The physical properties of an optical system are modified when experiencing changes in temperature. Thermo-elastic effects modify the dimensional characteristics, and thermo-optic effects change the index of refraction of the optical materials. Predicting optical performance in high-performance optical systems typically requires the coupling of the thermal, structural, and optical analyses to account for detailed thermal interactions. This chapter discusses integrating techniques along with thermal modeling methods to allow optical performance to be predicted as a function of complex temperature distributions.
5.1. Thermo-Elastic Analysis
Temperature changes in an optical system cause dimensional and positional changes in the optical components due to thermo-elastic effects. This includes changes in optical element thickness, diameter, radii of curvature, and higher-order surface deformations. These departures from the nominal optical system prescription affect optical performance.
The material property dictating the expansions and contractions is the linear coefficient of thermal expansion (CTE), denoted by Î±. The CTE varies considerably depending on the type of material. For instance, the CTE of common optical mounting materials include Invar 36 at ~ 1.0 ppm/C, titanium at 8.8 ppm/C, and aluminum at 23.6 ppm/C. The CTE of optical glasses include fused silica at 0.5 ppm/C, BK7 at 7.1 ppm/C, and FK54 at 14.6 ppm/C. The CTE of plastics and epoxies may be an order of magnitude greater than metals or glasses with CTEs in the hundreds of ppm/C.
5.1.1 CTE temperature dependence
The temperature dependence of the coefficient of thermal expansion must be accounted for in extremely sensitive optical systems or for optical systems experiencing large temperature swings. For example, the variation in CTE with temperature for aluminum, beryllium, and fused silica is shown in Fig. 5.1. A nonlinear finite element solution is required if the thermo-elastic response quantities are desired at incremental times as the optical instrument cools down or heats up.
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