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Basic Experimental Mechanics

 

Digital Photoelasticity

 

Structural Materials & Mechanics Research Group

 

 

Introduction

Automated photoelasticity has developed as a topic in the last ten to fifteen years during which time major advances have been made, partly as a result of the availability of new technology in computing and image processing. For a review of the subject see Ajovalasit et al [1] or Patterson [2] for work prior to 1988.  The major techniques of automated photoelasticity are described in the sections below:

 

Spectral Contents Analysis

Earlier developments were by Redner [3] and by Sanford and Igenyar [4].  Essentially, for the point of interest the light intensity is collected over a range of wavelengths to form a spectrum.  A theoretical model of the spectral contents of the point in a fringe pattern is fitted to the experimental data using the fringe order as the fitting parameter.  The maximum fringe order that can be recognised is approximately equal to the number of wavelengths at which intensity information is collected [5,6]. Hence an RGB camera can be used to obtain fringe orders up to about three [7].  No information about isoclinic angle is available.  Recent work has produced significantly faster algorithms which do not need any a priori knowledge of the range of fringe order being measured [8]. The University of Sheffield has implemented the technology in a number of novel instruments.

 

Fourier Analysis

Fourier analysis requires the collection of a large number of images, typical 90 for isoclinic map determination.  The methods used for determining isoclinic and isochromatic maps are different and have been developed by Morimoto et al [9] and Quan et al [10] respectively.  The grey-field polariscope developed by Lesniak et al [11] is not readily classified and falls between Fourier processing and phase-stepping.  These techniques produce periodic distributions of isoclinic and isochromatic fringe orders. The latter maps usually require unwrapping. See Ramesh [12]  for more details on digital photoelasticity and associated issues.

 

Phase-stepping

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 review [13] found that the six step algorithm pioneered by Wang and Patterson [14] 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 camera [15].

 

Concluding remarks

Early efforts to automate photoelastic analysis involved collection of monochromatic images followed by some form of fringe thinning, with the operator required to identify all the fringes and interpolation used to obtain values between the locations of fringes. The grey field polariscope falls across the boundaries between Fourier analysis and phase-stepping. Fourier analysis requires large numbers of images and so is often impractical. Spectral analysis can provide the absolute fringe order but no information about isoclinic angle. Thus its use in isolation produces significant drawbacks. The maximum fringe order that can be recognised is approximately equal to the number of wavelengths at which intensity information is collected. 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. 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.

 

References

1.        Ajovalasit, A., Barone, S., Petrucci, G., 1998, ‘A review of automated methods for the collection and analysis of photoelastic data’ J. Strain Analysis, 33(2):75-91.

2.        Patterson, E. A., 1988, 'Automated photoelastic analysis', Strain, 24(1): 15 - 20.

3.   Redner, A.S., 1984, ‘Photoelastic measurements by means of computer assisted spectral contents analysis’ Proc. 5th Int. Conf. Experimental Mechanics, Montreal, pp.421-7.

4.   Sanford, R.J., Igenyar, V., 1985, ‘The measurement of the complete photoelastic fringe order using a spectral scanner, Proc. SEM Spring Conf. Experimental Mechanics, pp. 160-8.

5.   Carazo-Alvarez, J., Haake, S.J., Patterson, E.A., 1994, 'Completely automated photoelastic fringe analysis', Optics & Lasers in Engineering, 21:133-149

6.   Bhat, G.K., Redner, A.S., 1999, ‘Minimizing number of images required in photoelastic multi-wavelength and phase-shifting analysis’, Proc. SEM Spring Conf. Theor. Exptl. & Comp. Mech., pp. 541-3.

7.   Petrucci etc

8.   Pacey, M.N., Wang, X.Z., Haake, S.J., Patterson, E.A., 1999,‘The application of evolutionary and maximum entropy algorithms to photoelastic spectral analysis’, Experimental Mechanics, 38(4): 265-273.

9.        Morimoto, Y., Morimoto Jr, Y., Hayashi, T., 1994, ‘Separation of isochromatics and isoclinics using fourier transform’ Experimental Techniques, 18(5):13-18.

10.     Quan, C., Bryanston-Cross, P.J., Judge, T.R., 1993, ‘Photoelasticity stress analysis using carrier fringe and FFT techniques’ Optics & Lasers in Engineering, 18:79-108.

11.     Lesniak, J., Zickel, M., Bazile, D., Boyce, B., 1999, ‘Assessment of grey-field photoelasticity’, Proc. 5th Int. Conf. Experimental Mechanics, Montreal, pp.856-9.

12.     Ramesh, Digital photoelasticity, Springer Verlag

13.     Ramesh, K., Ganapathy, V., 1996, ‘Phase-shifting methodologies in photoelastic analysis – the application of Jones calculus. J. Strain Analysis, 31(6):423-432.

14.     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.

15.     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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