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 sub-percent accuracy for precise cosmic shear measurements. We present a new differentiable implementation of our perturbation-based 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 utilizing 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 non-linear 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 $3\times 10^{-3}$ (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.

arXiv comment9 pages, 7 figures, Accepted for publication in MNRAS

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• Euclid preparation. LIII. LensMC, weak lensing cosmic shear measurement with forward modelling and Markov Chain Monte Carlo sampling
• DISCO-DJ I: a differentiable Einstein-Boltzmann solver for cosmology
• Chromatic Effects on the PSF and Shear Measurement for the Roman Space Telescope High-Latitude Wide Area Survey
• Simulating image coaddition with the Nancy Grace Roman Space Telescope: III. Software improvements and new linear algebra strategies
• Analytical Noise Bias Correction for Precise Weak Lensing Shear Inference
• Optimizing the Roman Space Telescope High-Latitude Wide Area Survey for mitigating chromatic PSF effects on shear measurement
• D${}_4$CNN$\times$AnaCal: Physics-Informed Machine Learning for Accurate and Precise Weak Lensing Shear Estimation