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d {\displaystyle d} represents the size of the film (or sensor) in the direction measured (see below: sensor effects). For example, for 35 mm film which is 36 mm wide and 24 mm high, d = 36 m m {\displaystyle d=36\,\mathrm {mm} } would be used to obtain the horizontal angle of view and d = 24 m m {\displaystyle d=24\,\mathrm {mm} } for the vertical angle.
Today, most lenses are multi-coated in order to minimize lens flare and other unwanted effects. Some lenses have a UV coating to keep out the ultraviolet light that could taint color. Most modern optical cements for bonding glass elements also block UV light, negating the need for a UV filter. However, this leaves an avenue for lens fungus to attack if lenses are not cared for appropriately. UV photographers must go to great lengths to find lenses with no cement or coatings.
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A macro lens used in macro or "close-up" photography (not to be confused with the compositional term close up) is any lens that produces an image on the focal plane (i.e., film or a digital sensor) that is one quarter of life size (1:4) to the same size (1:1) as the subject being imaged. There is no official standard to define a macro lens, usually a prime lens, but a 1:1 ratio is, typically, considered "true" macro. Magnification from life size to larger is called "Micro" photography (2:1, 3:1 etc.). This configuration is generally used to image close-up very small subjects. A macro lens may be of any focal length, the actual focus length being determined by its practical use, considering magnification, the required ratio, access to the subject, and illumination considerations. It can be a special lens corrected optically for close up work or it can be any lens modified (with adapters or spacers, which are also known as "extension tubes".) to bring the focal plane "forward" for very close photography. Depending on the camera to subject distance and aperture, the depth-of-field can be very narrow, limiting the linear depth of the area that will be in focus. Lenses are usually stopped down to give a greater depth-of-field.
Focal lengths are usually specified in millimetres (mm), but older lenses might be marked in centimetres (cm) or inches. For a given film or sensor size, specified by the length of the diagonal, a lens may be classified as a:
Glass is the most common material used to construct lens elements, due to its good optical properties and resistance to scratching. Other materials are also used, such as quartz glass, fluorite,[3][4][5][6] plastics like acrylic (Plexiglass), and even germanium and meteoritic glass.[citation needed] Plastics allow the manufacturing of strongly aspherical lens elements which are difficult or impossible to manufacture in glass, and which simplify or improve lens manufacturing and performance.[citation needed] Plastics are not used for the outermost elements of all but the cheapest lenses as they scratch easily. Molded plastic lenses have been used for the cheapest disposable cameras for many years, and have acquired a bad reputation: manufacturers of quality optics tend to use euphemisms such as "optical resin". However many modern, high performance (and high priced) lenses from popular manufacturers include molded or hybrid aspherical elements, so it is not true that all lenses with plastic elements are of low photographic quality.[citation needed]
For lenses projecting rectilinear (non-spatially-distorted) images of distant objects, the effective focal length and the image format dimensions completely define the angle of view. Calculations for lenses producing non-rectilinear images are much more complex and in the end not very useful in most practical applications. (In the case of a lens with distortion, e.g., a fisheye lens, a longer lens with distortion can have a wider angle of view than a shorter lens with low distortion)[3] Angle of view may be measured horizontally (from the left to right edge of the frame), vertically (from the top to bottom of the frame), or diagonally (from one corner of the frame to its opposite corner).
Field of view camera
The collimator's distant virtual image of the target subtends a certain angle, referred to as the angular extent of the target, that depends on the collimator focal length and the target size. Assuming the sensed image includes the whole target, the angle seen by the camera, its FOV, is this angular extent of the target times the ratio of full image size to target image size.[10]
The lens usually is focused by adjusting the distance from the lens assembly to the image plane, or by moving elements of the lens assembly. To improve performance, some lenses have a cam system that adjusts the distance between the groups as the lens is focused. Manufacturers call this different things: Nikon calls it CRC (close range correction); Canon calls it a floating system; and Hasselblad and Mamiya call it FLE (floating lens element).[2]
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Now α / 2 {\displaystyle \alpha /2} is the angle between the optical axis of the lens and the ray joining its optical center to the edge of the film. Here α {\displaystyle \alpha } is defined to be the angle-of-view, since it is the angle enclosing the largest object whose image can fit on the film. We want to find the relationship between:
Zoom lenses are a special case wherein the focal length, and hence angle of view, of the lens can be altered mechanically without removing the lens from the camera.
