Martin Kilbinger

Tobias Liaudat, Jean-Luc Starck, Martin Kilbinger et al.

In astronomy, upcoming space telescopes with wide-field optical instruments have a spatially varying point spread function (PSF). Specific scientific goals require a high-fidelity estimation of the PSF at target positions where no direct measurement of the PSF is provided. Even though observations of the PSF are available at some positions of the field of view (FOV), they are undersampled, noisy, and integrated into wavelength in the instrument's passband. PSF modeling represents a challenging ill-posed problem, as it requires building a model from degraded observations that can infer a super-resolved PSF at any wavelength and position in the FOV. Our model, coined WaveDiff, proposes a paradigm shift in the data-driven modeling of the point spread function field of telescopes. We change the data-driven modeling space from the pixels to the wavefront by adding a differentiable optical forward model into the modeling framework. This change allows the transfer of complexity from the instrumental response into the forward model. The proposed model relies on stochastic gradient descent to estimate its parameters. Our framework paves the way to building powerful, physically motivated models that do not require special calibration data. This paper demonstrates the WaveDiff model in a simplified setting of a space telescope. The proposed framework represents a performance breakthrough with respect to the existing state-of-the-art data-driven approach. The pixel reconstruction errors decrease 6-fold at observation resolution and 44-fold for a 3x super-resolution. The ellipticity errors are reduced at least 20 times, and the size error is reduced more than 250 times. By only using noisy broad-band in-focus observations, we successfully capture the PSF chromatic variations due to diffraction. Code available at https://github.com/tobias-liaudat/wf-psf.

Tobias Liaudat, Jean-Luc Starck, Martin Kilbinger

The accurate modelling of the Point Spread Function (PSF) is of paramount importance in astronomical observations, as it allows for the correction of distortions and blurring caused by the telescope and atmosphere. PSF modelling is crucial for accurately measuring celestial objects' properties. The last decades brought us a steady increase in the power and complexity of astronomical telescopes and instruments. Upcoming galaxy surveys like Euclid and LSST will observe an unprecedented amount and quality of data. Modelling the PSF for these new facilities and surveys requires novel modelling techniques that can cope with the ever-tightening error requirements. The purpose of this review is three-fold. First, we introduce the optical background required for a more physically-motivated PSF modelling and propose an observational model that can be reused for future developments. Second, we provide an overview of the different physical contributors of the PSF, including the optic- and detector-level contributors and the atmosphere. We expect that the overview will help better understand the modelled effects. Third, we discuss the different methods for PSF modelling from the parametric and non-parametric families for ground- and space-based telescopes, with their advantages and limitations. Validation methods for PSF models are then addressed, with several metrics related to weak lensing studies discussed in detail. Finally, we explore current challenges and future directions in PSF modelling for astronomical telescopes.

Tobias Liaudat, Jean-Luc Starck, Martin Kilbinger et al.

We propose a paradigm shift in the data-driven modeling of the instrumental response field of telescopes. By adding a differentiable optical forward model into the modeling framework, we change the data-driven modeling space from the pixels to the wavefront. This allows to transfer a great deal of complexity from the instrumental response into the forward model while being able to adapt to the observations, remaining data-driven. Our framework allows a way forward to building powerful models that are physically motivated, interpretable, and that do not require special calibration data. We show that for a simplified setting of a space telescope, this framework represents a real performance breakthrough compared to existing data-driven approaches with reconstruction errors decreasing 5 fold at observation resolution and more than 10 fold for a 3x super-resolution. We successfully model chromatic variations of the instrument's response only using noisy broad-band in-focus observations.