Elliptical Weighted HOLICs for Weak Lensing Shear Measurement part3:Random Count Noise Effect for Image's Moments in Weak Lensing Analysis

TL;DR

This paper addresses the impact of random count noise on weak lensing shear measurements, deriving correction equations to reduce systematic errors caused by Poisson noise in background images.

Contribution

It introduces new correction methods for second-order effects of Poisson noise on image moments and ellipticity measurements in weak lensing analysis.

Findings

Systematic error reduced to less than 1% for objects with S/N > 3

Derived equations effectively correct noise-induced moment errors

Validated correction methods through simulation tests

Abstract

This is the third paper on the improvements of systematic errors in our weak lensing analysis using an elliptical weight function, called E-HOLICs. In the previous papers we have succeeded in avoiding error which depends on ellipticity of background image. In this paper, we investigate the systematic error which depends on signal to noise ratio of background image. We find that the origin of the error is the random count noise which comes from Poisson noise of sky counts. Random count noise makes additional moments and centroid shift error, and those 1st orders are canceled in averaging, but 2nd orders are not canceled. We derived the equations which corrects these effects in measuring moments and ellipticity of the image and test their validity using simulation image. We find that the systematic error becomes less than 1% in the measured ellipticity for objects with $S/N>3$.