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Approche inverse pour la reconstruction des environnements circumstellaires en polarimétrie avec l’instrument d’imagerie directe ESO/VLT SPHERE IRDIS.

Abstract : Survey of circumstellar environments allows a better understanding of exoplanets formation. Despite instrumentation enhancement, allowing for a bigger resolution of these environments, their observation remains difficult due to high contrast between the environments and their host stars. In fact the host stars are 1000 to 10 000 times brighter than the environment, even 10 000 000 times brighter for exoplanets. When images of these circumstellars environments are acquired in direct imaging, the signal of the environments is mixed to star light residuals. Yet, the light of the environment is partially linearly polarized while the light of the star is unpolarized. The instrument Infrared Dual-band Imaging and Spectroscopy (IRDIS) of the European Southern Observatory’s (ESO) Spectro-Polarimeter High-contrast Expolanet REsearch (SPHERE) instrument, installed at one of the four Very Large Telescopes (VLT) in Atacama in Chile, acquires datasets where the polarization is modulated according to a known angle cycle. Then, combining these multivariate data, it is possible to extract the light scattered by the environment from the light of the stars. When data are combined with the state-of-the-art methods, neither the photon noise statistics of the data, witch dominate the signal of interest, nor the read out noise of the detector, nor the missing data. Moreover, if any image in an angle rotation cycle is missing, the rest of the cycle is note used. Finally, any centering, rotation, or deconvolution by the Point Spread Function are made independently of the data reduction. The bad pixels and dead pixels are interpolated before the processing. The issue of such a processing is that the propagation of the errors in the data is not handled. The « inverse problem » methods aim to estimate the light of the environment using a direct model of the data, while controlling the error propagation in the reconstruction. This approach is already used in several field in astronomy, but they have not been developed yet for high contrast direct imaging in polarimetry. The aim of my PhD thesis is to reconstruct, under a given quality criterion, a map of the polarized light of the circumstellar environments, a map of the corresponding polarization angles and a map of the residual star light and of the unpolarized light of the environment. To achieve this goal, in this thesis I develop a non-linear physical model of the data, pixelwise independent, based on Jones formalism and parameterized in the unpolarized intensity, the linearly polarized intensity and the linear polarization angle. Then, I derive an alternative formulation, parameterized in the Stokes parameters, providing the link between such a physical model and the state-of-the-art methods. Throughout this thesis, I extend this model to a pixelwise dependent formulation, without and with the convolution by the Point Spread Function (PSF). In the case without the convolution, I derive a new non-linear model, parameterized in the unpolarized intensity, and the Stokes parameters of the horizontal and vertical polarized intensities. For each of this model, I develop several methods to estimate the parameters, based on the minimization of a constrained criterion and, in the pixelwise dependent case, with regularizations. Among these regularizations, I compare differentiable and non-differentiable penalizations applied on horizontal and vertical image gradients coefficients and on the singular values of the pixels Hessian matrices. In the linear case, I impose an epigraphical constraint between the Stokes parameters. It corresponds in the linear case to a non-negative constraint on the polarized and unpolarized intensities. To auto-calibrate the regularization weights, I use the Stein Unbiased Risk Estimator (SURE). The whole methods are applied on simulated dataset, created to reproduce typical astrophysical datasets encountered in circumstellar environment polarimetrical direct imaging. Depending of the properties of the functions considered in the objective function, the research of its minimum is done with different algorithms. In the pixelwise independent case, I proceed with a direct inversion. In the non-linear case, the parameters of interest are estimated hierarchically. In the smooth pixelwise dependent case, I use a preconditionned gradient descent with with the limited memory preconditionnement of Broyden-Fletcher-Goldfarb-Shanno (BFGS). This algorithm is suitable to estimate the parameters under a non-negative constraint. In the linear case with an epigraphical constraint and a smooth regularization, I use the Forward-Backward with backtracking. The backtracking avoids us the calculus of the gradient Lipschitz constant which can be difficult. In the case of non-smooth regularization, I use the preconditionned primal-dual Condat-V\~u algorithm with a backtracking step. Then, I show that in the pixelwise independent case, taking into account the missing data allows us for the use of incomplete data cycle, reducing the maps estimation error. I also point out that in the pixelwise dependent case, taking the detector transformations (rotations, translations) and the dead pixels into account in the model reduce the error on the polarized and non-polarized intensities in the non-linear case of an independent regularization on both quantities. The error on the angle benefit from a linear model with a regularization on the Stokes parameters. I also show that in the cas of low disk polarization the auto-calibration of the regularization weights with SURE tend to over-regularize the estimation, giving a higher bound for a better manual choice. In the case of the deconvolution, I show that a smooth regularization with smoothing prior and edge preserving as the Total Variation hyperbolic approximation (TV-h) gives better result, in a given time, than than the non-smooth penalization of the Total Variation (TV) and the Shatten norm of the Hessian. I also show that the reconstructions estimated from the global model including the convolution have a smaller estimation error than reconstructions with a posterior deconvolution. Finally, I show on several astrophysical datasets the benefits of the best methods that I develop in this thesis, for the polarized intensity and the angle of polarization. I conclude that taking in account a global model including the convolution for the reconstruction of circumstellar environment, with several level of regularization, allows for a thinner resolution of bright polarized structures and a best detection of low polarized intensity structures.
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Submitted on : Friday, April 16, 2021 - 1:35:19 PM
Last modification on : Wednesday, November 3, 2021 - 6:52:29 AM
Long-term archiving on: : Saturday, July 17, 2021 - 6:41:56 PM

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Laurence Denneulin. Approche inverse pour la reconstruction des environnements circumstellaires en polarimétrie avec l’instrument d’imagerie directe ESO/VLT SPHERE IRDIS.. Instrumentation et méthodes pour l'astrophysique [astro-ph.IM]. Université Claude Bernard Lyon 1 (UCBL), 2020. Français. ⟨tel-03200282⟩

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