Application of principal component analysis in phase-shifting photoelasticity.

Juan A Quiroga,José A Gómez-Pedrero

doi:10.1364/oe.24.005984

Abstract

Principal component analysis phase shifting (PCA) is a useful tool for fringe pattern demodulation in phase shifting interferometry. The PCA has no restrictions on background intensity or fringe modulation, and it is a self-calibrating phase sampling algorithm (PSA). Moreover, the technique is well suited for analyzing arbitrary sets of phase-shifted interferograms due to its low computational cost. In this work, we have adapted the standard phase shifting algorithm based on the PCA to the particular case of photoelastic fringe patterns. Compared with conventional PSAs used in photoelasticity, the PCA method does not need calibrated phase steps and, given that it can deal with an arbitrary number of images, it presents good noise rejection properties, even for complicated cases such as low order isochromatic photoelastic patterns.

Highlights

Photoelasticity is a widely employed technique in the field of stress measurement in transparent samples [1]
If we set the sample under stress inside a polariscope, there will appear an interferogram formed by two fringe patterns modulating each other: the isochromatics, associated with the local retardation and the isoclinics associated with the local orientation of the birrefrinence axes [1]
In order to test the proposed method, we have carried out a photoelastic experiment in which we have measured the isoclinics and isochromatics for two different objects: a planar disk in diametrical compression and a plastic ophthalmic lens which have been cut oversized so it is pressed by its metallic frame

Summary

Introduction

Photoelasticity is a widely employed technique in the field of stress measurement in transparent samples [1]. A typical PSA employed in photoelasticity is the eight-step technique reported by Quiroga et al [4] In this case, a 4-step PSA is used for the isoclinics calculation and an 8-step PSA for the isochromatics. Deviation of the actual angular positions from the planned ones are translated into detuning errors for the PSA [2,3,4,5] This kind of error can be eliminated if we use self-tunable or wide-band PSAs for the fringe pattern demodulation. In both techniques, it is assumed that the phase step between interferograms is unknown but constant. In order to apply any PSA technique, including PCA, it is necessary to demodulate in two different steps the isoclinics and the isochromatic fringe patterns. We will first summarize the PCA method for phase demodulation [10]

PCA analysis of phase shifted interferograms

I1 n I2 n

Isoclinics demodulation

Isochromatics demodulation

Experimental results

Conclusions