Investigation of systematic relationship between spectrometry and white light photoelasticity by regression analysis

By integrating the white light photoelasticity and spectrometry, a novel method called transmissivity extremities theory of photoelasticity to determine the state of stress has been recently developed. The key of transmissivity extremities theory of photoelasticity is to establish the systematic relationship of transmissivity with stress and wavelength and further derive the stress quantifying formula. Based on the high resolution and sensitivity of the spectrometer and the high measurement accuracy of the white light photoelasticity, transmissivity extremities theory of photoelasticity can determine the low-level stress even in low birefringence materials. Before extending the application of transmissivity extremities theory of photoelasticity to determine the higher level stress, the correlation between different transmissivity extremities linear equations in the systematic relationship and the relationship between parameters in the stress quantifying formula and thicknesses of specimens need to be derived and investigated. Therefore, in this article, a regression analysis of the constant term and first-order harmonic terms of the Fourier series function was employed to obtain the transmissivity extremities linear equations and parameters in the stress quantifying formula from the database. Both PSM-1 and glass were used to confirm the derived correlation and relationship. The effectiveness and merits of transmissivity extremities theory of photoelasticity were demonstrated by comparing simulation results obtained by transmissivity extremities theory of photoelasticity and the conventional white light photoelasticity, comparison between theoretical and experimental results of a diametrically loaded circular disk as well as the determination of the residual stress distribution of a thin glass substrate used for liquid crystal display.