DOF Confusion!!!
Technology - Technology
There is lots of confusion out on the web about DOF. Namely, there are two different types of applets for determining DOF. One, like the one here at photozone, determines DOF based on sharpness, the other, at Shuttercity, bases DOF on format.

For some strange reason people have an allegiance to one or the other and deem the other as wrong! Yet, it is apparent from discussion boards that these same people don’t understand what each type of applet means and, more importantly when to use it. As I see it, the difference lies between physics and applied photography. In this essay, via a couple of easy example, I hope to make sense of these applets.

Before I get started I will give a couple of definitions that everyone agrees with:

DOF (Depth of Field): The area in front of and behind a focused subject in which the photographed image appears sharp. In other words, the depth of sharpness to the front of sharpness to the front and rear of the subject where image blur in the film plane falls within the limits of the permissible circle of confusion

Mathematically,

Front DOF = d • F • a2 / (f2 + d • F • a)
Rear DOF = d • F • a2 / (f2 – d • F • a)

f: focal length
F: F number
d: circle of confusion diameter
a: subject distance (distance from 1st principal point to subject)

COC (Circle of Confusion): Images are formed from a composite of dots (not points, though I’ll call them that for simplicity) having a certain area, or size. Since the image becomes less sharp as the size of these dots increases, the dots are called “circles of confusion.” Thus, one way of indicating the quality of a lens is by the smallest dot it can form, or its “minimum circle of confusion.”

The maximum allowable dot size in an image is called the “permissible circle of confusion.” In other words, how much can a point be magnified and still look like a point and not a disk.

Please note COC, thus DOF, depends on the use of the images and is somewhat subjective. This is no different that resolution.

Physics

I’ll explain what I call the physics by use of an example. Let’s say we take a picture of a point with a 4x5inch camera and crop out a 6x7cm, 6x4.5cm, and a 35mm frame sizes. (If you like, consider all these formats with the same focal length lens, at the same aperture, and the same distance to the point). According to the applets that take into account format size, the DOF changes for each crop. Does this make sense? Of course not! It is the same point on the same piece of film. As such, it can’t be magnified any more for each format and still look like a point and not a disk. Thus, we can conclude that COC is not a function of format. This leaves DOF as a property of the lens and focusing distance(review the above equations). Also note that the sharper the lens, the smaller the point is that can be produced on the film, the shallower the DOF (I’ll let you think about this), and the larger a print can be made and still have the point look like a point.

Photography

“But wait a minute,” you say, “why do some applets use format instead of sharpness?” These applets assume that in photography the subject will be framed the same regardless of format. In other words, to frame the subject from the same distance the larger format will need a longer focal length lens, or the smaller format will need to be moved further away from the subject (or vice-versa). Now consider making an 8x10 print once you do this. Each point in the larger format will need to be magnified less than with the smaller format. This is a fancy way of saying you can make larger prints from larger formats. As a concrete example let’s consider the Canon dslr’s d30, d60, 10d frame size verses a 35mm frame size. We all know by now that there is a 1.6x multiplier factor for angle of view (technically, using the term “magnification” is wrong) between the digital frame size of these and a 35mm film size. Ergo, a 100mm lens mounted on a 10D frames the subject the same as a (100x1.6 =) 160mm lens on a 35mm body but with 1.6x more DOF for a given aperture. Presuming the media is equivalent (I don’t want to get into a film vs. digital debate), the larger format, 35mm, can be made into a larger print because each point needs to be magnified less. There are pitfalls to this method. Consider macro photography. Magnification, e.g. 1:1 or “life size,” has nothing to do with format. To review this, consider 1:1 or life size. This implies that the object will be the same size on film as it really is. Moving the camera or changing lenses for the same angle view negates the 1:1 magnification which only occurs at one distance for a given lens from the lens to subject. So beware, applets that rely on format will fail you! Whereas, applets like at photozone will get this right to first order.

Summary

Hopefully I cleared up the differences between each type of applet and you can put them to work for you!

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