Finite element analysis of deformation in large optics due to space environment radiation

Dose gradients in large mirror substrates due to unequal exposure to the natural space radiation environment have been calculated for two circular orbits: 1200 km altitude/98 deg inclination and 3700 km/30 deg. Dose gradients were translated to density-change profiles based on experimentally determined density changes as a function of dose for fused silica and the low-CTE glass ceramic, Zerodur-M. Finite element analysis of deformation due to the radiation-induced density gradient was performed for a 4 meter by 0.5 cm disk representing a mirror faceplate. Displacements of nearly 2500 micrometers at the outer edge were calculated for a Zerodur faceplate after 10 yr at 3700 km/30 deg. Silica, which is much less sensitive, deformed by only a few angstroms. Reinforcement with a backing having the equivalent stiffness of 5 cm of SiC resulted in a 10-fold decrease in the calculated deformation.