PSFs of coadded images
 ORCID iD: 0000000322711527
 ORCID iD: 0000000241795175
 ORCID iD: 0000000316660962
 ORCID iD: 0000000327595764
 ORCID iD: 0000000187836529
 ORCID iD: 000000025596198X
Abstract
We provide a detailed exploration of the connection between choice of coaddition schemes and the pointspread function (PSF) of the resulting coadded images. In particular, we investigate what properties of the coaddition algorithm lead to the final coadded image having a welldefined PSF. The key elements of this discussion are as follows:

We provide an illustration of how linear coaddition schemes can produce a coadd that lacks a welldefined PSF even for relatively simple scenarios and choices of weight functions.

We provide a more formal demonstration of the fact that a linear coadd only has a welldefined PSF in the case that either (a) each input image has the same PSF or (b) the coadd is produced with weights that are independent of the signal.

We discuss some reasons that two plausible nonlinear coaddition algorithms (median and clippedmean) fail to produce a consistent PSF profile for stars.

We demonstrate that all nonlinear coaddition procedures fail to produce a welldefined PSF for extended objects.
In the end, we conclude that, for any purpose where a welldefined PSF is desired, one should use a linear coaddition scheme with weights that do not correlate with the signal and are approximately uniform across typical objects of interest.