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From the definition of magnification, m = S 2 / S 1 {\displaystyle m=S_{2}/S_{1}} , we can substitute S 1 {\displaystyle S_{1}} and with some algebra find: S 2 = F ⋅ ( 1 + m ) {\displaystyle S_{2}=F\cdot (1+m)}
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The lens mount design is an important issue for compatibility between cameras and lenses. There is no universal standard for lens mounts, and each major camera maker typically uses its own proprietary design, incompatible with other makers.[16] A few older manual focus lens mount designs, such as the Leica M39 lens mount for rangefinders, M42 lens mount for early SLRs, and the Pentax K mount are found across multiple brands, but this is not common today. A few mount designs, such as the Olympus/Kodak Four Thirds System mount for DSLRs, have also been licensed to other makers.[17] Most large-format cameras take interchangeable lenses as well, which are usually mounted in a lensboard or on the front standard.
This table shows the diagonal, horizontal, and vertical angles of view, in degrees, for lenses producing rectilinear images, when used with 36 mm × 24 mm format (that is, 135 film or full-frame 35 mm digital using width 36 mm, height 24 mm, and diagonal 43.3 mm for d in the formula above).[16] Digital compact cameras sometimes state the focal lengths of their lenses in 35 mm equivalents, which can be used in this table.
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FOVurban dictionary
UV/visible light from an integrating sphere (and/or other source such as a black body) is focused onto a square test target at the focal plane of a collimator (the mirrors in the diagram), such that a virtual image of the test target will be seen infinitely far away by the camera under test. The camera under test senses a real image of the virtual image of the target, and the sensed image is displayed on a monitor.[9]
A second effect which comes into play in macro photography is lens asymmetry (an asymmetric lens is a lens where the aperture appears to have different dimensions when viewed from the front and from the back). The lens asymmetry causes an offset between the nodal plane and pupil positions. The effect can be quantified using the ratio (P) between apparent exit pupil diameter and entrance pupil diameter. The full formula for angle of view now becomes:[7] α = 2 arctan d 2 F ⋅ ( 1 + m / P ) {\displaystyle \alpha =2\arctan {\frac {d}{2F\cdot (1+m/P)}}}
In the optical instrumentation industry the term field of view (FOV) is most often used, though the measurements are still expressed as angles.[8] Optical tests are commonly used for measuring the FOV of UV, visible, and infrared (wavelengths about 0.1–20 μm in the electromagnetic spectrum) sensors and cameras.
If the subject image size remains the same, then at any given aperture all lenses, wide angle and long lenses, will give the same depth of field.[15]
Field of view human eye
A camera's angle of view depends not only on the lens, but also on the sensor. Digital sensors are usually smaller than 35 mm film, and this causes the lens to have a narrower angle of view than with 35 mm film, by a constant factor for each sensor (called the crop factor). In everyday digital cameras, the crop factor can range from around 1 (professional digital SLRs), to 1.6 (consumer SLR), to 2 (Micro Four Thirds ILC) to 6 (most compact cameras). So a standard 50 mm lens for 35 mm photography acts like a 50 mm standard "film" lens on a professional digital SLR, but would act closer to an 80 mm lens (1.6×50mm) on many mid-market DSLRs, and the 40-degree angle of view of a standard 50 mm lens on a film camera is equivalent to an 80 mm lens on many digital SLRs.
