PSF photometry on just one star

[pllim]

Let's consider this work flow:

1. Select one star.
2. Construct a 2D model (e.g., Gaussian2D, Moffat2D, or a non-existent Lorentz2D).
3. Feed the model some rough initial estimates.
4. Fit the model to the star.
5. Obtain or derive the following values from fit:
   • Centroid
   • FWHM (X, Y, and overall?)
   • Brightness
   • Ellipticity
   • Background (sky level)

Is this something that PSF photometry can/should do? If not, is this something that photutils should support outside of PSF photometry domain?

More context: I discussed this with @larrybradley and @eteq offline. Erik suggested prepare_psf_model that seems to go with BasicPSFPhotometry. However, BasicPSFPhotometry requires things like group_maker, which does not seem very relevant for one-star use case, and I am unable to find a good example for the use case above given #557.

xref ejeschke/ginga#896 and https://github.com/ejeschke/ginga/blob/965d1ec23fdf02b7a48c86b428153346c6ce5cad/ginga/util/iqcalc.py#L466