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Depth of Field (DOF)

Introduction:
Depth of field (DOF) can often be a confusing topic, but it must be understood for a photographer to correctly compose and shoot photographs. This article will try to explain DOF and how it's applied to photography. Be aware that it is a very complicated topic and I will try to simplify it here somewhat to make it easier to understand.
 
Definition:
The depth of field is defined as the range in an image that appears to be in focus. Several ways to achieve more DOF are stopping down the lens (closing the aperture/choosing a bigger F number), using a wide angle lens, and focusing on the hyperfocal distance.
 
Circles of Confusion:
Depth of field (a measure of distance of acceptable sharpness usually in feet or meters) is calculated using the circle of confusion (COC). Lets explain the COC first so we can move on to depth of field.

The COC is the largest on-film (sensor) circle that you can see as a well defined point on an 8 x 10 print from a distance of 1 foot. As such, the circle of confusion (before the point appears to be a circle) is dependant on the size of the imaging sensor. This is because of the amount of enlargement that the sensor image has to undergo to reach the same print size. Smaller sensors have to be enlarged much more than larger ones. The maximum allowable circle of confusion is often simple referred to as the circle of confusion.

In a photograph, the spot you focus on is the only spot where the image will be in perfect focus. The focus begins to fade as you get further away from the point of focus in both directions, even though your eye might not be able to tell the difference. As this distance increases, that perfect spot of light will start to turn into a circle. At the point where these circles become apparent (when viewed on an 8 x 10 print from 1 foot distance) is called the maximum allowable circle of confusion or simply circle of confusion.
 
It could also be looked at this way. In the diagram below, the lens was focused on the red point of light. The lens gathers all this light and converges it on the film plane (sensor). As long as the focusing was correct, it will result in an image with a perfect point of light in the middle.
Focused
 
In the diagram below the lens remains focused on the red point of light distance. The yellow light is inside the plane of focus and after passing through the lens will converge in front of the film plane hence projecting a circle on the image. Once again to drive the point home, as soon as these circles are distinguishable in an 8x10 print from a distance of 1 foot you have reached the circle of confusion.
ForegroundC0C
 
The same is true of an point of light beyond the plane of focus, the only difference is that the light will converge beyond the film plane.
Background CoC
 
Depth of Field:
Now we come to depth of field. Depth of field is strictly an optical result. It is the area in front and behind the focus point which appears to be sharp within the limits of the COC. The COC defines where the depth of field begins and ends. For example, a Nikon D200 has a COC of 0.020mm (this is the point where the point becomes a circle). So, a D200 with a 12mm lens with an F-stop of 4 focused at 5 feet will result in a depth of field beginning at 2.72 feet and extending to 31.3 feet. The hyperfocal distance for this lens and aperture combination is 5.94 feet. So if you focused at 5.94 feet you would achieve a depth of field that begins at 2.97 feet and extends to infinity. This is the maximum possible DOF.

The diagram below shows what the depth of field is and how it extends beyond the focus point in both directions. Beyond the depth of field the circles of confusion no longer appear as points but as circles and are out of focus. The circle where this change happens is said to be the circle of confusion for that particular sensor. The circle of confusion thereby limits the depth of field in both directions from the point of focus. (see diagram below)
Circles of ConfusionHere you can see the DOF extend from the point of focus in both directions (foreground and background). The range of the DOF is limited by the circle of confusion
As a side note, the way a camera renders circles of confusion outside the depth of field is called Bokeh. You can find the article on it here.
 
Subject Distance:
Coming closer to a subject will decrease the depth of field as is evident in macro photography. This is where correct focusing is critical as the DOF is limited to fractions of an inch. At these close distances it is necessary to employ macro focusing rails and very sturdy tripods.

The reverse is also true. Moving away from a subject will create the appearance that the depth of field is getting bigger.
 
Focal Lengths:
Lenses with a longer focal length appear to have a shallower depth of field because they tend to flatten the perspective. The relation of foreground to background is not as apparent as in a wide angle lens. Telephoto lenses also shorten the subject distance, though this is done optically instead of actually walking closer but with the same effect.

A wide angle lens shows much more dimension of a scene because it "sees" a wider area and your subject is much smaller than in a telephoto lens. This is the same effect as if you were to walk further away from your subject to create more DOF. When you use a wide angle lens the DOF fades more gradually in behind the focus point which is why they are good for landscape photography.

These are just optical effects. If you were to take any 2 lenses at the same aperture and take a photo where the subject fills the frame to the same extent you will see virtually identical depth of field in both images. There is a slight difference as one comes closer to the extreme wide angle focal lengths, but it is negligible when you take into consideration the focusing distance and aperture. (the actual difference is around a 7.8 cm difference between 10 mm and 400 mm lenses)
 
Depth of Field Distribution:
The distribution of the depth of field changes with focal length. This is very important to keep in mind when employing longer lenses. Wide angle lenses (10-20 mm) are mostly used for landscape photography. In this range of focal lengths the distribution (Front : Rear)of the DOF varies between 30/70 for 10 mm and
40/60 for a 20 mm lens. This is the most drastic change. As you approach 600mm the relation changes to 50/50. This is something that you just have to remember when composing using a wide angle lens.
 
Below is a depth of field calculator that will allow you to compute the near and far focus as well as the hyperfocal distance for a particular focal length, aperture, and camera type.

 

Choose camera
Focal Length
Aperture
Focusing Distance
   
 
Near Depth of Field Limit
Far Depth of Field Limit
Hyperfocal Distance
circle of confusion

 

Remember that to achieve the maximum depth of field all the way to infinity you have to focus at the hyperfocal distance. This calculator will tell you what depth of field you will achieve with your camera, focal length, aperture, and focusing distance. The hyperfocal distance is independent of the focusing distance. Use it to achieve max DOF. The near and far DOF is affected by the focusing distance.
 
All Together:
Once the concepts of COC and DOF are understood, one can employ them to create amazing photographs. Whether you use shallow depth of field to emphasize your subject or use a huge depth of field to capture stunning landscapes it's all up to you. It's always a good idea to carry with you some hyperfocal tables for the focal lengths you use the most, especially if you often employ wide angle lenses.

Cheers

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