  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 provide
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 FIREBall telescope and 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 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.
