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Active Optics in Astronomy: Freeform Mirror for the MESSIER Telescope Proposal

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Active Optics in Astronomy: Freeform Mirror for the MESSIER Telescope Proposal Mathematical and Computational Applications Article Active Optics in Astronomy: Freeform Mirror for the MESSIER Telescope Proposal Gerard Rene Lemaitre *, Pascal Vola * and Eduard Muslimov * Laboratoire d’Astrophysique Marseille (LAM), Aix Marseille Université (AMU) and CNRS, 38 rue Frédéric Joliot-Curie, 13388 Marseille CX 13, France * Correspondence: [email protected] (G.R.L.); [email protected] (P.V.); [email protected] (E.M.) Received: 28 November 2018; Accepted: 20 December 2018; Published: 27 December 2018 Abstract: Active optics techniques in astronomy provide high imaging quality. This paper is dedicated to highly deformable active optics that can generate non-axisymmetric aspheric surfaces—or freeform surfaces—by use of a minimum number of actuators. The aspheric mirror is obtained from a single uniform load that acts over the surface of a closed-form substrate whilst under axial reaction to its elliptical perimeter ring during spherical polishing. MESSIER space proposal is a wide-field low-central-obstruction folded-two-mirror-anastigmat or here called briefly three-mirror-anastigmat (TMA) telescope. The optical design is a folded reflective Schmidt. Basic telescope features are 36 cm aperture, f /2.5, with 1.6◦ × 2.6◦ field of view and a curved field detector allowing null distortion aberration for drift-scan observations. The freeform mirror is generated by spherical stress polishing that provides super-polished freeform surfaces after elastic relaxation. Preliminary analysis required use of the optics theory of 3rd-order aberrations and elasticity theory of thin elliptical plates. Final cross-optimizations were carried out with Zemax raytracing code and Nastran FEA elasticity code in order to determine the complete geometry of a glass ceramic Zerodur deformable substrate. Keywords: telescope; active optics; aspherics; elasticity; optical design; deformable mirror 1. Introduction Technological advances in astronomical instrumentation during the second part of the twentieth century gave rise to 4 m, 8 m and 10 m class telescopes that were completed with close loop active optics control in monolithic mirrors [1], segmented primary mirrors [2] and segmented in-situ stressed active optics mirrors [3]. Further advances on ground-based telescopes allowed developments of adaptive optics for blurring the image degradation due to atmosphere. Both active and adaptive optics provided milestone progress in the detection of super-massive black holes, exoplanets and large-scale structure of galaxies. This paper is dedicated to highly deformable active optics that can generate non-axisymmetric aspheric surfaces—or freeform surfaces—by use of a minimum number of actuators: a single uniform load acts over the monolithic surface of a closed-form substrate whilst under reaction to its elliptical perimeter ring. These freeform surfaces are the basic aspheric components of dispersive/reflective Schmidt systems. Both reflective diffraction freeform gratings and freeform mirrors have been investigated by Lemaitre [4]. MESSIER proposal is a wide-field low-central-obstruction folded-two-mirror-anastigmat or here called briefly three-mirror-anastigmat (TMA) telescope based on a folded reflective Schmidt optical design. It is dedicated to the survey of extended astronomical objects with extremely low surface brightness. The proposal name is in homage to French astronomer Charles Messier (1730–1817) (Figure1) who published the first astronomical catalogue of nebulae and star clusters. The catalogue was known as Messier objects—for instance, M1 for the Crab nebulae, M31 for the Andromeda galaxy Math. Comput. Appl. 2019, 24, 2; doi:10.3390/mca24010002 www.mdpi.com/journal/mca Math. Comput. Appl. 2019, 24, 2 2 of 15 Math. Comput. Appl. 2018, 23, x FOR PEER REVIEW 2 of 15 andand so forth—and so forth—and distinguished distinguished between between permanent permanent and and transient transient diffuse diffuse objects, objects, then then helped helped in in sensingsensing or discovering or discovering comets. comets. FigureFigure 1. Charles 1. Charles Messier Messier (1730–1817) (1730–1817) (Wikipedia). (Wikipedia). MESSIERMESSIER optical optical design design would would provide provide a high a high imaging imaging quality quality without without any any diff diffractiveractive spider spider patternpattern in the in thebeams. beams. A preliminarily A preliminarily ground-based ground-based prototype prototype is planned is planned to serve to serve as a as fast-track a fast-track pathpathfinderfinder for fora future a future space-based space-based MESSIER MESSIER mission. mission. The The elliptical elliptical freeform freeform mirror