Simple treatments of the photon noise and the pixelation effect in weak lensing

We propose easy ways of correcting for the systematic errors caused by the photon noise and the pixelation effect in cosmic shear measurements. Our treatment of noise can reliably remove the noise contamination to the cosmic shear even when the flux density of the noise is comparable with those of the sources. For pixelated images, we find that one can accurately reconstruct their corresponding continuous images by interpolating the logarithms of the pixel readouts with either the Bicubic or the Bicubic Spline method as long as the pixel size is about less than the scale size of the point spread function (PSF; including the pixel response function), a condition which is almost always satisfied in practice. Our methodology is well defined regardless of the morphologies of the galaxies and the PSF. Despite that our discussion is based on the shear measurement method of Zhang, our way of treating the noise can in principle be considered in other methods, and the interpolation method that we introduce for reconstructing continuous images from pixelated ones is generally useful for digital image processing of all purposes.