A Tutorial on Depth of Field

Depth of field (DOF) is a concept which is absolutely fundamental to photography. Some people have a basic understanding of what it is, while others understand it at a scientific level. Still, most people struggle with it to one degree or another. I would like to cover DOF from one end to the other. I’ll explain it at a basic level so that everyone reading this article will understand what it is from a practical point of view and will understand how to control it and what affects it. I’ll also delve into it a little deeper so that those of you who are technically inclined can understand it a little more thoroughly.

Depth of Field—What is it?

DOF describes the area of an image which appears to be in focus, or which is acceptably sharp. Sometimes everything in an image appears in focus. This image is described as having great or large DOF. In other images, only a very narrow area appears to be in focus. Everything else is blurry. This image is said to have shallow DOF.

Let’s look at some specific examples. In this first example, we have a landscape photograph. Everything, from the closest rock to the most distant hill appears sharply in focus. This image has large DOF. Most landscape photographers will create photographs with large DOF. They want everything in the picture to be sharp and in focus.

In this next example, we have shallow DOF. This is a common technique used in portrait photography to help draw the viewer’s attention to the face of the subject. Everything else in the photograph is blurry so that it doesn't distract. Note that the part of the image that is in focus is a plane which is perpendicular to the axis of the lens. In this example, the husband and wife are both approximately on the same plane, so they are both in focus. The woman who is closer to the camera is out of focus and the objects in the background are out of focus. Objects get progressively more out of focus the farther they are from the plane or point of focus.

Depth of Field—What affects it and how to control it?

At the most fundamental level, DOF is a function of only two things. That is to say, only two things control how much DOF any particular image has—aperture and magnification. Let’s discuss these in order.
First, aperture, or lens opening. If you want shallow DOF, use a large aperture (small f-number). If you want great DOF, use a small aperture (large f-number). Let me put this more generally. The larger the aperture, the shallower the DOF. The smaller the aperture, the greater the DOF. I wanted to put this more generally because using a small aperture doesn’t necessarily guarantee a large DOF, which leads us to the other parameter affecting DOF...magnification.

Since we’re in the digital age, I’ll use the term "image sensor," or simply "sensor," in this discussion instead of film. Let’s say I take a picture of a rock and the image of the rock spans half the height of the sensor. In other words, half the pixels of the sensor (in the vertical direction) capture the image of the rock. Then, I proceed to move closer to the rock so that the image of the rock fills more of the frame. By moving closer to the subject (the rock, in this case), I have increased magnification. I have taken a higher-magnification photograph. The only thing on the camera that I have touched is the focus ring. I have adjusted it to focus at a closer distance, since I have moved closer to my subject. Saying that I have taken a higher-magnification image and that I have adjusted the focus ring to a focusing distance which is closer is saying essentially the same thing. The interesting thing to note is that the image which I took of the rock after moving closer to it has less DOF than the first image. The first image I took of the rock, when I was standing farther away (and thus when it was smaller or less magnified) has greater DOF.

In a nutshell, that’s it. Bigger lens opening, less DOF. Smaller lens opening, more DOF. More magnification, less DOF. Less magnification, more DOF. Specifically, if you double the f-number (e.g., f/8 to f/16), DOF doubles. Conversely, if you halve the f-number, DOF is cut in half. Magnification, however, affects DOF with the square of the distance. For example, doubling the distance to the subject from the camera gives 4 times the DOF. Tripling the distance gives 9 times the DOF. The converse is also true, of course.

Practically speaking, this is all you need to know. Based on this knowledge, you can control DOF in your photography and get the results you want. For a little more technical explanation of DOF, read on.

Depth of Field—A more technical investigation.

When a lens is focused onto a plane (an infinitely thin, invisible wall, perpendicular to the lens axis), it projects a perfectly focused image onto the sensor. However, that image is perfectly focused, perfectly sharp, at only one point—the plane on which the lens is focused. Each point on the in-focus plane corresponds to a point which is focused onto the sensor. Every point in front of or behind that plane on which the lens is focused is focused either in front of or behind the sensor in the camera body.

These points of light intersect the sensor, but as a cross section of a cone, not as a point. This cross section is larger than a point, depending on how far away from the sensor the focused point lies. In other words, objects that are far from the plane on which the lens is focused will project a large cross section of the cone onto the sensor. Objects that are closer to plane on which the lens is focused will project a smaller cross section of the cone onto the sensor. Again, the farther away from the sensor the focused point lies, the larger the cone’s cross section which intersects the sensor. The larger this cross section, the blurrier that point of the image appears. So, objects which are farther from the point on which the lens is focused will appear less in focus.

