three fringe photoelasticity - use of colour image processing hardware to automate ordering of...

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UDC: 620.171.5 Three fringe photoelasticity - use of colour image processing hardware to automate ordering of isochromatics by K. Ramesh and Sanjeev S. Deshmukh, Dept of Mechanical Engineering, Indian Institute of Technology, Kanpur, India 208016. Abstract The early application of digital image processing (DIP) technique to automate photoelastic analysis is based on black and white ( B & W ) image processing systenzs. The various methodologies reported can be traced to rely upon one or several features of u B & W DIP system. With the advancements in computer technology, nowadays colour image processing systems are available at affordable prices. A systematic study has been carried out on how to use the red green blue (RGB) value recorded using a colour image processing system for determining fringe orders up to 3 in afringefield. The study has revealed that instead of directly using RGB values corresponding to a dark field image, ifthe difference of RGB values between bright and darkfield images is used, the number of noise points is less. Experiments have been carried out for several arbitrary lines in a circular disk under diametral compression and the results are found to be good. Key words: Isochromatics,fringe ordering, photoelastic analysis, colour code, pixel, RGB colour model, colour image processing Notations B, e Least square error F, Material stress fringe value G, N Fringeorder R, B &W Black and white CCD Charge coupled device DIP Digital image processing Pixel Picture element representing a point RGB Red green blue SCA Spectral content analysis Introduction Grey scale value of the B plane Grey scale value of the G plane Grey scale value of the R plane Among the experimentaltechniques, opticalmethods have the advantageof yielding full field infermation in the form of fringes.Fringe ordering is one of the crucial steps in the process of determining quantitative information from the fringe field. The method of photoelasticity provides the information of difference in principal stresses (isochromatics) and their orientation (isoclinics) in the form of fringes. A large class of problems such as determination of stress concentration factor(SCF), stress intensity factor (SIF) and also evaluation of contact stress parameters require only the information of isochromatic fringe orders from the field. For several problems in which an evaluation has to be made between different designs, it is enough ifoneknows theisochromaticfringeorder'. Only in special cases where one is interested in determining individual components of stress tensor, one requires both isochromatic and isoclinic fringe orders. Automation of the ordering of photoelastic fringes is one of the challenging tasks even today. With the advent of digital imageprocessing (DIP), several attemptshave been made to obtain fringe orders for the entire field. The earlier investigatorshave essentially usedB & W imageprocessing systems in view of their easy availability and lower cost to devise their algorithms. The approach can be broadly classified into, (i) fringe thinning followed by fringe cl~stering~.~, (ii) intensitybased measurementtechnique in (a) spatial d ~ m a i n ~ - ~ and (b) frequency d ~ m a i n . ~ The use of fringe thinning followed by fringe clustering is applicableto both static and dynamicproblems as only one image needs to be processed. It is shown elsewhere3that among the fringe thinning techniques, intensity based algorithms are better in general and it has been established that the algorithm of Ramesh and Pramod is the best to extract the fringe skeletons. Though a class of fringe thinning algorithmsincluding that of Ramesh and Pramod uses intensity data, the intensity values are used to extract relative minimum intensity points forming the fringe skeleton. On theotherhand, inintensity basedmeasurement techniques,the intensityvalues are directly used to find out the fractional fringe order in one way or the other. One of theearliestapproachesin thisdirectionwas theintroduction of hayfringe photoelasticity by Voloshin and Burger"' in 1985. In this approach, the model material and the loading are so chosen that the maximum fringe order in the fringe field does not exceed 0.5. They digitised the image and establishedone toone correspondencebetweenthe intensity value and the fractionalfringeorder by properly calibrating the system. The restriction that maximum fringe order in the field should be only 0.5 while using half fringe photoelasticity is overcome with the introduction of phase shifting methodologies in photoelasticity6. These methods are basically restricted to static problems as one has to record up to six images for a given situation. Ramesh et a16 has brought out the elegance of the algorithm of Patterson and 'Strain', August I996 79

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UDC: 620.171.5

Three fringe photoelasticity - use of colour image processing hardware to automate ordering of isochromatics by K. Ramesh and Sanjeev S. Deshmukh, Dept of Mechanical Engineering, Indian Institute of Technology, Kanpur, India 208016.

