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Due to similarity in name and nature, depth of field (DOF) and depth of focus are commonly confused concepts. To simplify the definitions, DOF concerns the image quality of a stationary lens as an object is repositioned, whereas depth of focus concerns a stationary object and a sensor’s ability to maintain focus for different sensor positions, including tilt.

Focal length

Depth of focus is the image-space complement of DOF and is related to how the quality of focus changes on the sensor side of the lens as the sensor is moved, while the object remains in the same position. Depth of focus characterizes how much tip and tilt is tolerated between the lens image plane and the sensor plane itself. As f/# decreases, the depth of focus does as well, which increases the impact that tilt has on achieving best focus across the sensor. Without active alignment, there will always be some degree of variation in the orthogonality between the sensor and the lens that is used; Figure 6 shows how this issue arises. It is generally assumed that problems involving depth of focus only occur with large sensors.

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If you want to adapt lenses that wouldn’t otherwise fit because of their shorter flange focal distance, there’s another option. Optical adapters include a lens element that shifts the focus of the lens. That way, they can push infinity focus further away from the sensor. There’s a problem, though. Most of the time these adapters drastically decrease the optical quality. They may degrade sharpness, and introduce serious color shifting or fringing. Thus, we don’t recommend using them, unless not inescapable.

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The DOF of a lens is its ability to maintain a desired amount of image quality (spatial frequency at a specified contrast), without refocusing, if the object position is moved closer and farther from the plane of best focus. DOF also applies to objects with complex geometries or features of different height. As an object is placed closer to or farther than the set focus distance of a lens, the object blurs and both resolution and contrast suffer. As such, DOF only makes sense if it is defined with an associated resolution and contrast. Several targets can be used to directly measure and benchmark an imaging system’s DOF; these targets are detailed in Test Target Overview.

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When it comes to adaptation, mirrorless mounts have a significant advantage. Their flange distance is much shorter than anything before them. Thus, you can adapt practically any lens onto them. Sony’s E-mount, which is the most popular full frame mirrorless mount, is the leader in this game. You can find E-mount adapters to any almost any lens from the past century. For electronically controlled lenses (like Canon EF), there are adapters that transfer electronic data. So, you are able to autofocus and control the aperture of an EF lens from a Sony E-mount camera. Vintage lenses have come back to fashion in the past decade for the same reason. You can easily get a Helios 58mm f/2 lens for 20 dollars. A manual adapter costs another few bucks. You can have an excellent, special lens on a modern camera. If you ever wanted to know where your sensor is placed inside your camera, find the circle with a line through it on the top of your camera. The line shows the sensor’s plane.

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35mm equivalentfocal length

Figure 2 features the same lens as Figure 1a but at a different WD. Note an increase in DOF occurs at longer WDs. Eventually, as the lens focuses on objects infinitely far away, the hyperfocal condition occurs. This condition is reached at the distance in which everything appears in equal focus.

The red cone in Figure 3 is an angular representation of the system resolution. Where the lines of the red cone and dotted black cone intersect defines the total range of the DOF. The lower the f/#, the faster the black dotted lines expand, and the lower the DOF.

“Does this lens have good DOF?” It is difficult to quantify without specifying an object detail size or image space frequency. The smaller the detail, the higher the spatial frequency needed, and the smaller the DOF the lens can produce. A DOF curve can be used to see how a lens performs over a given depth at a specific detail’s size (Lens Performance Curves). These graphs not only consider theoretical limitations associated with the f/# setting, but also the aberrational effects of the lens design.

Focal length is the distance from the center of the lens to the image sensor (focal plane), and each lens has a different focal length.

To overcome these issues, cameras and lenses with tighter tolerances must be used. For sensors, some lenses have tip/tilt control mechanisms to overcome this factor. Note that some line scan sensors can have swale, meaning they are not fully flat; this cannot be mitigated or removed via tip/tilt control.

