Elliptical weighted holics for weak lensing shear measurement. III. the effect of random count noise on image moments in weak lensing analysis

This is the third paper on the improvement of systematic errors in weak lensing analysis using an elliptical weight function, referred to as E-HOLICs. In previous papers, we succeeded in avoiding errors that depend on the ellipticity of the background image. In this paper, we investigate the systematic error that depends on the signal-to-noise ratio of the background image. We find that the origin of this error is the random count noise that comes from the Poisson noise of sky counts. The random count noise makes additional moments and centroid shift error, and those first-order effects are canceled in averaging, but the second-order effects are not canceled. We derive the formulae that correct this systematic error due to the random count noise in measuring the moments and ellipticity of the background image. The correction formulae obtained are expressed as combinations of complex moments of the image, and thus can correct the systematic errors caused by each object. We test their validity using a simulated image and find that the systematic error becomes less than 1% in the measured ellipticity for objects with an IMCAT significance threshold of ν ∼ 11.7.