colour adaptation in three fringe photoelasticity using a single image

TECHNIQUES by B. Neethi Simon and K. Ramesh

COLOUR ADAPTATION IN THREE FRINGEPHOTOELASTICITY USING A SINGLE IMAGE

I n conventional photoelasticity, one often makes useof a colour code to identify fringe gradient directionand to approximately assign the total fringe order.Three fringe photoelasticity (TFP) is an extension of

this technique to the digital domain. The total fringe orderat a point of interest in the actual model is determined bycomparing the R,G, and B values at the point of interestwith that of a calibration table. As the colours tend to mergebeyond fringe-order three, the technique is termed as TFP.1Because R, G, and B values of a colour image are used, it isalso termed as RGB photoelasticity (RGBP).2 TFP comes invery handy for the analysis of transient problems3 becauseof its capability of single-shot data acquisition and it is alsovery industry-friendly.

It is well-known that in TFP, because only colour informationis used for the identification of fringe order, noise maybe introduced, which can be removed by imposing fringe-order continuity.4 Several researchers proposed variousmethodologies such as refined three fringe photoelasticity(RTFP),5 introducing a regularisation term6,7 and medianfiltering8 to ensure fringe-order continuity.

The fringe-order evaluation could be erroneous when thereis a colour mismatch between the calibration and applicationspecimens. Colour mismatch is inevitably caused by factorssuch as differences in ambient lighting, annealing, or stressfreezing the specimen. In order to overcome this difficulty,Madhu et al.9 proposed colour adaptation in TFP whereinno-load bright field images of the calibration and applicationspecimens need to be additionally recorded in order totune the calibration table to suit the tint variation of theapplication specimen. Although the technique is quite goodfor live-loaded models, this methodology cannot be used forstress-frozen slices as the no-load image will not be available.

In this paper, a new methodology is proposed by which colourmismatch between the calibration and application specimensis taken care of using only the single isochromatic fringefield of the application specimen. The result thus obtainedis further improved by RTFP. The proposed methodologyis validated using the benchmark problem of a disc underdiametral compression, and its robustness is demonstratedfor complicated stress-frozen slices of three aero-structuralcomponents.

METHODOLOGY OF TFPIn TFP/RGBP, first a calibration table needs to be generatedwith RGB values assigned with known fringe orders. A beamunder 4-point bending is conventionally used to generate thiscalibration table as the variation in fringe order is knownto be linear across the depth of the beam. Then, one has

B. Neethi Simon ([email protected]) is a research scholar and K. Ramesh(SEM member, [email protected]) is a professor with the Department of AppliedMechanics, Indian Institute of Technology, Madras, Chennai, India.

to compare the RGB values of a point on the applicationspecimen with the calibration table so as to determine itstotal fringe order. Ideally, RGB values have to be uniquefor any fringe order. However, in view of experimentaldifficulties, the RGB values corresponding to a data point maynot exactly coincide with the RGB values in the calibrationtable. For any test data point, an error term ‘‘e’’ is defined as:1

e =√

(Re − Rc)2 + (Ge − Gc)2 + (Be − Bc)2 (1)

where subscript ‘‘e’’ refers to the experimentally measuredvalues for the data point and ‘‘c’’ denotes the values in thecalibration table. The calibration table is to be searched untilthe error ‘‘e’’ is a minimum. For the Rc, Gc, and Bc valuesthus determined, the calibration table provides the totalfringe order. Total fringe order is thus estimated for eachpixel over the domain.

NEED FOR COLOUR ADAPTATIONBecause only colour information is used for estimating thetotal fringe order, any tint variation between the calibrationand application specimens leads to error in identification ofthe total fringe order. To demonstrate this, two beams ofthe same material (Epoxy) cast in-house with the ratio ofresin and hardener varied in order to create a considerabletint variation are prepared. Both the specimens (Specimen-1and Specimen-2) are subjected to 4-point bending such thatat the top and bottom edges of the specimens one observesa fringe order of 3. The dark-field isochromatics for the tophalf of the central zone are recorded using a 3CCD camera(Sony XC003P) for both the specimens and are shown inFig. 1a and b, respectively. In order to clearly visualise thecolour variation between the two specimens, R, G, and Bintensities for each of the specimens with respect to fringeorder are also plotted in Fig. 1c and d, respectively.

