Tolerance For the Pixelation Effect in Shear Measurement

Images taken by space telescopes typically have a superb spatial resolution, but a relatively poor sampling rate due to the finite CCD pixel size. Beyond the Nyquist limit, it becomes uncertain how much the pixelation effect may affect the accuracy of galaxy shape measurement. It is timely to study this issue given that a number of space-based large-scale weak lensing surveys are planned. Using the Fourier_Quad method, we quantify the shear recovery error as a function of the sampling factor Q, i.e., the ratio between the FWHM of the point-spread-function (PSF) and the pixel size of the CCD, for different PSFs and galaxies of different sizes and noise levels. We show that sub-percent-level accuracy in shear recovery is achievable with single-exposure images for $Q\lesssim 2$. The conclusion holds for galaxies much smaller than the PSF, and those with a significant level of noise.