  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
$(3.54\pm0.03)\times 10^{-7}$ 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.