A calibration table is generated using Specimen-1. Using this,the whole-field fringe order for the two recorded dark-fieldisochromatic images is determined. The result is representedin the form of an image by converting the fringe-order datainto a set of grey level equations as:1

g(x, y) = INT[

255B

× f (x, y)

]= INT[R] (2)

where f (x, y) is the fringe order at point (x, y), B is themaximum fringe order of the calibration table (three in thiscase), g(x, y) is the grey level value at the point (x, y) andINT [R] is the nearest integer of R.

Figure 2a shows the image representation of the total fringeorder evaluated by TFP for Specimen-1 using the calibrationtable generated from Specimen-1 itself, which is smoothand continuous. On the other hand, the total fringe orderevaluated by TFP for Specimen-2 using the calibration table

doi: 10.1111/j.1747-1567.2010.00646.x© 2010, Society for Experimental Mechanics September/October 2011 EXPERIMENTAL TECHNIQUES 59

COLOUR ADAPTATION IN TFP USING A SINGLE IMAGE

Fig. 1: Zoomed colour dark-field isochromatics (shown in black and white in the print version) for the top half ofthe central zone of four-point bend specimen (a) Specimen-1, (b) Specimen-2. Plot of RGB colour intensityvariation with fringe order for (c) Specimen-1, (d) Specimen-2

generated from Specimen-1 is seen in Fig. 2b. Owing to thecolour mismatch between the calibration and applicationspecimens, the evaluated fringe order is seen to be erroneousand discontinuous. This clearly illustrates that tint variationbetween calibration and application specimens needs to beaccounted for.

EQUIVALENT TABLE GENERATIONUSING A SINGLE IMAGEUse of a single calibration table can help to simplify the useof TFP in an industrial environment. This can be done by

suitably modifying the RGB variation of the calibration tablein such a way that it matches the application specimen. Tofully exploit the advantages of TFP, the methodology adoptedshould use the available dark-field isochromatic image itselfand require no additional images.

This method of generation of an equivalent table isdemonstrated for Specimen-2 using the calibration tableof Specimen-1. Basically, one intends to map the graph ofFig. 1c to the one shown in Fig. 1d. For this, the maximumand minimum intensity points in the image (RImageMax,GImageMax, BImageMax, RImageMin, GImageMin, BImageMin) and the

60 EXPERIMENTAL TECHNIQUES September/October 2011


Fig. 2: Image representation of thetotal fringe order evaluated (a) forSpecimen-1 using original calibrationtable, (b) for Specimen-2 using originalcalibration table, (c) for Specimen-2using colour adapted modified table.(d) RTFP applied for (c). (e) Variationof evaluated fringe order forSpecimen-2 for the central verticalline AB

calibration table (RTableMax, GTableMax, BTableMax, RTableMin,GTableMin, BTableMin) are needed. These are identified bysearching the image and table for maximum and minimumvalues for each colour. For the present case, these values aredetermined and tabulated (Table 1).

From Table 1, one is able to quantitatively appreciate thecolour variation between the two specimens. The modifiedtable for Specimen-2 is then generated by altering theRGB intensities of the calibration table generated fromSpecimen-1 as follows:

Rmi =[(

RImageMax − RImageMin

RTableMax − RTableMin

)

× (Rci − RTableMin)

]+ RImageMin

Gmi =[(

GImageMax − GImageMin

GTableMax − GTableMin

)

× (Gci − GTableMin)

]+ GImageMin (3)

Bmi =[(

BImageMax − BImageMin

BTableMax − BTableMin

)

× (Bci − BTableMin)

]+ BImageMin

Table 1—Maximum and minimum intensityvalues in the calibration table (generated fromSpecimen-1) and the dark-field isochromaticimage of Specimen-2

INTENSITY VALUES

R G B

Table Max 208 238 151

Min 40 55 41

Image Max 170 243 227

Min 32 58 64

where Rmi, Gmi, and Bmi are the RGB values in the modifiedcalibration table at ith row and Rci, Gci, and Bci are theRGB values at ith row of the original calibration table. Thefringe-order N for each row is not modified in the equivalenttable.

