On the Concept of Depth of Field

After reading Bernie Sumption’s blog post and his “better depth of field table” concept, I wanted to understand what he was doing. He asserts that you can estimate depth of field if you can estimate the subject’s size—rather than distance—regardless of the focal length. He doesn’t go into detail about the mathematical basis for this assertion, apart from one equation that has since been removed from the Wikipedia article from which it was sourced. Here it is:

It turns out the math isn’t all that mysterious, as it’s simply a matter of recognizing that similar triangles have proportional dimensions—specifically, that the ratio of focal length to subject distance is proportional to the ratio of sensor size to subject size (magnification). This is not my point though. The math works and that’s fine by me.

The point is that in the course of digging around the Internet (as one does) for answers I came across a lot of variations on the same old explanations of depth of field that I (and you, I suspect) have read many many times before. Some are better than others, like this article from BBC Academy Guides that includes a nice diagram of a nature photographer who is about to be eaten by a bear.

But then I found “Apparent Depth of Field: Practical Use in Landscape Photography” by Joe Englander. Mr Englander puts the concept into words in a way I’d not heard before. He got my attention right away with the first sentence:

Depth of field, sometime erroneously called depth of focus, is, like almost every other tool in photography, an illusion.

He goes on to say,

Focus occurs in one geometric plane, and only in that plane. From high school geometry, you may remember that a plane has no depth. In reality, there is no depth of focus or depth of field. Any image made with any lens can have focus only in one place; everything else is absolutely out of focus.

I knew about circle of confusion, its use in formulas like the one above, but I didn’t really grok its relationship to depth of field until I read those words. Now, it’s easy for me to see that depth of field is really just the range of distances over which the resulting image is acceptably sharp, but not truly in focus. And as the circle of confusion gets larger, so does depth of field.