We characterize the ability of the Dark Energy Camera (DECam) to perform
relative astrometry across its 500~Mpix, 3 deg^2 science field of view, and
across 4 years of operation. This is done using internal comparisons of ~4x10^7
measurements of high-S/N stellar images obtained in repeat visits to fields of
moderate stellar density, with the telescope dithered to move the sources
around the array. An empirical astrometric model includes terms for: optical
distortions; stray electric fields in the CCD detectors; chromatic terms in the
instrumental and atmospheric optics; shifts in CCD relative positions of up to
~10 um when the DECam temperature cycles; and low-order distortions to each
exposure from changes in atmospheric refraction and telescope alignment. Errors
in this astrometric model are dominated by stochastic variations with typical
amplitudes of 10-30 mas (in a 30 s exposure) and 5-10 arcmin coherence length,
plausibly attributed to Kolmogorov-spectrum atmospheric turbulence. The size of
these atmospheric distortions is not closely related to the seeing. Given an
astrometric reference catalog at density ~0.7 arcmin^{-2}, e.g. from Gaia, the
typical atmospheric distortions can be interpolated to 7 mas RMS accuracy (for
30 s exposures) with 1 arcmin coherence length for residual errors. Remaining
detectable error contributors are 2-4 mas RMS from unmodelled stray electric
fields in the devices, and another 2-4 mas RMS from focal plane shifts between
camera thermal cycles. Thus the astrometric solution for a single DECam
exposure is accurate to 3-6 mas (0.02 pixels, or 300 nm) on the focal plane,
plus the stochastic atmospheric distortion.Comment: Submitted to PAS
