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). 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 these observations that can infer a super-resolved PSF at any wavelength and 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. 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 a great deal of complexity from the instrumental response into the forward model. The proposed model relies on efficient automatic differentiation technology and modern stochastic first-order optimization techniques recently developed by the thriving machine-learning community. 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.

Reviews in astronomy and space sciences

“…• GalSim (Rowe et al, 2015): github.com/GalSim-developers/ GalSim • WebbPSF (Perrin et al, 2014): github.com/spacetelescope/ webbpsf • PhoSim (Peterson et al, 2015): bitbucket.org/phosim/phosim_ release/wiki/Home • WaveDiff (Liaudat et al, 2023): github.com/CosmoStat/wf-psf • ShapePipe (Farrens, S. et al, 2022): github.com/CosmoStat/ shapepipe • PIFF (Jarvis et al, 2020): github.com/rmjarvis/Piff • MCCD (Liaudat et al, 2021a): github.com/CosmoStat/mccd • RCA (Ngolè et al, 2016;Schmitz et al, 2020): github.com/ CosmoStat/rca • PSFEX (Bertin, 2011): github.com/astromatic/psfex • Tiny Tim (Krist et al, 2011): github.com/spacetelescope/ tinytim • Photutils (Bradley et al, 2022): github.com/astropy/photutils • ∂Lux (Desdoigts et al, 2023): github.com/LouisDesdoigts/ dLux • psf-weather-station: github.com/LSSTDESC/psf-weatherstation.…”

Differentiable optics with ∂Lux: I—deep calibration of flat field and phase retrieval with automatic differentiation

“…There are several other frameworks for automatically differentiable optics simulation: the most similar is WaveBlocks, 53 a PyTorch package for object-oriented modeling of fluorescence microscopy. The DeepOptics package has 54 been developed in TensorFlow for camera design and computational imaging, and WaveDiff in TensorFlow has been used for detector calibration 55 and PSF modeling 56 . We believe that ∂Lux fills a unique niche in this ecosystem as the most general modeling framework for physical optics.…”

HybPSF: Hybrid Point-spread Function Reconstruction for the Observed JWST NIRCam Image

“…However, there may be discrepancies between the model and data due to differences in instrument configurations between simulations and practical telescope status (Hoffmann & Anderson 2018). To obtain more accurate PSF models, some improved methods have been developed (Rhodes et al 2007;van der Wel et al 2012;Brooks et al 2019;Liaudat et al 2021Liaudat et al , 2023. For example, WaveDiff (Liaudat et al 2023) reconstructs the best-fit wave front based on a differentiable optical forward model according to the data to obtain better PSF models.…”

“…To obtain more accurate PSF models, some improved methods have been developed (Rhodes et al 2007;van der Wel et al 2012;Brooks et al 2019;Liaudat et al 2021Liaudat et al , 2023. For example, WaveDiff (Liaudat et al 2023) reconstructs the best-fit wave front based on a differentiable optical forward model according to the data to obtain better PSF models. WebbPSF calculates the PSF by using the results of in-flight wave-front sensing measurements (Optical Path Difference, OPD, files), which are produced by the JWST wave-front sensing subsystem roughly every 2 days in flight (Brooks et al 2019).…”