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At this viewing distance and print size, camera manufacturers assume a circle of confusion is negligible if no larger than 0.01 inches (when enlarged). As a result, camera manufacturers use the 0.01 inch standard when providing lens depth of field markers (shown below for f/22 on a 50mm lens). In reality, a person with 20/20 vision or better can distinguish features 1/3 this size, and so the circle of confusion has to be even smaller than this to achieve acceptable sharpness throughout.

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When does the circle of confusion become perceptible to our eyes? An acceptably sharp circle of confusion is loosely defined as one which would go unnoticed when enlarged to a standard 8x10 inch print, and observed from a standard viewing distance of about 1 foot.

If an unmounted aspheric lens is being used to collimate the light from a point source or laser diode, the side with the greater radius of curvature (i.e., the flatter surface) should face the point source or laser diode. To collimate light using one of our mounted aspheric lenses, orient the housing so that the externally threaded end of the mount faces the source.

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The key concept is this: when an object is in focus, light rays originating from that point converge at a point on the camera's sensor. If the light rays hit the sensor at slightly different locations (arriving at a disc instead of a point), then this object will be rendered as out of focus — and increasingly so depending on how far apart the light rays are.

Diagram depicting depth of focus versus camera aperture. The purple lines comprising the edge of each shaded region represent the extreme angles at which light could potentially enter the aperture. The interior of the purple shaded regions represents all other possible angles.

There is a line going through the center of the image, where both sides of the prism surfaces com together. This may cause reflections or spikes.

Thorlabs offers a large selection of mounted and unmounted aspheric lenses to choose from. The aspheric lens with a focal length that is closest to 16 mm has a focal length of 15.29 mm (Item # 354260-B or A260-B). This lens also has a clear aperture that is larger than the collimated beam diameter. Therefore, this option is the best choice given the initial parameters (i.e., a P1-630A-FC-2 single mode fiber and a collimated beam diameter of 3 mm). Remember, for optimal coupling, the spot size of the focused beam must be less than the MFD of the single mode fiber. As a result, if an aspheric lens is not available that provides an exact match, then choose one with a focal length that is shorter than the calculation above yields. Alternatively, if the clear aperture of the aspheric lens is large enough, the beam can be expanded before the aspheric lens, which has the result of reducing the spot size of the focus beam.

*Technical Note: We describe depth of field as being virtually constant because there are limiting cases where this does not hold true. For focal distances resulting in high magnification, or very near the hyperfocal distance, wide angle lenses may provide a greater DoF than telephoto lenses. On the other hand, at high magnification the traditional DoF calculation becomes inaccurate due to another factor: pupil magnification. This reduces the DoF advantage for most wide angle lenses, and increases it for telephoto and macro lenses. At the other limiting case, near the hyperfocal distance, the increase in DoF arises because the wide angle lens has a greater rear DoF, and can thus more easily attain critical sharpness at infinity.

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This exposes a limitation of the traditional DoF concept: it only accounts for the total DoF and not its distribution around the focal plane, even though both may contribute to the perception of sharpness. Note how a wide angle lens provides a more gradually fading DoF behind the focal plane than in front, which is important for traditional landscape photographs.

On the other hand, when standing in the same place and focusing on a subject at the same distance, a longer focal length lens will have a shallower depth of field (even though the pictures will frame the subject entirely differently). This is more representative of everyday use, but is an effect due to higher magnification, not focal length.

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These lenses can be purchased unmounted or premounted in non-magnetic 303 stainless steel lens cells that are engraved with the Item # for easy identification. All mounted aspheres have a metric thread that make them easy to integrate into an optical setup or OEM application; they can also be readily used with our SM1-threaded (1.035"-40) lens tubes by using our aspheric lens adapters. When combined with our microscope objective adapter extension tube, mounted aspheres can be used as a drop-in replacement for multi-element microscope objectives.

Depth of field refers to the range of distance that appears acceptably sharp. It varies depending on camera type, aperture and focusing distance, although print size and viewing distance can also influence our perception of depth of field. This tutorial is designed to give a better intuitive and technical understanding for photography, and provides a depth of field calculator to show how it varies with your camera settings.

