Shear nulling after PSF Gaussianisation: Moment-based weak lensing measurements with subpercent noise bias

Context. Current optical imaging surveys for cosmology cover large areas of sky. Exploiting the statistical power of these surveys for weak lensing measurements requires shape measurement methods with subpercent systematic errors. Aims. 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. 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. Results. 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