Cubic polynomial curve-guided method for isochromatic
determination in three-fringe photoelasticity
Xiaomeng Liu (刘晓蒙)* and Shuguang Dai (戴曙光)
School of Optical Electrical and Computer Engineering, University of Shanghai for Science and Technology,
Shanghai 200093, China
*Corresponding author: lxm798@163.com
Received June 6, 2015; accepted August 19, 2015; posted online September 17, 2015
A method for isochromatic determination in three-fringe photoelasticity is presented. It combines the phase-
shifting method with cubic polynomial curve-fitting technology to eliminate the errors caused by color repetition.
We perform a demonstration of the method on a circular disc subjected to compressive loading and an injection-
molded cover with residual stresses. The test results compare well with the theoretical results.
OCIS codes: 120.0120, 120.5050.
doi: 10.3788/COL201513.101202.
Photoelasticity is one of the most widely used experimen-
tal methods for whole-field stress analysis in mechanics
[1]
.
The isochromatic and isoclinic fringes correspond to the
principal stress differences and their orientations, respec-
tively. Many techniques have been developed to evaluate
isochromatic fringes; they can be broadly classified into
phase shifting, spectral content analysis, and the Fourier
transform approach
[2]
. Among the various techniques, red,
green, and blue (RGB) photoelasticity
[3]
is a useful photo-
elastic technique to obtain full-field isochromatic data.
Since color merging occurs in RGB photoelasticity beyond
three fringe orders when generic white light sources are
used, it is also known as three-fringe photoelasticity
(TFP)
[4,5]
.
The isochromatic fringe order at an interesting point in
the actual model is established by comparing the values of
R, G, and B at the point of interest with the calibration
table. Ideally, the same test specimen and lighting condi-
tions are used in both the calibration and the application
experiments, but this is not possible in some applications.
Color adaptation
[6,7]
is a simple way of suitably modifying
the calibration table. TFP was originally used to estimate
total fringe orders up to a value of three, as beyond this
point, the colors tend to merge; however, there have been
attempts to push this limit
[8,9]
.
Although the basic principle of TFP is not complicated,
it is difficult to accurately estimate all of the parameters in
practice, such as quarter-wave plate error, dispersion of
the stress-optic coefficient, the spectra l response of the
camera, the spectral composition of the light source,
and the transmission response of the polariscope compo-
nents
[10]
. The evaluation of fringe orders using the least
square error method is quite simple; however, it is prone
to error at some locations owing to the repetition of
colors
[11]
. This is a major problem in TFP.
This Letter concentrates on the determination of iso-
chromatic fringe orders using a plane polariscope with a
white light source. In this case, the isochromatic fringe
is not affected by the isoclinic fringe or the quarter-
wave plate error, which occurs when using a circular
polariscope
[12]
. Moreover, the influence of background light
is eliminated. A new scanning scheme is proposed to de-
termine the isochromatic fringe orders. The applicabil ity
of the new method in determining the fringe orders of a
loaded disc and an injection-molded cover with residual
stresses is demonstrated.
In conventional TFP, researchers use a circular polari-
scope with a white light source to obtain the full-field
isochromatic data
[13]
. As Fig. 1(a) shows, in white light,
the intensity emerging from a dark-field circular polari-
scope (α ¼ 90°, ξ ¼ 135°, ϕ ¼ 45°, and β ¼ 0°) can be
written as
[5]
Fig. 1. Optical arrangements: (a) circular polariscope and
(b) plane polariscope.
COL 13(10), 101202(2015) CHINESE OPTICS LETTERS October 10, 2015
1671-7694/2015/101202(5) 101202-1 © 2015 Chinese Optics Letters
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