## How do Depth of Field and Circle of Confusion relate to each other?

This is an advanced subject. You should have completed lessons DP-111C and DP-112C before trying to apply the information contained in this blog post.

The size of the camera sensor, the focal length of the lens, aperture size or f stop and the distance from the camera to the focus point all have an impact on the available Depth of Field (DOF).  All of these issues work together to either create a broad flat DOF curve or a steep DOF curve.

Broad flat DOF curves are an indication that image sharpness decreases very gradually over a large distance. This is the type of curve you see with very wide angle (short focal length) lenses.

Steep DOF curves are an indication that the DOF is falling off very rapidly and headed toward a complete out of focus situation in a shorter distance.

If your photographic vision includes an expansive DOF, choose a focal length, f stop and focus distance combination which gives you a flatter more horizontal curve.  On the other hand, a steep vertical DOF curve will have a higher probability of satisfying a photographic vision with the subject in focus and the background becoming more out of focus as the distance from the camera to the background increases. An application for this type of shooting scenario might be an outdoor portrait session. (Note: Sometimes the greatest challenges associated with this 2nd scenario is getting enough DOF to keep your main subject in focus with the background out of focus. You will often be working on the “Edge”.)

The technical basis for this is as follows:

The sharpest point in an image is the focus point or point of critically sharp focus. Sharpness gradually decreases from that point outward, both in front of and behind the point of critically sharp focus to a mathematically calculated point where a sharp point becomes a small blurry circle. That small blurry circle is called a Circle of Confusion (CoC). The Near and Far Focus limits are where you theoretically start to notice that the CoC has grown large enough that a picture object appears to be out of focus. The point at which the circle of confusion size becomes noticeably blurry varies based on the size of your camera’s sensor. That is why DOF calculators ask what type of camera you are using.

The size of the Circle of Confusion does not stop increasing at the outer limits of the DOF (Near and Far Focus limits).  The CoC continues to get larger and larger the farther away an object is away from the focus point.  As the CoC size increases with distance an object located at those increased distances becomes more and more out of focus.  Since we are concerned with the background being out of focus we will concentrate on the Far Focus Limit.

The following diagram shows a 50 mm and a 200 mm lens. These are the basic parameters for both lens charts:

• The camera was focused on an object 10 feet away.
• The DOF or Area of Acceptably Sharp Focus is shaded in red.
• The Near Focus Limit of the DOF is marked with an “N”.
• The Far Focus Limit of the DOF is marked with an “F”.
• The Circle of Confusion (CoC) at the Near and Far Focus Limits is .03mm for a full frame sensor.

The lines to the right of the DOF and Far Focus Limit approximately plot various CoC sizes at various f stops.  For example: The purple line with purple squares on the 200 mm lens chart shows the distance from the camera that the CoC is 2 mm in size at various f stops.  At f/4 the 200 mm lens will have a CoC of 2 mm about 23.2 feet away from the camera.

What does all of this mean?  There are number of conclusions you can derive from these illustrations with regard to the Far Focus Limit and objects behind or beyond the Focus Point. We will look at how rapidly an object becomes defocused or more Out of Focus (OOF).

Lenses with a shorter focal length tend to have shallow or flat DOF curves and the CoC size does not increase very rapidly. Thus objects tend to stay in focus or slightly out of focus for some distance behind the focal point. That is why shorter focal length (i.e.: 18 mm, 28mm etc) lenses are well suited to create images with lots of DOF. See the DOF graph for the 18mm lens above.

Longer focal length lenses tend to have steeper DOF curves and objects behind the Far Focus Limit tend to become more OOF more rapidly than with shorter focal length lenses. For example, at a distance of 30 feet from the camera, a 50 mm lens set at f/2.8 would have a CoC size of about .2 mm.  The 200 mm lens would have an approximate CoC size of 2.5 mm at 30 feet from the camera.  The 200 mm lens has a CoC that is about 12.5 times larger at that same distance and f stop. Because the curves are not linear the ratios of CoC sizes between the 50 mm and 200 mm lenses will vary, but the same principle still applies.

Another observation is, even though longer focal length lenses have a steep DOF curve, the CoC lines tend to flatten out the farther you are away from the camera and at larger f stop numbers. Even though the DOF fall off is greater with a longer focal length lens, the OOF effect seems to diminish as the distance increases. You seem to have a law of diminishing returns with increasing distance from the camera.

In conclusion:

If you want a lot of DOF, use a wider angle or shorter focal length lens. If you want a smaller DOF and rapid fall off of focus use a longer focal length or telephoto lens.

Note: you might be able to use a 50mm lens with a very small native aperture (f/1 etc) to do the same thing because the DOF curve for the f/1 to f/2 portion of the DOF is very steep. But your available DOF may not be adequate at focus short distances for portrait head shots. See the blog posting Are you using a 50mm f/1 native aperture lens for head and shoulder portraits?