Point Spread Function Modelling for Space Telescopes with a Differentiable Optical Model
Context
Weak gravitational lensing [1] is a powerful probe of the Large Scale Structure of our Universe. Cosmologists use weak lensing to study the nature of dark matter and its spatial distribution. Weak lensing missions require highly accurate shape measurements of galaxy images. The instrumental response of the telescope, called the point spread function (PSF), produces a deformation of the observed images. This deformation can be mistaken for the effects of weak lensing in the galaxy images, thus being one of the primary sources of systematic error when doing weak lensing science. Therefore, estimating a reliable and accurate PSF model is crucial for the success of any weak lensing mission [2]. The PSF field can be interpreted as a convolutional kernel that affects each of our observations of interest, which varies spatially, spectrally, and temporally. The PSF model needs to be able to cope with each of these variations. We use specific stars considered point sources in the field of view to constrain our PSF model. These stars, which are unresolved objects, provide us with degraded samples of the PSF field. The observations go through different degradations depending on the properties of the telescope. These degradations include undersampling, integration over the instrument passband, and additive noise. We finally build the PSF model using these degraded observations and then use the model to infer the PSF at the position of galaxies. This procedure constitutes the ill-posed inverse problem of PSF modelling. See [3] for a recent review on PSF modelling.
The recently launched Euclid survey represents one of the most complex challenges for PSF modelling. Because of the very broad passband of Euclid’s visible imager (VIS) ranging from 550nm to 900nm, PSF models need to capture not only the PSF field spatial variations but also its chromatic variations. Each star observation is integrated with the object’s spectral energy distribution (SED) over the whole VIS passband. As the observations are undersampled, a super-resolution step is also required. A recent model coined WaveDiff [4] was proposed to tackle the PSF modelling problem for Euclid and is based on a differentiable optical model. WaveDiff achieved state-of-the-art performance and is currently being tested with recent observations from the Euclid survey.
The James Webb Space Telescope (JWST) was recently launched and is producing outstanding observations. The COSMOS-Web collaboration [5] is a wide-field JWST treasury program that maps a contiguous 0.6 deg2 field. The COSMOS-Web observations are available and provide a unique opportunity to test and develop a precise PSF model for JWST. In this context, several science cases, on top of weak gravitational lensing studies, can vastly profit from a precise PSF model. For example, strong gravitational lensing [6], where the PSF plays a crucial role in reconstruction, and exoplanet imaging [7], where the PSF speckles can mimic the appearance of exoplanets, therefore subtracting an accurate and precise PSF model is essential to improve the imaging and detection of exoplanets.
PhD project
The candidate will aim to develop more accurate and performant PSF models for space-based telescopes exploiting a differentiable optical framework and focus the effort on Euclid and JWST.
The WaveDiff model is based on the wavefront space and does not consider pixel-based or detector-level effects. These pixel errors cannot be modelled accurately in the wavefront as they naturally arise directly on the detectors and are unrelated to the telescope’s optic aberrations. Therefore, as a first direction, we will extend the PSF modelling approach, considering the detector-level effect by combining a parametric and data-driven (learned) approach. We will exploit the automatic differentiation capabilities of machine learning frameworks (e.g. TensorFlow, Pytorch, JAX) of the WaveDiff PSF model to accomplish the objective.
As a second direction, we will consider the joint estimation of the PSF field and the stellar Spectral Energy Densities (SEDs) by exploiting repeated exposures or dithers. The goal is to improve and calibrate the original SED estimation by exploiting the PSF modelling information. We will rely on our PSF model, and repeated observations of the same object will change the star image (as it is imaged on different focal plane positions) but will share the same SEDs.
Another direction will be to extend WaveDiff for more general astronomical observatories like JWST with smaller fields of view. We will need to constrain the PSF model with observations from several bands to build a unique PSF model constrained by more information. The objective is to develop the next PSF model for JWST that is available for widespread use, which we will validate with the available real data from the COSMOS-Web JWST program.
The following direction will be to extend the performance of WaveDiff by including a continuous field in the form of an implicit neural representations [8], or neural fields (NeRF) [9], to address the spatial variations of the PSF in the wavefront space with a more powerful and flexible model.
Finally, throughout the PhD, the candidate will collaborate on Euclid’s data-driven PSF modelling effort, which consists of applying WaveDiff to real Euclid data, and the COSMOS-Web collaboration to exploit JWST observations.
References
[1] R. Mandelbaum. “Weak Lensing for Precision Cosmology”. In: Annual Review of Astronomy and Astro- physics 56 (2018), pp. 393–433. doi: 10.1146/annurev-astro-081817-051928. arXiv: 1710.03235.
[2] T. I. Liaudat et al. “Multi-CCD modelling of the point spread function”. In: A&A 646 (2021), A27. doi:10.1051/0004-6361/202039584.
[3] T. I. Liaudat, J.-L. Starck, and M. Kilbinger. “Point spread function modelling for astronomical telescopes: a review focused on weak gravitational lensing studies”. In: Frontiers in Astronomy and Space Sciences 10 (2023). doi: 10.3389/fspas.2023.1158213.
[4] T. I. Liaudat, J.-L. Starck, M. Kilbinger, and P.-A. Frugier. “Rethinking data-driven point spread function modeling with a differentiable optical model”. In: Inverse Problems 39.3 (Feb. 2023), p. 035008. doi:10.1088/1361-6420/acb664.
[5] C. M. Casey et al. “COSMOS-Web: An Overview of the JWST Cosmic Origins Survey”. In: The Astrophysical Journal 954.1 (Aug. 2023), p. 31. doi: 10.3847/1538-4357/acc2bc.