Abstract

The early application of digital image processing (DIP) technique to automate photoelastic analysis is based on black and white ( B & W ) image processing systenzs. The various methodologies reported can be traced to rely upon one or several features of u B & W DIP system. With the advancements in computer technology, nowadays colour image processing systems are available at affordable prices. A systematic study has been carried out on how to use the red green blue (RGB) value recorded using a colour image processing system for determining fringe orders up to 3 in afringefield. The study has revealed that instead of directly using RGB values corresponding to a dark field image, ifthe difference of RGB values between bright and darkfield images is used, the number of noise points is less. Experiments have been carried out for several arbitrary lines in a circular disk under diametral compression and the results are found to be good.

Key words: Isochromatics, fringe ordering, photoelastic analysis, colour code, pixel, RGB colour model, colour image processing

Notations

B, e Least square error F, Material stress fringe value G, N Fringeorder R, B &W Black and white CCD Charge coupled device DIP Digital image processing Pixel Picture element representing a point RGB Red green blue SCA Spectral content analysis

Introduction

Grey scale value of the B plane

Grey scale value of the G plane

Grey scale value of the R plane

Among the experimental techniques, optical methods have the advantage of yielding full field infermation in the form of fringes. Fringe ordering is one of the crucial steps in the process of determining quantitative information from the fringe field. The method of photoelasticity provides the information of difference in principal stresses (isochromatics) and their orientation (isoclinics) in the form of fringes. A large class of problems such as determination of stress concentration factor(SCF), stress

intensity factor (SIF) and also evaluation of contact stress parameters require only the information of isochromatic fringe orders from the field. For several problems in which an evaluation has to be made between different designs, it is enough ifoneknows theisochromaticfringeorder'. Only in special cases where one is interested in determining individual components of stress tensor, one requires both isochromatic and isoclinic fringe orders.

Automation of the ordering of photoelastic fringes is one of the challenging tasks even today. With the advent of digital image processing (DIP), several attempts have been made to obtain fringe orders for the entire field. The earlier investigators have essentially usedB & W image processing systems in view of their easy availability and lower cost to devise their algorithms. The approach can be broadly classified into, (i) fringe thinning followed by fringe cl~stering~.~, (ii) intensity based measurement technique in (a) spatial d ~ m a i n ~ - ~ and (b) frequency d ~ m a i n . ~

The use of fringe thinning followed by fringe clustering is applicable to both static and dynamic problems as only one image needs to be processed. It is shown elsewhere3 that among the fringe thinning techniques, intensity based algorithms are better in general and it has been established that the algorithm of Ramesh and Pramod is the best to extract the fringe skeletons. Though a class of fringe thinning algorithms including that of Ramesh and Pramod uses intensity data, the intensity values are used to extract relative minimum intensity points forming the fringe skeleton. On theotherhand, inintensity basedmeasurement techniques, the intensity values are directly used to find out the fractional fringe order in one way or the other. One of theearliestapproaches in thisdirection was theintroduction of hayfringe photoelasticity by Voloshin and Burger"' in 1985. In this approach, the model material and the loading are so chosen that the maximum fringe order in the fringe field does not exceed 0.5. They digitised the image and establishedone toone correspondencebetween the intensity value and the fractional fringeorder by properly calibrating the system.

The restriction that maximum fringe order in the field should be only 0.5 while using half fringe photoelasticity is overcome with the introduction of phase shifting methodologies in photoelasticity6. These methods are basically restricted to static problems as one has to record up to six images for a given situation. Ramesh et a16 has brought out the elegance of the algorithm of Patterson and

'Strain', August I996 79

Wang'. The phase shifting technique can yield both fractional fringe order and isoclinic angle (with some restriction) at every point in the fringe field. To find the absolute fringe order at any point one needs the total fringe order for at least one point in the fringe field to be supplied by auxiliary means.

Automated evaluation of fractional fringe order for every point in the fringe field by processing one photograph has also received attention in the literature. Quan et al' have shown that by using carrier fringes and operating in the frequency domain, it is possible to evaluate the fractional fringe orders using one photograph. The approach is computationally intensive as direct and inverse Fourier transforms have to be computed. The utility of the method is restricted by the availability of high density carrier fringes.

