When we share astronomical images, we expect the images to have standards-compliant descriptions of their astrometric calibration—the mapping between image position and sky position—in their headers. Naturally, it is just as important to have descriptions of the point-spread-function, for almost any astronomical activity (like photometry, source matching, or color measurement). And yet we have no standards. (Even the WCS standard for astrometry is seriously out of date). Develop a PSF standard!
Requirements include: It should be very flexible. It should permit variations of the PSF with position in the image. It should have a specified relationship between the stellar position and the position of the mean, median, or mode of the PSF itself. That latter point relates to the fact that astrometric distortions can be sucked up into PSF variations if you permit the mode of the PSF to drift relative to the star postion. I like that freedom, but whether you permit it or not it should be explicit.