I haven't gone as far as calculating the MTF, my chart is just based on my empirical judgement that visual degradation seems to set in at approx. 1.5x the sensel pitch. This is also often supported by an observed declining MTF score at higher spatial frequencies when using narrower apertures.

And that judgment should be pretty accurate. Many demosaicing algorithms use the green channel as an ersatz luminance channel for the purposes of interpolation, and the green pixels are spaced at sqrt2~1.4 times the pixel pitch, so when the diffraction spot exceeds this scale then diagonally nearby green pixels are blurred together.

An MTF degradation can be used to calculate a lowest limit of usefulness, and certainly a Sinc function is easier to use than an Airy pattern on an assumed square (sensel) aperture. I don't think we have to draw the line at a zero response, because at 10% MTF we're already pretty much at the practical limiting visual resolution (for average contrast subjects). The ISO also mentions a good correlation between 10% MTF and limiting visual resolution.

Right. I wasn't using a square sensel aperture, I had in mind a square lens aperture (usual "spherical cow" approximation we physicists use to simplify calculations). Agreed we don't have to draw the line at zero, but I was wanting to calculate how much the finite aperture degrades MTF for any aperture, even above the diffraction limit. I was surprised to find a linear relation, basically for an intensity pattern

I = I_0 cos^2 kx

and diffraction pattern sin^2ax/ax, the output of averaging the intensity pattern against the diffraction pattern is

I_diff = I_0 (1-a/k)

(for a<k), and

I_diff = 0

(for a>k)

I was merely expressing my surprise that the result was linear in the parameter _a_ which is proportional to the f-number. So MTF is decreasing directly with aperture even above the point where pixel-level resolution is diffraction limited (granted, not much for small _k_ but the amount of degradation doubles every time we stop down two stops).

I could also run a simulation in Mathematica (which I use to calculate a 2-D diffraction pattern PSF kernel), but it would still give a theoretical limit, because of the unknown properties of the AA-filter and residual optical aberrations. That's why I use the rule of thumb of 'sensel widths' which is useful enough to predict the visual on-set of diffraction degradation. Any narrower aperture will degrade the per pixel resolution, and reduce the chance of successful deconvolution to restore the losses.

Bart

Yes, doing the full integral against an Airy pattern is probably overkill. But it represents an upper bound on MTF. The MTF due to the AA filter simply multiplies that due to diffraction. Optical aberrations and diffraction effects might not cleanly factorize in this way, I'm not sure, since they arise from the same part of the optical pathway (the lens), in any case can only decrease overall MTF. In any case, these effects are present independent of diffraction and the influence of diffraction is I think reasonably modelled by the simple 1d calculation.