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Weak gravitational lensing studies aim to measure small distortions in theshapes of distant galaxies, and thus place very tight demands on theunderstanding of detector-induced systematic effects in astronomical images.The Wide-Field Infrared Survey Telescope (WFIRST) will carry out weak lensingmeasurements in the near infrared using the new Teledyne H4RG-10 detectorarrays, which makes the range of possible detector systematics very differentfrom traditional weak lensing measurements using optical CCDs. One of thenon-linear detector effects observed in CCDs is the brighter-fatter effect(BFE), in which charge already accumulated in a pixel alters the electric fieldgeometry and causes new charge to be deflected away from brighter pixels. Herewe describe the formalism for measuring the BFE using flat field correlationfunctions in infrared detector arrays. The auto-correlation of CCD flat fieldsis often used to measure the BFE, but because the infrared detector arrays areread out with the charge "in place," the flat field correlations are dominatedby capacitive cross-talk between neighboring pixels (the inter-pixelcapacitance, or IPC). Conversely, if the BFE is present and one does notaccount for it, it can bias correlation measurements of the IPC and photontransfer measurements of the gain. We show that because the infrared detectorarrays can be read out non-destructively, one can compute numerouscross-correlation functions between different time slices of the same flatexposures, and that correlations due to IPC and BFE leave distinct imprints. Wegenerate a suite of simulated flat fields and show that the underlying IPC andBFE 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 likelycaused by higher order terms that are dropped from this analysis.

Brighter-fatter effect in near-infrared detectors -- I. Theory of flat auto-correlations