The table below shows the horizontal, vertical and diagonal angles of view, in degrees, when used with 22.2 mm × 14.8 mm format (that is Canon's DSLR APS-C frame size) and a diagonal of 26.7 mm.
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The two fundamental parameters of an optical lens are the focal length and the maximum aperture. The lens' focal length determines the magnification of the image projected onto the image plane, and the aperture the light intensity of that image. For a given photographic system the focal length determines the angle of view, short focal lengths giving a wider field of view than longer focal length lenses. A wider aperture, identified by a smaller f-number, allows using a faster shutter speed for the same exposure. The camera equation, or G#, is the ratio of the radiance reaching the camera sensor to the irradiance on the focal plane of the camera lens.[8]
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A lens will most often have an aperture adjustment mechanism, usually an iris diaphragm, to regulate the amount of light that passes. In early camera models a rotating plate or slider with different sized holes was used. These Waterhouse stops may still be found on modern, specialized lenses. A shutter, to regulate the time during which light may pass, may be incorporated within the lens assembly (for better quality imagery), within the camera, or even, rarely, in front of the lens. Some cameras with leaf shutters in the lens omit the aperture, and the shutter does double duty.
The most common interchangeable lens mounts on the market today include the Canon EF, EF-S and EF-M autofocus lens mounts. Others include the Nikon F manual and autofocus mounts, the Olympus/Kodak Four Thirds and Olympus/Panasonic Micro Four Thirds digital-only mounts, the Pentax K mount and autofocus variants, the Sony Alpha mount (derived from the Minolta mount) and the Sony E digital-only mount.
The effective focal length is nearly equal to the stated focal length of the lens (F), except in macro photography where the lens-to-object distance is comparable to the focal length. In this case, the magnification factor (m) must be taken into account: f = F ⋅ ( 1 + m ) {\displaystyle f=F\cdot (1+m)}
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From the front of the camera, the small hole (the aperture), would be seen. The virtual image of the aperture as seen from the world is known as the lens's entrance pupil; ideally, all rays of light leaving a point on the object that enter the entrance pupil will be focused to the same point on the image sensor/film (provided the object point is in the field of view). If one were inside the camera, one would see the lens acting as a projector. The virtual image of the aperture from inside the camera is the lens's exit pupil. In this simple case, the aperture, entrance pupil, and exit pupil are all in the same place because the only optical element is in the plane of the aperture, but in general these three will be in different places. Practical photographic lenses include more lens elements. The additional elements allow lens designers to reduce various aberrations, but the principle of operation remains the same: pencils of rays are collected at the entrance pupil and focused down from the exit pupil onto the image plane.
Typical rectilinear lenses can be thought of as "improved" pinhole "lenses". As shown, a pinhole "lens" is simply a small aperture that blocks most rays of light, ideally selecting one ray to the object for each point on the image sensor. Pinhole lenses have a few severe limitations:
A side effect of using lenses of different focal lengths is the different distances from which a subject can be framed, resulting in a different perspective. Photographs can be taken of a person stretching out a hand with a wideangle, a normal lens, and a telephoto, which contain exactly the same image size by changing the distance from the subject. But the perspective will be different. With the wideangle, the hands will be exaggeratedly large relative to the head. As the focal length increases, the emphasis on the outstretched hand decreases. However, if pictures are taken from the same distance, and enlarged and cropped to contain the same view, the pictures will have identical perspective. A moderate long-focus (telephoto) lens is often recommended for portraiture because the perspective corresponding to the longer shooting distance is considered to look more flattering.
(In photography m {\displaystyle m} is usually defined to be positive, despite the inverted image.) For example, with a magnification ratio of 1:2, we find f = 1.5 ⋅ F {\displaystyle f=1.5\cdot F} and thus the angle of view is reduced by 33% compared to focusing on a distant object with the same lens.
The sensed image, which includes the target, is displayed on a monitor, where it can be measured. Dimensions of the full image display and of the portion of the image that is the target are determined by inspection (measurements are typically in pixels, but can just as well be inches or cm).
