Abstract
Elasticity theory and active optics led us to the discovery of three geometrical configurations of variable curvature mirrors (VCMs) that are either cycloid-like or tulip-like thickness distributions. Cycloid-like VCMs are generated by a uniform load—air pressure—applied over the mirror rear surface, and reacts without any bending moment along its circular contour. This particular VCM configuration is of practical interest because it smoothly generates accurate optical curvatures, varying from plane at rest to spherical curvatures up to f/2.9 over 16-mm aperture under 6.5-bar air pressure. Starting from the thin plate theory of elasticity and modeling with NASTRAN finite element analysis, one shows that 3-D optimizations—using a non-linear static flexural option—provide an accurate cycloid-like thickness distribution. VCM elasticity modeling in quenched stainless steel–chromium substrates allows the obtaining of diffraction-limited optical surfaces: Rayleigh’s criterion is achieved over a zoom range from flat to f/3.6 over 13-mm clear aperture up to 6-bar loading. These VCMs were originally developed and built at the Marseille Observatory in 1975 and implemented as a cat’s-eye mirror of IR Fourier-transform interferometers for laboratory recording of fast events in gas molecular spectroscopy. Later, for high-angular resolution astronomy with the ESO VLTI array—an interferometer made of 8 m Unit Telescopes (UTs) and 1.8 m Auxiliary Telescopes (ATs)—such VCMs were inevitable components to provide in a 3″ co-phased field-of-view since 1998. They were implemented (1) as cat’s eye mirrors of the height delay-lines beam recombination lab and (2) as ATs mirror-pair for output pupil conjugation of the movable x–y baseline. From the ESO-AMU approved convention of making 10 VCM spares up to 2024, the present modeling should provide a diffraction-limited extended field-of-view. It is pure coincidence that present results from modeling with an outer collarette are identical to results from analytic theory without collarette.
Highlights
Geometrical deformable configurations able to generate variable curvature mirrors (VCMs) were discovered by Lemaitre in 1976 [1]
In order to improve the mechanical design of cycloid-like VCMs, we presently show, from modeling with MSC-NASTRAN finite element analysis (FEA) code, as performed by one of us (Vola, in this paper), that 3-D optimizations with the non-linear static solution sequence SOL 106 can provide an accurate cycloid-like thickness distribution
Modeling of a cycloid-like VCM is investigated for the two following cases: (i) variable thickness distributions (VTD) plate alone and, (ii) VTD plate linked in a single piece with an outer rigid ring via a very thin collarette
Summary
Geometrical deformable configurations able to generate variable curvature mirrors (VCMs) were discovered by Lemaitre in 1976 [1]. The cycloid-like form manifold requires a uniform load—i.e., a gas or fluid pressure— applied over the mirror back surface that reacts without any bending moment along its circular contour This VCM configuration is of practical interest because it can generate accurate optical curvatures varying from the plane at rest up to f /3.5 or f /3 when under stress. The only other manifolds are two tulip-like forms that require, for static equilibrium, a combination of two sets of forces: a central axial force, a uniform load applied over the back surface, and an axial perimeter ring force These VCM configurations may provide a large zoom range up to f /3.5 or f /3 when under stress. These are constant thickness distribution (CTD) and variable thickness distribution (VTD) ([4] chapter 2)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
