A new shear estimator for weak-lensing observations

We present a new shear estimator for weak-lensing observations that properly accounts for the effects of a realistic point-spread function (PSF). Images of faint galaxies are subject to gravitational shearing, followed by smearing with the instrumental and/or atmospheric PSF. We construct a finite-resolution shear operator, which when applied to an observed image has the same effect as a gravitational shear applied prior to smearing. This operator allows one to calibrate essentially any shear estimator. We then specialize to the case of weighted second-moment shear estimators. We compute the shear polarizability, which gives the response of an individual galaxy's polarization to a gravitational shear. We then compute the response of the population of galaxies, and thereby construct an optimal weighting scheme for combining shear estimates from galaxies of various shapes, luminosities, and sizes. We define a figure of merit (an inverse shear variance per unit solid angle) that characterizes the quality of image data for shear measurement. The new method is tested with simulated image data. We discuss the correction for anisotropy of the PSF and propose a new technique involving measuring shapes from images that have been convolved with a recircularizing PSF. We draw attention to a hitherto ignored noise-related bias and show how this can be analyzed and corrected for. The analysis here draws heavily on the properties of real PSFs, and we include in Appendix A a brief review, highlighting those aspects that are relevant for weak lensing.