This cross section which intersects the sensor is called a circle of confusion. The larger a circle of confusion is, the blurrier the object it represents appears. The smaller a circle of confusion is, the sharper, or more in focus the object it represents appears. In the photographic community, smart individuals have specified how small a circle of confusion must be to be considered acceptably sharp. Any circle of confusion which is that size or smaller is considered acceptably sharp. Any circle of confusion which is larger than the specified size is considered unacceptably sharp. The areas which are unacceptably sharp are not in the DOF of the image. Conversely, the DOF contains or is defined by all parts of the image which have circles of confusion which are less than or equal to the size specified by that smart guy as being the appropriate size...a small enough size to be considered acceptably sharp. Here are a couple visuals to help.

In the first example, the diaphragm, or aperture, is wide open (let's say it's f/3.5). You can see that there are three different objects which the camera lens sees. The lens is focused on the blue object. Thus, it is focused onto the image sensor. The green object is beyond the plane of focus, so the lens focuses it behind the sensor. The red object is in front of the plane of focus, so the lens focuses it in front of the sensor. You can see that the green and red objects create large circles of confusion. So, they appear blurry in the final image. If you use your imagination, you can also see that, had the green object been farther away, the lens would have focused it even farther behind the lens, creating an even larger circle of confusion, and causing it to appear even more out of focus. The closer the green (or red) object had been to the blue object, the closer to the sensor the lens would have focused it, thus creating a smaller circle of confusion, or even a point, if the object were on the same plane of focus as the blue object.

In this next example, the diaphragm, or aperture, has been closed down some (let's say it's f/11). You can see how the circles of confusion have also been reduced in size as they intersect the sensor. The concept that objects which are farther or closer to the point of focus create larger and smaller circles of confusion, respectively, still applies.

Diameters of Just Acceptable Circles of Confusion

(These numbers will vary depending on your source or on whom you ask!!!)



NOTE: Circles of confusion are subjective gizmos. For 35mm, Kodak says 0.002" (0.0012" for critical use), or 1/1000 the focal length of the lens. Ansel Adams says 0.001" on the negative or between 1/100 to 1/200 in the final print.

NOTE: These data (some of them, at least) were taken from Kodak's Book of Large-Format Photography (ISBN 0-87985-771-4).

NOTE: There are a couple different sensors on the market which are considered APS-C. They vary only slightly in size and give crop factors which are marginally different.

How Lens Focal Length Affects DOF (or IF it does!)

Many people think that the focal length of the lens affects DOF. This is not true. Of course, some of you are thinking right now that I am either wrong or that I am splitting hairs. I might confess to being a hair-splitter, if you press me. It’s just that I want to reduce the problem to its most fundamental level so that the reader has the purest understanding of the issue. Let me explain.

I take a picture of a rock which is 10 feet away with a 50mm lens mounted on the camera. I then step back 10 feet so that the rock is 20 feet away. I proceed to attach a 100mm lens to the camera. Although I am now using a 100mm lens instead of a 50mm lens, the photograph has the exact same DOF as the first one. This proves that the focal length of the lens does not affect DOF.

If, however, I were to remain in my original location and switch lenses from the 50mm to the 100mm, the new image size would be double that of the original image. What I have done is to increase magnification, thus reducing DOF. Remember, the greater the magnification, the less the DOF, while the less the magnification, the greater the DOF.

Just to make sure it's clear, let me beat the example to death. If I remained in my original location, 10 feet away from the rock, and replaced the 50mm lens with a 25mm lens, DOF would be increased since magnification has just been cut in half. If, however, I were to move 5 feet closer to the subject, to a distance of 5 feet, I would have just cut the camera-to-subject distance in half (along with cutting the lens focal length in half), thus maintaining the original magnification and keeping DOF the same as in the original image.

So, you see, it may be spitting hairs to state that lens focal length doesn’t affect DOF, but I think it’s an important distinction to make, if one really wants to understand what’s happening.

I should note that, at high magnification (e.g., 1:1), DOF does change with lenses of different focal length.

Is There a Third Parameter Affecting DOF?

Well, sort of. Remember those confusing things called circles of confusion? A circle of confusion that we consider acceptably sharp might measure 1/1000” on the sensor. That’s the diameter of the cross section of the cone of light which intersects the sensor. When we enlarge that image, an image measuring, say, 15mm tall and 22mm wide, as on an APS-C sensor, to a common print size, say, 4” tall 6” wide, the circles of confusion are also enlarged proportionately. If we enlarge that same image to 20” tall and 30” wide, the circles of confusion are enlarged even more.

If a circle of confusion measuring 1/1000” on the sensor is considered acceptably sharp, this means it is considered acceptably sharp to produce a certain size print viewed at a certain distance. That's how the figure 1/1000" was arrived at in the first place. For example, let’s say we have a landscape image which contains no circles of confusion larger than 1/1000” (on the image sensor). So, the entire image is considered sharp…well, within certain limits. If we make a 4” x 6” print and view it at 18”, the image looks sharp. If we make an 8” x 10” print and view it at 36”, it will still look sharp. As long as we keep increasing our viewing distance proportionately to the image enlargement, it will appear sharp, by the standard we have given. If, however, we make a 40” x 60” print and view it at 18”, for example, the circles of confusion will have been enlarged so much that, at this close viewing distance, they will be large enough to render the image unacceptably sharp. The industry standard is to view an image at a distance which is equal to its diagonal. The viewing distance, then, for an 8" x 10" print should be around 13".