Sanford'reintroducedtheuseofwhitelightin transmission photoelastic analysis in 1986 and proposed a method of identifying fringe orders by analysing the spectral content of the transmitted light using a spectroscope. The method is based on the premise that each fringe order has a distinct spectral signature. For each data point, the transmission spectrum as a function of wavelength is experimentally obtained. A theoretical equation has been developed for the transmission spectrum as a function of retardation. The valueofretardation in the theoretical equation is iteratively changed until the theoretical and experimental curves are close in a least squares sense. It is to be noted that the retardation at each point is determined iteratively. Further, this approach is essentially a point by point technique.

Voloshin and Redner' came up with commercial equipment based on spectral content analysis (SCA). Carazo-Alvarez et allo combined SCA and phase shifting technique to completely automate the photoelastic analysis. They used SCA to determine total fringe order at just one point in the fringe field which is used as an input to unwrap the phases in phase shifting technique. They have also conducted some studies on how precisely one has to measure the s p e c m experimentally. The white light source used, in general, emits wavelengths in the range of 450 to 750 nm. They compared the use of collecting experimental data in steps of 40 nm and also in steps of 5 nm. They established that collecting dataat 40nm intervals is reasonably accurate for problems where fringe order gradient is less than 1.4 fringe/mm. Extending this idea, Haake and Patterson1I proposed a new approach wherein the use of a spectroscope is replaced by using eight high quality optical filters in conjunction with a B & W CCD camera. This has made the method wholefield. However, unlike phase stepping, here for each pixel, the fringe order has to be determined iteratively in a least squares sense and thus is computationally intensive. The error introduced due to mismatch of quarter wave plates in SCA was studied by Ajovalasit et all2 in 1995. They have used colour image processing system for their analysis.

A colour image processing system can be configured to

capture images in RGB mode. In RGB mode, the image is identified as a superposition of the image planes of red, green and blue. Similar to a B & W image processing system, the intensity is quantifiedin the range of 0-255, but for each image plane of R,G and B. Thus, for each point on the colour image, identified as a picture element (pixel), three numbers are specified to represent the colour at that point (pixel).

Voloshin and Burgefl exploited the hardware feature of the B & W image processing system to identify 256 grey level shades between pitch black and pure white to directly find the fractional fringe order between 0 to 0.5 or any fringe field in which the difference between maximum and minimum fringe order is 0.5. This imposed severe restrictions on selection of model material and loading. Despite this, several successful applications for solving practical problems are reported in the literature. While using colour images, in principle, one can identify fringe orders up to three using a colour code.

In this paper, a systematic study is undertaken to explore the use of RGB values of acolour image to unambiguously identify fringe orders up to three. Ajovalasit et a l l z have reported to a limited extent the use of RGB values to identify fringeorders. However, they weremore concerned with the error introduced in the theoretical estimation of intensity of light transmitted due to mismatch of quarter wave plates while using white light.

System con figuration

The system consists of a colour CCD camera (TMC-76 RGB PULNiX) giving RGB output. The camera has a pixel resolution of 512 x 512 pixels and it digitises the image at video rates. The camera is connected to a PC based image processing system equipped with a colour image processing card (MVP-AT, Matrox corporation) connected to a high resolution video monitor. The system can be configured to have four 512 x 512 pixels x 8 bits monochrome frame buffers or two 512 x 512 pixels x 16 bits colour frame buffers or one 5 12 x 5 12 pixels x 24 bits colour frame buffer. The 24 bit colour frame buffer is generated by overlapping of three 8 bit monochrome frame buffers.

Determination of RGB calibration table

The basic methodology proposed here is to compare the RGB values of a point with unknown fringe order with the calibrated RGB values assigned with known fringe orders so as to determine the fringe order at a given data point. The calibration table containing RGB values associated with known fringe orders is prepared using a beam under four point bending. The beam under four point bending was chosen because the fringe order variation is linear over its depth. The calibration table is generated upto fringe order three, as beyond this, the colours merge and it is difficult to use a colour code. Figure 1 shows abeam under bending and it is clearly seen that the fringes are exactly horizontal.