The modified table thereby generated for Specimen-2(Fig. 1b) from the calibration table of Specimen-1 (Fig. 1a)is used to evaluate the total fringe order for the dark-fieldisochromatic of Specimen-2, and the result is plotted as

September/October 2011 EXPERIMENTAL TECHNIQUES 61


an image in Fig. 2c. There is a good improvement in theestimation of fringe order from Fig. 2b and its variation isfairly continuous except for the presence of few streaks,showing the validity of the proposed colour adaptationscheme.

In order to remove these streaks and ensure continuousvariation of fringe order, the methodology of RTFP is used.In this, fringe-order continuity is imposed by modifying Eq. 1as:5

e =√

(Re − Rc)2 + (Ge − Gc)

2 + (Be − Bc)2

+(Np − N)2 × K2 (4)

where Np is the fringe order obtained for the neighbourhoodpixel to the point under consideration in the applicationspecimen and N is the fringe order at the current checkingpoint of the calibration table. A multiplication factor K

is used to have control on the performance of Eq. 4. Themagnitude of K is problem-dependant and needs to beselected by trial and error, interactively. As a thumb rule, K

must be selected as the minimum value, which removes allthe streaks present. For this problem, a value of 20 is foundto be suitable. The modified equation is applied only for theerroneous zone to effect refinement. This can be achievedby creating a tile or boundary around the erroneous zone.The fringe-order variation for Specimen-2 after refinement isshown in Fig. 2d. The intensity variation is found to be verysmooth, indicating good fringe-order continuity.

In order to quantitatively appreciate the improvement infringe-order estimation using the newly proposed colouradaptation scheme, the variation of fringe order with distancein Specimen-2 for a central vertical line is shown in Fig. 2e.When the original calibration table of Specimen-1 is used,the fringe-order estimate is highly erroneous. Once thecolour table is modified using the proposed colour adaptationscheme, the fringe-order estimate is linear as expected,except for two peaks, which are removed by RTFP. Thus,RTFP combined with the newly proposed colour adaptationscheme work very well for fringe-order estimation.

APPLICATION TO A BENCHMARKPROBLEMFigure 3a shows the colour dark-field isochromatic imageof a disc under diametral compression (diameter = 60 mm,load = 280 N and Fσ = 10.5 N/mm/fringe). The originalcalibration table is used to estimate the total fringe orderby TFP. The image representation of total fringe ordershown in Fig. 3b is found to be erroneous and discontinuous.Subsequently, a new modified table is generated usingthe procedure described earlier. Figure 3c shows the imagerepresentation of total fringe order evaluated using the newmodified table where the fringe-order variation is continuousexcept for the presence of a few small streaks, which areremoved using RTFP taking the multiplication factor K as30 (Fig. 3d).

The principal stress difference σ1 − σ2 can be computed fromthe total fringe-order N using the stress-optic law10

σ1 − σ2 = NFσ

h(5)

where h is the specimen thickness, and Fσ is the materialstress fringe value in N/mm/fringe. The graph in Fig. 3eshows the variation in principal stress difference for ahorizontal line at y/R = −0.44. It is seen to be highlydiscontinuous and erroneous when colour adaptation is notperformed, and improves significantly when the new colouradaptation scheme is used. The principal stress difference isalso computed analytically from the closed form solution10

for the same line and plotted in the same graph. It is seenthat the experimental values of RTFP combined with colouradaptation matches the analytical solution very closely,proving the effectiveness of the proposed method.

APPLICATION TO STRESS-FROZENSLICESThe newly developed colour adaptation technique makes useof only the single dark-field isochromatic image and doesnot require the no-load bright field image. Hence, it findsapplicability in the evaluation of total fringe order even forstress-frozen slices, and is a boon to the industry.

