Transmissive windows designed to operate at low temperatures are subject to repeated thermal cycling, which may crack the window. This paper derives a simple expression for the stresses developed at the edge of a circular window. These stresses depend upon the lowest service temperature, the elastic moduli of window and holder, the mismatch in the coefficients of thermal expansion, and the holder and window thicknesses. For a given material pair, there is a critical holder thickness that will initiate fracture in the window. A graph is provided to facilitate the determination of holder thickness.
V. Biricikoglu, "Thermal Stresses In Cryogenic Windows," Appl. Opt. 12, 1831-1833 (1973)