80 'Strain', August 1996

It may be noted that the digitised colour image of the beam is photographed using a B & W negative. In order to account for the fringe gradient, the calibration tables corresponding to 0-1 (low fringe gradient), 0-2 (medium fringe gradient) and 0-3 (high fringe gradient) fringe orders are obtained. Initially, the load is applied such that, the farthest fringe order seen is one. Data of RGB values were collected along a vertical line starting from fringe order zero to fringe order one. In view of the linear variation of the fringe gradient, the fractional fringe order is easily calculated for each pixel, which is then used to construct the calibration table. Care was taken while preparing a calibration table, so that the table would not include a noise point with sudden change in the RGB values. This was ensured by collecting data from the central region of the beam and by taking the average of 40 pixels horizontally for each fringe order. Similarly, load was increased in steps such that the farthest fringe order seen is two and then three. Data was collected in a similar fashion for fringe order variations of 0 to 2 and 0 to 3. Tables I and I1 show the calibration tables for fringe order variation of 0 to 1 and 0 to 3 respectively.

86 1 0 4 208 209 85 106

Fig.1 Beam under four point bending (Please note that, the colour image on the video monitor is captured using a 6 B W film.)

. . . ~ ~ ~ 1.0000

The calibration tables were prepared initially for the dark field arrangement of a circular polariscope. Other combinations were also prepared so as to minimise the effect of non-uniform illumination in actual experimental situations. Two approaches were adopted. In one, the RGB values of the unloaded model were subtracted from RGB values of the loaded model. In another approach, the RGB values of dark field are subtracted from the bright field intensity values. Tables 111 and IV show the calibration tables for a bright-dark combination for fringe order variations of 0-1 and 0-3.

Evaluation of fringe order at a point in a least squares sense

By comparing RGB values of any data point with Ihe RGB values in the calibration table, fringe order at that point can be determined. Ideally, RGB values have to be unique for any fringe order. However, in view of experimental difficulties, the RGB values corresponding to a data point may not exactly coincide with the RGB values in the calibration table. For any test data point, an error term ‘e’ is defined as,

e= (R,-Rc)’ + (Gc-Gc)’ + (Be-Bc)’

RGB Table: Dark field 10-1)

R G B N

68 70 67 67 72 73 76 76 81 80 84 89 90 96 98

103 109 110 1 1 4 121 124 1 3 0 130 138 14 3 147 147 152 155 158 158 1 6 1 160 162 162 163 165 167 166 168 167 169 170 1 7 1 169 169 168 170 170 170 169 170 168 165 163 164 1 6 1 162 159 156 156 153 150 145 147 143 137 137 138 12 8 129 123 1 2 1 126 112 106 100 106

95 92 94 88 83 84 86

91 86 90 93 90 97

1 0 1 108 1 1 3 122 128 134 142 148 157 1 6 1 164 172 180 1 8 1 190 192 202 203 208 212 219 2 2 1 225 227 235 234 24 0 242 246 247 247 248 2 5 1 2 5 1 2 5 1 2 5 1 2 5 1 24 9 2 5 1 250 250 245 243 24 0 239 236 233 230 228 222 2 2 0 213 210 206 200 192 189 185 173 170 166 158 149 146 135 1 3 0 123 108 113 108 107

94 98 95 93 94

103 102 103

77 82 86 83 95 89 94 93

108 100 117 113 124 120 125 1 3 0 14 9 1 4 5 145 157 158 160 1 6 1 168 173 172 177 178 180 184 171 185 173 173 166 165 167 166 165 156 158 148 1 5 1 146 138 132 127 130 128 120 111 102

99 9 1 83 73 64 62 58 42 37 52 36 26 45 28 34 34 4 2 37 63 58 64 99 88

100 106 134 134 147 160 165 169 178 194

0 .00000 0 .01163 0 .02326 0 .03488 0 . 0 4 6 5 1 0.05814 0 .06977 0 .08140 0 .09302 0.10465 0.11628 0 . 1 2 7 9 1 0.13953 0 .15116 0 .16279 0 .17412 0 .18605 0 .19767 0 .20930 0 .22093 0.23256 0 .24419 0 .25581 0.26744 0 .27907 0.29070 0.30233 0.31395 0.32558 0 .33721 0.34884 0.3604 7 0.37209 0.38372 0 .39535 0 .40698 0.41860 0.43023 0.44186 0.45349 0 .46512 0.47674 0 .48837 0 .50000 0.51163 0 .52326 0.53488 0 . 5 4 6 5 1 0.55814 0 .56977 0 .58140 0;59302 0.60465 0 .61628 0 .62791 0.63953 0.65116 0 .66279 0.67442 0.68605 0 .69761 0 .70930 0.72093 0.73256 0 .14419 0 .75581 0 .76744 0 .77907 0 .79070 0 .80233 0 .81395 0 .82558 0 .83721 0.84884 0 .86047 0 .87209 0.88372 0.89535 0.90698 0 .91860 0 .93023 0 .94186 0 .95349 0.96512 0.97674 0.98837

