Norman Koren depth of field formula

[TonyW]

I have been looking at the web page www.normankoren.com on depth of field. He quotes the formula
DOT ~= 2NC(1+M)/M^2, where N is the f number, C the diameter of the circle of confusion and M the magnification. This looks to be a useful formula but when I look at the approximations it's validity looks doubtful. I have not worked through all the algebra but I find it hard to believe the formula that he quotes as being exact.

Does anyone know the status of this article?

[benm]

That formula is an approximation when M > 1/20.

The more "exact" formulas are given above in the same article. I put "exact" in quotes because sharpness does not simply end when you get to the DOF limit, it just gradually gets less sharp. Within the DOF range it is acceptably sharp for most people. It will also depend on print size (or monitor magnification) and viewing distance.

[Glenn NK]

I have been looking at the web page www.normankoren.com on depth of field. He quotes the formula
DOT ~= 2NC(1+M)/M^2, where N is the f number, C the diameter of the circle of confusion and M the magnification.

This looks to be a useful formula but when I look at the approximations it's validity looks doubtful. I have not worked through all the algebra but I find it hard to believe the formula that he quotes as being exact.

Does anyone know the status of this article?

There is no exact expression for DOF because it's basis is arbitrary; to quote Wikipedia:
DOF is the distance between the nearest and farthest objects of a scene that appear acceptably sharp in an image.

Acceptably sharp has no strict mathematical or physical definition (there is standard that is used but it's often cast into doubt as to its usefulness - as I recall it's based on viewing a print of a standard size at a standard distance - and then determining if it's sharp enough - seems quite arbitrary to me, a bit like "how high is up").

DOF is fine as a concept, but it cannot have precisely defined limits (near and far) because sharpness doesn't suddenly stop at one point - as Ben stated, it gradually softens from the one point where the lens is focused (and this doesn't even take field curvature into consideration - which is very real with some lenses.)

This site might be of more use:

http://www.dofmaster.com/dofjs.html

Several interesting/useful links on the left. Seven years ago I printed out the charts for my lenses/cameras, and might have used them twice. Some people use the downloadable app for their I-phone.

LV (live view) is more useful and seems to have replaced the use of DOF charts in the field.

Glenn