Adaptive Quality Guided Phase Unwrapping Algorithm for Whole‐Field Digital Photoelastic Parameter Estimation of Complex Models

Abstract

With advancements in digital image processing and data acquisition, a separate branch of photoelasticity namely digital photoelasticity came into existence. Here, intensity information of the acquired image is used for the evaluation of whole‐field photoelastic parameters. Digital photoelasticity provides only wrapped phasemaps of isoclinics and isochromatics and they have to be unwrapped in different ways for getting the continuous‐phase values. In the case of the isochromatic phasemap, ambiguity removal prior to unwrapping is essential. In this paper, a 10‐step phase‐shifting methodology is proposed and a new strategy for obtaining the isochromatic phasemap free of ambiguity is demonstrated. Isoclinic unwrapping is performed by a new adaptive quality guided algorithm. Adaptive in the sense that isoclinic phase unwrapping is done autonomously even in the presence of isotropic points/π jumps occurring in the isoclinic phasemap. The isochromatic phasemap is also unwrapped using the quality guided path follower. The methodology is validated for the problem of a ring under diametral compression and later shown for three other models which have complex stress fields. Wherever possible, the parameters obtained by the new methodology are compared with analytical or numerical methods and the comparison is quite good.

Finite Element Simulation of Isoclinic and Isochromatic Phasemaps for Use in Digital Photoelasticity

“…Though one gets experimentally only a phasemap with ambiguous zones, numerically getting a phasemap with ambiguous zones is little involved. The presence of inconsistent zones in isoclinic phasemap leads to the formation of ambiguous zones in the isochromatic phasemap 2,10,11 . It has been shown recently 12 that in ambiguous zones, a simple reversal of fractional fringe order values clears this.…”

“…To validate the results obtained by FE, an experiment is carried out. The isoclinic values and isochromatic values are obtained by using a 10‐step phase‐shifting method 2,10,11 . The various optical arrangements necessary to get the 10 phase‐shifted images are shown in Table 1.…”

“…One of the main issues in wrapped isoclinic phasemaps is that the isoclinic values obtained do not uniformly represent the direction of one of the principal stresses over the entire domain. The zones where the phasemap refers to the other principal stress direction are labelled as inconsistent zones in the isoclinic phasemap 2 . These zones lead to the formation of ambiguous zones in the isochromatic phasemap where the sign of the fractional retardation has to be judiciously selected.…”

Mathematical Morphology Guided Automatic Unwrapping Isoclinic Phase Map in White Light Photoelasticity

“…In order to unwrap the isoclinic phase map, researchers [12][13][14][15][16] reported several methods to make the continuous isoclinic phase map in the true phase interval. Siegmann et al [12] proposed a robust unwrapping approach that was based on processing areas or regions rather than pixels, but the process for choosing the initial area for unwrapping was not clearly described.…”

“…Pinit and Umezaki [13] introduced an isoclinic phase unwrapping algorithm to account for isotropic points, the presence of isotropic points is initially detected by a cumbersome procedure and then unwrapping is done. Ramji and Ramesh [14] developed a quality guided approach for isoclinic unwrapping and by the phase map smoothing algorithm [8,15,16] phase map unwrapping method guided by morphological techniques is introduced. The motivation of this work is to produce an algorithm to resolve the ambiguity in isoclinic phase map that use a simple approach but retains the correctly demodulated regions of the isoclinic phase map.…”