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

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.