  Current optical imaging surveys for cosmology are covering large areas of
sky. To exploit the statistical power of these surveys for weak lensing
measurements requires shape measurement methods with subpercent systematic
errors. We introduce a new weak lensing shear measurement algorithm, Shear
Nulling after PSF Gaussianisation (SNAPG), designed to avoid the noise biases
that affect most other methods. SNAPG operates on images that have been
convolved with a kernel that renders the Point Spread Function (PSF) a circular
Gaussian, and uses weighted second moments of the sources. The response of such
second moments to a shear of the pre-seeing galaxy image can be predicted
analytically, allowing us to construct a shear nulling scheme that finds the
shear parameters for which the observed galaxies are consistent with an
unsheared, isotropically oriented population of sources. The inverse of this
nulling shear is then an estimate of the gravitational lensing shear. We
identify the uncertainty of the estimated centre of each galaxy as the source
of noise bias, and incorporate an approximate estimate of the centroid
covariance into the scheme. We test the method on extensive suites of simulated
galaxies of increasing complexity, and find that it is capable of shear
measurements with multiplicative bias below 0.5 percent.
