Quote Originally Posted by Q.G. View Post
"Lots of choices. Pick one." "Define" (in the "pick one" sense). "[...] perceptible by a person"
And still "an objective scale"?

Doesn't work.

The second approach, based on arbitrarily chosen ("let us say") dimensions, does no better.

As you say: "The criteria may be arbitrary"
And there the whole things come falling down. DOF is not an objective thing.

A statement like "The second method is independent of factors such as magnification, viewing distance, photo size, etc." even cannot be a thing related in any way to DOF.
DOF, in essence, is dependent on factors such as magnification, [etc.]
I think you are, perhaps, confusing the concept of "objectivity" with the concept of arbitrariness.

In most cases a standard is arbitrary, even though it may be objective. For example, a licensing body may decide that a passing grade on a professional certification exam is 70%. That is an arbitrary choice. (Why not 72%?) However, it is an objective criteria. In other words, once the standard is determined one does not have to subjectively discuss whether a score of, say 69% is a passing score.

Choices for standards are almost always arbitrary. For example, a definition of optical resolution based on the Rayleigh criterion is arbitrary. However, it is objective because two different people can perform the measurement and come up with the same result without having to apply subjective judgment.

Similarly, choices in definitions of depth of field that I discussed above may be arbitrary, such as the choice of a standard viewing distance. However, they are objective in the sense that they can be unambiguously measured.