I’ve been testing the Fujifilm 120/4 GF macro lens at 1:1, using the Fuji 45 mm extension tube. I found that the corners were soft. I’ve been using the lens for a long time, and I never noticed this before. But I’ve never used it for repro work, where such a flaw could well be a big problem. I was asked to post some images of three dimensional subjects where the soft corners showed up. I didn’t have any in my Lightroom catalog. In fact, I didn’t even have images at 1:2 where there was supposed to be sharp detail in the edges and corners.

I got to thinking about why, and realized that the math behind 3D work at 1:1 is cruel.

First, some basic principles. Depth of focus at a given f-stop is dependent on the stop and independent of focal length. Therefore, for macro work, depth of field at a given magnification and f-stop is independent of focal length. At 1:1, DOF equals depth of focus.

With excellent lenses, for critical sharpness, the circle of confusion (CoC) due to misfocus should be held about one and a half times the pixel pitch. For the GFX 100 and GFX 100S, that’s five or six micrometers (um). Let’s say we have a macro lens that we can get to 1:1, either on its own, or with tubes or bellows. Let’s further say that it’s a great — almost perfect — lens. To have acceptable diffraction for critical work, we need to use the lens at an effective aperture of f/8 or wider. If the lens doesn’t have internal focusing, that means that we’ll set the lens to f/4, since the bellows draw for 1:1 will make the effective f-stop two stops narrower than the f-stop on the lens. That means that the depth of field — and the depth of focus — will be 5*8, or 40 um.

For a worst-case CoC in a focusing stack, we’ll have to move the focal plane by 2*40 or 80 um between each shot. That means we need 12.5 shots for every millimeter (mm) of subject depth.

If the subject depth is an inch, we need 12.5*25.4, or a bit over 317 shots. If the subject depth is two inches, we need 635 shots.

Ilya Zakharevich says

Your numbers do not click. Why do you allow 1.5 px for defocus, but only 1 px for diffraction? Or do you mean “the marked f-number” (as opposed to “the physical one” = angular size of the exit pupil)?

JimK says

At f/8, at 530 nm, the Sparrow distance is 5.2 um.

Ilya Zakharevich says

.47 * .53 * 2 * 8 = 3.99. Which gives?!

JimK says

Yeah, you’re right. My bad. I was thinking Rayleigh. So let’s say that we’re at f/8 and want the worst-case defocus blur to be the same as the diffraction blur. That means we need even finer steps, and even more of them. If the criterion is average defocus blur, then we can loosen up on the step size a bit. The numbers are still cruel.

Ilya Zakharevich says

Anyway, I’m puzzled why you use the pre-DSP criteria of resolution. Rayleigh’s is XIX century, Sparrow’s seems to be early XX century. (BTW, thanks — I knew this limit “as a concept”, but without the name!)

Myself, I think in terms of MTF. — And I do not see how ANY other approach would make sense in presence of DSP.

For example, it seems that demosaicers you use do not resolve above 0.5 cycles/px. So a reasonable metric would be MTF at about 1/2√2 cycles/px. Say:

The defocus for which MTF at 1/2√2 cycles/px goes down at most 1.5 times.