ignored. Lens specifications normally instead measure field focus distance from the sensor, so you could subtract a few inches from your subject distance (to be at that node) to compute Field of View, but normally this is not significant except at extremely close focus and macro distances. It is more significant for macro distances. Example, the Nikon 105mm f/2.8 VR macro lens has specification "Minimum focus distance: 31.4 cm (1.03 feet), which is measured to the sensor plane at rear of the camera top. There's a small measuring symbol on top of the camera there, an O with a line through it (shown on this Nikon DSLR, or is often on the side of the pentaprism dome) to mark the sensor focal plane location. But at 1:1, a reliable chart of macro lens working distances says that 105 mm lens has a Working Distance (in front of lens) at 1:1, which is significantly less, 14.8 cm (5.8 inches), which differs by 16.6 mm due to the length of the lens and thickness of the camera body. SO NOTE: the terms Focal Length and lens focus distance are measured to the sensor plane, to that mark just mentioned. But Field of View and Depth of Field are computed to a node inside or near the lens. However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Aug 13, 2023 — A camera lens is an optical body that features a single lens or an assembly of lenses that mounts to a camera — Camera lenses explained.

Currently, endoscopic aspiration is most frequently used to obtain intestinal fluid. The aspiration and culture of small intestinal fluid are usually supposed to be the gold standard for the diagnosis of small intestinal bacterial overgrowth, which is defined as ≥ 105 colony-forming units per milliliter (CFU/mL) upon the culture of aspirated fluid (Khoshini et al., 2008; Grace et al., 2013; Erdogan et al., 2015). A recent study based on the culture of duodenal aspirate demonstrated that SIBO is associated with an overgrowth of anaerobes and that the microbial composition of the small intestine in symptomatic patients changed significantly, which was inconsistent with the results of aspiration culture (Saffouri et al., 2019).

SO NOTE: the terms Focal Length and lens focus distance are measured to the sensor plane, to that mark just mentioned. But Field of View and Depth of Field are computed to a node inside or near the lens. However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Additionally, under certain conditions, fresh stool samples cannot be analyzed immediately and need to be preserved for a while. Fecal materials instantly frozen at −80°C that can maintain microbial integrity without preservatives have been widely regarded as the gold standard for gut microbiota profiling. This approach retains microbial components similar to those of fresh samples and refrains from the potential impact of preservatives (Fouhy et al., 2015). For large-scale population studies, appropriate methods are important for patient compliance and the collection of optimal samples. Sometimes the ideal condition for immediate storage of specimens at −80°C cannot be met. Therefore, valid collection methods must be considered to minimize systematic bias that can be introduced in preprocessing steps (Flores et al., 2015). Jocelyn M et al. reported that the storage and transportation of samples at 4°C can minimize the changes to the microbial composition if ultralow-temperature storage is unavailable (Choo et al., 2015).

Laser capture microdissection (LCM) was developed to overcome the drawbacks of tissue microdissection techniques. LCM selectively adheres materials of interest to the thin transparent film over the tissue section by a pulse from the infrared laser (Emmert-Buck et al., 1996). Then, the thin film with the obtained tissue is removed from the slice and treated directly with DNA, RNA or enzyme buffer. Therefore, this ability to selectively transfer the small focal region of tissue or cell clusters to film can be used to obtain mucous gel layers on the surface of intestinal biopsy samples. Before LCM samples can be analyzed, frozen biopsy samples need to be cut into 10-micron sections and then put onto nuclease- and nucleic-acid-free membrane slides and air-dried overnight. To capture interfold microbes of the mouse colon with high precision, Nava et al. used LCM to find that microbes in the interfold region were significantly different from those in the central luminal compartment (Nava et al., 2011). Although the maximum size of the interfold region is ~100 μm, the high resolution of LCM of ~5 μm allows easy and accurate sampling. Differentiation was evident between the luminal and mucosal intervals by using LCM to capture specimens of the mucus gel layer from snap-frozen biopsy samples (Lavelle et al., 2015). The detectable bacterial load of UC patients measured by targeted LCM and qPCR was lower than that of the control group (Rowan et al., 2010). Thus, LCM provides an easy, precise, and efficient method to obtain the bacteria in the mucosal region for the analysis of host-mucosa-associated microbiota interactions. LCM may be suitable for precision medicine, but the tedious procedure limits its use in large-scale studies. What limits the accuracy of LCM may be that the source of the sample is from biopsy, which has its own drawbacks, largely nucleic acid degradation, e.g., RNA, and an insufficient sample amount.

FOV to mm calculator

Also if at 1:1 magnification (equal image size on both sides of lens), then s1 = s2, saying that the working macro distance in front of the lens node (extended at 1:1) is equal to the distance to the sensor image plane (both sides at 2x focal length). This makes f/stop number be 2x, which is 2 EV light loss. Those are basics. Internal focusing macro lenses can slightly reduce this light loss, but it is still near 2 EV. The Math Sensor dimension / 2focal length  =  Field dimension / 2distance This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Trig functions in software programming languages (including Excel, Javascript, C, Python, etc.) use radians instead of degrees. Calculators normally offer the choice of using degrees. To convert radians to degrees, multiply radians by 180/Pi, which is 57.2958 degrees per radian. Or for degrees to radians, multiply degrees by Pi/180. Field size and focal length are linear in field of view (half of sensor dimension or twice the focal length both produce half the field dimension). But the angle is a tangent function, which is Not straight-line linear (the angle is approximately linear if angle is not more than about 10 degrees (called the Small-Angle Approximation).

The Thin Lens Equations use the distance d in front of the lens node, but the lens specifications are "focused distance" (marked s in the diagram) which is to the sensor plane. Working Distance = d = S1 (distance in front of lens) Focal Length = f = S2 (distance behind lens) Focus Distance = d + f (subject distance to the sensor plane) The Thin Lens Model simplifies, and is practical and adequate for most computing, even if this model has one glass element and one central node point. Camera lenses have multiple glass elements, and are "thick lenses", much more complex, and have two node points, often called H for the field view side node, and H' for the sensor view side node. These two nodes might be designed a few inches apart, but they necessarily still see the same angle. The actual node position normally only matters to us for close macro distances, or perhaps in efforts to correct panoramic parallax. Sensor focal plane marking ϴ This front node is often a point inside the lens, perhaps crudely assumed about the middle of the lens (but it does move with zoom), but it is small and can often be ignored. Lens specifications normally instead measure field focus distance from the sensor, so you could subtract a few inches from your subject distance (to be at that node) to compute Field of View, but normally this is not significant except at extremely close focus and macro distances. It is more significant for macro distances. Example, the Nikon 105mm f/2.8 VR macro lens has specification "Minimum focus distance: 31.4 cm (1.03 feet), which is measured to the sensor plane at rear of the camera top. There's a small measuring symbol on top of the camera there, an O with a line through it (shown on this Nikon DSLR, or is often on the side of the pentaprism dome) to mark the sensor focal plane location. But at 1:1, a reliable chart of macro lens working distances says that 105 mm lens has a Working Distance (in front of lens) at 1:1, which is significantly less, 14.8 cm (5.8 inches), which differs by 16.6 mm due to the length of the lens and thickness of the camera body. SO NOTE: the terms Focal Length and lens focus distance are measured to the sensor plane, to that mark just mentioned. But Field of View and Depth of Field are computed to a node inside or near the lens. However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

QT, GJ, GW, BW, and HC designed the research. QT, GJ, GW, TL, and XL collected and analyzed relevant information. QT, GJ, GW, and HC wrote the paper. All authors were involved in the final approval of the article.

