  Uncertainty in the wide-angle Point Spread Function (PSF) at large angles
(tens of arcseconds and beyond) is one of the dominant sources of error in a
number of important quantities in observational astronomy. Examples include the
stellar mass and shape of galactic halos and the maximum extent of starlight in
the disks of nearby galaxies. However, modeling the wide-angle PSF has long
been a challenge in astronomical imaging. In this paper, we present a
self-consistent method to model the wide-angle PSF in images. Scattered light
from multiple bright stars is fitted simultaneously with a background model to
characterize the extended wing of the PSF using a Bayesian framework operating
on pixel-by-pixel level. The method is demonstrated using our software
elderflower and is applied to data from the Dragonfly Telephoto Array to model
its PSF out to 20-25 arcminutes. We compare the wide-angle PSF of Dragonfly to
that of a number of other telescopes, including the SDSS PSF, and show that on
scales of arcminutes the scattered light in the Dragonfly PSF is markedly lower
than that of other wide-field imaging telescopes. The energy in the wings of
the Dragonfly point-spread function is sufficiently low that optical
cleanliness plays an important role in defining the PSF. This component of the
PSF can be modelled accurately, highlighting the power of our self-contained
approach.
