Analytic PSF Correction for Gravitational Flexion Studies

TL;DR

This paper develops an analytic method to correct for PSF effects in gravitational flexion measurements, accounting for atmospheric and optical distortions, improving the accuracy of lensing studies.

Contribution

It introduces a fully analytic mapping from observed galaxy flexions to true gravitational flexions, considering complex PSF distortions and their impact.

Findings

PSF distortions significantly affect flexion measurements.

PSF size causes greater dilution of flexion signals than shear.

Correcting for PSF patterns can improve flexion measurement accuracy.

Abstract

Given a galaxy image, one cannot simply measure its flexion. An image's spin one and three shape properties, typically associated with F- and G-flexion, are actually complicated functions of the galaxy's intrinsic shape and the telescope's PSF, in addition to the lensing properties. The same is true for shear. In this work we create a completely analytic mapping from apparent measured galaxy flexions to gravitational flexions by (1) creating simple models for a lensed galaxy and for a PSF whose distortions are dominated by atmospheric smearing and optical aberrations, (2) convolving the two models, and (3) comparing the pre- and post-convolved flexion-like shape variations of the final image. For completeness, we do the same for shear. As expected, telescope astigmatism, coma, and trefoil can corrupt measurements of shear, F- flexion, and G-flexion, especially for small galaxies. We additionally find that PSF size dilutes the flexion signal more rapidly than the shear signal. Moreover, mixing between shears, flexions, and asymmetric aberrations can create additive offsets in lensing measurements that vary with both galaxy size and galaxy ellipticity and flexion values. But all is not lost; by measuring the patterns, we can correct for them.