Development of Birefringence Analysis Code for Single Crystal Optical Elements

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Steady state creep constitutive equation was formulated using the experimental data on compressive tests under constant strain rates at elevated temperatures. Residual stress in a calcium fluoride single crystal ingot after ingot annealing was calculated by the nonlinear finite element analysis using the steady state creep constitutive equation. In the birefringence analysis, optical path difference was obtained from the residual stress. The distributions of the optical path difference obtained from the analysis were compared with those of experimental measurements. It is found that analysis results agree well with experimental measurements. Thus the subsystem for residual stress estimation was verified. The birefringence was estimated for a calcium fluoride single crystal chamber window of an ArF excimer laser light source with a wave a length of 193nm used in a semiconductor lithography system.