  We implement the Elliptical Gauss-Laguerre (EGL) galaxy-shape measurement
method proposed by Bernstein & Jarvis (2002) and quantify the shear recovery
accuracy in weak lensing analysis. This method uses a deconvolution fitting
scheme to remove the effects of the point-spread function (PSF). The test
simulates >10^7 noisy galaxy images convolved with anisotropic PSFs, and
attempts to recover an input shear. The tests are designed to be immune to
shape noise, selection biases, and crowding. The systematic error in shear
recovery is divided into two classes, calibration (multiplicative) and
additive, with the latter arising from PSF anisotropy. At S/N > 50, the
deconvolution method measures the galaxy shape and input shear to ~ 1%
multiplicative accuracy, and suppresses > 99% of the PSF anisotropy. These
systematic errors increase to ~ 4% for the worst conditions, with poorly
resolved galaxies at S/N ~ 20. The EGL weak lensing analysis has the best
demonstrated accuracy to date, sufficient for the next generation of weak
lensing surveys.
