On Point Spread Function modelling: towards optimal interpolation

TL;DR

This paper compares various PSF interpolation methods for astronomy, finding Kriging to be the most reliable, which is crucial for improving weak lensing measurements and understanding dark energy.

Contribution

It introduces a simulation-based comparison of interpolation schemes for PSF modeling, highlighting Kriging's superior performance over polynomial methods.

Findings

Kriging outperforms polynomial interpolation in PSF modeling.

Current Kriging methods suffice for present surveys, but future needs require more advanced techniques.

Simulations based on PCA of real images effectively evaluate interpolation schemes.

Abstract

Point Spread Function (PSF) modeling is a central part of any astronomy data analysis relying on measuring the shapes of objects. It is especially crucial for weak gravitational lensing, in order to beat down systematics and allow one to reach the full potential of weak lensing in measuring dark energy. A PSF modeling pipeline is made of two main steps: the first one is to assess its shape on stars, and the second is to interpolate it at any desired position (usually galaxies). We focus on the second part, and compare different interpolation schemes, including polynomial interpolation, radial basis functions, Delaunay triangulation and Kriging. For that purpose, we develop simulations of PSF fields, in which stars are built from a set of basis functions defined from a Principal Components Analysis of a real ground-based image. We find that Kriging gives the most reliable interpolation, significantly better than the traditionally used polynomial interpolation. We also note that although a Kriging interpolation on individual images is enough to control systematics at the level necessary for current weak lensing surveys, more elaborate techniques will have to be developed to reach future ambitious surveys' requirements.