Active optics in astronomy – modeling of deformable substrates: freeform surfaces for FIREBall and MESSIER

Active optics techniques on large telescopes and astronomical instrumentations provide high imaging quality. For ground-based astronomy, the co-addition of adaptive optics again increases angular resolution up to providing diffraction-limited imaging at least in the infrared. Active and adaptive optics marked milestone progress in the detection of exoplanets, super-massive black holes, 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 surface of a vase-form substrate whilst under reaction to its elliptical perimeter ring. Two such instruments are presented: (1) the Faint Intergalactic Redshifted Emission Balloon (FIREBall) telescope and multi object spectrograph (MOS) where the freeform reflective diffraction grating is generated by replication of a deformable master grating, and (2) the MESSIER wide-field low-central-obstruction three-mirror-anastigmat (TMA) telescope proposal where the freeform mirror is generated by stress figuring and elastic relaxation. Freeform surfaces were obtained by plane super-polishing. 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 geometry of the deformable substrates.