Weak weak lensing:correcting weak shear measurements accurately for PSF anisotropy

We have developed a new technique for weak lensing analysis, specifically designed to correct accurately for the effect of the point spread function (PSF) on the shapes of small galaxy images. This method does not rely on weighted second moments of detected images, which we show can leave residuals at the level of a percent in the shear; rather, we directly fit observed galaxy images as PSF-convolved, sheared circular sources. We show by means of simulations that this technique is able to recover shears with systematic errors well below the percent level for representative PSF shapes, while its noise properties are similar to existing methods.