A New Estimator for Phase Statistics

TL;DR

This paper introduces a new phase statistic for 2D weak lensing convergence fields that provides independent information, improves signal-to-noise ratio, and is adaptable to noise and masks, with applications to lensed CMB maps.

Contribution

A novel phase statistic for 2D weak lensing that offers independent information, better noise performance, and ease of implementation, with extensions to higher-order and importance of post-Born corrections.

Findings

Good agreement with theoretical predictions across redshifts

Achieves better signal-to-noise than line correlation function

Effective in noisy and masked data environments

Abstract

We introduce a novel statistic to probe the statistics of phases of Fourier modes in two-dimensions (2D) for weak lensing convergence field $\kappa$. This statistic contains completely independent information compared to that contained in observed power spectrum. We compare our results against state-of-the-art numerical simulations as a function of source redshift and find good agreement with theoretical predictions. We show that our estimator can achieve better signal-to-noise compared to the commonly employed statistics known as the line correlation function (LCF). Being a two-point statistics, our estimator is also easy to implement in the presence of complicated noise and mask, and can also be generalised to higher-order. While applying this estimator for the study of lensed CMB maps, we show that it is important to include post-Born corrections in the study of statistics of phase.