Back to the general ideas, of all above: This Distance to Field doesn't necessarily mean to subject or to focus point. Here it means the distance to the point where you want field size calculated (perhaps the background, computing what will show in the picture). As noted, use either meters or feet (the units all cancel out). And/or substitute width for height if appropriate. Just be consistent, and solve for the unknown. FWIW, cameras report focus distance as s, measured to the sensor surface. Lens calculations however compute with distance d, in front of the lens node (which except for telephoto lenses, is normally inside the lens body). The Thin Lens Equations use the distance d in front of the lens node, but the lens specifications are "focused distance" (marked s in the diagram) which is to the sensor plane. Working Distance = d = S1 (distance in front of lens) Focal Length = f = S2 (distance behind lens) Focus Distance = d + f (subject distance to the sensor plane) The Thin Lens Model simplifies, and is practical and adequate for most computing, even if this model has one glass element and one central node point. Camera lenses have multiple glass elements, and are "thick lenses", much more complex, and have two node points, often called H for the field view side node, and H' for the sensor view side node. These two nodes might be designed a few inches apart, but they necessarily still see the same angle. The actual node position normally only matters to us for close macro distances, or perhaps in efforts to correct panoramic parallax. Sensor focal plane marking ϴ This front node is often a point inside the lens, perhaps crudely assumed about the middle of the lens (but it does move with zoom), but it is small and can often be ignored. Lens specifications normally instead measure field focus distance from the sensor, so you could subtract a few inches from your subject distance (to be at that node) to compute Field of View, but normally this is not significant except at extremely close focus and macro distances. It is more significant for macro distances. Example, the Nikon 105mm f/2.8 VR macro lens has specification "Minimum focus distance: 31.4 cm (1.03 feet), which is measured to the sensor plane at rear of the camera top. There's a small measuring symbol on top of the camera there, an O with a line through it (shown on this Nikon DSLR, or is often on the side of the pentaprism dome) to mark the sensor focal plane location. But at 1:1, a reliable chart of macro lens working distances says that 105 mm lens has a Working Distance (in front of lens) at 1:1, which is significantly less, 14.8 cm (5.8 inches), which differs by 16.6 mm due to the length of the lens and thickness of the camera body. SO NOTE: the terms Focal Length and lens focus distance are measured to the sensor plane, to that mark just mentioned. But Field of View and Depth of Field are computed to a node inside or near the lens. However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

There are approximations in calculations. The math is precise, but the data is less so. The required Focal length and Sensor Size are rounded specifications, losing a bit of precision. This little difference at the small sensor gets magnified in the field and scene. However, the results certainly are close enough to be very useful in any practical case. My experience is that the field is fairly accurate (at distances of at least a meter or so), assuming you actually know your parameters. Some problems are: You absolutely must know the actual correct sensor size in mm. Or the FOV calculator here can make a reasonable approximation of sensor size from the accurate Crop Factor. If not accurate, the field of view calculation will not be accurate. If you're guessing, your results will likely be troubled. Please see this summary of Issues determining Sensor Size which might help. You must know the actual correct lens focal length in mm. Zoom lens focal length is different at each and every zoom position. The image EXIF data may show focal length (but it is rounded in some degree). And of course just guessing about the field distance may be an approximation, or may not be at all accurate. Field of View calculators do NOT work for macro distances. Macro uses reproduction ration, like 1:1. Thin Lens Equation The Marked focal length of any lens is a rounded nominal number, like 50 or 60 mm. The actual can be a few percent different. Furthermore, the Marked focal length is only applicable to focus at infinity. Focal length normally increases when lens is extended forward to focus closer. Lens specs normally indicate this internal extension at closest focus distance. But internal focusing lenses can do internal tricks with focal length (some zooms and macro lenses can be shorter when up close, instead of longer). But generally speaking, focal length becomes a little longer at very close distances (2x longer at 1:1), so field of view could be a little smaller, but should be insignificant as long as magnification is greater than 0.1x, which in regular lenses is normally near their Minimum focus distance. But this calculation does not include macro distances. We are only seeking a ballpark FOV number anyway, we adjust small differences with our subject framing or cropping, but vague guesses about your distance and sensor size or focal length don't help FOV accuracy. And a fisheye lens is a different animal, wider view than this formula predicts. A regular lens is rectilinear, meaning it shows straight lines as straight lines, not curved. A fisheye is rather unconcerned about this distortion, and can show a wider view, poorly purists might say, but very wide, and very possibly interesting. Focal Length varies with zoom, and the Exif data with the image should report focal length (in coarse zoom steps, as best it can). Actual focal length could be determined by the Magnification (Wikipedia) and distance. The distance from the front nodal point to the object in the subject plane (s1), and the distance from the rear nodal point to the image plane (s2) (when focused) are related by this Thin Lens equation (Wikipedia), which the diagram and formulas below simplify. If OK with a little geometry and algebra, you can see the derivation of this classic Thin Lens Equation at the Khan Academy. In this equation, we can see that if the subject at s1 is at infinity, then 1/s1 is zero, so then s2 = f. This is the marked focal length that applies when focused at infinity. What camera lenses call the focused distance is s = s1 + s2, from subject to the sensor plane. Also if at 1:1 magnification (equal image size on both sides of lens), then s1 = s2, saying that the working macro distance in front of the lens node (extended at 1:1) is equal to the distance to the sensor image plane (both sides at 2x focal length). This makes f/stop number be 2x, which is 2 EV light loss. Those are basics. Internal focusing macro lenses can slightly reduce this light loss, but it is still near 2 EV. The Math Sensor dimension / 2focal length  =  Field dimension / 2distance This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

A bowel preparation usually requires a quantity of laxatives, such as polyethylene glycol (PEG) or sulfate, to clean out most of the digesta from the GI tract. Adequate bowel preparation requires the feces to present clear liquid without any solid particles within it. In mice with osmotic diarrhea induced by PEG aqueous solution, however, the intestinal epithelium, mucosa and gut environment of the host were destroyed in a short period of time, and the gut microbiota was still significantly changed for a long period of time. The changes in gut microbiota mainly included that the alpha diversity significantly decreased, and it was still significantly lower than the baseline level 2 weeks after diarrhea and was difficult to completely recover. Moreover, some high-abundance bacteria disappeared (e.g., the S24-7 family) and were replaced by other low-abundance taxa (Tropini et al., 2018). A previous study demonstrated that bowel preparation with PEG has the potential to result in significant morphological alterations in the colon, including the loss of epithelial cells and superficial mucus (Bucher et al., 2006). Shobar et al. reported that the diversity and composition of the luminal and mucosal microbiomes are affected by bowel preparation (Shobar et al., 2016). It has also been found that lavage before colonoscopy causes a 31-fold reduction in the total microbial load and the loss of the subject specificity of the microbiota in 22% of the participants (Jalanka et al., 2015).

There are other storage methods with or without preservatives that are utilized to achieve microbiome compositions similar to those of fresh samples. As no-additive methods, fecal samples stored at room temperature for 24 h, −20°C for 1 week and in Eppendorf tubes at room temperature for 3 days did not significantly influence fecal microbiome profiles (Carroll et al., 2012; Tedjo et al., 2015). Additionally, fecal occult blood test cards, FTA cards (Whatman), and the OMNIgene Gut kit (DNA Genotek) have also been proven to be effective for samples stored for several days at room temperature (Dominianni et al., 2014; Song et al., 2016; Vogtmann et al., 2017). For using preservatives to store fecal specimens stably, 95% ethanol and RNAlater are worthy of recommendation (Flores et al., 2015; Song et al., 2016; Vogtmann et al., 2017; Wang et al., 2018). Storage conditions may significantly alter the characteristics of the microbial community. In the absence of ultralow-temperature conditions, storage and transportation by the methods mentioned above can minimize changes in microbial composition. The choice of collection and storage methods must be based on the purpose, scope, and conditions of the study.

Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Substituting size of an Object in the field, instead of overall Field size. Using these two steps may be convenient: Object height on sensor (mm)  =   Sensor height (mm) × Object height (pixels) Sensor height (pixels) Object height on sensor (mm)Focal length (mm)  =   Real Object size *Distance to Object * Rearrange this ratio to compute desired unknown value. Examples: Distance to Object *  =   Real Object height * × Focal Length (mm) Object height on sensor (mm) Real Object height *  =   Distance to Object * × Object height on sensor (mm) Focal Length (mm) * feet or meters (but both same units) There are Other possible arrangements. But this next one must use Field dimension and Height converted to mm (304.8 mm per foot), because each ratio must be a dimensionless number. Magnification =  Distance to Object (mm) Focal Length (mm) =  Real Object height (mm) Object height on sensor (mm) This is magnification on the sensor or film. The image must still be enlarged for viewing.1:1 macro reproduction at 1× is when these two top and bottom values are equal.Distant object size is reduced greatly, like perhaps maybe magnification of 0.001x or less. Back to the general ideas, of all above: This Distance to Field doesn't necessarily mean to subject or to focus point. Here it means the distance to the point where you want field size calculated (perhaps the background, computing what will show in the picture). As noted, use either meters or feet (the units all cancel out). And/or substitute width for height if appropriate. Just be consistent, and solve for the unknown. FWIW, cameras report focus distance as s, measured to the sensor surface. Lens calculations however compute with distance d, in front of the lens node (which except for telephoto lenses, is normally inside the lens body). The Thin Lens Equations use the distance d in front of the lens node, but the lens specifications are "focused distance" (marked s in the diagram) which is to the sensor plane. Working Distance = d = S1 (distance in front of lens) Focal Length = f = S2 (distance behind lens) Focus Distance = d + f (subject distance to the sensor plane) The Thin Lens Model simplifies, and is practical and adequate for most computing, even if this model has one glass element and one central node point. Camera lenses have multiple glass elements, and are "thick lenses", much more complex, and have two node points, often called H for the field view side node, and H' for the sensor view side node. These two nodes might be designed a few inches apart, but they necessarily still see the same angle. The actual node position normally only matters to us for close macro distances, or perhaps in efforts to correct panoramic parallax. Sensor focal plane marking ϴ This front node is often a point inside the lens, perhaps crudely assumed about the middle of the lens (but it does move with zoom), but it is small and can often be ignored. Lens specifications normally instead measure field focus distance from the sensor, so you could subtract a few inches from your subject distance (to be at that node) to compute Field of View, but normally this is not significant except at extremely close focus and macro distances. It is more significant for macro distances. Example, the Nikon 105mm f/2.8 VR macro lens has specification "Minimum focus distance: 31.4 cm (1.03 feet), which is measured to the sensor plane at rear of the camera top. There's a small measuring symbol on top of the camera there, an O with a line through it (shown on this Nikon DSLR, or is often on the side of the pentaprism dome) to mark the sensor focal plane location. But at 1:1, a reliable chart of macro lens working distances says that 105 mm lens has a Working Distance (in front of lens) at 1:1, which is significantly less, 14.8 cm (5.8 inches), which differs by 16.6 mm due to the length of the lens and thickness of the camera body. SO NOTE: the terms Focal Length and lens focus distance are measured to the sensor plane, to that mark just mentioned. But Field of View and Depth of Field are computed to a node inside or near the lens. However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here Copyright © 2018-2024 by Wayne Fulton - All rights are reserved.

1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Field Width × Focal Length mm Sensor Width mm  = Distance    This looks simple because it is (but correct sensor size and focal length are required). Twice the focal length is half the field, or twice the distance is twice the field dimension. And assuming use of a proper lens designed for the sensor, twice the sensor dimension is twice the field, which is why a smaller "cropped" sensor sees a smaller field unless compensated with a shorter lens. These ratios above are just the trig tangent (opposite over adjacent), necessarily equal for the equal angles, but using the ratios is simpler math for the field dimensions. But computing the angle of view requires trigonometry, for dimensions of Width, Height, or Diagonal angles of view. The 2's do NOT cancel out for this trig tangent. Field angle of view = 2 x arctan ((sensor dimension (mm) / 2) / focal length (mm)) 2 × arctan(  Sensor Width mm 2 × Focal Length mm )  =  Degrees

In brief, the drawbacks of using fecal samples as substitutions for gut microbiota can be summarized in the following aspects. First, the possibility of incomplete separation of fecal bacteria and intestinal flora cannot be eliminated. Physiological variations containing chemical and nutrient gradients and the division of host immune activity are different among the lengths of the small and large intestine, all of which are known to influence the microbial composition. The families Lactobacillaceae and Enterobacteriaceae predominate in the small intestine, whereas the colon is dominated by the families Prevotellaceae, Bacteroidaceae, Rikenellaceae, Ruminococcaceae, and Lachnospiraceae (Donaldson et al., 2016). Therefore, it is not comprehensive to study intestinal flora with fecal bacteria. Second, homogenization before the collection of fecal samples perturbs fecal biostructure, and if not homogenizing, representativeness of samples may be inadequate. Swidsinski et al. used a plastic drinking straw to punch the stool to obtain fecal cylinders that successfully retained the biostructure of fecal microbiota and demonstrated that fecal microbiota is highly structured (Swidsinski et al., 2008). However, another study has reported that homogenization can significantly reduce the intraindividual variation in the detection of each fecal microbiota component (Hsieh et al., 2016). This leads to a controversy over which method should be adopted. Finally, in most cases, it is unrealistic to analyze fresh samples immediately. Then, the effect of the storage method, which may cause microbial DNA degradation, overgrowth, and the death of some species, on the fecal sample components must be considered.

This looks simple because it is (but correct sensor size and focal length are required). Twice the focal length is half the field, or twice the distance is twice the field dimension. And assuming use of a proper lens designed for the sensor, twice the sensor dimension is twice the field, which is why a smaller "cropped" sensor sees a smaller field unless compensated with a shorter lens. These ratios above are just the trig tangent (opposite over adjacent), necessarily equal for the equal angles, but using the ratios is simpler math for the field dimensions. But computing the angle of view requires trigonometry, for dimensions of Width, Height, or Diagonal angles of view. The 2's do NOT cancel out for this trig tangent. Field angle of view = 2 x arctan ((sensor dimension (mm) / 2) / focal length (mm)) 2 × arctan(  Sensor Width mm 2 × Focal Length mm )  =  Degrees

There are Other possible arrangements. But this next one must use Field dimension and Height converted to mm (304.8 mm per foot), because each ratio must be a dimensionless number. Magnification =  Distance to Object (mm) Focal Length (mm) =  Real Object height (mm) Object height on sensor (mm) This is magnification on the sensor or film. The image must still be enlarged for viewing.1:1 macro reproduction at 1× is when these two top and bottom values are equal.Distant object size is reduced greatly, like perhaps maybe magnification of 0.001x or less.

Thin Lens Equation The Marked focal length of any lens is a rounded nominal number, like 50 or 60 mm. The actual can be a few percent different. Furthermore, the Marked focal length is only applicable to focus at infinity. Focal length normally increases when lens is extended forward to focus closer. Lens specs normally indicate this internal extension at closest focus distance. But internal focusing lenses can do internal tricks with focal length (some zooms and macro lenses can be shorter when up close, instead of longer). But generally speaking, focal length becomes a little longer at very close distances (2x longer at 1:1), so field of view could be a little smaller, but should be insignificant as long as magnification is greater than 0.1x, which in regular lenses is normally near their Minimum focus distance. But this calculation does not include macro distances. We are only seeking a ballpark FOV number anyway, we adjust small differences with our subject framing or cropping, but vague guesses about your distance and sensor size or focal length don't help FOV accuracy. And a fisheye lens is a different animal, wider view than this formula predicts. A regular lens is rectilinear, meaning it shows straight lines as straight lines, not curved. A fisheye is rather unconcerned about this distortion, and can show a wider view, poorly purists might say, but very wide, and very possibly interesting. Focal Length varies with zoom, and the Exif data with the image should report focal length (in coarse zoom steps, as best it can). Actual focal length could be determined by the Magnification (Wikipedia) and distance. The distance from the front nodal point to the object in the subject plane (s1), and the distance from the rear nodal point to the image plane (s2) (when focused) are related by this Thin Lens equation (Wikipedia), which the diagram and formulas below simplify. If OK with a little geometry and algebra, you can see the derivation of this classic Thin Lens Equation at the Khan Academy. In this equation, we can see that if the subject at s1 is at infinity, then 1/s1 is zero, so then s2 = f. This is the marked focal length that applies when focused at infinity. What camera lenses call the focused distance is s = s1 + s2, from subject to the sensor plane. Also if at 1:1 magnification (equal image size on both sides of lens), then s1 = s2, saying that the working macro distance in front of the lens node (extended at 1:1) is equal to the distance to the sensor image plane (both sides at 2x focal length). This makes f/stop number be 2x, which is 2 EV light loss. Those are basics. Internal focusing macro lenses can slightly reduce this light loss, but it is still near 2 EV. The Math Sensor dimension / 2focal length  =  Field dimension / 2distance This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

The development of next-generation sequencing technology has enabled researchers to explore and understand the gut microbiome from a broader and deeper perspective. However, the results of different studies on gut microbiota are highly variable even in the same disease, which makes it difficult to guide clinical diagnosis and treatment. The ideal sampling method should be non-invasive, involve little cross-contamination or bowel preparation, and collect gut microbiota at different sites. Currently, sequencing technologies are usually based on samples collected from feces, mucosal biopsy, intestinal fluid, etc. However, different parts of the gastrointestinal tract possess various physiological characteristics that are essential for particular species of living microbiota. Moreover, current sampling methods are somewhat defective. For example, fecal samples are just a proxy for intestinal microbiota, while biopsies are invasive for patients and not suitable for healthy controls. In this review, we summarize the current sampling methods and their advantages and shortcomings. New sampling technologies, such as the Brisbane Aseptic Biopsy Device and the intelligent capsule, are also mentioned to inspire the development of future precise description methods of the gut microbiome.