Table - I

‘Strain’, August 1996 81

RGB Table: Dark Fieldlo-31

t

R c B N

69 16 1 8 82 88 93 99 111 117 125 135 I41 150 155 160 161 166 168 168 171 168 1 1 0 161 168 166 166 160 155 152 148 I51 131 132 121 I19 110 98 89 85 83 81 83 82 82 89 99 103 110 115 124 131 136 142 144 148 153 157 159 160 159 163 166 170 167 166 169 113 164 168 166 165 148 132 132 122 111 99 95 91 87 81 87 88 81 94 98 102 105 109 112 117 119 124 130 134 131 142 141 149 150 154 158 155 159 162 168 164 161 160 146 143 125 116 101 96 90 91

104 107 I15 I27 I41 155 168 117 190 201 209 221 226 233 239 244 241 249 251 250 251 246 246 239 234 224 218 209 I97 183 164 155 142 125 115 I07 106 106 106 112 124 133 147 165 177 184 198 211 221 227 234 241 246 251 252 252 251 250 249 248 241 234 227 219 212 195 182 114 156 14 3 130 129 131 119 121 125 131 340 148 151 166 171 181 202 206 213 223 229 231 242 248 251 252 251 252 251 248 241 239 234 227 218 212 201 191 113 168 156 149 149 144 151 151 I10

191 209

102

74 80 96

I08 109 I17 125 151 I53 1 6 1 168 170 178 175 112 174 169 162 150 152 139 131 I13 110 94 85 67 52 42 40 52 55 62 92 108 133 150 166 195 216 213 225 231 215 213 222 202 189 181 116 165 151 I41 121 119 111 101 97 83 71 13 63 52 55 44 62 70 80 113 133 156 161 112 206 214 121 232 219 215 1 1 8 204 198 184 162 163 160 142 143 125 118 100 95 96 92 84 83 84 1 8 82 81 86 90 91

101 107 138 131 155 165 161 119 179 119 171 151 136 111

0.00000 0.02586 0.05172 0.07759 0.10345 0.12931 0.15517 O.l810? 0.20690 0.23176 0.25862 0.2844P 0.31034 0.33621 0.36207 0.38193 0.41319 0.43966 0.46552 0.49138 0.51724 0.54310 0.56897 0.59483 0.62069 0.64655 0.67241 0.69828 0.12414 0.15000 0.11586 0.80172 0.82159 0.85345 0.81931 0.90511 0.93103 0.95690 0.98276 1.00862 1.03448 I. 06034 1.08621 1.11207 1.13793 1.16319 1.18966 1.21552 1.24138 1.26721 1.29310 1 .)I897 1.34483 1.31069 1.39655 1.42241 1.44828 1.41414 1.50000 1.52586 1.55172 1.51159 1.60345 1.62931 1.65511 1.68103 1.10690 1.13276 1.75862 1.18448 1.81034 1.83621 1.86207

1.91319 1.93966 1.96552 1.99138 2.01124 2.04310 2.06191 2.09483 1.12069 2.14655 2.11241

1.12414 2.25000

2.30172 2.32159 2.35345 2.37931 2 A0511

2.45690 2.48276 2.50862 2.53448 2.56034 2.58621 2.61207 2.63193 2.66319 2.68966 2.71552 2.74138 2.16124 2.79310 2.81897 2.84483 2.81069

2.92241 2.94828 2.91414 3 . O O O O O

i.08i93

2.19020

2.27506

a .a3103

2.09655

Table - I1

where, subscript ‘e’ refers to the experimentally measured values for the data point and ‘c’ denotes the values in the calibration table. All the three calibration tables corresponding to 0- 1,O-2, 0-3 fringe orders are searched to minimise the error ‘e’. The fringe order corresponding to the RGB values thus determined from the calibration table, is then assigned to that test point. There are instances when one of the three RGB intensity values saturates and its intensity value is equal to 255. If there are adjacent data points with an intensity value of 255, then it is likely to give an erroneous match. In such cases, it is proposed to use the difference between component values like (R - B),(G - B),(R - G) as the case may be instead of directly comparing RGB values as in equation (1). The approach was found to be viable in an actual experimental situation.