The specifications for the P1-630A-FC-2, 630 nm, FC/PC single mode patch cable indicate that the mode field diameter (MFD) is 4.3 μm. This specification should be matched to the diffraction-limited spot size given by the following equation:

Aspheric lenses focus or collimate light without introducing spherical aberration into the transmitted wavefront. For monochromatic sources, spherical aberration often prevents a single spherical lens from achieving diffraction-limited performance when focusing or collimating light. Aspheric lenses are designed to mitigate the impacts of spherical aberration and are often the best single element solution for many applications including collimating the output of a fiber or laser diode, coupling light into a fiber, spatial filtering, or imaging light onto a detector.

Using the laser diode and aspheric lens chosen above, we can use an anamorphic prism pair to convert our collimated, elliptical beam into a circular beam.

Alternatively, we can use the PS871-B unmounted prism pair to achieve the precise magnification of the minor diameter necessary to produce a circular beam. Using the data available here, we see that the PS871-B achieves a magnification of 4.0 when the prisms are positioned at the following angles for a 670 nm wavelength beam:

Note how there is indeed a subtle change for the smallest focal lengths. This is a real effect, but is negligible compared to both aperture and focusing distance. Even though the total depth of field is virtually constant, the fraction of the depth of field which is in front of and behind the focus distance does change with focal length, as demonstrated below:

Since there is no critical point of transition, a more rigorous term called the "circle of confusion" is used to define how much a point needs to be blurred in order to be perceived as unsharp. When the circle of confusion becomes perceptible to our eyes, this region is said to be outside the depth of field and thus no longer "acceptably sharp." The circle of confusion above has been exaggerated for clarity; in reality this would be only a tiny fraction of the camera sensor's area.

Aspheric lenses are commonly chosen to couple incident light with a diameter of 1 - 5 mm into a single mode fiber. A simple example will illustrate the key specifications to consider when trying to choose the correct lens.

Due to the rotational symmetry of the lens surface, only even powers of Y are contained in the polynomial expansion above. The target values of the aspheric coefficients for each product can be found by clicking either on the blue Info Icons in the tables below () or on the red documents icon () next to each lens sold below.

The aspheric surfaces of these lenses may be described using a polynomial expansion in Y, the radial distance from the optical axis. The surface profile or sagitta (often abbreviated as sag) is denoted by z, and is given by the following expression:

For macro photography (high magnification), the depth of field is actually influenced by another factor: pupil magnification. This is equal to one for lenses which are internally symmetric, although for wide angle and telephoto lenses this is greater or less than one, respectively. A greater depth of field is achieved (than would be ordinarily calculated) for a pupil magnification less than one, whereas the pupil magnification does not change the calculation when it is equal to one. The problem is that the pupil magnification is usually not provided by lens manufacturers, and one can only roughly estimate it visually.

where R is the radius of curvature, k is the conic constant, and the An are the nth order aspheric coefficients. The sign of R is determined by whether the center of curvature for the lens surface is located to the right or left of the lens' vertex; a positive R indicates that the center of curvature is located to the right of the vertex, while a negative R indicates that the center of curvature is located to the left of the vertex. For example, the radius of curvature for the left surface of a biconvex lens would be specified as positive, while the radius of curvature for its right surface would be specified as negative.

Whereas earlier we considered only the larger divergence angle, we now look at the smaller beam divergence of 8°. From this, and using the effective focal length of the A390-B aspheric lens chosen in Example 1, we can determine the length of the semi-minor axis of the elliptical beam after collimation:

A selection of the lenses sold on this page are designed for collimating laser diodes. As seen in the tables below, a compatible laser window thickness is listed for these lenses. In these instances, the numerical aperture (NA), working distance (WD), and wavefront error of these lenses are defined based on the presence of a laser window of the indicated thickness (not included).

