Thermal deformation noise in large optical systems

Abstract

Future large space-based telescope systems require precise optical surface quality and wave-front stability. One source of noise for very large precise optical systems is ambient thermal energy which induces statistical fluctuations in the strain energy state of the structure. We broadly model such optical systems as bending energy dominated or membrane in-plane energy dominated and derive analytical expressions for the governing parameters that determine noise magnitude. It is shown that for bending-based systems thermal noise increases as aperture is increased and as bending stiffness is decreased, while for membrane mirror systems it is the in-plane pretension level that determines the noise magnitude. The analysis is extended to numerical finite element techniques to illustrate the effects on very general large damped structures where we address the form of equivalent thermal loading density required in modeling such distributed structures. Calculations show that temporal rms deformation noise on the order of a picometer or less can be expected for apertures up to about 10 m and therefore is probably not significant. For lightweight precision aperture systems greater than 10 m, thermal noise may need to be considered in the design.