Back to the general ideas, of all above: This Distance to Field doesn't necessarily mean to subject or to focus point. Here it means the distance to the point where you want field size calculated (perhaps the background, computing what will show in the picture). As noted, use either meters or feet (the units all cancel out). And/or substitute width for height if appropriate. Just be consistent, and solve for the unknown. FWIW, cameras report focus distance as s, measured to the sensor surface. Lens calculations however compute with distance d, in front of the lens node (which except for telephoto lenses, is normally inside the lens body). The Thin Lens Equations use the distance d in front of the lens node, but the lens specifications are "focused distance" (marked s in the diagram) which is to the sensor plane. Working Distance = d = S1 (distance in front of lens) Focal Length = f = S2 (distance behind lens) Focus Distance = d + f (subject distance to the sensor plane) The Thin Lens Model simplifies, and is practical and adequate for most computing, even if this model has one glass element and one central node point. Camera lenses have multiple glass elements, and are "thick lenses", much more complex, and have two node points, often called H for the field view side node, and H' for the sensor view side node. These two nodes might be designed a few inches apart, but they necessarily still see the same angle. The actual node position normally only matters to us for close macro distances, or perhaps in efforts to correct panoramic parallax. Sensor focal plane marking ϴ This front node is often a point inside the lens, perhaps crudely assumed about the middle of the lens (but it does move with zoom), but it is small and can often be ignored. Lens specifications normally instead measure field focus distance from the sensor, so you could subtract a few inches from your subject distance (to be at that node) to compute Field of View, but normally this is not significant except at extremely close focus and macro distances. It is more significant for macro distances. Example, the Nikon 105mm f/2.8 VR macro lens has specification "Minimum focus distance: 31.4 cm (1.03 feet), which is measured to the sensor plane at rear of the camera top. There's a small measuring symbol on top of the camera there, an O with a line through it (shown on this Nikon DSLR, or is often on the side of the pentaprism dome) to mark the sensor focal plane location. But at 1:1, a reliable chart of macro lens working distances says that 105 mm lens has a Working Distance (in front of lens) at 1:1, which is significantly less, 14.8 cm (5.8 inches), which differs by 16.6 mm due to the length of the lens and thickness of the camera body. SO NOTE: the terms Focal Length and lens focus distance are measured to the sensor plane, to that mark just mentioned. But Field of View and Depth of Field are computed to a node inside or near the lens. However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

This is magnification on the sensor or film. The image must still be enlarged for viewing.1:1 macro reproduction at 1× is when these two top and bottom values are equal.Distant object size is reduced greatly, like perhaps maybe magnification of 0.001x or less.

In addition to the composition and diversity of gut microbiota, their spatial organization also reflects the host-microbiota relationship. To obtain the complete structure of the intestine and its contents, Johansson et al. improved the histological preparations that successfully preserved intestinal mucus and located bacteria with fluorescence in situ hybridization (FISH) (Johansson and Hansson, 2012). Using FISH technology, the location of the bacteria of interest labeled by a fluorescent DNA probe can be observed under a fluorescence microscope. However, due to the difficulties in sampling, ethical problems and the huge individual differences in microbial composition, the research and manipulation of human gut microbial communities in situ are limited. As an alternative, the transplantation of human gut microbiota into germ-free mice has been widely used (Goodman et al., 2011; McNulty et al., 2013). To explore the spatial organization of the human gut microbiota, Earle et al. developed a new approach that visualizes the bacteria in human microbiota-colonized gnotobiotic mice by FISH (Earle et al., 2015). They inoculated the fluorescent probe corresponding to the bacteria of interest to the fixed gut cross-sections of mouse intestine. However, a single field of view in a section cannot represent the entire intestine. To solve this problem, Bacspace software was developed to stitch the overlapping images of multiple fields of view into a continuous image that represents the entire gut, distinguish host epithelial cells from bacteria and measure the distance between bacterial cells and between bacterial cells and the epithelium. Using Bacspace, they revealed homologous clustering within Bacteroidales or Firmicutes, which clusters of Bacteroidales that exclude Firmicutes and vice versa. Moreover, the application of FISH combined with spectral imaging analysis methods uncovered the spatial organization of gnotobiotic mice colonized with 15-member human gut microbiota (Welch et al., 2017). There are two densely colonized regions in the colon: one adjacent to the mucosa and the other bordered by food particles within the lumen. Modest differences in the composition of the microbiota in these two regions suggest that the lumen and mucosa should not be defined as stratified compartments. Owing to orders-of-magnitude differences in the microbial density between the small intestine and colon, the number of microbes in the cross-section of the small intestine is 10 to 1 million times less than that in the colon. That is, compared with 1,000 bacteria per field of view in the colon, there are almost no bacteria in the small intestine. Because of its higher microbial density, the histological method is more suitable for the colon. Improper sample preparation can also result in the loss of intestinal contents in sections. Compared with other methods, the Technovit h8100 embedding method can successfully preserve the three-dimensional structure of the intestine and is compatible with FISH and other labeling techniques for the visualization of microbial cells in the mouse intestines along with mucus and fecal pellets (Hasegawa et al., 2017). These imaging techniques can simultaneously locate some cultivable microbes with fluorescent probes that need predesign, but they cannot deal with complex and diverse microbiomes. For unbiased high-taxonomic-resolution dissection of the complex gut microbial biogeography, Ravi et al. developed metagenomic plot sampling by sequencing that can analyze the spatial location of various microbes without advance specification (Sheth et al., 2019). They found that a strong association between Bacteroides in all intestinal cavities and the local areas of bacterial phylogeny and aggregation were related to dietary disturbance. Although the establishment of human gut microbiota in germ-free mice provides us with a solution to the difficulty of sampling in the human intestine, the influence of the difference in gene background on the composition of microbiota should not be ignored (Wos-Oxley et al., 2012). At the same time, the establishment of human intestinal microflora in germ-free mice will also be affected by the operation of bacterial transplantation. There are several points to be paid attention to for oral gavage. Because of the presence of anaerobic bacteria in the human flora, they need to be rapidly infused into the digestive tract. A larger volume of administration will promote the distribution and colonization of the mouse intestinal microbial community and protect the microbiota from intestinal enzymes and pH changes, and some rodent diets may also promote or inhibit the growth of some bacteria (Rodriguez-Palacios et al., 2019) Compared with controls, germ-free mice have a significantly longer gut transit time along with lower levels of SCFAs that are produced by the fermentation of indigestible carbohydrates by commensal bacteria and can promote bowel movement (Vincent et al., 2018). Colonization of different strains in germ-free mice may affect intestinal motility by influencing the level of SCFAs, resulting in different amount of fecal pellets in the colon. Therefore, the relationship between the bacteria and fecal pellets in the colon section may be slightly different.

The endoscopic working channel is easily contaminated by oral and GI contents. Rubber was used to cover the distal tip of the catheter to block the infiltration of intestinal fluid (Uno et al., 1998). Inspired by previous studies, Quintanilha et al. used a membrane of microfilm to protect the distal tip to avoid internal contamination (Quintanilha et al., 2007). As endoscopic biopsy is aggressive for healthy people, the suction of intestinal fluid has become an alternative option. Nevertheless, intestinal fluid suction is sometimes time-consuming, which increases the time of endoscopy and sometimes fails due to sparse intestinal fluid (Riordan et al., 1995). Although previous studies have made great efforts to minimize co-contamination during intestinal fluid suction, innate defects in endoscopic sampling are unavoidable, as mentioned above. Moreover, the uncertainty of sampling sites also poses challenges for obtaining reliable samples.

Real Object height *  =   Distance to Object * × Object height on sensor (mm) Focal Length (mm) * feet or meters (but both same units) There are Other possible arrangements. But this next one must use Field dimension and Height converted to mm (304.8 mm per foot), because each ratio must be a dimensionless number. Magnification =  Distance to Object (mm) Focal Length (mm) =  Real Object height (mm) Object height on sensor (mm) This is magnification on the sensor or film. The image must still be enlarged for viewing.1:1 macro reproduction at 1× is when these two top and bottom values are equal.Distant object size is reduced greatly, like perhaps maybe magnification of 0.001x or less.

Calculate field of viewmicroscope

Fiber optic connections are capable of providing very high speeds which can lead to improved gaming experiences. They provide a faster connection and reduce lag ...

