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.
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