The LSST M1/M3 combines an 8.4 m primary mirror and a 5.1 m tertiary mirror on one glass substrate. The combined mirror was completed at the Richard F. Caris Mirror Lab at the University of Arizona in October 2014. Interferometric measurements show that both mirrors have surface accuracy better than 20 nm rms over their clear apertures, in near-simultaneous tests, and that both mirrors meet their stringent structure function specifications. Acceptance tests showed that the radii of curvature, conic constants, and alignment of the 2 optical axes are within the specified tolerances. The mirror figures are obtained by combining the lab measurements with a model of the telescope's active optics system that uses the 156 support actuators to bend the glass substrate. This correction affects both mirror surfaces simultaneously. We showed that both mirrors have excellent figures and meet their specifications with a single bending of the substrate and correction forces that are well within the allowed magnitude. The interferometers do not resolve some small surface features with high slope errors. We used a new instrument based on deflectometry to measure many of these features with sub-millimeter spatial resolution, and nanometer accuracy for small features, over 12.5 cm apertures. Mirror Lab and LSST staff created synthetic models of both mirrors by combining the interferometric maps and the small high-resolution maps, and used these to show the impact of the small features on images is acceptably small.

The Richard F. Caris Mirror Lab at the University of Arizona is responsible for production of the eight 8.4 m segments for the primary mirror of the Giant Magellan Telescope, including one spare off-axis segment. We report on the successful casting of Segment 4, the center segment. Prior to generating the optical surface of Segment 2, we carried out a major upgrade of our 8.4 m Large Optical Generator. The upgrade includes new hardware and software to improve accuracy, safety, reliability and ease of use. We are currently carrying out an upgrade of our 8.4 m polishing machine that includes improved orbital polishing capabilities. We added and modified several components of the optical tests during the manufacture of Segment 1, and we have continued to improve the systems in preparation for Segments 2-8. We completed two projects that were prior commitments before GMT Segment 2: casting and polishing the combined primary and tertiary mirrors for the LSST, and casting and generating a 6.5 m mirror for the Tokyo Atacama Observatory.

Les surfaces complexes ont des applications dans divers domaines tels que ceux de la photonique, de l'énergie, du biomédical, du transport... Par contre, elles posent de véritables défis quant à leur spécification, fabrication et mesure ainsi que lors de l'évaluation de leur défaut de forme. Les processus de fabrication et de mesure de surfaces complexes sont fortement tributaires des dimensions, des tolérances et des formes spécifiées. Afin de rendre exploitable les informations données par le système de mesure, une étape importante de traitement s'impose. Il s'agit ici de la reconstruction de surfaces afin de reconstituer la géométrie et la topologie de la surface sous-jacente et d'en extraire les informations nécessaires pour des besoins de métrologie dimensionnelle (caractéristiques dimensionnelles et évaluation des défauts de forme). Dans la catégorie des surfaces asphériques pour lesquelles un modèle mathématique est associé, le processus de traitement de données géométriques, non nécessairement organisées, se fait par l'association du modèle aux données. Les résidus d'association recherchés en optique sont typiquement de l'ordre du nanomètre. Dans ce cadre, nous proposons l'utilisation de l'algorithme L-BFGS qui n'a encore jamais été utilisé en métrologie. Ce dernier permet de résoudre des problèmes d'optimisation non-linéaires, sans contraintes et d'une manière robuste, automatique et rapide. La méthode L-BFGS reste efficace pour des données contenant plusieurs millions de points. Dans la catégorie des surfaces gauches et notamment des aubes de turbines, la fabrication, la mesure et le traitement sont à une toute autre échelle, sub-micrométrique. Les surfaces gauches ne sont généralement pas définies par un modèle mathématique mais sont représentées par des modèles paramétriques de type B-Spline et/ou NURBS. Dans ce cadre, nous exposons un état de l'art détaillé et proposons une nouvelle approche itérative d'association B-Spline. L'algorithme s'affranchit de tous les problèmes liés à l'initialisation et au paramétrage initial. Par conséquent, un tel algorithme constitue une nouveauté dans ce domaine. Nous établissons une étude approfondie en évoquant les avantages et les limites actuelles de cette approche sur des exemples de courbes fermées en 2D. Nous complétons ensuite cette étude par des perspectives d'amélioration et de généralisation aux surfaces en 3D. / Complex surfaces exhibit real challenges in regard to their design specification, their manufacturing, their measurement and the evaluation of their manufacturing defects. They are classified according to their geometric/shape complexity as well as to their required tolerance. Thus, the manufacturing and measurement processes used are selected accordingly. In order to transcribe significant information from the measured data, a data processing scheme is essential. Here, processing involves surface reconstruction in the aim of reconstituting the underlying geometry and topology to the points and extracting the necessary metrological information (form and/or dimensional errors). For the category of aspherical surfaces, where a mathematical model is available, the processing of the data, which are not necessarily organized, is done by fitting/associating the aspherical model to the data. The sought precision in optics is typically nanometric. In this context, we propose the L-BFGS optimization algorithm, first time used in metrological applications and which allows solving unconstrained, non-linear optimization problems precisely, automatically and fast. The L-BFGS method remains efficient and performs well even in the presence of very large amounts of data.In the category of general freeform surfaces and particularly turbine blades, the manufacturing, measurement and data processing are all at a different scale and require sub-micrometric precision. Freeform surfaces are generally not defined by a mathematical formula but are rather represented using parametric models such as B-Splines and NURBS. We expose a detailed state-of-the-art review of existing reconstruction algorithms in this field and then propose a new active contour deformation of B-Splines approach. The algorithm is independent of problems related to initialization and initial parameterization. Consequently, it is a new algorithm with promising results. We then establish a thorough study and a series of tests to show the advantages and limitations of our approach on examples of closed curves in the plane. We conclude the study with perspectives regarding improvements of the method and its extension to surfaces in 3D.