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Longer focal lengths may also appear to have a shallower depth of field because they enlarge the background relative to the foreground (due to their narrower angle of view). This can make an out of focus background look even more out of focus because its blur has become enlarged. However, this is another concept entirely, since depth of field only describes the sharp region of a photo — not the blurred regions.

The depth of field does not abruptly change from sharp to unsharp, but instead occurs as a gradual transition. In fact, everything immediately in front of or in back of the focusing distance begins to lose sharpness — even if this is not perceived by our eyes or by the resolution of the camera.

Depth of field also appears shallower for SLR cameras than for compact digital cameras, because SLR cameras require a longer focal length to achieve the same field of view (see the tutorial on digital camera sensor sizes for more on this topic).

Refer to the diagram to the right for α1 and α2 definitions. Our 780 nm laser will experience slightly less magnification than a 670 nm beam passing through the prisms at these angles. Some trial and error may be required to achieve the exact desired magnification. In general:

Here, f is the focal length of the lens, λ is the wavelength of the input light, and D is the diameter of collimated beam incident on the lens. Solving for the desired focal length of the collimating lens yields

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The minor beam diameter is double the semi-minor axis, or 0.64 mm. In order to magnify the minor diameter to be equal to the major diameter of 2.5 mm, we will need an anamorphic prism pair that yields a magnification of 3.9. Thorlabs offers both mounted and unmounted prism pairs. Mounted prism pairs provide the benefit of a stable housing to preserve alignment, while unmounted prism pairs can be positioned at any angle to achieve the exact desired magnification.

Assuming that the thickness of the lens is small compared to the radius of curvature, the thin lens approximation can be used to determine the appropriate focal length for the asphere. Assuming a divergence angle of 30° (FWHM) and desired beam diameter of 3 mm:

The PS883-B mounted prism pair provides a magnification of 4.0 for a 950 nm wavelength beam. Because shorter wavelengths undergo greater magnification when passing through the prism pair, we can expect our 780 nm beam to be magnified by slightly more than 4.0X. Thus, the beam will still maintain a small degree of ellipticity.

Since the output of a laser diode is highly divergent, collimating optics are necessary. Aspheric lenses do not introduce spherical aberration and therefore are commonly chosen when the collimated laser beam is to be between one and five millimeters. A simple example will illustrate the key specifications to consider when choosing the correct lens for a given application. The second example below is an extension of the procedure, which will show how to circularize an elliptical beam.

All of the molded glass lenses featured on this page are available with an antireflection coating for either the 600 - 1050 nm or 650 - 1050 nm range deposited on both sides. Other AR coating options are listed in the Aspheric Lens Selection Guide table at right.

With this information known, it is now time to choose the appropriate collimating lens. Thorlabs offers a large selection of aspheric lenses. For this application, the ideal lens is a molded glass aspheric lens with focal length near 5.6 mm and our -B antireflection coating, which covers 780 nm. The C171TMD-B (mounted) or 354171-B (unmounted) aspheric lenses have a focal length of 6.20 mm, which will result in a collimated beam diameter (major axis) of 3.3 mm. Next, check to see if the numerical aperture (NA) of the diode is smaller than the NA of the lens:

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A different maximum circle of confusion also applies for each print size and viewing distance combination. In the earlier example of blurred dots, the circle of confusion is actually smaller than the resolution of your screen for the two dots on either side of the focal point, and so these are considered within the depth of field. Alternatively, the depth of field can be based on when the circle of confusion becomes larger than the size of your digital camera's pixels.

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Note that depth of field only sets a maximum value for the circle of confusion, and does not describe what happens to regions once they become out of focus. These regions are also called "bokeh," from Japanese (pronounced bo-ké). Two images with identical depth of field may have significantly different bokeh, as this depends on the shape of the lens diaphragm. In reality, the circle of confusion is usually not actually a circle, but is only approximated as such when it is very small. When it becomes large, most lenses will render it as a polygonal shape with 5-8 sides.

Note: Depth of field calculations are at f/4.0 on a camera with a 1.6X crop factor,using a circle of confusion of 0.0206 mm.

