Experimental Mechanics @ Michigan State University

 

 

EM Basics: Phase-stepping in PEA

 

 

 

 

§             Generally monochromatic light is used in phase-stepping to produce maps of isoclinic angle and isochromatic fringe order from a theoretical minimum of three images. In practice an over-deterministic system is preferable and a recent review1 found that the six step algorithm pioneered by Wang and Patterson2 gave the best results.

§             The technique produces periodic maps of isoclinic and isochromatic fringe order, and the latter normally require unwrapping. Various algorithms for demodulating the isoclinic and isochromatics and unwrapping them have been developed.

§             The disadvantage of phase-stepping is that, whilst multiple fringes can be dealt with by phase unwrapping, the fringe order must provided at a pair of points in order to fix the absolute value of the fringe order map. In transmission photoelasticity this has been achieved by using a small probe based on spectral contents analysis3 and by using white light with a colour CCD camera4.

§             Images show data for a disc subject to diametric compression and viewed in a monochromatic transmission polariscope. The six phase stepped images are shown in pseudo colour (left), with the results of processing using Wang and Patterson algorithm (centre) to produce periodic isoclinic (top) and isochromatic (top) maps. The unwrapped maps of isoclinic angle (top) and calibrated fringe order (bottom) are also shown (right)

Six phase-stepped images

Fractional fringe pattern of a compression disk

Fringe order map of a compression disk
  1. Ramesh, K., Ganapathy, V., 1996, ‘Phase-shifting methodologies in photoelastic analysis – the application of Jones calculus. J. Strain Analysis, 31(6):423-432.
  2. Patterson, E.A., Wang, Z.F., 1995, 'Use of phase stepping with demodulation and fuzzy sets for birefringence measurement', Optics and Lasers in Engineering, 22:91-104.
  3. Carazo-Alvarez, J., Haake, S.J., Patterson, E.A., 1994, 'Completely automated photoelastic fringe analysis', Optics & Lasers in Engineering, 21:133-149.

4.      Wang, Z.F., Patterson, E.A., 1999, ‘Integration of spectral and phase-stepping methods in photoelasticity’, J. Strain Analysis, 34(1): 59-64.

 

 

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