Shallowdepth of field

Figure 9 shows the change in MTF performance at the corner of the image for this 35mm lens assuming 25µm of tilt, seen in Figure 8. Figure 9a shows the new performance of the lens at f/2.8; note the decrease in performance from Figure 9a. Figure 9b shows the performance shift at f/5.6, which is minor compared to 9a. Most importantly, the lens at f/5.6 will now outperform the one at f/2.8. The drawback to running systems at f/5.6 is three times less light relative to f/2.8 and this can be problematic in high speed or line scan applications. Finally, if the sensor is tilted about the its center, performance decrease occurs at both the top and bottom of the sensor (and the corresponding points in the FOV), since the ray bundles expand after the best focus. No two camera and lens combinations are identical. When building multiple systems, this fact can manifest at different degrees of magnitude.

Depth of fieldsimulator

2023216 — The longer the focal length, or the higher the mm of the lens, the narrower the angle of view is and the higher the magnification of the image.

In general, when lenses are focused at short WDs, the large cone angles cause the cones to diverge very quickly on either side of best focus, leading to limited DOF. For objects in focus at longer WDs, the transition rate of the bundles decreases and DOF will increase.

And there you have it. There are many different lenses you can use with different camera systems. And if you can’t buy them, there is a chance you can always make one. If you are looking for more information, we have a great article on lens mounts.

However, this issue is independent of sensor size. As the derivation in Equation 3 shows, depth of focus, $\delta $, is heavily dependent on the number of pixels or pixel count, $ p $, and has little to do with array or pixel size, $ s $. As sensors increase in pixel count, this issue is more evident. Particularly in many line scan applications, the large arrays and low f/#s emphasize the need for careful alignment between the object, lens, and sensor.

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Changing the f/# of a lens changes DOF, shown in Figure 3. For each configuration shown in Figure 3 there are two bundles of rays. The bundle represented by dotted black lines shows how well the lens is focused. As an object moves away from the best focus position (where the dotted lines cross), object details move into a wider area of the cone. The wider the spread of the cone, the more the image blurs into the surroundings. The f/# of the lens controls how quickly the cone expands and how much information or detail is blurred together at a given distance. Figure 3a shows a lens with a shallow DOF, where Figure 3b shows a lens with a large DOF.

Figure 8 analyzes the depth of focus for the two cases in Figure 7. In both cases, the far right vertical line is at the best focus for the full image. Each semi-vertical line to the left of best focus represents a position 12.5µm closer to the back of the lens. These simulate the positions of the pixels, assuming a tip/tilt of 12.5µm and 25µm respectively from the center to the corner of the sensor. The blue ray bundle shows the image center and the yellow and red ray bundles show the corners of the image. The yellow and red bundles represent one line pair cycle on the sensor assuming 3.45µm pixels. Notice in Figure 8a, that for f/2.8 there is already bleed-over between the yellow and red ray bundles at the shift to the 12.5µm tilt position. Moving out to 25µm, the red bundle now covers two full pixels and about half the yellow bundle as well. This causes significant blurring. In Figure 8b, for f/5.6, the yellow and red ray bundles stay within one pixel over the full 25µm tilt range. Note that the blue pixel’s position does not change, as the tip/ tilt is centered on this pixel.

Flange distance defines if a certain lens can be adapted to a certain camera body. Here’s the essence: a lens can be adapted to a camera if its intended flange distance is longer than the camera body’s flange distance. There are a few additions to this. Even if an adaptation is possible in theory, it may not work in reality. Lens Adapters are exactly as thick as the difference between the flanges distances of the camera and the lens. Therefore, the difference must be significant enough to let an adapter fit. For instance, you can’t adapt an MFT lens to a Sony E-mount camera. Their difference is only 1.25mm, an adapter that thin is hardly feasible. In general, adapters for mirrorless lenses rarely exist. The difference is only 2.5mm between the Canon EF and Nikon F mounts. That’s fairly short, but it allows for a non-electronic adapter. This means that you can adapt Nikon lenses to Canon cameras, but you won’t have aperture control and have to focus manually. But, it does not work reversed, so you can’t easily put a Canon lens on a Nikon camera. If you plan to adapt vintage lenses that have extending parts rearwards, be careful too. You might have to physically modify the lens to fit the adapter.

