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. The cosmic
shears measured from the interpolated continuous images contain negligible
systematic errors 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 (2008),
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.
