In modeling space optical systems, an important property affecting the wave front error is the coefficient of thermal expansion (CTE) of the materials. The change of deformation that an optical element experiences due to thermal loads is proportional to both the CTE and the change in temperature gradient. This deformation affects the performance of the optical system by introducing error in the wave front. The deformation can be reduced in part by using materials with low CTE. Alternatively, using high conductivity materials to minimize temperature gradients through the mirror can also reduce deformation. Usually, a combination of these approaches is used to optimize the performance and meet the requirements of the system. Even with the utmost attention to thermal control, often the temperature gradients cannot be completely avoided. Low CTE materials have been developed to reduce thermal deformation, including ULE (Ultra-low Expansion), Zerodur, and Silicon Carbide. However, the manufacturing process can result in non-uniformities throughout the optics. For optical systems requiring highly precise performance, modeling these non-uniformities becomes important. The non-uniformity in the CTE of a material in effect compounds the deformation in the same manner as introducing additional temperature gradient through the optics. This paper describes the methodology for integrated thermal/mechanical modeling to predict the deformation response of an optical element with assumed CTE variations and thermal disturbances. A mirror with an assumed CTE variation was modeled in a changing thermal environment and using IDEAS/TMG analysis tools, thermal deformations were predicted. Results show excellent agreement with engineering predictions. Clearly knowing the CTE variation of the material is a critical step for modeling. However, measuring and specifying the material CTE is out of the scope of this paper.
Effect of Residual Stress on Thermal Deformation Behavior