Experimental validation The problem of acircular disc under diametral compression was taken up for fringe order determination using the RGB calibration tables. The circular disc made up of the same material as the beam, was loaded to a known load. The models were made by mixing CY230 resin and hardener HY95 1 in the ratio 100:9.The F, value was determined for asodium vapoursourceof589.3nmbyan overdeterministic least squares technique. A theoretically reconstructed image with the data points echoed, is shown in Fig. 2. It is reportedLs that, while using white light, the first fringe order occurs at a retardation of 577 nm. This is accounted for while estimating the theoretical fringe orders in the present study. Initially the unloaded disk is viewed in a dark field arrangement torecord the background intensity. Then, the disk is digitised in both dark and bright field arrangements. Using these, data is generated for a dark field background and bright-dark combinations. Initially, data along the diameter of the disc is analysed to see which set of calibration tables gives good results. The RGB values for points along the diameter are compared with all the three sets of calibration tables and the fringe order is determined.

Fig2 Theoretically reconstructed fringe pattern of circular disk(dia:€Qmm; thickness:6mm) for monochromatic light (A = 589.3 nm), F, = 13.52 Wmdringe

82 ‘Strain’, August I996

RCB Table: Bright-Dark 10-11

4- R d

84 83 86 86 79 76 75 71 67 68 60 55 54 45 42 33 23 23 13 2

-5 -9

-15 -26 -32 -33 -38 -48 -47 -57 - 54 -65 -63 -71 - 74 -81 -80 -82 - 8 7 -93 -91 -91 - 91 - 94 - 92 -92 -89 - 92 -88 -90 -85 - 84 -80 -77 - 71 - 74 -67 -70 -64 -58 -54 -53 -44 -43 -35 -33 -26 -22 -19 -8 -9 0 6

-1 14 23 28 29 37 43 42 50 56 56 55 55 59

133 138 136 132 135 129 121 114 106 95 89 80 67 60 48 41 34 21 12 8

-5 - 13 -23 -31 -40 - 54 - 62 - 70 -85 -86

-106 -105 -119 -124 -130 -132 -140 -146 -147 -145 -149 -153 -153 -147 -147 -143 -140 -128 -128 -117 -113 -108 - 98 -87 - 82 -71 - 64 - 50 -40 -33 -23 -6 -2 12 23 32 42 53 63 70 86 69 99

119 117 121 126 137 137 139 143 141 132 133 132

4-0, Bl-Bd N

130 120 .~ 1.00000

86 79 69 73 61 58 63 61 50 49 35 35 25 19 13 7

-13 -11 -20 - 34 -36 -46 -60 -62 -73 -64 -81 -78 -67 - 91 -63 -82 -67 -65 -61 -68 -58 -4 9 -43 -45 -36 -6 0 0

17 26 40 32 56 56 75 95 95 97

119 132 137 141 134 161 162 14 1 167 164 153 163 154 153 148 150 119 130 121 71 83 68 55 31 19 7

-16 -25 -32 -47 -70 -91 -90

0.00000 0.01163 0.02326 0.03488 0.04651 0.05814 0.06977 0.08140 0.09302 0.10465 0.11628 0.12791 0.13953 0.15116 0.16279 0.17442 0.18605 0.19767 0.20930 0.22093 0.23256 0.24419 0.25581 0.26744 0.27907 0.29070 0.30233 0.31395 0.32558 0.33721 0.34884 0.36047 0.37209 0.38372 0.39535 0.40698 0.41860 0.43023 0.44186 0.45349 0.46512 0.47674 0.48837 0.50000 0.51163 0.52326 0.53488 0.54651 0.55814 0.56977 0.58140 0.59302 0.60465 0.61628 0.62791 0.63953 0.65116 0.66279 0.67442 0.68605 0.69167 0.70930 0.72093 0.73256 0.7441 9 0.75581 0.16744 0.71907 0.79070 0.80233 0.81395 0.82558 0.83721 0. 84884 0.86047 0. 81209 0.88372 0.89535 0.90698 0.91860 0.93023 0.94186 0.95349 0.96512 0.97674 0.98837