This Distance to Field doesn't necessarily mean to subject or to focus point. Here it means the distance to the point where you want field size calculated (perhaps the background, computing what will show in the picture). As noted, use either meters or feet (the units all cancel out). And/or substitute width for height if appropriate. Just be consistent, and solve for the unknown. FWIW, cameras report focus distance as s, measured to the sensor surface. Lens calculations however compute with distance d, in front of the lens node (which except for telephoto lenses, is normally inside the lens body). The Thin Lens Equations use the distance d in front of the lens node, but the lens specifications are "focused distance" (marked s in the diagram) which is to the sensor plane. Working Distance = d = S1 (distance in front of lens) Focal Length = f = S2 (distance behind lens) Focus Distance = d + f (subject distance to the sensor plane) The Thin Lens Model simplifies, and is practical and adequate for most computing, even if this model has one glass element and one central node point. Camera lenses have multiple glass elements, and are "thick lenses", much more complex, and have two node points, often called H for the field view side node, and H' for the sensor view side node. These two nodes might be designed a few inches apart, but they necessarily still see the same angle. The actual node position normally only matters to us for close macro distances, or perhaps in efforts to correct panoramic parallax. Sensor focal plane marking ϴ This front node is often a point inside the lens, perhaps crudely assumed about the middle of the lens (but it does move with zoom), but it is small and can often be ignored. Lens specifications normally instead measure field focus distance from the sensor, so you could subtract a few inches from your subject distance (to be at that node) to compute Field of View, but normally this is not significant except at extremely close focus and macro distances. It is more significant for macro distances. Example, the Nikon 105mm f/2.8 VR macro lens has specification "Minimum focus distance: 31.4 cm (1.03 feet), which is measured to the sensor plane at rear of the camera top. There's a small measuring symbol on top of the camera there, an O with a line through it (shown on this Nikon DSLR, or is often on the side of the pentaprism dome) to mark the sensor focal plane location. But at 1:1, a reliable chart of macro lens working distances says that 105 mm lens has a Working Distance (in front of lens) at 1:1, which is significantly less, 14.8 cm (5.8 inches), which differs by 16.6 mm due to the length of the lens and thickness of the camera body. SO NOTE: the terms Focal Length and lens focus distance are measured to the sensor plane, to that mark just mentioned. But Field of View and Depth of Field are computed to a node inside or near the lens. However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

For pragmatic reasons, fecal specimens are frequently used as proxies for gut microbiota. Fecal specimens are naturally collected, non-invasive and can be sampled repeatedly, so they are the source of samples for most intestinal microbiota studies. However, it is becoming increasingly clear that there may be significant differences in microbial composition between mucosa and feces (Zoetendal et al., 2002; Carroll et al., 2010). Feces were deemed to be substitutes for GI lumen contents, but their components uncertainly reflect direct interaction with mucosa. In recent studies, it has been demonstrated that the fecal and mucosal-associated microbiota are two distinct microbial niches (Rangel et al., 2015; Ringel et al., 2015; Tap et al., 2017). Fecal samples could not be indicators of the composition and metagenomic function of mucosa-associated microbiota distributed among multiple sites of the intestine (Zmora et al., 2018). Therefore, there is a bias in the estimation of intestinal microbiota with feces. Moreover, the fecal microbiota is not equally distributed within feces and has its own biostructure (Swidsinski et al., 2008). Wu et al. reported that 35% of low-abundance taxa, which account for 0.2–0.4% of the total microbiome in one replicate, were not found in a second fecal sample (Wu et al., 2010). The intraindividual variation in the detected bacteria was significantly reduced in the majority of studies that homogenized fecal samples or smears and ignored their structure (Hsieh et al., 2016). In the case of fecal subsampling, the results of microbial taxa detected by qPCR were highly variable (Gorzelak et al., 2015).

Focal Length varies with zoom, and the Exif data with the image should report focal length (in coarse zoom steps, as best it can). Actual focal length could be determined by the Magnification (Wikipedia) and distance. The distance from the front nodal point to the object in the subject plane (s1), and the distance from the rear nodal point to the image plane (s2) (when focused) are related by this Thin Lens equation (Wikipedia), which the diagram and formulas below simplify. If OK with a little geometry and algebra, you can see the derivation of this classic Thin Lens Equation at the Khan Academy. In this equation, we can see that if the subject at s1 is at infinity, then 1/s1 is zero, so then s2 = f. This is the marked focal length that applies when focused at infinity. What camera lenses call the focused distance is s = s1 + s2, from subject to the sensor plane. Also if at 1:1 magnification (equal image size on both sides of lens), then s1 = s2, saying that the working macro distance in front of the lens node (extended at 1:1) is equal to the distance to the sensor image plane (both sides at 2x focal length). This makes f/stop number be 2x, which is 2 EV light loss. Those are basics. Internal focusing macro lenses can slightly reduce this light loss, but it is still near 2 EV. The Math Sensor dimension / 2focal length  =  Field dimension / 2distance This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

In 1979, Wimberley and colleagues first used the protected specimen brush (PSB) technique to collect infectious samples from the lower respiratory tract by the fiberoptic bronchoscope (Wimberley et al., 1979). These brush specimens are not easily contaminated by the normal flora of the upper respiratory tract, which is of greater significance for the diagnosis of lower respiratory tract infection. In recent years, Lavelle et al. promoted and validated techniques for repeated assessment of colonic microbial population spatial variability by combining mucosal biopsy with the PSB technique, which is used to sample the lumen-associated microbiota (Lavelle et al., 2013). The PSB is a sterile disposable sheath brush with a distal plug at the top, which is sealed in the sheath when inserted and retracted through the colonoscopic channel. In contrast to biopsy, mucosal brushing can reduce the risks associated with mucosal biopsy (bleeding and infection) and provide a more representative sample of the mucosal surface, and brush sampling has obtained a relatively large ratio of bacterial to host DNA (Huse et al., 2014). Although it has been reported that alpha diversities of samples collected by BABD and the PSB technique are similar at the phylum level, the PSB technique provides samples with a higher proportion of bacterial gDNA (Shanahan et al., 2016). Another study, however, suggested that there were spatial variations between luminal and mucosal microbiota (Lavelle et al., 2015). As sampling applying PSB technology depends on endoscopy, this method has the same defects as biopsies, such as bowel preparation influence, inevitable contamination, and invasion.

7/32" Hex Key Wrench ... Allen head cap screws are everywhere, which makes this wrench a necessity. • Extra long for added leverage and accessibility. ... Meets ...

Field size and focal length are linear in field of view (half of sensor dimension or twice the focal length both produce half the field dimension). But the angle is a tangent function, which is Not straight-line linear (the angle is approximately linear if angle is not more than about 10 degrees (called the Small-Angle Approximation).

In this equation, we can see that if the subject at s1 is at infinity, then 1/s1 is zero, so then s2 = f. This is the marked focal length that applies when focused at infinity. What camera lenses call the focused distance is s = s1 + s2, from subject to the sensor plane. Also if at 1:1 magnification (equal image size on both sides of lens), then s1 = s2, saying that the working macro distance in front of the lens node (extended at 1:1) is equal to the distance to the sensor image plane (both sides at 2x focal length). This makes f/stop number be 2x, which is 2 EV light loss. Those are basics. Internal focusing macro lenses can slightly reduce this light loss, but it is still near 2 EV. The Math Sensor dimension / 2focal length  =  Field dimension / 2distance This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