mirror is generated is generated by by stressstress polishing polishing and and elastic elastic relaxation relaxation technique technique [4,5]. [4 ,5 ]. Super-polishingSuper-polishing of freeform of freeform surfaces surfaces is obtained is obtained from from spherical spherical polishing polishing after after elastic elastic relaxation. relaxation. PreliminaryPreliminary analysis analysis required required use use of ofthe the optics optics theo theoryry of of3rd-order 3rd-order aberrations aberrations and and elasticity elasticity theory theory of of thinthin elliptical elliptical plates. plates. The The fi finalnal cross-optimizations cross-optimizations were carriedcarried outout withwith ZemaxZemax ray-tracingray-tracing code code and andNastran Nastran FEA FEA elasticity elasticity code code that that provides provides accurate accurate determination determination of of the the substrate substrate geometry geometry of of a glassa glassceramic ceramic Zerodur Zerodur material. material. 2. Optical2. Optical Design Design with with a Re a Reflectiveflective Schmidt Schmidt Concept Concept A reflectiveA reflective Schmidt Schmidt design design is isa wide- a wide-fieldfield system system and and basically basically a a two-mirror two-mirror anastigmat. WithWith one onefreeform freeform surface surface correcting correcting all threeall three primary primary aberrations, aberrations, such asuch system a system has been has widely been investigated widely investigatedas well as as for well telescope as for or telescope spectrograph or sp designs.ectrograph The correctordesigns. mirrorThe corrector or reflective mirror diffraction or reflective grating is diffalwaysraction locatedgrating atis always the centre located of curvature at the centre of aspherical of curvature concave of a spherical mirror. concave mirror. ComparedCompared to toa aSchmidt Schmidt with with aa refractor-correctingrefractor-correcting element, element, which which is a is centred-system, a centred-system, a reflective a reflectiveSchmidt Schmidt necessarily necessarily requires requires a tilt a oftilt theof the optics. optics. TheThe inclination of of the the mirrors mirrors then then forms forms a a non-centred-systemnon-centred-system. For. Foran f an/2.5f /2.5focal-ratio, focal-ratio, the tilt the angle tilt angle of the of aspheric the aspheric primary primary mirror mirror is typically is typically of of ◦ aboutabout 10° 10andand somewhat somewhat depending depending on the on theFoV FoV size. size. For Fora re aflective reflective Schmidt Schmidt optical optical design, design, as MESSIER as MESSIER telescope telescope proposal proposal at f at/2.5,f /2.5, a supplementary a supplementary folding-folding-flatflat mirror mirror was was found found necessary. necessary. This This third third mirror mirror provides: provides: (i) an (i) easy an easy access access to the to thedetector detector for forminimal minimal central central obstruction; obstruction; and and (ii)(ii) avoidavoid any any spider spider inside inside the beamsthe beams that wouldthat would cause diffractivecause diffractiveartefact artefact cross-like cross-like images images at the focal at the image focal ofimage bright of stars.bright Thisstars. led This us led to a us three-mirror to a three-mirror design or designTMA or telescope.TMA telescope. InvestigationsInvestigations of ofthe the plane-aspheric plane-aspheric mirror mirror havehave beenbeen discussed discussed to defineto define the bestthe shapebest shape freeform freeformsurface surface of this of non-centred this non-centred system. system. The freeform The freeform surface surface is with is ellipticalwith elliptical symmetry symmetry and provides and providesbalance balance of the of quadratic the quadratic terms terms with respect with respect to the to bi-quadratic the bi-quadratic terms. terms. TemporarilyTemporarily avoiding avoiding the the folding-flat folding-flat mirror, mirror, let assumeassumea a two-mirror two-mirror non-centred non-centred system system where wherethe the primary primary mirror mirror M1 isM1 a freeformis a freeform and theand secondary the secondary mirror mirror M2 is aM2 concave is a concave spherical spherical surface of surfaceradius of ofradius curvature of curvatureR. The inputR. The beams input arebeams circular are circular collimated collimated beams merging beams merging at various at fieldvarious angles fieldof angles a telescope of a andtelescope define and along de thefine M1 along freeform the M1 mirror freeform an elliptical mirror pupil an elliptical due to inclination pupil due angle to i. inclinationA convenient angle valuei. A convenient of the inclination value angleof the allows inclination the M2 angle mirror allows to avoid the anyM2 obstructionmirror to avoid and provideany obstruction and provide focusing very closely to mid-distance between M1 and M2, then
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