  Weak gravitational lensing studies aim to measure small distortions in the
shapes of distant galaxies, and thus place very tight demands on the
understanding of detector-induced systematic effects in astronomical images.
The Wide-Field Infrared Survey Telescope (WFIRST) will carry out weak lensing
measurements in the near infrared using the new Teledyne H4RG-10 detector
arrays, which makes the range of possible detector systematics very different
from traditional weak lensing measurements using optical CCDs. One of the
non-linear detector effects observed in CCDs is the brighter-fatter effect
(BFE), in which charge already accumulated in a pixel alters the electric field
geometry and causes new charge to be deflected away from brighter pixels. Here
we describe the formalism for measuring the BFE using flat field correlation
functions in infrared detector arrays. The auto-correlation of CCD flat fields
is often used to measure the BFE, but because the infrared detector arrays are
read out with the charge "in place," the flat field correlations are dominated
by capacitive cross-talk between neighboring pixels (the inter-pixel
capacitance, or IPC). Conversely, if the BFE is present and one does not
account for it, it can bias correlation measurements of the IPC and photon
transfer measurements of the gain. We show that because the infrared detector
arrays can be read out non-destructively, one can compute numerous
cross-correlation functions between different time slices of the same flat
exposures, and that correlations due to IPC and BFE leave distinct imprints. We
generate a suite of simulated flat fields and show that the underlying IPC and
BFE parameters can be extracted, even when both are present in the simulation.
There are some biases in the BFE coefficients up to 12%, which are likely
caused by higher order terms that are dropped from this analysis.
