Weak lensing measurements: A revisited method and application to Hubble Space Telescope images

The weak distortions produced by gravitational lensing in the images of bac kground galaxies provide a unique method to measure directly the distributi on of mass in the universe. However, because the induced distortions are on ly of a few percent, this technique requires high-precision measurements of the lensing shear and cautious corrections for systematic effects. Kaiser, Squires, & Broadhurst proposed a method to calibrate the ellipticity-shear relation in the presence of point-spread function (PSF) anisotropies and c amera distortions. Here, we revisit the Kaiser, Squires, & Broadhurst metho d in the context of the demanding search for weak lensing by large-scale st ructure. We show that both the PSF and the camera distortions can be correc ted for using source moments, as opposed to ellipticities. We clarify the a pplicability of some of the approximations made in this method. We derive e xpressions for the corrections that involve only the galaxy moments. By dec omposing the moments into spinors, we derive an explicit relation between t he shear and the average ellipticity. We discuss the shortcomings of the me thod and test its validity using numerical simulations. As an application o f the method, we repeat the analysis of the Hubble Space Telescope (HST) WF PC2 camera performed by Hoekstra et al. We confirm the presence of sizable (similar to 10%) PSF ellipticities at the edge of the WFPC2 chips. However, we find that the camera distortion is radial, rather than tangential. We a lso show that the PSF ellipticity varies by as much as 2% over time. We use these measurements to correct the shape of galaxies in the HST Survey Stri p (the "Groth" Strip). By considering the dependence of the ellipticities o n object size, we show that, after corrections, the residual systematic unc ertainty for galaxies with radii greater than 0 ".15 is about 0.4% when ave raged over each chip. We discuss how these results provide good prospects f or measuring weak lensing by large-scale structure with deep HST surveys.