We have some excellent data from observing the star Markab, in Pegasus. We have 334 images at 4 seconds exposure, and each is bordered by dark frames of the same expsoure time - thus we can subtract bias and any dark current easily.
We did this, and aligned and coadded the many images. Then we inspect the PSF by cosnidering the intensity around teh star in concentric rings:
We see that the core of the PSF is about 2.5-3 orders of magnitude above the point where the wings start. We see the wings drop off and join the sky level. The red crosses are median bin values. The blue curve is a polynomial fit, the coefficient of which are given in the table. The polynomial is found for a fit to 1/radius against PSF for the wings, and a Voigt function for the core out to about 1 arc minute.
Some points: The curve is not the PSF - because there are remnants of sky brightness - about 0.88 counts [star scaled to 50000 counts at the peak]. The PSF would be well approximated by the above polynomial without offset (first coefficient).
The part of the PSF from 1-3 arc minutes is roughly linear, as if a simple 1/r ^alfa power-law applies. This is not the case when we consider the above.
We might revisit the extended halo we see in lunar images with the above insight into the effect of a sky level.