Stress coefficient calibration from correlating longitudinal wave velocity and stress birefringence in ultra-low expansion quartz glass

Ultra-low expansion quartz glass serves as a critical material for large-aperture telescope mirrors, yet its imaging quality and dimensional stability are often compromised by residual stresses generated during manufacturing. In response to this problem, we developed a stress coefficient calibration method that combines acoustoelastic and photoelastic effects, establishing a direct correlation between longitudinal wave velocity and stress birefringence. The feasibility and accuracy of the ultrasonic immersion pulse-echo method in capturing the acoustoelastic effect were verified through finite-element simulation, thereby laying a solid foundation for the subsequent experimental design. To realistically replicate the stress state during actual fabrication, we introduced a wide-range composite stress field in samples possessing intrinsic structural stresses through the quenching treatment. Experimental results reveal a clear linear relationship with <i>R</i>²≥0.967 between longitudinal wave velocity and stress birefringence within a stress birefringence range of 0-40 nm/cm, yielding a stress coefficient of approximately -0.43884(<i>m</i>/<i>s</i>)/(<i>n</i><i>m</i>/<i>c</i><i>m</i>) with a standard deviation of 0.00965 (m/s)/(nm/cm). This method eliminates the need for complex mechanical loading and is both non-contact and non-destructive, thereby providing, to our knowledge, a new approach for the non-destructive testing of residual stress and the optimization of manufacturing processes in ultra-low expansion quartz glass.