| CVS $Revision: 2.2 $Date: 2001/10/10 02:28:52 Accepted to AJ Shapes and Shears, Stars and Smears: Optimal Measurements for Weak (2007) | |||||||||||||
Abstract | |||||||||||||
| We present the theoretical and analytical bases of optimal techniques to measure weak gravitational shear from images of galaxies. We rst characterize the geometric space of shears and ellipticity, then use this geometric interpretation to analyse images. The steps of this analysis include: measurement of object shapes on images, combining measurements of a given galaxy on dierent images, estimating the underlying shear from an ensemble of galaxy shapes, and compensating for the systematic eects of image distortion, bias from PSF asymmetries, and \dilution " of the signal by the seeing. These methods minimize the ellipticity measurement noise, provide calculable shear uncertainty estimates, and allow removal of systematic contamination by PSF eects to arbitrary precision. Galaxy images and PSFs are expressed as \Laguerre expansions, " a 2d generalization of the Edgeworth expansion, making the PSF correction and shape measurement relatively straightforward and computationally ecient. We also discuss sources of noise-induced bias in weak lensing measurements|selection biases, and \centroid " biases arising from noise rectication|and provide a solution for these and previously identied biases. Subject headings: gravitational lensing|methods: data analysis|techniques: image processing 1. | |||||||||||||
Publication details | |||||||||||||
| |||||||||||||