A METHOD FOR WEAK LENSING OBSERVATIONS

We develop and test a method for measuring the gravitational lensing-i nduced distortion of faint background galaxies. We first describe how we locate the galaxies and measure two-component ''polarization'' or e llipticity statistic e(alpha), whose expectation value should be propo rtional to the gravitational shear gamma(alpha). We then show that an anisotropic instrumental point-spread function (PSF) perturbs the pola rization by delta e(alpha) = P-alpha beta p beta(s), where p(alpha) is a measure of the PSF anisotropy and P-alpha beta(s) is the ''lineariz ed smear polarizability tensor.'' By estimating P-alpha beta(s) for ea ch object we can determine p(alpha) from the foreground stars and appl y a correction -P-alpha beta p beta(s) to the galaxies. We test this p rocedure using deep high-resolution images from the Hubble Space Teles cope (HST) which are smeared with an anisotropic PSF and then have noi se added to simulate ground-based observations. We find that the proce dure works very well. A similar analysis yields a linear shear polariz ability tensor P-alpha beta(gamma) which describes the response to a g ravitational shear. This calibrates the polarization-shear relation, b ut only for galaxies which are well resolved. To empirically calibrate the effect of seeing on the smaller galaxies we artificially stretch HST images to simulate lensing and then degrade them as before. These experiments provide a rigorous and exacting test of the method under r ealistic conditions. They show that it is possible to remove the effec t of instrumental PSF anisotropy and that the method provides an effic ient and quantitative measurement of the gravitational shear.