  With the recent detection of cosmic shear, the most challenging effect of
weak gravitational lensing has been observed. The main difficulties for this
detection were the need for a large amount of high quality data and the control
of systematics during the gravitational shear measurement process, in
particular those coming from the Point Spread Function anisotropy. In this
paper we perform detailed simulations with the state-of-the-art algorithm
developed by Kaiser, Squires and Broadhurst (KSB) to measure gravitational
shear. We show that for realistic PSF profiles the KSB algorithm can recover
any shear amplitude in the range $0.012 < |\gammavec |<0.32$ with a relative,
systematic error of $10-15%$. We give quantitative limits on the PSF correction
method as a function of shear strength, object size, signal-to-noise and PSF
anisotropy amplitude, and we provide an automatic procedure to get a reliable
object catalog for shear measurements out of the raw images.
