Modeling of speckle noise in the interferometric phase-stepping photoelastic-coating stress analysis

An interferometric phase-shifting photoelasticity is an effective approach to separate the stress components in engineering structures with mechanical and geometrical complexity, especially when the photoelastic coating method is applied. A series of photoelastic fringe patterns are recorded with a circular polariscope to obtain the phase map proportional to the difference of the principal stresses in the tested specimen. In addition, holographic recording of fringe patterns is applied for retrieval of isopachic fringes which give the sum of the principal stresses. The easiest way to perform a combined polariscopic and holographic measurement for full-field stress analysis is to use a laser light source. However, the speckle noise at coherent illumination could severely violate the requirement for high signal-to-noise ratio in the recorded patterns. Thus, task-oriented preprocessing and denoising algorithms become mandatory for accurate phase estimation and unwrapping. Development of such algorithms is impossible without an adequate signal-and-noise model, which is the goal of this paper. The paper presents simulation of an interferometric photoelastic measurement that is based on calculation of the complex amplitudes at the output of a Mach-Zender interferometer combined with a circular polariscope. The model is used for simulation of speckled fringe patterns for an epoxy disk under concentrated diametral compression. Comparison with experimental fringe patterns which have been recorded at pure tensile load for PhotoStress coated samples with a hole as a mechanical stress concentrator is also included.