Figure 4a shows the dark-field isochromatic image of astress-frozen slice cut from one half of an aero-structuralcomponent with a crack. The image representation of thetotal fringe-order variation evaluated for various cases aregiven in Fig. 4b–j. Figure 4b is obtained by TFP using theoriginal calibration table which does not account for tintvariation of the stress-frozen slice, and the result is quitepoor. Figure 4c is obtained using the modified equivalenttable which accounts for the tint variation and it has streaksindicating the presence of noise.

These streaks need to be removed using RTFP to getcontinuity in fringe order. The choice of the value of themultiplication factor K in Eq. 4 needs to be done carefully.When the value of K is higher, fringe-order continuity getsmore precedence over colour matching. Thus, the magnitudeof K must be just the right value to remove all the streakspresent. If it is too high, the fringe-order continuity may getover-emphasised leading to erroneous results.

The effect of variation of K on fringe-order estimation isillustrated for this stress-frozen slice. RTFP is applied onFig. 4c for various values of K and the results are shown inFig. 4d–j. It is observed that when K is increased from 0 to 40(Fig. 4c–e), although the number of streaks get progressivelyreduced, still some streaks are present. For K = 60, thesestreaks are removed (Fig. 4f). When K is increased furtheruntil 80 (Fig. 4g), no perceptible change is seen; but beyond100 (Figs. 4h–j), fringe-order continuity gains precedenceand the fringe-order estimation becomes incorrect. Thus, avalue of K = 60 is found to be suitable for this problem.

As another application problem, a bolt-connected lap jointmodel is stress frozen and the colour dark-field isochromatic



Fig. 3: (a) Colour dark-field isochromaticimage of a disc under diametralcompression. Image representation of thetotal fringe order evaluated by (b) TFPusing the calibration table generated fromSpecimen-1. (c) TFP using the colouradapted modified table (d) RTFP appliedfor (c). (e) Comparison of experimentallyevaluated and analytical variation ofprincipal stress difference for a horizontalline (y/R = −0.44)

image of the central slice is shown in Fig. 5a. The totalfringe order evaluated using the original calibration tableof Specimen-1 seen in Fig. 5b is almost uniformly zero andcompletely erroneous because there is a considerable colourvariation between Specimen-1 and the present stress-frozenslice. When the newly proposed methodology is used togenerate a modified table for fringe-order estimation, thereis a remarkable improvement (Fig. 5c). Especially for suchcomplex problems, one must keep in mind that the intensityvalues in the background must not be allowed to affect thecolour adaptation procedure. This is easily accomplished byselecting a suitable tile encompassing a region in the imagewhere fringe-order transition from 0 to 0.5 is present. Streakspresent in Fig. 5c are then removed using RTFP with thechoice of the value of multiplication factor K as 55 (Fig. 5d).

The dark-field isochromatics of a stress-frozen slice froma fuselage square lug is shown in Fig. 6a, and it is

observed that the fringe-order variation here is only above∼0.7. The total fringe-order variation obtained using theoriginal calibration table of Specimen-1 seen in Fig. 6bis highly erroneous due to considerable tint variation. Inorder to perform colour adaptation for such a problemwhere only higher fringe orders are present, one can usethe proposed method simply by matching minimum andmaximum intensity points of two higher fringe orders, say 1and 1.5. A tile is selected which encompasses fringe orders1 and 1.5 and within this tile, maximum and minimumintensity points (RImageMax, GImageMax, BImageMax, RImageMin,GImageMin, BImageMin) are determined. The calibration tableis also searched for its maximum and minimum intensitypoints (RTableMax, GTableMax, BTableMax, RTableMin, GTableMin,BTableMin) subject to the condition that the fringe order isgreater than 0.7. Once these values are determined, theentire modified colour table is generated using the sameequations; this modified table is used to evaluate the total



Fig. 4: (a) Colour dark-field isochromatic image of a stress-frozen slice. Image representation of the total fringeorder evaluated by (b) TFP using the calibration table generated from Specimen-1. (c) TFP using the colouradapted modified table. RTFP applied for (c) with multiplication factor K taken as (d) 20, (e) 40, (f) 60, (g) 80,(h) 100, (i) 150, (j) 350

