Theoretical compensation of static deformations of freeform multimirror substrates.

Varying temperatures influence the figure errors of freeform metal mirrors by thermal expansion. Furthermore, different materials lead to thermo-elastic bending effects. The paper presents a derivation of a compensation approach for general static loads. Utilizing perturbation theory, this approach works for shape compensation of substrates that operate in various temperature environments. Verification is made using a finite element analysis, which is further used to produce manufacturable CAD models. The remaining low spatial frequency errors are deterministically correctable using diamond turning or polishing techniques.