
Basic Experimental Mechanics 


Digital Photoelasticity 




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. 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 greyfield polariscope developed by Lesniak et al [11]
is not readily classified and falls between Fourier processing and
phasestepping. 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. Phasestepping Generally monochromatic light
is used in phasestepping to produce maps of isoclinic angle and isochromatic
fringe order from a theoretical minimum of three images. In practice an
overdeterministic 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
phasestepping 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 analysis^{3} 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 phasestepping.
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 phasestepping to produce
maps of isoclinic angle and isochromatic fringe order from a theoretical
minimum of three images. The disadvantage of phasestepping 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):7591. 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.4217. 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. 1608. 5. CarazoAlvarez,
J., Haake,
S.J., Patterson, E.A., 1994, 'Completely automated photoelastic fringe
analysis', Optics & Lasers in Engineering, 21:133149 6. Bhat,
G.K., Redner,
A.S., 1999, ‘Minimizing number of images required in photoelastic
multiwavelength and phaseshifting analysis’,
Proc. SEM Spring Conf. Theor. Exptl. & Comp. Mech., pp. 5413. 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): 265273. 9.
Morimoto, Y., Morimoto Jr,
Y., Hayashi, T., 1994, ‘Separation of isochromatics and isoclinics using fourier transform’ Experimental
Techniques, 18(5):1318. 10.
Quan,
C., BryanstonCross, P.J., Judge, T.R., 1993,
‘Photoelasticity stress analysis using carrier fringe and FFT techniques’
Optics & Lasers in Engineering, 18:79108. 11.
Lesniak,
J., Zickel, M., Bazile,
D., Boyce, B., 1999, ‘Assessment of greyfield photoelasticity’, Proc. 5th
Int. Conf. Experimental Mechanics, Montreal, pp.8569. 12. Ramesh, Digital photoelasticity, Springer Verlag 13.
Ramesh,
K., Ganapathy, V., 1996, ‘Phaseshifting
methodologies in photoelastic analysis – the application of Jones calculus.
J. Strain Analysis, 31(6):423432. 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, 22:91104. 15.
Wang, Z.F., Patterson, E.A., 1999,
‘Integration of spectral and phasestepping methods in photoelasticity’, J.
Strain Analysis, 34(1): 5964. 