ELLIPTICALLY WEIGHTED HOLICs FOR WEAK-LENSING SHEAR MEASUREMENT. I. DEFINITIONS AND ISOTROPIC POINT-SPREAD FUNCTION CORRECTION

Abstract

We develop a new method of estimating gravitational shear by adopting an elliptical weight function to measure background galaxy images. In doing so, we introduce the new concept of "zero plane," which is an imaginary source plane where shapes of all sources are perfect circles, and regard the intrinsic shear as the result of an imaginary lensing distortion. This makes the relation between the observed shear, intrinsic shear, and lensing distortion much simpler, and thus higher-order calculations are easier. The elliptical weight function allows us to measure the multipole moments of the shapes of background galaxies more precisely by weighting brighter parts of the image highly, and to reduce systematic error due to insufficient expansion of the weight function in the original approach of Kaiser et al. (KSB). Point-spread function (PSF) correction in the elliptically weighted higher-order lensing image characteristics (E-HOLICs) method becomes more complicated than in the KSB method. In this paper, we study 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 the E-HOLICs method reduces to solve a polynomial in the absolute magnitude of the distortion. We compare the systematic errors between our approach and that of KSB using the Shear Testing Programme 2 simulation. It is confirmed that the KSB method overestimates the input shear for images with large ellipticities, and E-HOLICs correctly estimates the input shear even for such images. Anisotropic PSF correction and analysis of real data will be presented in a forthcoming paper.

A study of the sensitivity of shape measurements to the input parameters of weak-lensing image simulations

“…A further sophistication would be to try to match the shape of the weight function (e.g. Melchior et al 2011;Okura & Futamase 2011). This optimization slows down the shape measurement algorithm and increases the sensitivity to the input ellipticity distribution.…”

Analytical noise bias correction for weak lensing shear analysis with ERA

“…Among them, the photon noise bias which is bias due to random count from Poisson noise of sky brightness is known to be critical for the measurement of cosmic shear. Comments, investigation and development about the bias can be seen in Bernstein & Jarvis 2002, Hirata et al 2003, Miller et al 2007, Bridle et al 2010, Refregier et al 2012, Melchior & Viola 2012, Kacprzak et al 2012, Bernstein & Armstrong 2014, Jarvis et al 2016, Bernstein et al 2016, Simon & Schneider 2016, Conti et al 2017, Hall & Taylor 2017, Hoekstra 2017 We have also developed a new weak lensing shear analysis method called EHOLICs (Okura and Futamase 2011, 2013) based on KSB (Kaiser et al 1995) method, The method uses an elliptical weight function in order to avoid for the systematic error caused by the approximation of the weight function. We have then developed a new method of PSF correction called ERA (Okura and Fuatase 2014, 2016.…”

The Systematic Error Test for PSF Correction in Weak Gravitational Lensing Shear Measurement by the Era Method by Idealizing PSF

“…Previous approaches of PSF correction adopted some sort of approximation for the form of PSF which prevents from an accurate correction in some cases. Recently, we have proposed a new approximation free method of PSF correction called ERA method (ERA1: Futamase 2014, ERA2:Okura andFutamase 2015) based on E-HOLICs method (Okura and Futamase 2011, Okura and Futamase 2012, Okura and Futamase 2013 which is a generalization of KSB method (Kaiser at al. 1995) and uses an elliptical weight function to avoid expansion of weight function in measuring ellipticity.…”