How does focus breathing affect DOF?

Question

Like explained in this question

Does focus breathing make a lens slower when close focusing?

focus breathing does change the effective F-stop. At the same time, the lens behaves, as if it was a shorter focal length.

Since both these factors affect DOF, how can one determine the overall effect on the DOF ?

Answer 1

As you close focus you are racking the lens further and further from film/senor. This now elongated distance is no longer called focal length; it is the back focus distance. The focal length is a measurement taken when the lens is imaging an object at infinity (as far as the eye can see).

As you close focus and approach a magnification factor of 1 (life-size often called unity or 1:1), the back focus distance increases one complete focal length. As an example, at unity, a 50mm lens will have a back focus distance of 100mm. The subject to film/sensor distance will be 4× the focal length.

At close focusing distances the depth of field is computed based on the back focus distance. Additionally a revised f-number is plugged into the equation.

At unity the back focus is 2× the focal length, and the f-number is 2 f-stops more stopped down. These revisions must be taken into account when computing depth of field.

Given the following definitions,

P = distance to object
P_d = distant point sharply defined
P_n = near point sharply defined
D = diameter of circle of confusion
f = f-number (revised when close focusing)
F = focal length (back focus when close focusing)

Then:

P_n = P ÷ (1 + P∙D∙f/F²)

P_d = P ÷ (1 - P∙D∙f/F²)