Because different lenses generally require a different camera–subject distance to preserve the size of a subject, changing the angle of view can indirectly distort perspective, changing the apparent relative size of the subject and foreground.
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The target's angular extent is: α = 2 arctan L 2 f c {\displaystyle \alpha =2\arctan {\frac {L}{2f_{c}}}} where L {\displaystyle L} is the dimension of the target and f c {\displaystyle f_{c}} is the focal length of collimator.
For macro photography, we cannot neglect the difference between S 2 {\displaystyle S_{2}} and F {\displaystyle F} . From the thin lens formula, 1 F = 1 S 1 + 1 S 2 . {\displaystyle {\frac {1}{F}}={\frac {1}{S_{1}}}+{\frac {1}{S_{2}}}.}
Because this is a trigonometric function, the angle of view does not vary quite linearly with the reciprocal of the focal length. However, except for wide-angle lenses, it is reasonable to approximate α ≈ d f {\displaystyle \alpha \approx {\frac {d}{f}}} radians or 180 d π f {\displaystyle {\frac {180d}{\pi f}}} degrees.
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The maximum usable aperture of a lens is specified as the focal ratio or f-number, defined as the lens's focal length divided by the effective aperture (or entrance pupil), a dimensionless number. The lower the f-number, the higher light intensity at the focal plane. Larger apertures (smaller f-numbers) provide a much shallower depth of field than smaller apertures, other conditions being equal. Practical lens assemblies may also contain mechanisms to deal with measuring light, secondary apertures for flare reduction,[9] and mechanisms to hold the aperture open until the instant of exposure to allow SLR cameras to focus with a brighter image with shallower depth of field, theoretically allowing better focus accuracy.
Modifying the angle of view over time (known as zooming), is a frequently used cinematic technique, often combined with camera movement to produce a "dolly zoom" effect, made famous by the film Vertigo. Using a wide angle of view can exaggerate the camera's perceived speed, and is a common technique in tracking shots, phantom rides, and racing video games. See also Field of view in video games.
A camera lens may be made from a number of elements: from one, as in the Box Brownie's meniscus lens, to over 20 in the more complex zooms. These elements may themselves comprise a group of lenses cemented together.
The widest aperture lens in history of photography is believed to be the Carl Zeiss Planar 50mm f/0.7,[11] which was designed and made specifically for the NASA Apollo lunar program to capture the far side of the Moon in 1966. Three of these lenses were purchased by filmmaker Stanley Kubrick in order to film scenes in his 1975 film Barry Lyndon, using candlelight as the sole light source.[12][13][14]
Practical lenses can be thought of as an answer to the question: "how can a pinhole lens be modified to admit more light and give a smaller spot size?". A first step is to put a simple convex lens at the pinhole with a focal length equal to the distance to the film plane (assuming the camera will take pictures of distant objects[1]). This allows the pinhole to be opened up significantly (fourth image) because a thin convex lens bends light rays in proportion to their distance to the axis of the lens, with rays striking the center of the lens passing straight through. The geometry is almost the same as with a simple pinhole lens, but rather than being illuminated by single rays of light, each image point is illuminated by a focused "pencil" of light rays.
Many single-lens reflex cameras and some rangefinder cameras have detachable lenses. A few other types do as well, notably the Mamiya TLR cameras and SLR, medium format cameras (RZ67, RB67, 645-1000s)other companies that produce medium format equipment such as Bronica, Hasselblad and Fuji have similar camera styles that allow interchangeability in the lenses as well, and mirrorless interchangeable-lens cameras. The lenses attach to the camera using a lens mount, which contains mechanical linkages and often also electrical contacts between the lens and camera body.
Note that the angle of view varies slightly when the focus is not at infinity (See breathing (lens)), given by S 2 = S 1 f S 1 − f {\displaystyle S_{2}={\frac {S_{1}f}{S_{1}-f}}} rearranging the lens equation.
