Modeling the Extremely Lightweight Zerodur Mirror (ELZM) Thermal Soak Test

Exoplanet science requires extreme wavefront stability (10 pm change/10 minutes), so every source of wavefront error (WFE) must be characterized in detail. This work illustrates the testing and characterization process that will be used to determine how much surface figure error (SFE) is produced by mirror substrate materials' CTE distributions. Schott's extremely lightweight Zerodur mirror (ELZM) was polished to a sphere, mounted, and tested at Marshall Space Flight Center (MSFC) in the X-Ray and Cryogenic Test Facility (XRCF). The test transitioned the mirror's temperature from an isothermal state at 292K to isothermal states at 275K, 250K and 230K to isolate the effects of the mirror's CTE distribution. The SFE was measured interferometrically at each temperature state and finite element analysis (FEA) has been completed to assess the predictability of the change in the mirror's surface due to a change in the mirror's temperature. The coefficient of thermal expansion (CTE) distribution in the ELZM is unknown, so the analysis has been correlated to the test data. The correlation process requires finding the sensitivity of SFE to a given CTE distribution in the mirror. A novel hand calculation is proposed to use these sensitivities to estimate thermally induced SFE. The correlation process was successful and is documented in this paper. The CTE map that produces the measured SFE is in line with the measured data of typical boules of Schott's Zerodur glass.