Euclid: Nonparametric point spread function field recovery through interpolation on a graph Laplacian^⋆

¹ AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, 91191 Gif-sur-Yvette, France
e-mail: morgan.schmitz@astro.princeton.edu
² Institut LIST, CEA, Université Paris-Saclay, 91191 Gif-Sur-Yvette Cedex, France
³ INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
⁴ Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal
⁵ Leiden Observatory, Leiden University, Niels Bohrweg 2, 2333, CA Leiden, The Netherlands
⁶ INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy
⁷ Centre National d’Etudes Spatiales, Toulouse, France
⁸ ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
⁹ Aix-Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
¹⁰ INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34131 Trieste, Italy
¹¹ INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy
¹² von Hoerner & Sulger GmbH, SchloßPlatz 8, 68723 Schwetzingen, Germany
¹³ Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK
¹⁴ Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany
¹⁵ Institut de Physique Nucléaire de Lyon, 4, rue Enrico Fermi, 69622 Villeurbanne cedex, France
¹⁶ Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 quai Ernest-Ansermet, 1211 Genève 4, Switzerland
¹⁷ Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029 Blindern, 0315 Oslo, Norway
¹⁸ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain
¹⁹ Institut d’Estudis Espacials de Catalunya (IEEC), 08034 Barcelona, Spain
²⁰ Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
²¹ Centre for Extragalactic Astronomy, Department of Physics, Durham University, South Road, Durham DH1 3LE, UK
²² Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
²³ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
²⁴ Dipartimento di Fisica e Astronomia, Universitá di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
²⁵ Institute of Space Sciences (IEEC-CSIC), c/Can Magrans s/n, 08193 Cerdanyola del Vallés Barcelona, Spain
²⁶ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
²⁷ Depto. de Electrónica y Tecnología de Computadoras Universidad Politécnica de Cartagena, 30202 Cartagena, Spain

Received: 13 June 2019
Accepted: 27 February 2020

Abstract

Context. Future weak lensing surveys, such as the Euclid mission, will attempt to measure the shapes of billions of galaxies in order to derive cosmological information. These surveys will attain very low levels of statistical error, and systematic errors must be extremely well controlled. In particular, the point spread function (PSF) must be estimated using stars in the field, and recovered with high accuracy.

Aims. The aims of this paper are twofold. Firstly, we took steps toward a nonparametric method to address the issue of recovering the PSF field, namely that of finding the correct PSF at the position of any galaxy in the field, applicable to Euclid. Our approach relies solely on the data, as opposed to parametric methods that make use of our knowledge of the instrument. Secondly, we studied the impact of imperfect PSF models on the shape measurement of galaxies themselves, and whether common assumptions about this impact hold true in an Euclid scenario.

Methods. We extended the recently proposed resolved components analysis approach, which performs super-resolution on a field of under-sampled observations of a spatially varying, image-valued function. We added a spatial interpolation component to the method, making it a true 2-dimensional PSF model. We compared our approach to PSFEx, then quantified the impact of PSF recovery errors on galaxy shape measurements through image simulations.

Results. Our approach yields an improvement over PSFEx in terms of the PSF model and on observed galaxy shape errors, though it is at present far from reaching the required Euclid accuracy. We also find that the usual formalism used for the propagation of PSF model errors to weak lensing quantities no longer holds in the case of an Euclid-like PSF. In particular, different shape measurement approaches can react differently to the same PSF modeling errors.