Simple Treatments of the Photon Noise and the Pixelation Effect in Weak Lensing

TL;DR

This paper introduces simple, effective correction methods for photon noise and pixelation effects in weak lensing measurements, improving accuracy in cosmic shear analysis regardless of galaxy or PSF shapes.

Contribution

It presents novel correction techniques for photon noise and pixelation in cosmic shear measurements, applicable across various shear measurement methods.

Findings

Reliable noise removal even when noise flux density is high

Accurate reconstruction of continuous images from pixelated data

Negligible systematic errors with appropriate pixel size

Abstract

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.