Erin Sheldon and Matt Becker have long reported that DM's CoaddPsf is not as accurate as it could be, in that they get significantly better agreement between the coadded image and PSF by rendering the input PSF at integer coadd positions (and hence fractional input-image positions) and then warping with the fractional translation included.

A conversation at the DESC Sprint Week of 2021-10-25 helped us at least mostly wrap our heads around the problem; we had not taken action on this problem because it wasn't clear which of our assumptions about Nyquist sampling and Lanczos were breaking down, and hence whether simply adopting their approach would address our more general problem of needing to provide coadd PSFs at arbitrary (i.e. not just integer) pixel positions. The short answer is it looks like it should - even if their approach still isn't quite right, it's more right than what we're doing, and we should modify CoaddPsf and WarpedPsf to operate the same way.

This won't actually affect the metadetect development effort, because we don't plan to use CoaddPsf or WarpedPsf for cell-based coadds anyway, but it still seems worth doing before any major production run that does not use cell-based coadds for all measurements.

As part of this ticket, we should also actually do the math to try to get an even more complete understanding of what's going on. I'm thinking specifically of writing down both approaches and Fourier transforming them, applying the Poisson summation formula as needed, without assuming that the warping kernel is Sinc or even well-sampled. I'm particularly curious whether this observed discrepancy tells us anything about how much we should expect coadd noise to be correlated, and whether we can pin the problem squarely on differences between Lanczos and sinc either inside or outside the band limit.