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m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Object height on sensor (mm)  =   Sensor height (mm) × Object height (pixels) Sensor height (pixels) Object height on sensor (mm)Focal length (mm)  =   Real Object size *Distance to Object * Rearrange this ratio to compute desired unknown value. Examples: Distance to Object *  =   Real Object height * × Focal Length (mm) Object height on sensor (mm) Real Object height *  =   Distance to Object * × Object height on sensor (mm) Focal Length (mm) * feet or meters (but both same units) There are Other possible arrangements. But this next one must use Field dimension and Height converted to mm (304.8 mm per foot), because each ratio must be a dimensionless number. Magnification =  Distance to Object (mm) Focal Length (mm) =  Real Object height (mm) Object height on sensor (mm) This is magnification on the sensor or film. The image must still be enlarged for viewing.1:1 macro reproduction at 1× is when these two top and bottom values are equal.Distant object size is reduced greatly, like perhaps maybe magnification of 0.001x or less. Back to the general ideas, of all above: This Distance to Field doesn't necessarily mean to subject or to focus point. Here it means the distance to the point where you want field size calculated (perhaps the background, computing what will show in the picture). As noted, use either meters or feet (the units all cancel out). And/or substitute width for height if appropriate. Just be consistent, and solve for the unknown. FWIW, cameras report focus distance as s, measured to the sensor surface. Lens calculations however compute with distance d, in front of the lens node (which except for telephoto lenses, is normally inside the lens body). The Thin Lens Equations use the distance d in front of the lens node, but the lens specifications are "focused distance" (marked s in the diagram) which is to the sensor plane. Working Distance = d = S1 (distance in front of lens) Focal Length = f = S2 (distance behind lens) Focus Distance = d + f (subject distance to the sensor plane) The Thin Lens Model simplifies, and is practical and adequate for most computing, even if this model has one glass element and one central node point. Camera lenses have multiple glass elements, and are "thick lenses", much more complex, and have two node points, often called H for the field view side node, and H' for the sensor view side node. These two nodes might be designed a few inches apart, but they necessarily still see the same angle. The actual node position normally only matters to us for close macro distances, or perhaps in efforts to correct panoramic parallax. Sensor focal plane marking ϴ This front node is often a point inside the lens, perhaps crudely assumed about the middle of the lens (but it does move with zoom), but it is small and can often be ignored. Lens specifications normally instead measure field focus distance from the sensor, so you could subtract a few inches from your subject distance (to be at that node) to compute Field of View, but normally this is not significant except at extremely close focus and macro distances. It is more significant for macro distances. Example, the Nikon 105mm f/2.8 VR macro lens has specification "Minimum focus distance: 31.4 cm (1.03 feet), which is measured to the sensor plane at rear of the camera top. There's a small measuring symbol on top of the camera there, an O with a line through it (shown on this Nikon DSLR, or is often on the side of the pentaprism dome) to mark the sensor focal plane location. But at 1:1, a reliable chart of macro lens working distances says that 105 mm lens has a Working Distance (in front of lens) at 1:1, which is significantly less, 14.8 cm (5.8 inches), which differs by 16.6 mm due to the length of the lens and thickness of the camera body. SO NOTE: the terms Focal Length and lens focus distance are measured to the sensor plane, to that mark just mentioned. But Field of View and Depth of Field are computed to a node inside or near the lens. However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here Copyright © 2018-2024 by Wayne Fulton - All rights are reserved.

Due to the influence of bowel preparation and contamination during the procedure, invasion, the limitation of sampling sites, the risk of bleeding and infection and its unsuitability for healthy people, biopsy, although deemed to be the gold standard for the collection of mucosal microbiota, is not appropriate for future gut microbiota analysis.

For aspirating uncontaminated intestinal fluid, Shiner invented a stainless-steel capsule fitted with a cap at its distal end and a hollow connection at the proximal end (SHINER, 1963). The proximal end of the capsule is connected to the negative-pressure source through a tube. When reaching the sampling site, the negative-pressure suction results in the opening of the sampling channel of the capsule, and the surrounding fluid entered the capsule chamber. After aspiration, the capsule is closed again, and the collected samples are isolated from the external fluid. The advantage of this device is to prevent the collected samples from being contaminated by the contents of the GI tract at the non-sampling sites. Due to the complex structure, this method has not been widely utilized. After that, the progress of obtaining GI fluid was in the development of a specially manufactured double-lumen tube with multiple aspirating ports in various locations and a mercury-filled bag at its distal end (Kalser et al., 1966). Subjects swallowed the tube, and then aspirates were sucked by a sterile syringe when ports were located in the proper position (75 cm distal to the ligament of Treitz for jejunal aspirates and 75 cm proximal to the ileocecal valve for ileal aspirates). Belov et al. aspirated intestinal fluid through nasojejunal tubes inserted routinely for enteral feeding (Belov et al., 1999). However, intestinal viscous fluid and blockages in the tubing made the collection procedure difficult and time-consuming.

* feet or meters (but both same units) Meaning, if you use Feet for Distance, then the Field Width will also be feet. Or meters if you use meters. Rearrange ratios to compute desired unknown value. The actual Field of View Calculator will be much more versatile, and can help find sensor size from crop factor, but math examples are shown here for Width. The computed Dimension can be Width, Height, or Diagonal. Sensor Width mm × Distance Focal Length mm  = Field Width   Field Width × Focal Length mm Sensor Width mm  = Distance    This looks simple because it is (but correct sensor size and focal length are required). Twice the focal length is half the field, or twice the distance is twice the field dimension. And assuming use of a proper lens designed for the sensor, twice the sensor dimension is twice the field, which is why a smaller "cropped" sensor sees a smaller field unless compensated with a shorter lens. These ratios above are just the trig tangent (opposite over adjacent), necessarily equal for the equal angles, but using the ratios is simpler math for the field dimensions. But computing the angle of view requires trigonometry, for dimensions of Width, Height, or Diagonal angles of view. The 2's do NOT cancel out for this trig tangent. Field angle of view = 2 x arctan ((sensor dimension (mm) / 2) / focal length (mm)) 2 × arctan(  Sensor Width mm 2 × Focal Length mm )  =  Degrees

Field of viewcamera

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For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

These ratios above are just the trig tangent (opposite over adjacent), necessarily equal for the equal angles, but using the ratios is simpler math for the field dimensions. But computing the angle of view requires trigonometry, for dimensions of Width, Height, or Diagonal angles of view. The 2's do NOT cancel out for this trig tangent.

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Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

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This article was submitted to Microbiome in Health and Disease, a section of the journal Frontiers in Cellular and Infection Microbiology

In addition to the effects induced by bowel preparation, mucosal biopsies performed during standard endoscopic procedures may be contaminated by GI luminal fluid in the endoscopic channel. To minimize contamination during the sampling of mucosa-associated microbiota, the Brisbane Aseptic Biopsy Device (BABD), which consists of sterile forceps covered by a sheath and sealed by a plug at the ends, has been developed. Biopsies obtained by standard forceps have a greater diversity of mucosa-associated microbiota than samples collected using BABD (Shanahan et al., 2016). Even so, contamination may still happen before sampling. When the endoscopy tube enters the sampling site from the mouth or anus, it is inevitable for bacteria located in non-sampling sites to be brought to the sampling site. Moreover, the endoscope cannot reach all segments of the whole intestine, such as the distal small intestine, so the biopsy sections are restricted. Modern multi-omics technologies require different starting materials, including DNA, RNA, and proteins, and biopsy may not yield enough material to cope with the demands of these technologies. For this reason, Watt et al. demonstrated that colonic lavage offers a sample type similar to that of biopsy and generates significantly higher DNA than that of biopsies, with median DNA yields of 48.5 and 1.95 μg for colonic lavage and biopsy, respectively (Watt et al., 2016).

Distance to Object *  =   Real Object height * × Focal Length (mm) Object height on sensor (mm) Real Object height *  =   Distance to Object * × Object height on sensor (mm) Focal Length (mm) * feet or meters (but both same units) There are Other possible arrangements. But this next one must use Field dimension and Height converted to mm (304.8 mm per foot), because each ratio must be a dimensionless number. Magnification =  Distance to Object (mm) Focal Length (mm) =  Real Object height (mm) Object height on sensor (mm) This is magnification on the sensor or film. The image must still be enlarged for viewing.1:1 macro reproduction at 1× is when these two top and bottom values are equal.Distant object size is reduced greatly, like perhaps maybe magnification of 0.001x or less.

As there are numerous associations between gut microbiota and human health, it is particularly important to analyze the relationship between changes in gut microbiota and disease occurrence, progression, and prognosis. In the past, gut microbiome analysis depended on the isolation and cultures, but the difficulty in cultivating anaerobic bacteria, which are abundant in the intestine, seriously affected the accuracy of the analysis. In recent years, the progression of next-generation sequencing (NGS), which can accurately analyze microbial components without culture, has attracted attention in research on the intestinal microbiome. However, it is critical to collect appropriate samples of gut microbiota for NGS. Current sampling methods for obtaining specimens from feces, mucosal biopsy, and intestinal aspiration, all of which may have some defects, cannot accurately reflect the composition of the intestinal microbiome (Table 1). In this review, we summarize current methods for the collection of gut microbiota and their possible deficiencies to explore the difficulties that need to be overcome in gut microbiota collection technologies.

