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
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
Comment: 13 pages, 4 figures; pedagogical article for submission to the Open
Journal of Astrophysics
Subject: Astrophysics - Instrumentation and Methods for Astrophysics