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Thales Alenia Space is designing and developing space observation instruments since more than 40 years. This paper explains why active optics is needed for next generation of instruments for Earth observation. It describes what kind of solution is preferred and gives an overview of the development status on the associated technologies. Indeed, the future missions will have to deal with better performance, better optical quality while from manufacturing point of view, the total mass, the development schedule and the final cost have to be reduced. These constraints induce a new generation of solutions based on large entrance optics associated to high lightweight ratio which naturally provide solutions sensitive to gravity deformation. In these conditions, the enhancement of the final performance can only be guaranteed by using active optics in flight. A deformable mirror is therefore foreseen to be implemented in future large telescopes in order to correct manufacturing residues and ground/flight evolution, including gravity. Moreover, low mass and low cost require more compact designs which entail solutions more sensitive to misalignment. An active positioning mechanism is then also needed in order to correct the telescope alignment during operation conditions. Thales Alenia Space has been selected by CNES to develop and qualify active optics building blocks and then to test and demonstrate the improvement that new active technologies can bring in a full size instrument representative of the next generation of observation instruments. An overview of the current development status and the achieved performances is given for each building block (Primary Mirror, deformable mirror, 6-dof mechanism, wavefront sensor).

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 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.

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 Earth's 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.

The irrigation problem is the problem of finding an efficient way to transport a mea- sure µ + onto a measure µ � . By efficient, we mean that a structure that achieves the transport (which, following (Bernot, Caselles and Morel, Publ. Mat. 49 (2005) 417-451), we call traffic plan) is better if it carries the mass in a grouped way rather than in a separate way. This is formalized by considering costs functionals that favorize this property. The aim of this paper is to introduce a dynamical cost functional on traffic plans that we argue to be more realistic. The existence of minimizers is proved in two ways: in some cases, we can deduce it from a classical semicontinuity argument; the other cases are treated by studying the link between our cost and the one introduced in (Bernot, Caselles and Morel, Publ. Mat. 49 (2005) 417-451). Finally, we discuss the stability of minimizers with respect to specific variations of the cost functional.

The transportation problem can be formalized as the problem of finding the optimal paths to transport a measure μ + onto a measure μ − with the same mass. In contrast with the Monge–Kantorovich formalization, recent approaches model the branched structure of such supply networks by an energy functional whose essential feature is to favor wide roads. Given a flow s in a road or a tube or a wire, the transportation cost per unit length is supposed to be proportional to s α with 0 1-\frac 1N$$ such structures can irrigate a whole bounded open set of $${\mathbb{R}}^N$$ . The aim of this paper is to give a mathematical proof of several structure and regularity properties empirically observed in transportation networks. It is first proven that optimal transportation networks have a tree structure and can be monotonically approximated by finite graphs. An interior regularity result is then proven according to which an optimal network is a finite graph away from the irrigated measure. It is also proven that the branching number of optimal networks has everywhere a universal explicit bound. These results answer questions raised in two recent papers by Xia.

International audience; The model of a robot may not be able to consider all the physical phenomena influencing the manipulator performances since they are too numerous and/or difficult to measure: this is model discrepancy. For a highly-accurate active space telescope, an important source of inaccuracy was measured using photogrammetry: the deformation of its mobile platform. This deformation cannot be directly measured in space and needs to be properly modeled in order to enable the telescope calibration with the available measurements. Two incremental models are proposed and the parameter observability is discussed. After experimental calibration, a micrometer accuracy can be reached. The influence of model discrepancy on the experimental parameter identification is finally discussed.

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.

International audience; In this paper we study generalized solutions (in the Brenier's sense) for the Euler equations. We prove that uniqueness holds in dimension one whenever the pressure field is smooth, while we show that in dimension two uniqueness is far from being true. In the case of the two-dimensional disc we study solutions to Euler equations where particles located at a point $x$ go to $-x$ in a time $\pi$, and we give a quite general description of the (large) set of such solutions. As a byproduct, we can construct a new class of classical solutions to Euler equations in the disc.