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A robust approach to demodulating and unwrapping phase-stepped photoelastic data

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Abstract

New algorithms are proposed for processing wrapped isochromatic and isoclinic fringe data generated by the digital photoelastic technique of phase-stepping. The new algorithms are based on processing areas rather than individual pixels to demodulate the data and employing quality assessments of the data to guide the unwrapping procedure. Comparisons with an existing algorithm, manual analysis, and finite element modeling have been used to demonstrate that the new approach is more robust without any reduction in speed or accuracy. This represents a significant advance for processing complex fringe patterns, which are often encountered in the aerospace industry from which the exemplars are drawn.

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Abbreviations

A(j) :

current area for processing

A(j+1) :

next area for processing

H :

threshold height used in spike removal process applied to partial derivative data

i1 ...i6:

intensity measured in polariscope orientated as shown in Table 1

i m :

intensity term to account for stray light entering the polariscope

i v :

intensity observed in a polariscope when the fast axes of all the elements are aligned

I c :

i4−i6

I d :

i1−i2

I s :

i5−i3

n, m :

coordinates of pixel of interest

N, M :

number of pixels inx, y direction in data map

Qθ(n, m):

quality value for the pixel located at (n, m)

w 1 :

window dimension used in evaluating quality map

w 2 :

window dimension used in reducing number of areas to be processed

α:

relative retardation

Δψ x (i, j), Δψ y (i, j):

difference in partial derivative of the phase data with respect to thex, y directions

\(\overline {\Delta \psi _x } (n,m),\overline {\Delta \psi _y } (n,m)\) :

mean of the differences in partial derivative of the phase data with respect to thex, y directions within the window

θ:

isoclinic angle

ρ:

percentage area left unwrapped

σ1, σ2 :

maximum and minimum principal stresses

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Author notes

  1. E. A. Patterson (Research Officer)

    Present address: Department of Mechanical Engineering, Michigan State University, 2555 Engineering Building, 48824-1226, East Lansing, MI, USA

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Sheffield, S1 3JD, Sheffield, UK

    P. Siegmann (Research Associate) & E. A. Patterson (Research Officer)

  2. Institute for Aerospace Research, NRC Canada, Ottawa, Canada

    D. Backman (Professor)

Authors
  1. P. Siegmann
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  2. D. Backman
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  3. E. A. Patterson
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Siegmann, P., Backman, D. & Patterson, E.A. A robust approach to demodulating and unwrapping phase-stepped photoelastic data. Experimental Mechanics 45, 278–289 (2005). https://doi.org/10.1007/BF02427952

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  • DOI: https://doi.org/10.1007/BF02427952

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