Hmmm.... I feel like my previous comment got lost somewhere.... I'll try to recreate:

I've managed to fit a full focal plane worth of donuts. (See attached scatter plots of fit coefficients). Looks mostly like what I would have expected. E.g., the Z4-Z10 coefficients make Z4-Z10-ish looking polynomials over the field. There are some interesting trends in the higher order coefficients too.

The Z4 coefficients don't match the surface height metrology very well.

The r0 coefficient, which is to model the extra bluriness due to the atmosphere, is flat over most of the focal plane, but has a steep deviation towards the edge of the focal plane in quadrants I, II, and IV. I believe r0 should be flat over the full focal plane. I'll look at the individual donut fits to see if anything looks weird there. This same region of the focal plane shows deviations in many other coefficients too.

Another aspect that I'm not sure I understand is whether or not distortion affects either the donut images or the pinhole images used to model the pupil function. It may be worth trying to model this out.

roodman, if you're watching, I'm particularly interested in your thoughts.

Finally, before marking this ticket as done, in addition to the above, I'd like to be able to fit a focal plane with an arbitrary rotator angle, instead of only a focal plane with a convenient rotator angle, as has been done so far.

Do you have a feeling from how the surface and Z4 can fail to match, except "the surface is wrong"?

Distortion possibly? I'd be interested if DECam has done this comparison already.

Z4 is mostly a measure of the size of the donut, so if the pixel size is varying radially, I think this might look like the Z4 variation.

I think I'm ready to declare this one finished. Two updates since last post: I can now process donuts taken at any rotator angle. I can process both intra-focal and extra-focal donuts. I'm attaching a few figures showing the Z5 field-of-view dependence for exposures with different rotator angles (51412 has rotator ~ 45 degrees, 69016 has rotator ~ -90 degrees) and different focus values (51412 has FOC-VAL = 4.68, 51416 has FOC-VAL = 2.88, i.e., 1800 microns different, meaning both images are ~900 microns out-of-focus in different directions).

The rotator differences between the two images at the same FOC-VAL but different rotator angle are pretty small. The intra-vs-extra differences at the same rotation are a bit more dramatic (even after accounting for the sign flip). Will need to look at more of these to decide if that's meaningful or not.

reference image

intra <-> extra focal, same rotator position

change rotator, same focus position