A techie follow-up, if I may!

How low does the lens's MTF have to drop before one sees a significant decrease in the limiting resolution (or increase in the 92 pixel diameter) - and is there some MTF value associated with this "limiting resolution"?

Hi Andy,

Good questions, but hard ones to answer with a single number.

First of all, with my proposed target one doesn't test optical MTF alone, but rather the system MTF (lens (de)focus, residual aberrations, veiling glare, diffraction, OLPF, microlenses, sensel aperture). When the system MTF goes to zero, that's the limit. But it is of course not that simple, because MTF is a function of contrast reduction with increasing spatial frequency. Therefore, if one increases the input contrast enough, then there will be more residual contrast. I've designed the target to produce a moderate contrast, but one would need to spot measure it after printing (which is beyond my control) to get a more accurate input value.

Second, as for an MTF value associated with the limiting resolution, the ISO standard for digital camera resolution and the ones for scanner resolution used to have a remark that 10% MTF (or SFR) corresponds well with the limiting resolution of the human eye. I don't know if the more recent standard copies still mention that.

I Think that the limiting resolution is near the Rayleigh limit, which is often quoted at around 10% MTF, but some calculations by Bart indicate the Rayleigh limit is closer to 20%. Hopefully, he will comment.

Yes, Bill is correct. The difference is due to accidental alignment with the sensel grid. When the Rayleigh limit gap between two diffraction PSF peaks aligns with the sensel between the diffraction patterns then the MTF can be something like 26%, when however the peaks of the ajacent diffraction patterns happen to be aligned with the sensels then the gap could have almost zero MTF, depending on sensel pitch. So on average, one could say it's 10%, but in practice it varies between approx. 26% and 0%, depending on the particular parameters (wavelength, aperture number, sensel pitch, sensel grid alignment).

EDIT

I'll illustrate it a bit better. This is how the Rayleigh criterion of f/5.6, assuming a 564nm wavelength, looks when sampled at a 0.1 micron pitch.

Now imagine area sampling that same Rayleigh criterion with 1 to 6 micron sensels, which will look like this:

When you magnify the images, it becomes apparent that due to the area sampling of our sensels, it becomes quickly impossible to find any contrast between the diffraction peaks. In fact, in order to reliably resolve the two diffraction patterns according to the Rayleigh criterion, we require more than 4 pixels per diffraction pattern diameter. In other words, to resolve the two diffraction patterns of f/5.6 (assuming a 564nm wavelength), we require a sensel pitch of less than (2.44 x 0.564 x 5.6) / 4 = 1.93 micron, and even then the alignment of the diffraction patterns may blend them to a uniform brightness in the worst case.

Fortunately, my resolution target is relatively insensitive to hor/ver sensel alignment because it tests the resolution at various angles, not just the ones that happen to align with the grid.

Cheers,

Bart

P.S. I've been working on a webpage that illustrates it with visual examples. Although it basically works, one needs to continuously confirm that it is okay that the Javascript takes more time to finish, so I also need some more time to get things sorted out and sped up.