  In this paper we present results from the weak lensing shape measurement
GRavitational lEnsing Accuracy Testing 2010 (GREAT10) Galaxy Challenge. This
marks an order of magnitude step change in the level of scrutiny employed in
weak lensing shape measurement analysis. We provide descriptions of each method
tested and include 10 evaluation metrics over 24 simulation branches. GREAT10
was the first shape measurement challenge to include variable fields; both the
shear field and the Point Spread Function (PSF) vary across the images in a
realistic manner. The variable fields enable a variety of metrics that are
inaccessible to constant shear simulations including a direct measure of the
impact of shape measurement inaccuracies, and the impact of PSF size and
ellipticity, on the shear power spectrum. To assess the impact of shape
measurement bias for cosmic shear we present a general pseudo-Cl formalism,
that propagates spatially varying systematics in cosmic shear through to power
spectrum estimates. We also show how one-point estimators of bias can be
extracted from variable shear simulations. The GREAT10 Galaxy Challenge
received 95 submissions and saw a factor of 3 improvement in the accuracy
achieved by shape measurement methods. The best methods achieve sub-percent
average biases. We find a strong dependence in accuracy as a function of
signal-to-noise, and indications of a weak dependence on galaxy type and size.
Some requirements for the most ambitious cosmic shear experiments are met above
a signal-to-noise ratio of 20. These results have the caveat that the simulated
PSF was a ground-based PSF. Our results are a snapshot of the accuracy of
current shape measurement methods and are a benchmark upon which improvement
can continue. This provides a foundation for a better understanding of the
strengths and limitations of shape measurement methods.
