Weak gravitational lensing has emerged as a leading probe of the growth of cosmic structure. However, the shear signal is very small and accurate measurement depends critically on our ability to understand how non-ideal instrumental effects affect astronomical images. WFIRST will fly a focal plane containing 18 Teledyne H4RG-10 near infrared detector arrays, which present different instrument calibration challenges from previous weak lensing observations. Previous work has shown that correlation functions of flat field images are effective tools for disentangling linear and non-linear inter-pixel capacitance (IPC) and the brighter-fatter effect (BFE). Here we present a Fourier-domain treatment of the flat field correlations, which allows us to expand the previous formalism to all orders in IPC, BFE, and classical non-linearity. We show that biases in simulated flat field analyses in Paper I are greatly reduced through the use of this formalism. We then apply this updated formalism to flat field data from three WFIRST flight candidate detectors, and explore the robustness to variations in the analysis. We find that the BFE is present in all three detectors, and that its contribution to the flat field correlations dominates over the non-linear IPC. The magnitude of the BFE is such that the effective area of a pixel is increased by $(3.54pm0.03)times 10^{-7}$ for every electron deposited in a neighboring pixel. We compare IPC maps from flat field autocorrelation measurements to those obtained from the single pixel reset method and find a median difference of 0.113%. After further diagnosis of this difference, we ascribe it largely to an additional source of cross-talk, the vertical trailing pixel effect, and recommend further work to develop a model for this effect. These results represent a significant step toward calibration of the non-ideal effects in WFIRST detectors.
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