Elliptical Weighted HOLICs for Weak Lensing Shear Measurement. part1:Definitions and isotropic PSF correction

Abstract

We develop a new method to estimate gravitational shear by adopting an elliptical weight function to measure background galaxy images. In doing so, we introduce a new concept of "zero plane" which is an imaginal source plane where shapes of all sources are perfect circles, and regard the intrinsic shear as the result of an imaginal lensing distortion. This makes the relation between the observed shear, the intrinsic shear and lensing distortion more simple and thus higher-order calculation more easy. The elliptical weight function allows us to measure the mutiplemoment of shape of background galaxies more precisely by weighting highly to brighter parts of image and moreover to reduce systematic error due to insufficient expansion of the weight function in the original approach of KSB. Point Spread Function(PSF) correction in E-HOLICs methods becomes more complicated than those in KSB methods. In this paper we studied isotropic PSF correction in detail. By adopting the lensing distortion as the ellipticity of the weight function, we are able to show that the shear estimation in E-HOLICs method reduces to solve a polynomial in the absolute magnitude of the distortion. We compare the systematic errors between our approach and KSB using STEP2 simulation. It is confirmed that KSB method overestimate the input shear for images with large ellipticities, and E-HOLICs correctly estimate the input shear even for such images. Anisotropic PSF correction and analysis of real data will be presented in forthcoming paper.