Originally posted by clackers You can see that focal length is much more important than the F number because it's a squared quantity.

If you take the formula

DOF = 2*u^2 * N * c / f^2

and insert the definition of N

N = f/D

you get

DOF = 2*u^2 * c / (f * D)

This suggests that the DOF decreases linearly with focal length (not with the square of the focal length), if we keep D constant (which we must in order to create comparable images).

For two different formats that require two different focal lengths (f1 & f2) to achieve the same framing, we have

DOF1 = 2*u^2 *c / (f1 * D)

DOF2 = 2*u^2 *c / (f2 * D)

with DOF1 being the DOF for the small format and DOF2 being the DOF for the larger format.

However, we must also consider the enlargement factor required for producing an output at a certain size.

For a smaller format, the enlargement factor is larger, precisely by a factor k, the crop factor k = sqrt(larger format area / smaller format area).

This neutralises the "f" differences in the denominator in the above DOF formulas, as the focal length f2 required for the larger format is exactly k * f1, with f1 being the focal length for the smaller format.

In formulas:

Output-referred-DOF1 = DOF1 / ef1

Output-referred-DOF2 = DOF2 / ef2

with ef1 and ef2 being the required enlargement factors for achieving a certain print size respectively.

Now as we have

ef1 = k * ef2

and

f2 = k * f1

we get

Output-referred-DOF1 = 2*u^2 *c / (f1 * D) / (k * ef2) = 2*u^2 *c / ((f1 * D) * (k * ef2))

Output-referred-DOF2 = 2*u^2 *c / (k * f1 * D) / ef2 = 2*u^2 *c / ((k * f1 * D * ef2))

i.e., Output-referred-DOF1 = Output-referred-DOF2.

Do you now see how the focal length has no impact, when changing the format size at the same time (and using equivalent focal lengths)?

Do you also see that we had to keep D (the entrance pupil diameter) constant to achieve the same DOF?

Due to the fact that D needs to be kept constant, we need to change the f-stop (f/D) from f-stop1 (= f1/D) to f-stop2 = (f2/D) when changing the format size. In other words, we need to stop down (using the crop factor k as a multiplier) when using a larger format.

So, yes, taken out of context, technically my statement that focal length does not influence DOF is not correct.

However, I hope it was always clear that the context I was assuming was a change in format size.

Originally posted by clackers Also note the sentences: "Sensor size affects DOF only in that changing the sensor size on a camera requires changing the focal length to get the same picture. It is the change in focal length that then affects the DOF."

It is quite useless of this 'Equivalence' tosh to suggest otherwise!

The "equivalence tosh" agrees that sensor size per se does not change the DOF.

Arguably, that's one of the main messages of the "equivalence tosh".

It agrees that the

*lens *defines the DOF.

It states that by using equivalent lens parameters that the DOF does not change (which it demonstrably does not).

There are various ways in which one can express the influence of lens parameters on DOF. I find considering the subject magnification and the entrance pupil diameter more helpful compared to focal length (the latter is not helpful anymore in macro situations), but these are details.