The Math Sensor dimension / 2focal length  =  Field dimension / 2distance This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

Sensor focal plane marking ϴ This front node is often a point inside the lens, perhaps crudely assumed about the middle of the lens (but it does move with zoom), but it is small and can often be ignored. Lens specifications normally instead measure field focus distance from the sensor, so you could subtract a few inches from your subject distance (to be at that node) to compute Field of View, but normally this is not significant except at extremely close focus and macro distances. It is more significant for macro distances. Example, the Nikon 105mm f/2.8 VR macro lens has specification "Minimum focus distance: 31.4 cm (1.03 feet), which is measured to the sensor plane at rear of the camera top. There's a small measuring symbol on top of the camera there, an O with a line through it (shown on this Nikon DSLR, or is often on the side of the pentaprism dome) to mark the sensor focal plane location. But at 1:1, a reliable chart of macro lens working distances says that 105 mm lens has a Working Distance (in front of lens) at 1:1, which is significantly less, 14.8 cm (5.8 inches), which differs by 16.6 mm due to the length of the lens and thickness of the camera body. SO NOTE: the terms Focal Length and lens focus distance are measured to the sensor plane, to that mark just mentioned. But Field of View and Depth of Field are computed to a node inside or near the lens. However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Focal Length varies with zoom, and the Exif data with the image should report focal length (in coarse zoom steps, as best it can). Actual focal length could be determined by the Magnification (Wikipedia) and distance. The distance from the front nodal point to the object in the subject plane (s1), and the distance from the rear nodal point to the image plane (s2) (when focused) are related by this Thin Lens equation (Wikipedia), which the diagram and formulas below simplify. If OK with a little geometry and algebra, you can see the derivation of this classic Thin Lens Equation at the Khan Academy. In this equation, we can see that if the subject at s1 is at infinity, then 1/s1 is zero, so then s2 = f. This is the marked focal length that applies when focused at infinity. What camera lenses call the focused distance is s = s1 + s2, from subject to the sensor plane. Also if at 1:1 magnification (equal image size on both sides of lens), then s1 = s2, saying that the working macro distance in front of the lens node (extended at 1:1) is equal to the distance to the sensor image plane (both sides at 2x focal length). This makes f/stop number be 2x, which is 2 EV light loss. Those are basics. Internal focusing macro lenses can slightly reduce this light loss, but it is still near 2 EV. The Math Sensor dimension / 2focal length  =  Field dimension / 2distance This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

Sensor Width mm × Distance Focal Length mm  = Field Width   Field Width × Focal Length mm Sensor Width mm  = Distance    This looks simple because it is (but correct sensor size and focal length are required). Twice the focal length is half the field, or twice the distance is twice the field dimension. And assuming use of a proper lens designed for the sensor, twice the sensor dimension is twice the field, which is why a smaller "cropped" sensor sees a smaller field unless compensated with a shorter lens. These ratios above are just the trig tangent (opposite over adjacent), necessarily equal for the equal angles, but using the ratios is simpler math for the field dimensions. But computing the angle of view requires trigonometry, for dimensions of Width, Height, or Diagonal angles of view. The 2's do NOT cancel out for this trig tangent. Field angle of view = 2 x arctan ((sensor dimension (mm) / 2) / focal length (mm)) 2 × arctan(  Sensor Width mm 2 × Focal Length mm )  =  Degrees

1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

The drawbacks of the above methods seem to be insurmountable, and researchers are putting forth effort to develop new devices for sampling. To date, many swallowable devices have been used to observe the intestine and deliver drugs. Due to the non-invasive characteristics of swallowable devices, their use is increasingly considered to collect intestinal contents. Based on microelectromechanical systems (MEMS) technology, Cui et al. invented a swallowable capsule that can deliver drugs and collect intestinal fluid (Cui et al., 2008). The characteristics of gastrointestinal tract positioning, wireless communication and large sample size give the capsule the ability to automatically collect intestinal fluid. However, the limitation of this device is that the collected sample is easily polluted by the downstream liquid. In recent years, NIZO has developed an intelligent capsule for small intestinal sampling of the microbiomeby combining the IntelliCap® system and the quencher. The IntelliCap® system is a swallowable capsule that contains pH and temperature sensors, communication units, μ-computers, motors and batteries. The quencher is a container placed in the capsule for qualitative and quantitative preservation of microbiota. The capsules can be positioned by measuring significant changes in pH in the GI tract (Koziolek et al., 2015). When the swallowed capsule reaches the designated region of the small intestine, the aspiration of the intestinal fluid can be initiated. Aspirated intestinal fluid can be collected after the capsule is discharged from the body. Recently, Rezaei Nejad et al. also reported a 3D-printed pill for aspirating small intestinal fluid (Rezaei Nejad et al., 2019). This pill comprises a semipermeable membrane to separate the helical channels and salt chamber. The higher osmotic pressure on the side of the salt chamber drives the liquid in the helical channels to flow to the chamber through the semipermeable membrane. Then, the intestinal fluid can be aspirated from the inlets connected to the helical channels. The outer enteric capsule shell ensures that the collection begins in the small intestine. Compared to NIZO's capsule, the cost of this battery-less pill will certainly be much lower. However, the problem of sample preservation after collection seems to have not been solved, which may lead to the contamination of samples with intestinal fluid from non-collected sites.

However, the Field of View calculator and the Depth of Field calculators instead are designed around the Thin Lens Model, and are measured to a node point inside a "Normal" lens, perhaps near its middle. So calculated distances are measured to the designed focal nodes. We are rarely told where the nodes are designed, often both are inside the lens body somewhere, but some are outside. For telephoto lenses, the rear node H' (focal length from sensor plane) is instead designed just outside the front lens element, and its field H node is the focal length dimension approximately in front of the front lens surface (see an example). The designer's term "telephoto" is about this reposition of the nodal point so that the physical lens is NOT longer than its focal length. And in wide angle lenses for DSLR, the rear node H' is generally designed behind the rear lens surface, at least for SLR (lens is moved well forward to provide room to allow the larger SLR mirror to rise... 12 mm lens but 24 mm mirror, etc). This difference is only a few inches, but it affects where the focused distance is measured to the sensor. And it shifts a bit as the lens is focused much closer. Repeating, the focal length marked on the lens is specified for when focus at infinity, and focal length is longer when focused closer. But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Camerafield of viewsimulator

Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

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Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used.

The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

The Math Sensor dimension / 2focal length  =  Field dimension / 2distance This diagram is the basis of Field of View and Depth of Field calculations. The half angles form geometry's Similar Triangles from the equal angles on each side of the lens. The /2 cancels out on both sides. This equation simply says that the equal angles have the same trigonometry tangent (opposite / adjacent) on each side of lens (but the /2 must be included then). The lens is simply an enlargement device (actually a size reduction) proportionally to the ratio of focal length / field distance. But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

Rearrange this ratio to compute desired unknown value. Examples: Distance to Object *  =   Real Object height * × Focal Length (mm) Object height on sensor (mm) Real Object height *  =   Distance to Object * × Object height on sensor (mm) Focal Length (mm) * feet or meters (but both same units) There are Other possible arrangements. But this next one must use Field dimension and Height converted to mm (304.8 mm per foot), because each ratio must be a dimensionless number. Magnification =  Distance to Object (mm) Focal Length (mm) =  Real Object height (mm) Object height on sensor (mm) This is magnification on the sensor or film. The image must still be enlarged for viewing.1:1 macro reproduction at 1× is when these two top and bottom values are equal.Distant object size is reduced greatly, like perhaps maybe magnification of 0.001x or less.

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And a fisheye lens is a different animal, wider view than this formula predicts. A regular lens is rectilinear, meaning it shows straight lines as straight lines, not curved. A fisheye is rather unconcerned about this distortion, and can show a wider view, poorly purists might say, but very wide, and very possibly interesting.

