Document scheme for measuring cobra offset, brightness and PSF

As mentioned on slack:

https://sumire-pfs.slack.com/archives/C9TDPMVHT/p1664334936041159

RHL proposed a means by which the cobra offsets, source brightness and PSFs can be measured using sky objects:

Unfortunately, I think I really just remembered Eddie Schlafly’s good idea (or was it David Schlegel – that's where I heard about something very similar). I've written to David asking for a reference.
Start by assuming that we can find a field where all the stars are equally bright and exactly at the expected positions on PFI. We can then design a plate and offset the fibre positions into (say) a 5x5 dither on a 0.5" grid or (better) a hexagonal close-pack; say 19 positions. If we then observe the field the individual fibres (observing different stars) will give us an image of the PSF with a single exposure. Note that we don't move any cobras after the initial setup.
Unfortunately we don't have access to such a field, but fortunately we don't need it. There are 3 unknown numbers associated with each star: the flux, the offset in x and y from the expected position (presumably due to problems in our mapping from (ra, dec) to mm). So if we take four dithered exposures of the field, each with the fibres offset to my 19 positions, we can solve for the brightness and offset of every star, and also the PSF.
In reality of course there may be spatial structure in the PSF and noise so we'd probably want more than four exposures.
For a focus sweep we'd only need one exposure for each focal position once we'd solved for the brightness/offset with a 4-dither sequence. We might want more if we're worried that changing the focus would move the stars on the PFI focal plane.
Unless I've missed something this is definitely something to use in November.

Please document this scheme.