Fonction d'étalement du point

NOTOC La fonction d'étalement du point (point spread function ou PSF en anglais), ou réponse impulsionnelle spatiale, est une fonction mathématique qui décrit la réponse d'un système d'imagerie à une source ponctuelle. Elle est utilisée dans divers domaines pouvant relever de l'optique (astronomie, microscopie, ophtalmologie) ou d'autres techniques d'imagerie (radiographie, échographie, ). Dans le cadre de l'optique, un système optique et ses différents éléments présentent des défauts qui ont pour effet, pour un point objet, un « étalement » du point lumineux image. Pour un système optique sans aberration, seule la diffraction intervient et l'image formée est une tache d'Airy pour une ouverture circulaire. La fonction d'étalement du point est l'équivalent bidimensionnel de la réponse impulsionnelle utilisée en traitement du signal. Cette fonction étant connue, des opérations de déconvolution permettent de renverser le processus pour améliorer la résolution du système d'imagerie.

Radial expansion for spinning conformal blocks

This paper develops a method to compute any bosonic conformal block as a series expansion in the optimal radial coordinate introduced by Hogervorst and Rychkov. The method reduces to the known result when the external operators are all the same scalar operator, but it allows to compute conformal blocks for external operators with spin. Moreover, we explain how to write closed form recursion relations for the coefficients of the expansions. We study three examples of four point functions in detail: one vector and three scalars; two vectors and two scalars; two spin 2 tensors and two scalars. Finally, for the case of two external vectors, we also provide a more efficient way to generate the series expansion using the analytic structure of the blocks as a function of the scaling dimension of the exchanged operator.

Springer2016

Machine-learning methods for weak lensing analysis of the ESA Euclid sky survey

Thibault Adrien Kuntzer

A clear picture has emerged from the last three decades of research: our Universe is expanding at an accelerated rate. The cause of this expansion remains elusive, but in essence acts as a repulsive force. This so-called dark energy represents about 69% of the energy content in the Universe. A further 26% of the energy is contained in dark matter, a form of matter that is invisible electromagnetically. Understanding the nature of these two major components of the Universe is at the top of the list of unsolved problems. To unveil answers, ambitious experiments are devised to survey an ever larger and deeper fraction of the sky. One such project is the European Space Agency (ESA) telescope Euclid, which will probe dark matter and infer desperately needed information about dark energy. Because light bundles follow null geodesics, their trajectories are affected by the mass distribution along the line of sight, which includes dark matter. This is gravitational lensing. In the vast majority of cases, deformations of the source objects are weak, and profiles are slightly sheared. The nature of the dark components can be fathomed by measuring the shear over a large fraction of the sky. The shear can be recovered by a statistical analysis of a large number of objects. In this thesis, we take on the development of the necessary tools to measure the shear. Shear measurement techniques have been developed and improved for more than two decades. Their performance, however, do not meet the unprecedented requirements imposed by future surveys. Requirements trickle down from the targeted determination of the cosmological parameters. We aim at preparing novel and innovative methods. These methods are tested against the Euclid requirements. Contributions can be classified into two major themes. A key step in the processing of weak gravitational lensing data is the correction of image deformations generated by the instrument itself. This point spread function (PSF) correction is the first theme. The second is the shear measurement itself, and in particular, producing accurate measurements. We explore machine-learning methods, and notably artificial neural networks. These methods are, for the most part, data-driven. Schemes must first be trained against a representative sample of data. Crafting optimal training sets and choosing the method parameters can be crucial for the performance. We dedicate an important fraction of this dissertation to describing simulations behind the datasets and motivating our parameter choices. We propose schemes to build a clean selection of stars and model the PSF to the Euclid requirements in the first part of this thesis. Shear measurements are notoriously biased because of their small size and their low intensity. We introduce an approach that produces unbiased estimates of shear. This is achieved by processing data from any shape measurement technique with artificial neural networks, and predicting corrected estimates of the shape of the galaxies, or directly the shear. We demonstrate that simple networks with simple trainings are sufficient to reach the Euclid requirements on shear measurements.

EPFL2018

SALSA: a tool to estimate the stray light contamination for low-Earth orbit observatories

Thibault Adrien Kuntzer

Stray light contamination reduces considerably the precision of photometric of faint stars for low altitude space-borne observatories. When measuring faint objects, the necessity of coping with stray light contamination arises in order to avoid systematic impacts on low signal-to-noise images. Stray light contamination can be represented by a flat offset in CCD data. Mitigation techniques begin by a comprehensive study during the design phase, followed by the use of target pointing optimisation and post-processing methods. We present a code that aims at simulating the stray-light contamination in low-Earth orbit coming from reflexion of solar light by the Earth. StrAy Light SimulAtor (SALSA) is a tool intended to be used at an early stage as a tool to evaluate the effective visible region in the sky and, therefore to optimise the observation sequence. SALSA can compute Earth stray light contamination for significant periods of time allowing mission-wide parameters to be optimised (e.g. impose constraints on the point source transmission function (PST) and/or on the altitude of the satellite). It can also be used to study the behaviour of the stray light at different seasons or latitudes. Given the position of the satellite with respect to the Earth and the Sun, SALSA computes the stray light at the entrance of the telescope following a geometrical technique. After characterising the illuminated region of the Earth, the portion of illuminated Earth that affects the satellite is calculated. Then, the flux of reflected solar photons is evaluated at the entrance of the telescope. Using the PST of the instrument, the final stray light contamination at the detector is calculated. The analysis tools include time series analysis of the contamination, evaluation of the sky coverage and an objects visibility predictor. Effects of the South Atlantic Anomaly and of any shutdown periods of the instrument can be added. Several designs or mission concepts can be easily tested and compared. The code is not thought as a stand-alone mission designer. Its mandatory inputs are a time series describing the trajectory of the satellite and the characteristics of the instrument. This software suite has been applied to the design and analysis of CHEOPS (CHaracterizing ExoPlanet Satellite). This mission requires very high precision photometry to detect very shallow transits of exoplanets. Different altitudes and characteristics of the detector have been studied in order to find the best parameters, that reduce the effect of contamination.

Spie-Int Soc Optical Engineering2014

Machine-learning methods for weak lensing analysis of the ESA Euclid sky survey

Thibault Adrien Kuntzer

EPFL2018

SALSA: a tool to estimate the stray light contamination for low-Earth orbit observatories

Thibault Adrien Kuntzer

Spie-Int Soc Optical Engineering2014