A Differentiable Perturbation-based Weak Lensing Shear Estimator

Abstract

Upcoming imaging surveys will use weak gravitational lensing to study the large-scale structure of the Universe, demanding subpercent accuracy for precise cosmic shear measurements. We present a new differentiable implementation of our perturbationbased shear estimator (FPFS), using JAX, which is publicly available as part of a new suite of analytic shear algorithms called AnaCal. This code can analytically calibrate the shear response of any nonlinear observable constructed with the FPFS shapelets and detection modes utilising auto-differentiation (AD), generalizing the formalism to include a family of shear estimators with corrections for detection and selection biases. Using the AD capability of JAX, it calculates the full Hessian matrix of the nonlinear observables, which improves the previously presented second-order noise bias correction in the shear estimation. As an illustration of the power of the new AnaCal framework, we optimize the effective galaxy number density in the space of the generalized shear estimators using an LSST-like galaxy image simulation for the ten-year LSST. For the generic shear estimator, the magnitude of the multiplicative bias |m| is below 3 × 10−3 (99.7% confidence interval), and the effective galaxy number density is improved by 5% . We also discuss some planned future additions to the AnaCal software suite to extend its applicability beyond the FPFS measurements.