RGB Tab1e:Bright-Dark[O-31

118 114 106 91 74 56 36 20 1

~ 18 -41 -65 -711 - 97 -109 -130 -140 - 146 -152 -149 - 143 -134 -124 -111 - 92 -67 -53 -33 -11 12 17 55 74 96 109 120 124 125 124 116 102 91 70 44 30 11 -13 -19 -56 -77 - 94 -116 -123 -114 -141 -138 -131 -132 -130 -126 - 107 -92 -76 -57 -38 -11 10 27 55 74 87 95 97 113 109 106 101 89 80 61 49 34 16 -6 -22 - 3 5 -54 -61 - 84 -99 -110 -117 -116 - 115 -119 -117 -105 -101

- 1 5 -78 -64 -47 - 35 - 10

0 26 3I 52 69

76 7c 64 45 27

- 1 9

.ra

97 84 62 43 37 18 3

- 3 5 -41 -66 -70 -75 - 82 -79 -87 -75 -60 -45 -28 - 15 5 20 56 80 102 104 130 141 152 149 138 124 109 76 53 20 -5 -37 -70 -103 -105 -133 -144 -137 -145 -159 -132 -115 -101 -81 -55 -21 0 34 64 72 96 115 137 157 156 164 172 161 156 129 114 91 42

-4 -16 -46 -97 -101 -119 -117 -124 -132 -127 -113 -111 -92 -61 -55 -50 -28 -11 17 39 76 91 89 100 124 129 122 129 116 121 111 91 88 71 55 11 4 - 8 -37 - 4 0 -56 - 5 8 - 5 8 -59 - 14 - 1 5 14

Table - IV

1. 00000 1.02586 1.05172 1.07759 1.10145 1.12911 1.15517 ).18103 1.20690 1.23276 1 . 25862 I . 20448 I . 31014 I . 33621 1.36207 1. 38793 1.41379 1.43966 1.46552 1.49138 I . 51724 I . 54310 1. 56897 1. 59483 I .62069 I . 64655 1.67241 I . 69828 1.72414 I . 75000 1.77586 I . 80172 1.82759 I .85145 I . 117931 I . 90517 3.91103 3,95690 1.98276 1.00862 1 .OM48 1.06014 1.08621 1.11207 1.11791 1.163'19 I . 10966 1.21552 1.24138 1.26724 1.29310 1.31897 1.34483 1.37069 1.39655 1.42241 1.44818 1.47414 1.50000 1.52586 1.55172 1.57759 1.60345 1.62931 1.65517 1.61103

1.70690 1.73276 1.75162 1.78448 1,81034 1.83621 1.86207 1.88793 1.91379 1.93966 1.96552 1.99118 2.01724 2.04310 2.06897 2.09483 2.12069 2.14655

2.19818

2.15000 2.27586 2.10172 2.32759 2.15345 2.37911 2.40517 2.43101 2.45690 2.48276 1.50862 2.5144a 2.56014 2.58621 2.61207 2.61791 2.66379 2.68966 2.71552 2.74138 2.76714 2.79310 1.84481 2.87069 2.89655 2.92241 2 94828 2.97414 1.00000

a . 17241 2.21414

a . 81897

83

Figure 3(a) shows the comparison of the fringe orders obtained using the dark field calibration table with theory, Fig.3(b) shows the comparison using the loaded - unloaded table and Fig.3(c) shows the comparison using (bright - dark) table.

In Fig.3, no smoothing is done whilst plotting the curves. It is seen that there exists a number of noise points and these are least when a (bright - dark) combination is used, maximum when RGB values are directly used and are midway when the loaded-unloaded table is used.

In Figs 3(b) and 3(c), non-uniform illumination is accounted. However, theadvantageis seenonlyinFig.3(~). The models are made of epoxies which undergo considerable deformation after load is applied. Hence, there may be a mismatch between the corresponding pixels of the loaded image and unloaded image. However, suchaproblemdoesnot existinFig.3(c).Further,referring toFigs (4-6), whileusing (bright-dark)combination (Fig.6), the variation of intensity as a function of fringe order does not have local oscillations.

