Weak Lensing Measurements: the KSB Method Revisited and Application to HST Images

The weak distortions produced by gravitational lensing in the images of background galaxies provide a unique method to measure directly the distribution of mass in the universe. However, because the induced distortions are only of a few percent, this technique requires high precision measurements of the lensing shear and cautious corrections for systematic effects. Kaiser, Squires, & Broadhurst (1995) proposed a method to calibrate the ellipticity–shear relation in the presence of Point Spread Function (PSF) anisotropies and camera distortions. Here, we revisit the KSB method in the context of the demanding search for weak lensing by large-scale structure. We show that both the PSF and the camera distortions can be corrected for using source moments, as opposed to ellipticities. We clarify the applicability of some of the approximations made in this method. We derive expressions for the corrections which only involve the galaxy moments. By decomposing the moments into spinors, we derive an explicit relation between the shear and the average ellipticity. As an application, we repeat the analysis of the HST–WFPC2 camera performed by Hoekstra et al. (1998). We confirm the presence of sizable (∼ 10%) PSF ellipticities at the edge of the WFPC2 present address: Institute of Astronomy, Madingley Road, Cambridge, CB3 OHA, U.K., email: [email protected]