Fig. 5: (a) Colour dark-fieldisochromatic image of a centralstress-frozen slice of a lapmodel with a bolted connection.Image representation of thetotal fringe order evaluated by(b) TFP using the calibrationtable generated fromSpecimen-1. (c) TFP using thecolour adapted modified table(d) RTFP applied for (c)

fringe order and the result is plotted in Fig. 6c. The variationin total fringe order is fairly continuous except for thepresence of few streaks, which are removed using RTFP

taking K as 70 (Fig. 6d). Thus, the proposed method workswell when fringe orders 0 and 0.5 are absent. In a similarmanner, the proposed colour adaptation procedure can be



Fig. 6: (a) Colour dark-fieldisochromatic image of a stressfrozen slice of a fuselage square lugshowing tile used for colouradaptation. Image representation ofthe total fringe order evaluated by(b) TFP using the calibration tablegenerated from Specimen-1. (c)TFP using the colour adaptedmodified table (d) RTFP applied for(c)

extended to cases where fringe-order transitions from 1.5 to2 or 2 to 2.5 are present.

CONCLUSIONA new technique is proposed to tune the colour code tabledeveloped for one specimen in TFP for another specimenthat may have some colour variation. For this no extraimage is required; the colour dark-field isochromatic imageof the specimen under test alone is sufficient. Hence, theadvantage of TFP to use a single image for total fringe-orderevaluation is preserved. Thereby, the proposed method findsapplicability in analysing stress-frozen slices and can beextended for transient problems as well. The validity ofthe proposed technique is demonstrated using a 4-pointbend specimen and the benchmark problem of a disc underdiametral compression. The industrial application of theproposed method is also demonstrated for complicated stress-frozen slices of three aero-structural components.

ACKNOWLEDGMENTThe authors acknowledge Dr. S. A. Annamalai Pillaiof Vikram Sarabhai Space Center (VSSC), Trivandrumfor providing the stress-frozen slices of aero-structuralcomponents for analysis.

References

1. Ramesh, K., and Deshmukh, S.S., ‘‘Three Fringe Photoelas-ticity—Use of Colour Image Processing Hardware to AutomateOrdering of Isochromatics,’’ Strain 32:79–86 (1996).

2. Ajovalasit, A., Barone, S., and Petrucci, G., ‘‘Towards RGBPhotoelasticity: Full-field Automated Photoelasticity in WhiteLight,’’ Experimental Mechanics 35:193–200 (1995).

3. Neethi Simon, B., Prasath, R.G.R., and Ramesh, K., ‘‘Tran-sient Thermal Stress Intensity Factors of Bimaterial InterfaceCracks Using Refined Three-fringe Photoelasticity,’’ Journal ofStrain Analysis 44:427–438 (2009).

4. Ajovalasit, A., Petrucci G., and Scafidi, M., ‘‘RGB photoelas-ticity: Review and Improvements,’’ Strain 46:137–147 (2010).

5. Madhu, K.R., and Ramesh, K., ‘‘Noise Removal in Three-fringe Photoelasticity by Adaptive Colour Difference Estimation,’’Optics and Lasers in Engineering 45:175–182 (2007).

6. Quiroga, J., Botella, A., and Gomez-Pedrero, J., ‘‘ImprovedMethod for Isochromatic Demodulation by RGB Calibration,’’Applied Optics 41:3461–3468 (2002).

7. Quiroga, J., Servin, M., and Marroquin, J., ‘‘RegularizationPhase Tracking Technique for Demodulation of Isochromaticsfrom a Single-tricolor Image,’’ Measurement Science Technology13:132–140 (2002).

8. Dubey, V.N., and Grewal, G.S., ‘‘Noise Removal in ThreeFringe Photoelasticity by Median Filtering,’’ Optics and Lasers inEngineering 47:1226–1230 (2009).

9. Madhu, K.R., Prasath, R.G.R., and Ramesh, K., ‘‘ColourAdaptation in Three Fringe Photoelasticity,’’ Experimental Mechan-ics 47:271–276 (2007).

10. Ramesh, K., Digital Photoelasticity: Advanced Techniquesand Applications, Springer-Verlag, Berlin, Germany (2000). �


colour adaptation in three fringe photoelasticity using a single image

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