Astronomical telescopes and instruments enable astronomers to see into deep space and unravel the mysteries of the universe. Freeform mirror surfaces – surfaces with a shape more complex than a symmetrical conventional mirror surface (as for example, sphere, parabola, hyperbola, etc.) - offer substantial benefits by providing additional degrees of freedom that make it possible to improve the optical performances of the instrument, reducing the overall instrument mass and size.
The hydroforming process is difficult to design and optimize because the mirror undergoes plastic deformation to provide a freeform optical surface. While the elastic behavior of materials is well known and frequently modeled in optical manufacturing, the analysis of materials under stress in the plastic domain is much more difficult because it involves both material and geometric nonlinearities. One particular importance is the quantifying of the springback effect, in order to control the final shape of the mirror.