Biases in, and corrections to, KSB shear measurements

TL;DR

This paper critically examines the KSB method for measuring gravitational shear, identifying key assumptions that cause bias, and proposes a third-order extension that significantly reduces these biases.

Contribution

The authors analyze the biases in the KSB shear measurement method and develop a third-order extension to improve accuracy in weak lensing studies.

Findings

KSB yields biased shear estimates due to non-commuting averaging operations.

Assumptions of small ellipticity and approximate PSF correction contribute to biases.

Third-order extension of KSB reduces biases substantially.

Abstract

We analyse the KSB method to estimate gravitational shear from surface-brightness moments of small and noisy galaxy images. We identify three potentially problematic assumptions. These are: (1) While gravitational shear must be estimated from averaged galaxy images, KSB derives a shear estimate from each individual image and then takes the average. Since the two operations do not commute, KSB gives biased results. (2) KSB implicitly assumes that galaxy ellipticities are small, while weak gravitational lensing assures only that the change in ellipticity due to the shear is small. (3) KSB does not invert the convolution with the point-spread function, but gives an approximate PSF correction which - even for a circular PSF - holds only in the limit of circular sources. The effects of assumptions (2) and (3) partially counter-act in a way dependent on the width of the weight function and of the PSF. We quantitatively demonstrate the biases due to all assumptions, extend the KSB approach consistently to third order in the shear and ellipticity and show that this extension lowers the biases substantially. The issue of proper PSF deconvolution will be addressed in a forthcoming paper.