Marc Bernot

Wasserstein barycenter and its application to texture mixing

This paper proposes a new definition of the averaging of discrete probability distributions as a barycenter over the Monge-Kantorovich optimal transport space. To overcome the time complexity involved by the numerical solving of such problem, the original Wasserstein metric is replaced by a sliced approximation over 1D distributions. This enables us to introduce a new fast gradient descent algorithm to compute Wasserstein barycenters of point clouds. This new notion of barycenter of probabilities is likely to find applications in computer vision where one wants to average features defined as distributions. We show an application to texture synthesis and mixing, where a texture is characterized by the distribution of the response to a multi-scale oriented filter bank. This leads to a simple way to navigate over a convex domain of color textures.

Comparative theoretical and experimental study of a Shack-Hartmann and a Phase Diversity SENSOR, for high-precision wavefront sensing dedicated to Space Active Optics

Earth-imaging or Universe Science satellites are always in need of higher spatial resolutions, in order to discern finer and finer details in images. This means that every new generation of satellites must have a larger main mirror than the previous one, because of the diffraction. Since it allows the use of larger mirrors, active optics is presently studied for the next generation of satellites. To measure the aberrations of such an active telescope, the Shack-Hartmann (SH), and the phase-diversity (PD) are the two wavefront sensors (WFS) considered preferentially because they are able to work with an extended source like the Earths surface, as well as point sources like stars. The RASCASSE project was commissioned by the French spatial agency (CNES) to study the SH and PD sensors for high-performance wavefront sensing. It involved ONERA and Thales Alenia Space (TAS), and LAM. Papers by TAS and LAM on the same project are available in this conference, too [1,2]. The purpose of our work at ONERA was to explore what the best performance both wavefront sensors can achieve in a space optics context. So we first performed a theoretical study in order to identify the main sources of errors and quantify them — then we validated those results experimentally. The outline of this paper follows this approach: we first discuss phase diversity theoretical results, then Shack-Hartmann’s, then experimental results — to finally conclude on each sensor’s performance, and compare their weak and strong points.

Wave-front sensing for space active optics: Rascasse project

The payloads for Earth Observation and Universe Science are currently based on very stiff opto-mechanical structures with very tight tolerances. The introduction of active optics in such an instrument would relax the constraints on the thermo-mechanical architecture and on the mirrors polishing. A reduction of the global mass/cost of the telescope is therefore expected. Active optics is based on two key-components: the wave-front sensor and the wave-front corrector.

The LAM space active optics facility

The next generation of large lightweight space telescopes will require the use of active optics systems to enhance the performance and increase the spatial resolution. Since almost 10 years now, LAM, CNES, THALES and ONERA conjugate their experience and efforts for the development of space active optics through the validation of key technological building blocks: correcting devices, metrology components and control strategies. This article presents the work done so far on active correcting mirrors and wave front sensing, as well as all the facilities implemented. The last part of this paper focuses on the merging of the MADRAS and RASCASSE test-set up. This unique combination will provide to the active optics community an automated, flexible and versatile facility able to feed and characterise space active optics components.