[6] A. Acebron et al. “The Next Step in Galaxy Cluster Strong Lensing: Modeling the Surface Brightness of Multiply Imaged Sources”. In: ApJ 976.1, 110 (Nov. 2024), p. 110. doi: 10.3847/1538-4357/ad8343. arXiv: 2410.01883 [astro-ph.GA].
[7] B. Y. Feng et al. “Exoplanet Imaging via Differentiable Rendering”. In: IEEE Transactions on Computational Imaging 11 (2025), pp. 36–51. doi: 10.1109/TCI.2025.3525971.
[8] Y. Xie et al. “Neural Fields in Visual Computing and Beyond”. In: arXiv e-prints, arXiv:2111.11426 (Nov.2021), arXiv:2111.11426. doi: 10.48550/arXiv.2111.11426. arXiv: 2111.11426 [cs.CV].
[9] B. Mildenhall et al. “NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis”. In: arXiv e-prints, arXiv:2003.08934 (Mar. 2020), arXiv:2003.08934. doi: 10.48550/arXiv.2003.08934. arXiv:2003.08934 [cs.CV].
Analysis and experimental study of capillary structures to mitigate the influence of magnetogravitational forces on liquid helium cooling for future HTS superconducting magnets
As physics requires increasingly higher magnetic fields, CEA is called upon to develop and produce superconducting magnets capable of generating magnetic field of more than 30 T. The windings of these electromagnets are made from superconducting materials whose electrical resistance is extremely low at cryogenic temperatures (a few Kelvins). This enables them to carry high currents (>10 kA) while dissipating a minimum of heat by Joule effect. Cooling at these low temperatures is achieved using liquid helium. But helium is diamagnetic. Magnetic fields will therefore induce volumetric forces that add to or oppose gravity within the helium. These magneto-gravity forces disrupt the convective phenomena required to cool the superconducting magnet. This can lead to a rise in their temperature and a loss of their superconducting state, which is essential for their proper operation. In order to circumvent this phenomenon, a new cooling system never used in cryomagnetism will be studied. This cooling system will be developed using heat pipes whose operation is based on capillary forces that are theoretically independent of the magneto-gravity forces induced by strong magnetic fields. These capillary structures can take several forms (microchannels, foam, mesh, etc.). In the framework of the thesis these different structures will be studied theoretically and then experimentally, both with and without magnetic forces, in order to determine the most suitable structures for the future superconducting magnets.
Mesure de la réponse intra-pixel de détecteur infrarouge à base de HgCdTe avec des rayons X pour l’astrophysique
In the field of infrared astrophysics, the most commonly used photon sensors are detector arrays based on the HgCdTe absorbing material. The manufacturing of such detectors is a globally recognized expertise of CEA/Leti in Grenoble. As for the Astrophysics Department (DAp) of CEA/IRFU, it holds renowned expertise in the characterization of this type of detector. A key characteristic is the pixel spatial response (PSR), which describes the response of an individual pixel in the array to the point-like generation of carriers within the absorbing material at various locations inside the pixel. Today, this detector characteristic has become a critical parameter for instrument performance. It is particularly crucial in applications such as measuring galaxy distortion or conducting high-precision astrometry. Various methods exist to measure this quantity, including the projection of point light sources and interferometric techniques. These methods, however, are complex to implement, especially at the cryogenic operating temperatures of the detectors.
At the DAp, we propose a new method based on the use of X-ray photons to measure the PSR of infrared detectors. By interacting with the HgCdTe material, the X-ray photon generates carriers locally. These carriers then diffuse before being collected. The goal is to derive the PSR by analyzing the resulting images. We suggest a two-pronged approach that integrates both experimental methods and simulations. Data analysis methods will also be developed. Thus, the ultimate objective of this thesis is to develop a new, robust, elegant, and fast method for measuring the intra-pixel response of infrared detectors for space instrumentation. The student will be based at the DAp. This work also involves collaboration with CEA/Leti, combining the instrumental expertise of the DAp with the technological knowledge of CEA/Leti.
First observations of the TeV gamma-ray sky with the NectarCAM camera for the CTA observatory
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ARTIFICIAL INTELLIGENCE TO SIMULATE BIG DATA AND SEARCH FOR THE HIGGS BOSON DECAY TO A PAIR OF MUONS WITH THE ATLAS EXPERIMENT AT THE LARGE HADRON COLLIDER
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SEARCH FOR DIFFUSE EMISSIONS AND SEARCHES IN VERY-HIGH-ENERGY GAMMA RAYS AND FUNDAMENTAL PHYSICS WITH H.E.S.S. AND CTAO
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STUDY OF THE MULTI-SCALE VARIABILITY OF THE VERY HIGH ENERGY GAMMA-RAY SKY
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H.E.S.S. allows measuring the direction, the energy and the arrival time of each detected photon. The time measurement makes it possible to highlight sources which present significant temporal or periodic flux variations. The study of these variable
Direction de la Recherche Fondamentale
Institut de recherche
sur les lois fondamentales de l’univers
emissions (transient or periodic), either towards the Galactic Center or active nuclei of galaxies (AGN) at cosmological distance allows for a better understanding of the emission processes at work in these sources. It also helps characterizing the medium in which the photons propagate and testing the validity of some fundamental physical laws such as Lorentz invariance. It is possible to probe a wide range of time scales variations in the flux of astrophysical sources. These time scales range from a few seconds (gamma ray bursts, primordial black holes) to a few years (binary systems of high mass, active galaxy nuclei).
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