Pixelation Effects in Weak Lensing

Weak gravitational lensing is a promising probe of dark matter and dark energy requiring accurate measurement of the shapes of faint, distant galaxies. Such measures are hindered by the finite resolution and pixel scale of typical cameras. On the other hand, as imaging telescopes are practically limited to a fixed number of pixels and operational life-span, so the survey area increases with pixel size. We investigate the optimum choice of pixel scale in this trade-off for a space-based mission, using the full engineering model and survey strategy of the proposed SuperNova/Acceleration Probe as an example. Our methodology is to simulate realistic astronomical images of known shear and to evaluate the surface density of sources where the shear is accurately recovered using the Rhodes, Refregier, & Groth algorithm in the context of the derived dark matter power spectrum. In addition to considering single exposures, we also examine the benefits of sub-pixel dithering. Although some of our results depend upon the adopted shape measurement method, the relative trends, particularly those involving the surface density of resolved galaxies, are robust. Our approach provides a practical counterpart to studies which consider the effects of pixelation from analytic principles, which necessarily assume an idealized shape measurement method. We find that the statistical error on the mass power spectrum is minimized with a pixel scale equal to 75-80% of the FWHM of the point-spread function, and that dithering is marginally beneficial at larger pixel scales.