So, whether or not an image has adequate DOF is determined, in part, by how much we enlarge that image and by how close we are to the image when we view it. This applies equally to a digital camera with an APS-C-sized sensor and to an 8” x 10” view camera. These are all just different places on a continuum. An 8" x 10" piece of film could have larger circles of confusion than an APS-C-sized sensor and still be produce a final print which appears sharp, since we would be enlarging the film less than we would the digital image to achieve a given final size print.

Hyperfocal Distance, or How to Achieve Maximum DOF

Hyperfocal distance is the nearest distance in a scene that appears sharply in focus when the lens is focused at infinity. In other words, focus your lens on infinity and read the number on the DOF scale which is across from the applicable aperture reading. That is the hyperfocal distance for that lens at that aperture. Hyperfocal distance applies for a given aperture and focal length. In other words, the hyperfocal distance is different at f/22 than it is at f/11, for example. Also, the hyperfocal distance is different for a 50mm lens than it is for a 200mm lens, for example.

Focus the lens on infinity. For this lens, which is a Rokkor, set the infinity sign so that it is across from the white triangle below the focusing ring. Note that this lens is set for an aperture of f/16. This is accomplished by turning the aperture ring at the base of the lens so that the 16 lines up with the white circle just above it (just below the white triangle). Now, note that the white number 5 (meters) or green 15 (actually more like 17 or 18, in feet) is above the 16 to the left of the triangle. That's the hyperfocal distance for this lens (50mm) at this aperture (f/16).

To achieve maximum DOF, focus on the hyperfocal distance. The number we found in the previous image (5 meters, or roughly 15 feet) should be moved so that it lines up with the white triangle. Now, if we read the DOF scale, we can see that, based on the fact that the aperture is set at f/16, our DOF stretches from about 9 feet (the distance which lines up with the 16 on the left) to infinity (which lines up with the 16 on the right).

An easier way to accomplish the same thing is simply to set infinity to line up with the appropriate aperture on the right side of the focus tick mark. So, clearly, the far limit of DOF would then be infinity, and you can then simply read what the near limit would be by looking to the left side of the focus tick mark to see what distance lines up with whatever aperture you have set.

Setting the focus in this manner is important only if you want near objects to appear in focus. Most landscape photographers want everything to be in focus, from flowers very near the camera to the most distant hill, so they use this technique quite frequently. In fact, most landscape photographers don't even use auto-focus, for this very reason.

If your lens doesn't have a DOF scale on it, you can buy or print out charts which list DOF for various lenses at various apertures. Keep in mind that when you use 35mm lenses on a digital SLR, if the digital SLR you are using has a sensor which is smaller than full-size (i.e., a 35mm frame of film), the image will need to be enlarged more to get a given print size than would the 35mm frame of film. For this reason, you need to use a higher standard when setting focus than the 35mm lens indicates. For example, in the illustration above, you might use the markings for f/11 (the tick mark between f/8 and f/16), or even f/8, as a more conservative technique. The closest thing that would be in focus would be around 10 feet, or so, so you'd lose a few feet of close focus ability, but that's just the way it goes when you have to enlarge your original more to get your final print. You'd be guaranteeing that everything out to infinity was still sharply in focus. You would just lose some close focusing capability.

If you want to compute the hyperfocal distance for a lens of a given focal length at a given aperture, you can use the following equation.



where:

H = hyperfocal distance
F = focal length
f = aperture
d = diameter of circle of confusion

Make sure to use consistent units for hyperfocal distance, focal length, and circle of confusion—either inches or millimeters.

Here's an example for a 50mm lens at f/16 (35mm camera).

H = 2^2 / (16 x 0.002)

H = 125 inches, or 10 feet, 5 inches.

So, if I take my 35mm camera with 50mm lens set at f/16, I should focus it at 10 feet 5 inches (the hyperfocal distance) to obtain maximum DOF. Everything from 5 feet 2.5 inches (half the hyperfocal distance) to infinity will be in focus, or acceptably sharp...at least at normal print sizes and normal viewing distances!

Summary

When you take a picture, remember to use a smaller aperture for greater DOF or a larger aperture for smaller DOF. Also, remember that higher magnification gives less DOF, and less magnification gives greater DOF. Keep this in mind the next time you take a macro photograph of a flower or insect. Notice how incredibly tiny DOF can become at such high magnification. Last, remember that shallow DOF may become excessively noticeable when you create very large prints or view your prints at close distance. In this case, just make sure you use the smallest aperture possible.

Additional Resources

• Luminous Landscape—Understanding Depth of Field


• Bob Atkins—Digital Depth of Field


• Paul van Walree—Depth of Field