Field of view definition microscope
The purpose of this test is to measure the horizontal and vertical FOV of a lens and sensor used in an imaging system, when the lens focal length or sensor size is not known (that is, when the calculation above is not immediately applicable). Although this is one typical method that the optics industry uses to measure the FOV, there exist many other possible methods.
The total field of view is then approximately: F O V = α D d {\displaystyle \mathrm {FOV} =\alpha {\frac {D}{d}}} or more precisely, if the imaging system is rectilinear: F O V = 2 arctan L D 2 f c d {\displaystyle \mathrm {FOV} =2\arctan {\frac {LD}{2f_{c}d}}}
For a lens projecting a rectilinear image (focused at infinity, see derivation), the angle of view (α) can be calculated from the chosen dimension (d), and effective focal length (f) as follows:[4] α = 2 arctan d 2 f {\displaystyle \alpha =2\arctan {\frac {d}{2f}}}
The complexity of a lens — the number of elements and their degree of asphericity — depends upon the angle of view, the maximum aperture, and intended price point, among other variables. An extreme wideangle lens of large aperture must be of very complex construction to correct for optical aberrations, which are worse at the edge of the field and when the edge of a large lens is used for image-forming. A long-focus lens of small aperture can be of very simple construction to attain comparable image quality: a doublet (two elements) will often suffice. Some older cameras were fitted with convertible lenses (German: Satzobjektiv) of normal focal length. The front element could be unscrewed, leaving a lens of twice the focal length, and half the angle of view and half the aperture. The simpler half-lens was of adequate quality for the narrow angle of view and small relative aperture. This would require the bellows had to be extended to twice the normal length.
Consider a rectilinear lens in a camera used to photograph an object at a distance S 1 {\displaystyle S_{1}} , and forming an image that just barely fits in the dimension, d {\displaystyle d} , of the frame (the film or image sensor). Treat the lens as if it were a pinhole at distance S 2 {\displaystyle S_{2}} from the image plane (technically, the center of perspective of a rectilinear lens is at the center of its entrance pupil):[6]
In photography, angle of view (AOV)[1] describes the angular extent of a given scene that is imaged by a camera. It is used interchangeably with the more general term field of view.
Using basic trigonometry, we find: tan ( α / 2 ) = d / 2 S 2 . {\displaystyle \tan(\alpha /2)={\frac {d/2}{S_{2}}}.} which we can solve for α, giving: α = 2 arctan d 2 S 2 {\displaystyle \alpha =2\arctan {\frac {d}{2S_{2}}}}
Another result of using a wide angle lens is a greater apparent perspective distortion when the camera is not aligned perpendicularly to the subject: parallel lines converge at the same rate as with a normal lens, but converge more due to the wider total field. For example, buildings appear to be falling backwards much more severely when the camera is pointed upward from ground level than they would if photographed with a normal lens at the same distance from the subject, because more of the subject building is visible in the wide-angle shot.
It is important to distinguish the angle of view from the angle of coverage, which describes the angle range that a lens can image. Typically the image circle produced by a lens is large enough to cover the film or sensor completely, possibly including some vignetting toward the edge. If the angle of coverage of the lens does not fill the sensor, the image circle will be visible, typically with strong vignetting toward the edge, and the effective angle of view will be limited to the angle of coverage.
The front element is critical to the performance of the whole assembly. In all modern lenses the surface is coated to reduce abrasion, flare, and surface reflectance, and to adjust color balance. To minimize aberration, the curvature is usually set so that the angle of incidence and the angle of refraction are equal. In a prime lens this is easy, but in a zoom there is always a compromise.
Consider a 35 mm camera with a lens having a focal length of F = 50 mm. The dimensions of the 35 mm image format are 24 mm (vertically) × 36 mm (horizontal), giving a diagonal of about 43.3 mm.
