Rethinking data-driven point spread function modeling with a differentiable optical model

Abstract

In astronomy, upcoming space telescopes with wide-field optical instruments have a spatially varying point spread function (PSF). Certain scientific goals require a highfidelity 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 in wavelength in the instrument's passband. PSF modeling represents a challenging ill-posed problem, as it requires building a model from these observations that can infer a super-resolved PSF at any wavelength and any position in the FOV. Current data-driven PSF models can tackle spatial variations and super-resolution. However, they are not capable of capturing PSF chromatic variations.Our model, coined WaveDiff, proposes a paradigm shift in the data-driven modeling of the point spread function 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 change allows the transfer of a great deal of complexity from the instrumental response into the forward model. The proposed model relies on efficient automatic differentiation technology as well as modern stochastic first-order optimization techniques recently developed by the thriving machine-learning community. Our framework paves the way to building powerful models that are physically motivated and do not require special calibration data.This paper demonstrates the WaveDiff model on 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 by a factor of at least 20 and the size error by a factor of more than 250. By only using noisy broad-band in-focus observations, we successfully capture the PSF chromatic variations due to diffraction. WaveDiff source code and examples associated with this paper are available at this link .

Deep learning-based galaxy image deconvolution

“…It was shown by Sureau et al (2020) that Tikhonet can handle such data by deconvolving each galaxy in the field independently and using the PSF corresponding to the center of the galaxy. The PSF field is generally not known, but can be reconstructed from observed stars present in the image (Liaudat et al, 2021;Liaudat et al, 2022). • Many galaxies share very similar morphologies.…”