Factors that contribute to the temperature dependence of a resonant frequency in a low-expansion optical cavity are discussed, including deformation at the cavity ends due to different coefficients of thermal expansion (CTE) of the spacer, optically-contacted mirror substrate and coating. A model of the temperature dependence is presented that incorporates finite-element-analysis of the cavity ends. A measurement of frequency versus temperature of a cavity mode is used along with the model to deduce a spacers CTE versus temperature profile. The measured profile correlates very well with a separate experiment utilizing a temporary surface-mounted Fabry-Perot cavity fabricated on the outside of the spacer with hydroxy-catalysis bonding.
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