The point spread function (PSF) describes how the light of a point-like source is affected by several optical scattering effects (atmosphere, telescope, instrument, etc.). Since the light of all astrophysical sources undergoes all these effects, characterizing the PSF is key in astronomical analysis (for small and large objects). Consequently, having a good characterization of the PSF is fundamental to any analysis.
In some situations234 a parametric (analytical) model is sufficient for the PSF (such as Gaussian or Moffat, see Point spread function). However, once you are interested in objects that are larger than a handful of pixels, it is almost impossible to find an analytic function to adequately characterize the PSF. Therefore, it is necessary to obtain an empirical (non-parametric) and extended PSF. In this section we describe a set of installed scrips in Gnuastro that will let you construct the non-parametric PSF using point-like sources. They allow you to derive the PSF from the same astronomical images that the science is derived from (without assuming any analytical function).
The scripts are based on the concepts described in Infante-Sainz et al. (2020, https://arxiv.org/abs/1911.01430). But to be complete, we first give a summary of the logic and overview of their combined usage in Overview of the PSF scripts. Furthermore, before going into the technical details of each script, we encourage you to go through the tutorial that is devoted to this at Building the extended PSF. The tutorial uses a real dataset and includes all the logic and reasoning behind every step of the usage in every installed script.
An example scenario where a parametric PSF may be enough: you are only interested in very small, high redshift objects that only extended a handful of pixels.