Euclid: Precise inference of defocus wavefront error from image diffraction spike measurements
Abstract
The success of the Euclid cosmological weak lensing measurements requires unprecedented knowledge of the point spread function (PSF) shape. Defocus wavefront errors induce variations in PSF size that directly bias inferred galaxy shapes. We present a rapid, model-independent estimator of the Euclid visible instrument defocus based on measuring subpixel shifts in diffraction spikes from bright stars, arising from the non-mirror-symmetric placement of the telescope spiders. This estimate requires no a-priori PSF model and can be directly inferred from individual survey exposures within seconds. We express defocus as the secondary mirror displacement along the optical axis, $Δz$, achieving a per-exposure precision of $σ(Δz) = 0.022\,μ\text{m}$ in standard Euclid wide-survey images, corresponding to a peak-to-valley optical-path difference of $0.75\,\text{nm}$. This sensitivity resolves thermally induced shifts, typically 0.1-0.3$\,μ\text{m}$, and enables tracking of temporal evolution and field-of-view variations when combining exposures within periods of stability. Since July 2024, the Euclid telescope has been exceptionally stable, while changes to defocus are effectively homogeneous across the field of view. By correlating defocus with PSF size, we find that the Euclid DR3 requirement of a fractional PSF size bias of $\left|ΔR_\mathrm{PSF}^2/R_\mathrm{PSF}^2\right|<10^{-3}$ corresponds to field-averaged secondary mirror displacements exceeding $\langle Δz_\mathrm{thr}\rangle = (0.0683 \pm 0.0024)\,μ\text{m}$. Our estimator provides a robust real-time monitoring tool, supplies a stringent prior for computationally intensive PSF model fitting, and is applicable not only to the Euclid telescope, but to other telescopes whose spider vanes are not mirror-symmetrically arranged.
Authors 98
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Leiden University · Leiden Observatory
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Leiden Observatory, Leiden University, Einsteinweg 55, 2333 CC Leiden, The Netherlands
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Leiden University · Leiden Observatory
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Leiden Observatory, Leiden University, Einsteinweg 55, 2333 CC Leiden, The Netherlands
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University of Oxford · University of the Western Cape
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Department of Physics, Oxford University, Keble Road, Oxford OX1 3RH, UK
Department of Physics and Astronomy, University of the Western Cape, Bellville, Cape Town, 7535, South Africa
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Leiden University · Utrecht University · Leiden Observatory
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Institute for Theoretical Physics, Utrecht University, Princetonplein 5, 3584 CE Utrecht, The Netherlands
Leiden Observatory, Leiden University, Einsteinweg 55, 2333 CC Leiden, The Netherlands
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Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
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European Space Astronomy Centre
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ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
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School of Mathematics and Physics, University of Surrey, Guildford, Surrey, GU2 7XH, UK
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Brera Astronomical Observatory
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INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
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Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics
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INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
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Scuola Internazionale Superiore di Studi Avanzati · Trieste Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Trieste · Institute for Fundamental Physics of the Universe
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IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy
INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy
SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste TS, Italy
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Istituto Nazionale di Fisica Nucleare, Sezione di Bologna · Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics · University of Bologna
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Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
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INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
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Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics
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Centre National d'Études Spatiales
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Trieste Astronomical Observatory · Institute for Fundamental Physics of the Universe
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Brera Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Genova · University of Genoa
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Astronomical Observatory of Capodimonte · University of Naples Federico II
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Istituto Nazionale di Fisica Nucleare, Sezione di Torino · Osservatorio Astrofisico di Torino · University of Turin · National Institute for Astrophysics
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Istituto Nazionale di Fisica Nucleare, Sezione di Bologna · Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics · University of Bologna
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Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics
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