As details get smaller (represented by a smaller red cone), the bundles in Figure 3a and 3b move closer together. Eventually, increasing the f/# too much causes smaller details to blur due to reaching the lens diffraction limit, since the limiting resolution of the lens is inversely proportional to f/#. This limitation means that while increasing the f/# will always increase the DOF, the minimum resolvable feature size (even at best focus) increases. For more information on the diffraction limit and its relationship to f/#, see The Airy Disk and Diffraction Limit. Using short wavelengths helps to salvage some of this resolution. Learn more about how wavelength affects system performance in MTF Curves and Lens Performance. Note that this diffraction effect is not viewable in Figure 3, but that it is mentioned here as something to mind.

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You might wonder why we can’t always interchange lenses between different brands and types of cameras. Canon lenses are for Canon systems and Nikon lenses only work with Nikon systems. Even within the same manufacturer, specific lenses are for specific cameras. Besides different protocols of connection, this all comes down to a camera’s flange distance. Read below to find out what it is.

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Flange distance is the distance between the lens mount and the sensor in a camera. It varies between manufacturers, and between types of cameras, too. The most important factor that determines a camera’s flange distance is whether it has a mirror. A mirror mechanism increases the minimum required flange distance for a camera system. If one would place the lens mount (and thus the rear glass elements) too far back, the mirror would hit it every time it flips. Typically, SLR and DSLR systems, which include a mirror, have flange distances around 45mm. Specifically, Canon’s EF mount is 44mm, Nikon’s F is 46.5mm. Other DSLR mounts are similar, too. (We’ll get back soon to what this means in practice.) Digital mirrorless (MILC) systems, which don’t have a mirror, can reduce it to less than 20mm. Sony’s E-mount has an 18mm, the MFT system has a 19.25mm flange distance.

Figure 5 shows the same concept as Figure 4, but the cones represent multiple points in the FOV. Each detail and subsequent space represent one line pair. The overlap in the bundles in Figure 5a shows how the information blends together faster than that of Figure 4b and shows how two different object details can blur together due to a lower f/#. In Figure 5b, this does not occur due to the higher f/# of the lens.

Depth of field

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Camera lenses work very similarly to our eyes. If fitted correctly, they can focus to infinity (anything that’s far away), and they can focus close-up. Most lenses focus with their rear element(s) moving. To achieve close focus, the rear element is further away from the sensor. When focusing to infinity, that element is closer to the sensor. If the lens can’t get close enough to the sensor, it will be impossible to focus to infinity. This strongly limits the practical use of any lens, except macro lenses. This phenomenon determines what lenses can be adapted to different camera mounts.

Figure 4a illustrates the ray bundle at the center of an object under inspection at f/2.8 (a) and f/8 (b). The vertical lines represent 2mm increments away from best focus. On each vertical line, a square represents the discrete feature size of single pixel of detail. Figure 4a shows that as the width of the ray bundle spreads out, more rays miss the detail. In Figure 4b, the bundle expands more slowly and the rays all strike the detail which is larger than the bundle diameter for all depths shown.

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In Figure 1, contrast values (y-axis) are seen over a WD range (x-axis) at a fixed frequency of 20$ \small{\tfrac{\text{lp}}{\text{mm}}} $ (image detail). Note the difference in DOF between Figure 1a, which is set at f/2.8, and Figure 1b, which is set at f/4. Also note that there is more usable DOF beyond the best focus than between the best focus and the lens, due to magnification decreasing. The graphs themselves contain different colored lines denoting different sensor positions. These types of asymmetric DOF curves are common in fixed focal length lenses.

Figure 7 shows a 35mm lens using 470nm illumination. Figure 7a is set to f/2.8 and Figure 7b is set to f/5.6. Both graphs go out to 150$ \small{\tfrac{\text{lp}}{\text{mm}}} $—the Nyquist limit of a sensor with 3.45µm pixels. It is easy to see that the performance of Figure 7a is far better than Figure 7b, using this lens at a setting of f/2.8 provides the highest level of imaging quality in a given object plane. However, as discussed in the previous section, sensor tilt will negatively impact the image quality produced, and the higher the number of pixels, the more pronounced the effect.