Depth of Field -- Part I

Article and Photography by Ron Bigelow

www.ronbigelow.com

When we, as photographers, plan a shot, one of the fundamental decisions that we must make is what we want to be in sharp focus. What we desire to be in focus can vary radically from one image to another. For an expansive vista of the Grand Canyon, we may desire that everything from the foreground to the farthest recesses of the canyon be sharp. For a macro shot of a flower, we may want a very narrow range of focus so that the viewers' attention is concentrated at a specific point in the image.

The issue of what is and is not in focus is referred to as depth of field (DOF). From a practical point of view, DOF can be defined as the nearest point to the farthest point that appears sharp in an image. Figures 1 -- 2 demonstrate the concept of DOF. Figure 1 has a very narrow DOF. Figure 2 has a much greater DOF.

Figure 1: Narrow DOF
Figure 2: Large DOF

The definition above seems rather innocuous. However, hidden within this definition are some rather subtle points. First, the definition refers to the sharpness "in an image". Now, at first glance, this may seem rather obvious. On the contrary, however, this point is often misunderstood. DOF refers to the sharpness of the image in its final form (such as a print). DOF is not something that is inherent in only the camera and lens. For instance, in the case of a print, DOF depends on how large the image is printed. Thus, a 20" x 30" print will have a smaller DOF than an 8" x 10" print if both prints are viewed from the same distance. Second, the definition contains the phrase "appears sharp". The definition uses the phrase "appears sharp" instead of "is sharp" because DOF is intractably tied to the nuances of the human visual system. What appears sharp is determined by the human eye and brain. Thus, the DOF of an image depends on what a viewer's eye can resolve. For instance, the DOF of an image depends on how far away a viewer is from the image. If an individual looks at a billboard at the far end of a football stadium, all parts of the image may appear to be sharp because the eye can not resolve fine detail at that distance. In other words, the image will appear to have a large DOF. On the other hand, if the individual stands only a few yards from the billboard, the DOF will be much smaller because the individual's eyes can resolve fine detail much better at this distance, and the individual can better differentiate the sharpness of the various parts of the image.

This last paragraph may seem a bit confusing to those photographers that use DOF tables, DOF calculators, or the DOF scales on their lenses (many modern lenses no longer have DOF scales). After all, the scales don't reference anything related to print size or viewing distance. In addition, the DOF tables and calculators generally only require information such as the focal length of the lens, aperture, and distance from the subject. How can this be? How can things like print size and viewing distance affect DOF when these DOF devices don't even consider them? The answer is rather simple. The people who created these devices, as well as the people that manufacture cameras and lenses, make assumptions when they evaluate DOF. A typical assumption for a full-frame digital camera or a 35mm film camera is that the photographer will make an 8"x 10" inch print that will be viewed at about 12".

This can lead to some serious errors for any photographer that blindly depends on these DOF devices. For example, a photographer that uses the DOF table and then blows a 35mm negative up to a 16" x 24" print will discover that the DOF of the print is smaller than what was indicated in the table. Additionally, a photographer that uses the DOF scales on a lens while using a sub-full-frame digital camera (i.e. the sensor is smaller than a full-frame sensor) will find that the DOF of the printed image is, likely, different than expected (the lens designers probably assumed that 35mm film or a full-frame sensor were being used when they created the lens).

Does this mean that a photographer can not estimate the DOF before an image is shot? Absolutely not. The DOF devices are of considerable value in estimating DOF (I use them myself). What it does mean is that a photographer needs to understand some of the details behind DOF to interpret the DOF numbers given by DOF devices and to use that information to properly estimate the DOF for a specific application. Thus, the purpose of this article is to delve into the details behind DOF and to evaluate how they impact the sharpness of an image.

Circle of Confusion

To understand DOF, it is necessary to understand the circle of confusion (CoC). Figure 3 shows a subject that is being photographed. The subject is at a distance from the lens (identified by the letter S in the diagram). Light from a point on the subject travels to the lens and is focused at the plane of the sensor. In a perfect world (i.e., a world with perfect lenses that have no aberrations), a point on the subject would be focused as a perfect point at the plane of the sensor. Unfortunately, this is not a perfect world, and the point on the subject will not be focused as a perfect point at the sensor plane. Rather, it will be focused as a small circle. Now, one might be tempted to think that we would see this circle as a circle (which is what it is) rather than a point. However, since this is not a perfect world, our eyes are not perfect either. Our eyes can only resolve detail down to a certain level. If the circle is small enough, our eyes will see the circle as a point.

Figure 3: Subject Forming an Image on a sensor

So, the question now becomes, "how small does the circle have to be so that it appears as a point to a person that is viewing it?" The photographic industry has settled on a standard of about four lines per mm (the human eye can actually resolve somewhat finer than that, but this is the standard that is used). That means that the human eye can barely see a circle with a diameter of about 0.25mm (up close). Any circle with a diameter smaller than that will appear as a point. Earlier, it was mentioned that DOF calculations for full sensor and 35mm cameras usually assume that a photographer would be making an 8" x 10" print. So, a 0.25 mm circle on an 8" x 10" print would barely be recognizable.