Up to this point, we have been using the full-width at half maximum (FWHM) beam diameter to characterize the beam. However, a better practice is to use the 1/e2 beam diameter. For a Gaussian beam profile, the 1/e2 diameter is almost equal to 1.7X the FWHM diameter. The 1/e2 beam diameter therefore captures more of the laser diode's output light (for greater power delivery) and minimizes far-field diffraction (by clipping less of the incident light).

Molded glass aspheres are manufactured from a variety of optical glasses to yield the indicated performance. The molding process will cause the properties of the glass (e.g., Abbe number) to deviate slightly from those given by glass manufacturers. Specific material properties for each lens can be found by clicking on the Info Icon  in the tables below and selecting the Glass tab.

When choosing a collimation lens, it is essential to know the divergence angle of the source being used and the desired output diameter. The specifications for the L780P010 laser diode indicate that the typical parallel and perpendicular FWHM beam divergences are 8° and 30°, respectively. Therefore, as the light diverges, an elliptical beam will result. To collect as much light as possible during the collimation process, consider the larger of these two divergence angles in any calculations (i.e., in this case, use 30°). If you wish to convert your elliptical beam into a round one, we suggest using an anamorphic prism pair, which magnifies one axis of your beam; for details, see Example 2 below.

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Another implication of the circle of confusion is the concept of depth of focus (also called the "focus spread"). It differs from depth of field because it describes the distance over which light is focused at the camera's sensor, as opposed to the subject:

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Why not just use the smallest aperture (largest number) to achieve the best possible depth of field? Other than the fact that this may require prohibitively long shutter speeds without a camera tripod, too small of an aperture softens the image by creating a larger circle of confusion (or "Airy disk") due to an effect called diffraction — even within the plane of focus. Diffraction quickly becomes more of a limiting factor than depth of field as the aperture gets smaller. Despite their extreme depth of field, this is also why "pinhole cameras" have limited resolution.

The table below contains all molded visible and near-IR aspheric lenses offered by Thorlabs. For our selection of IR molded aspheres, click here. The Item # listed is that of the unmounted, uncoated lens. An "X" in any of the five AR Coating Columns indicates the lens is available with that coating (note that the V coating availability is indicated with the AR coating wavelength). The table to the right defines each letter and lists the specified AR coating range. Clicking on the X takes you to the landing page where that lens (mounted or unmounted) can be purchased.

Note that focal length has not been listed as influencing depth of field, contrary to popular belief. Even though telephoto lenses appear to create a much shallower depth of field, this is mainly because they are often used to magnify the subject when one is unable to get closer. If the subject occupies the same fraction of the image (constant magnification) for both a telephoto and a wide angle lens, the total depth of field is virtually* constant with focal length! This would of course require you to either get much closer with a wide angle lens or much farther with a telephoto lens, as demonstrated in the following chart:

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In order to calculate the depth of field, one needs to first decide on an appropriate value for the maximum allowable circle of confusion. This is based on both the camera type (sensor or film size), and on the viewing distance / print size combination. Needless to say, knowing what this will be ahead of time often isn't straightforward. Try out the depth of field calculator tool to help you find this for your specific situation.

Although print size and viewing distance influence how large the circle of confusion appears to our eyes, aperture and focusing distance are the two main factors that determine how big the circle of confusion will be on your camera's sensor. Larger apertures (smaller F-stop number) and closer focusing distances produce a shallower depth of field. The following test maintains the same focus distance, but changes the aperture setting:

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A good rule of thumb is to pick a lens with an NA twice that of the laser diode NA. For example, either the A390-B or the A390TM-B could be used as these lenses each have an NA of 0.53, which is more than twice the approximate NA of our laser diode (0.26). These lenses each have a focal length of 4.6 mm, resulting in an approximate major beam diameter of 2.5 mm. In general, using a collimating lens with a short focal length will result in a small collimated beam diameter and a large beam divergence, while a lens with a large focal length will result in a large collimated beam diameter and a small divergence.