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