The 1951 USAF resolution test chart is one way to measure the resolving power of a lens. The quality of the material, coatings, and build affect the resolution. Lens resolution is ultimately limited by diffraction, and very few photographic lenses approach this resolution. Ones that do are called "diffraction limited" and are usually extremely expensive.[7]
There is no major difference in principle between a lens used for a still camera, a video camera, a telescope, a microscope, or other apparatus, but the details of design and construction are different. A lens might be permanently fixed to a camera, or it might be interchangeable with lenses of different focal lengths, apertures, and other properties.
Some lenses, called zoom lenses, have a focal length that varies as internal elements are moved, typically by rotating the barrel or pressing a button which activates an electric motor. Commonly, the lens may zoom from moderate wide-angle, through normal, to moderate telephoto; or from normal to extreme telephoto. The zoom range is limited by manufacturing constraints; the ideal of a lens of large maximum aperture which will zoom from extreme wideangle to extreme telephoto is not attainable. Zoom lenses are widely used for small-format cameras of all types: still and cine cameras with fixed or interchangeable lenses. Bulk and price limit their use for larger film sizes. Motorized zoom lenses may also have the focus, iris, and other functions motorized.
To project a sharp image of distant objects, S 2 {\displaystyle S_{2}} needs to be equal to the focal length, F {\displaystyle F} , which is attained by setting the lens for infinity focus. Then the angle of view is given by:
Defining f = S 2 {\displaystyle f=S_{2}} as the "effective focal length", we get the formula presented above: α = 2 arctan d 2 f {\displaystyle \alpha =2\arctan {\frac {d}{2f}}} where f = F ⋅ ( 1 + m ) {\displaystyle f=F\cdot (1+m)} .
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While in principle a simple convex lens will suffice, in practice a compound lens made up of a number of optical lens elements is required to correct (as much as possible) the many optical aberrations that arise. Some aberrations will be present in any lens system. It is the job of the lens designer to balance these and produce a design that is suitable for photographic use and possibly mass production.
For a given camera–subject distance, longer lenses magnify the subject more. For a given subject magnification (and thus different camera–subject distances), longer lenses appear to compress distance; wider lenses appear to expand the distance between objects.
A camera lens (also known as photographic lens or photographic objective) is an optical lens or assembly of lenses used in conjunction with a camera body and mechanism to make images of objects either on photographic film or on other media capable of storing an image chemically or electronically.
As noted above, a camera's angle level of view depends not only on the lens, but also on the sensor used. Digital sensors are usually smaller than 35 mm film, causing the lens to usually behave as a longer focal length lens would behave, and have a narrower angle of view than with 35 mm film, by a constant factor for each sensor (called the crop factor). In everyday digital cameras, the crop factor can range from around 1 (professional digital SLRs), to 1.6 (mid-market SLRs), to around 3 to 6 for compact cameras. So a standard 50 mm lens for 35 mm photography acts like a 50 mm standard "film" lens even on a professional digital SLR, but would act closer to a 75 mm (1.5×50 mm Nikon) or 80 mm lens (1.6×50mm Canon) on many mid-market DSLRs, and the 40-degree angle of view of a standard 50 mm lens on a film camera is equivalent to a 28–35 mm lens on many digital SLRs.
Good-quality lenses with maximum aperture no greater than f/2.8 and fixed, normal, focal length need at least three (triplet) or four elements (the trade name "Tessar" derives from the Greek tessera, meaning "four"). The widest-range zooms often have fifteen or more. The reflection of light at each of the many interfaces between different optical media (air, glass, plastic) seriously degraded the contrast and color saturation of early lenses, particularly zoom lenses, especially where the lens was directly illuminated by a light source. The introduction many years ago of optical coatings, and advances in coating technology over the years, have resulted in major improvements, and modern high-quality zoom lenses give images of quite acceptable contrast, although zoom lenses with many elements will transmit less light than lenses made with fewer elements (all other factors such as aperture, focal length, and coatings being equal).[15]