Reviewed by: Gyanendra Prakash Dubey, Institut Pasteur, France; Kun Zhang, Virginia Commonwealth University, United States

But be aware that focal length lengthens with closer focus distance (and is generally unknown then (focal length is 2x at 1:1 magnification, but lens internal focusing can make changes). Focusing and zooms and especially internal focusing change focal length internally. The focal length marked on the lens is at infinity focus. Focal length is generally near close enough at the closest focus of a regular lens, but calculations will be more accurate if focus is out a bit further. But macro work uses Magnification instead of subject distance. This Thin Lens Model simplifies, as if it were a simple one glass element (like a handheld magnifying lens) with only the one central node point. Multi-element “Thick” camera lenses have two nodes for each side of lens (see the fstop page). But camera lenses normally have several (to many) glass lens elements (a thick lens), designed to correct optical aberrations and distortions, and also to zoom. The Thin Lens Model does still work well for practical computing purposes, at least at distances of at least maybe a meter or two, making a few mm dimension to the node be less important (a bit more description below). The focal length is measured from the sensor plane to the lens node H' (often inside the lens, but not always). Technically, the focal length Marked on the lens applies when focused at infinity, but it will be a bit longer when focused closer. Lens equations use distance d in front of the field node, however note that specifications of lens focus-distance (like minimum closest focus) specify s to the sensor, the sum of d and f. The standard camera magnification geometry uses the standard ratios of the similar triangles shown above. The field dimension angle in front of this lens node is the same angle (opposite angles) as the sensor dimension angle behind the lens. The ratio of distances on each side of the lens are the same as the ratio of the size dimensions on each side of the lens. These ratios (as shown first below) are simply the trigonometry tangents of the same angle on each side of the lens (tangent is opposite side over adjacent side). In this equation, rearrangement will compute any one term from the other three. But one mm of error in focal length or sensor size is magnified in the field, so input accuracy is critical. The math is simple, but the difficult part of computing this will be to first accurately determine the correct sensor dimensions, and/or the zoom lens focal length (small errors get magnified at the larger distant field). Trigonometry does also work for this, but we don't need trig except to compute the actual angles of Field of View. Because Field of View dimensions are just similar triangles (shown gray above). The three field or sensor dimensions are Height, Width, or Diagonal, each are computed individually. Using the (opposite dimension / 2) to create right angles for trig, these ratios are the trig tangent of the half angles, which is the same opposite angle on both sides of lens (the two formula ratios are necessarily equal). The /2 cancels out on both sides, and any unit conversions to feet or meters on the right side cancel out. It becomes a very simple equation. Do be consistent with units, but then there is no conversion of units needed (same ratio on both sides). Basics of lens optics in all of these equations(similar triangles on both sides of the lens)

But the "Subject Distance" (S in diagram) is measured to the sensor focal plane (it is the "focus distance"), where we see a small line symbol like ϴ marked on the top of the camera (often near top LCD on right side, but some are on left side of camera). The line across the circle indicates the location of the film or sensor plane (for focus measurements). However, the Thin Lens Equation uses the working distance d in front of the lens. This is why we often see in equations: (S - f) used for d.  Again, three points. Simple cameras typically do not give specifications about the sensor size in mm (the 1/xx inch number is near meaningless dimensionally). However crop factor might be determined, and can compute sensor size. The focal length is a nominal number, rounded, not precisely exact. And the marked focal length applies at infinity, and it will be a little different if focused close, so the focus distance should not be too close, at least a meter or two. Normally lenses won't focus close enough to matter much (except macro lenses). Camcorder 16:9 fits the full view circle from the lens. But 16:9 video on a 3:2 or 4:3 camera sensor (or a 4:3 image from a 16:9 camcorder) is cropped and resampled, instead of fitting the lens full view circle. The Field of View calculator handles that, always with the assumption that the maximum possible area of the sensor is always used. Some cameras make exceptions to that, unknown to me. Or if you know, you can specify the exact size of the sensor used. For Macro, computing Field size from magnification is more convenient than from focal length, since we don't really know focal length at macro extension. The math above WILL BE INACCURATE at macro distances, because the Focal Length has changed there. For example, we do know the Thin Lens Formula specifies focal length at 1:1 is extended to 2x the marked focal length at infinity. So FWIW, for the calculator Option 8 for magnification 1 (1:1) for a 50 mm lens at 2x, we could enter it as 100 mm, and compute field width for a full frame sensor as 0.11811 feet (which x12 and x25.4 is the expected 36 mm full frame width for 1:1). Subject distance becomes 0.32808 feet (both are feet if we use feet), which x12 is 3.9 inches. But this distance is measured to the Principle Point typically inside the lens somewhere, which we really don't know where that is, and it becomes very significant for macro. Which is why field of view for macro is instead computed from magnification (reproduction ratio, like 1:1). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

But computing the angle of view requires trigonometry, for dimensions of Width, Height, or Diagonal angles of view. The 2's do NOT cancel out for this trig tangent.

Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or the ratio of size of sensor to the size of the remote field. We could compute for magnification here, but we likely don't know new focal length at that close magnification. Just using magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification. However Magnification is simply:     m = s2/s1.   Or m = f/d.   Or m = f/(S-f). Other macro ideas: Actual focal length = Sensor dimension × Working distance / Field dimension Those are all in the same units. Note that working dimension is to the lenses internal node, and NOT just to the front of the lens. Which is probably only an inch or two difference, but it becomes very significant at macro distances. Field dimension = Sensor dimension / Magnification Let's say it this way: 1:1 macro, the focal length f is same as the distance d in front of lens (each with its own node). 1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 1:2 macro (magnification 0.5), the field of view is twice the size of the sensor. 1:4 macro (magnification 0.25), the field of view is four times the size of the sensor. This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro. The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24 mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity). The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why. But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or so, reducing the focal length error to be insignificant. Menu of the other Photo and Flash pages here

Rearrange this ratio to compute desired unknown value. Examples: Distance to Object *  =   Real Object height * × Focal Length (mm) Object height on sensor (mm) Real Object height *  =   Distance to Object * × Object height on sensor (mm) Focal Length (mm) * feet or meters (but both same units) There are Other possible arrangements. But this next one must use Field dimension and Height converted to mm (304.8 mm per foot), because each ratio must be a dimensionless number. Magnification =  Distance to Object (mm) Focal Length (mm) =  Real Object height (mm) Object height on sensor (mm) This is magnification on the sensor or film. The image must still be enlarged for viewing.1:1 macro reproduction at 1× is when these two top and bottom values are equal.Distant object size is reduced greatly, like perhaps maybe magnification of 0.001x or less.

Field angle of view = 2 x arctan ((sensor dimension (mm) / 2) / focal length (mm)) 2 × arctan(  Sensor Width mm 2 × Focal Length mm )  =  Degrees

The Marked focal length of any lens is a rounded nominal number, like 50 or 60 mm. The actual can be a few percent different. Furthermore, the Marked focal length is only applicable to focus at infinity. Focal length normally increases when lens is extended forward to focus closer. Lens specs normally indicate this internal extension at closest focus distance. But internal focusing lenses can do internal tricks with focal length (some zooms and macro lenses can be shorter when up close, instead of longer). But generally speaking, focal length becomes a little longer at very close distances (2x longer at 1:1), so field of view could be a little smaller, but should be insignificant as long as magnification is greater than 0.1x, which in regular lenses is normally near their Minimum focus distance. But this calculation does not include macro distances. We are only seeking a ballpark FOV number anyway, we adjust small differences with our subject framing or cropping, but vague guesses about your distance and sensor size or focal length don't help FOV accuracy. And a fisheye lens is a different animal, wider view than this formula predicts. A regular lens is rectilinear, meaning it shows straight lines as straight lines, not curved. A fisheye is rather unconcerned about this distortion, and can show a wider view, poorly purists might say, but very wide, and very possibly interesting.

The gut microbiota changes gradually with time, and differences have been found between younger and older adults (O'Toole and Jeffery, 2015). The gut microbiota differs between individuals due to many factors, such as genes and diet. Studies have shown that high-carbohydrate and high-fiber diets could increase the abundance and diversity of intestinal microorganisms, especially in individuals with reduced microbial diversity (Tap et al., 2015; Sheflin et al., 2017). Low-carbohydrate diets can significantly reduce the number of butyric-acid-producing bacteria (such as Roseburia and Bifidobacterium), thereby reducing the production of butyric acid and reducing the protective effect on the intestine (Duncan et al., 2007; Russell et al., 2011). The immature gut microbiota is considered to be one of the causes of malnutrition, and human milk oligosaccharides can ameliorate malnutrition by regulating the microbiome (Blanton et al., 2016; Charbonneau et al., 2016). Moreover, the occurrence of many diseases, such as Clostridium difficile infection, inflammatory bowel disease (IBD) and irritable bowel syndrome (IBS), is also related to an alteration of gut microbiota. Long-term use of a large number of broad-spectrum antibiotics can lead to dysbiosis, such as C. difficile infection (Stanley and Burns, 2010). Compared with the control group, studies of intestinal microflora in IBD patients have consistently shown changes in microflora composition and reduced overall biodiversity, for instance, an increase in facultative anaerobes and a decrease in obligate anaerobes (Shim, 2013; Lloyd-Price et al., 2019). The occurrence of IBS is thought to be associated with the microbial effect on gut-brain communication (Eisenstein, 2016).