However, that 0.25mm circle is on the print. It is necessary to figure out the size of a circle on the sensor that, when enlarged, will be 0.25mm on the print. This involves some simple math. An 8" x 10" print has a diagonal of 325.28mm. A full sized sensor is 24 mm x 36mm and has a diagonal of 43.27mm. Dividing these two numbers shows that the sensor has a diagonal that is 7.5 times smaller than the diagonal of the 8" x 10" print. Thus, the circle on the sensor must be 7.5 times smaller than the circle on the 8" x 10" print. This works out to a circle of 0.033mm on the sensor. Thus, the diameter of a circle on a full sized sensor below which the eye can no longer resolve detail when the image is printed at 8" x 10" is 0.033mm. This diameter is referred to as the circle of confusion and is critical to understanding DOF.

With an understanding of CoC, a technical definition of DOF can now be created. Figure 4 shows a DOF diagram. This is similar to the previous diagram, but it has some additional detail. The subject is, again, at a distance, S, from the lens. A point on the subject will form a circle on the plane of the sensor (see the yellow lines). Since the light from the subject is focused at the sensor, the circle that is formed should be very small (smaller than the circle of confusion). Thus, the image of the subject will appear sharp.

Figure 4: DOF Diagram
So, how much of the area in front of the subject will appear sharp in the 8" x 10" print? The diagram shows a location nearer to the lens than the subject. It can be seen that the light from this location (see the green lines) is focused behind the sensor. Consequently, light from a point at this location forms a larger circle on the sensor than the light from a point on the subject. However, as long as the diameter of this circle is smaller than the CoC, the print will appear sharp. As the location moves closer to the lens, the circle becomes larger. When the location becomes close enough to the lens that a point at the location forms a circle on the sensor that has a diameter that reaches the CoC, the near edge of acceptable sharpness has been reached. The distance at which this occurs is identified as Sn. Thus, Sn is the nearest distance from the lens that will form a circle on the sensor that has a diameter equal to the CoC.

Then, how much of the area behind the subject will appear sharp in the 8" x 10" print? The diagram shows a location farther from the lens than the subject. It can be seen that the light from this location (see the blue lines) is focused in front of the sensor. Consequently, light from a point at this location forms a larger circle on the sensor than the light from a point on the subject. However, as long as the diameter of this circle is smaller than the CoC, the print will also appear sharp. As the location moves farther from the lens, the circle becomes larger. When the location becomes far enough from the lens that a point at the location forms a circle on the sensor that has a diameter that reaches the CoC, the far edge of acceptable sharpness has been reached. The distance at which this occurs is identified as Sf. Thus, Sf is the farthest distance from the lens that will form a circle on the sensor that has a diameter equal to the CoC.

Accordingly, the DOF is the area between Sn and Sf -- the area that produces circles on the sensor with diameters smaller than the CoC.

Things that Affect the DOF

Of course, photographers want to know what things affect the DOF. They can use this information to manipulate the DOF to create the effects that they want. Actually, there are several factors that affect the DOF.

Aperture: Aperture has a very large impact on DOF. The smaller the aperture, the greater the DOF.

Focal Length: Increasing the focal length reduces the DOF. Conversely, decreasing the focal length increases the DOF. Thus, long lenses typically have small DOFs and wide angle lenses have large DOFs. This is one of the reasons that landscape photographers often use wide angle lenses. A wide angle lens combined with a small aperture produces a very large DOF.

Distance: The greater the distance from the subject, the greater the DOF.

Lens Sharpness: Lens sharpness has an impact on DOF. Sharp lenses create smaller circles at the sensor plane than do lenses that are less sharp. Thus, Sn and Sf move farther away from the subject before the circles reach the CoC. Consequently, the DOF increases.

Sensor/Film Size: The size of the sensor or film also has an affect on the DOF. For instance, most DSLRs have sub-full-frame sensors. A typical sub-full-frame sensor might have dimensions of around 22.5mm x 15mm. Such a sensor would have a diagonal of 27.04mm. The ratio of the diagonal of the print to the diagonal of the sensor is 12. Thus, the CoC is 12 times smaller than 0.25mm. This works out to a CoC of 0.021. This smaller CoC reduces the DOF.

However, the CoC is not the only thing that changes with the sensor size. Photographers who use cameras with sub-full-frame sensors generally use shorter lenses than photographers that use full-frame cameras. For example, many sub-full-frame DSLRs have a multiplication factor of 1.5 to 1.6. This increases the effective focal length of any lens that is used with the camera. A case in point, when a 200mm lens is placed on a camera with a multiplication factor of 1.5, the lens will give the same magnification as a 300mm lens on a full-frame camera. Thus, a photographer using this sub-full-frame camera would only need a 200mm lens while the photographer with the full frame camera would need a 300 mm lens.

As mentioned above, shorter focal lengths increase DOF. So, with sub-full-frame sensors, the smaller CoC reduces DOF, but the shorter lenses increase DOF. So, what is the final result? Actually, the shorter focal lengths used on the sub-full-frame cameras increases the DOF more than the smaller CoC decreases it. Consequently, sub-full-frame cameras have a greater depth of field, at any given aperture, than full frame cameras.

Print Size and Viewing Distance: As mentioned previously, the DOF scales and tables are calculated based on a CoC that assumes that a photographer will make an 8"x 10" inch print that will be viewed at about 12". If the print size or viewing distance changes, the CoC and the DOF change. As the print size becomes larger, the DOF decreases. However, larger prints are generally viewed from greater distances, and greater distances increase DOF. However, the general rule is that the larger the print, the smaller the DOF.

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Depth of Field -- Part II