  Weak gravitational lensing (WL) is one of the most powerful techniques to
learn about the dark sector of the universe. To extract the WL signal from
astronomical observations, galaxy shapes must be measured and corrected for the
point spread function (PSF) of the imaging system with extreme accuracy. Future
WL missions (such as the Wide-Field Infrared Survey Telescope, WFIRST) will use
a family of hybrid nearinfrared CMOS detectors (HAWAII-4RG) that are untested
for accurate WL measurements. Like all image sensors, these devices are subject
to conversion gain nonlinearities (voltage response to collected photo-charge)
that bias the shape and size of bright objects such as reference stars that are
used in PSF determination. We study this type of detector nonlinearity (NL) and
show how to derive requirements on it from WFIRST PSF size and ellipticity
requirements. We simulate the PSF optical profiles expected for WFIRST and
measure the fractional error in the PSF size and the absolute error in the PSF
ellipticity as a function of star magnitude and the NL model. For our nominal
NL model (a quadratic correction), we find that, uncalibrated, NL can induce an
error of 0.01 (fractional size) and 0.00175 (absolute ellipticity error) in the
H158 bandpass for the brightest unsaturated stars in WFIRST. In addition, our
simulations show that to limit the bias of the size and ellipticity errors in
the H158 band to approximately 10% of the estimated WFIRST error budget, the
parameter of our quadratic NL model must be calibrated to about 1% and 2.4%,
respectively. We present a fitting formula that can be used to estimate WFIRST
detector NL requirements once a true PSF error budget is established.
