PSFs of coadded images

TL;DR

This paper examines how different coaddition schemes affect the point-spread function in combined images, highlighting conditions for well-defined PSFs and limitations of nonlinear methods.

Contribution

It formally demonstrates when linear coaddition produces a well-defined PSF and analyzes the failure of nonlinear methods for stars and extended objects.

Findings

Linear coaddition yields well-defined PSF only under specific conditions.

Nonlinear methods like median and clipped-mean fail to produce consistent PSFs for stars.

All nonlinear coaddition methods fail to produce a well-defined PSF for extended objects.

Abstract

We provide a detailed exploration of the connection between choice of coaddition schemes and the point-spread 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 well-defined PSF. The key elements of this discussion are as follows: 1. We provide an illustration of how linear coaddition schemes can produce a coadd that lacks a well-defined PSF even for relatively simple scenarios and choices of weight functions. 2. We provide a more formal demonstration of the fact that a linear coadd only has a well-defined 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. 3. We discuss some reasons that two plausible nonlinear coaddition algorithms (median and clipped-mean) fail to produce a consistent PSF profile for stars. 4. We demonstrate that all nonlinear coaddition procedures fail to produce a well-defined PSF for extended objects. In the end, we conclude that, for any purpose where a well-defined 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.