Plxals

Pixels

- Using Bri ht Dark Tab: -

Fig3 Fringe order determination using RGB intensity values without noim removal by various calibration tables. a) dark field table, b) loaded-unloaded table, c) (bright-

dark) table

84

Fringe Order

Fig.4 Intensity 01 RGB planes as a lunction of lringe order for bright field

O L , I , , , I , , , , , , I I , , , , 1 1 1 , , I ,

0.60 0.Jo 1.b 1.h 2.h 2.30 3.60 3.h Fringe Order

Fig.5 Intensity 01 RGB planes as n lunction 01 lringe order lor darklield

Fringe Order

Fig.6 Intensity d RGB planes as a luncllon of lringe order lor (bright - dark) field

'Stnrin I, August 1996

FIg.7 intensity of (R-G).G.B planes BS a functim of fringe order for (brlghtdark) field

_ _ _ _ Theory. J - Experimental

along line 1

C 'E LA

_ _ _ _ Theory.

- Experimental along line 1

Pixels

Fig.8 The fringe order determined experimentally along the horizontal diameter (line 1)of the disc using (R-G),G,E combination of (bright-dark) table (a) wRh

noise points (b) after noise removal

Existence of noise points can be attributed to the fact that, the least squares error may be a minimum at some other point due to sinusoidal variation of RGB values. It was felt that if substantial variation in intensity values could be obtained as a function of fringe order, it could to some extent alleviate this problem. Several combinations were tried and it was found that within the (bright-dark) table, instead of using RGB, if (R-G), G and B values were considered, the results were much better. Figure 7 shows the intensity variation as a function of fringe order for R- G,G and B . The fringe order variation along the diameter is obtained using this table and the results are shown in Fig &a). Comparing to Fig. 3, the nolse in Fig .8 is the least. However, the results have to be further improved by eliminating noise points.

_ _ _ _ Theory.

- Along Une 2. .A

_ _ _ _ Theory.

- Along Line 3.

st,:,, I I I , 1

d \E35 I \

Pixels

F1g.Q Experimental fringe order for two dlfferent horizontal lines along the disk (dia: €4 mm; thickness: 6 wn) (a) fory = 13.5mm (b) fory = 17Amm

It caii be seen that, in all the cases the noise points are distinct. These ;re easily ideiitified by using a toler'mce value aund it is found out hat in the present study a value of 0.25 W;LS found to be sufficient. IJse ofa direction tlag to keep track of the fringe gradient direction along with the use of at tolerance value has helped in devising a simple 'md efficient noiseremovitl aIlgorilhin. Theresultsaw shown in

efficient noise removal algorithm. The results are shown in Fig. 8(b). Using this procedure, the results for two lines with y = 13.5 mm and y = 17.4 mm respectively were calculated and are shown in Figs 9(a) and (b).

The noise points seen at the beginning and end of the curves along the three different lines are only because the noise removal algorithm is not applied for the first and the last 15 pixels. Hence, noise points occurring in this region areskipped. Theremainingpartofthecurves show excellent matching with the theoretical curves.

Conclusions

A systematic study has been carried out on how to use the RGB value recorded using a colour image processing system for determining fringe orders up to 3 in a fringe field. The study has revealed that instead of directly using RGB values corresponding to a dark field image, if the difference of RGB values between bright and dark field image is used, the number of noise points is less. This is because the approach accounts for the non-uniform illumination. The noise points are further reduced if in a (bright - dark) combination, (R-G),G and B are used in equation (1) rather than simply RGB . The method proposed is very simple and easy to implement. Unlike SCA, the computational demand is almost negligible and hence, is easily adaptable for devising automatic polariscopes.

Further, the use of a CCD camera to capture images makes it a whole field technique. The method can be used in conjunction with phase shifting techniques, if in the fringe field several fringes occur beyond third fringe order. The method can be directly applied for analysing slices from 3D models and also can be used with success while analysing fringe patterns from the photoelastic coating technique. Using this method, theleast fringe order variation that can be detected is 0.012 fringe order in 0-1 range, 0.017 in 1-2 range and 0.026 in 2-3 range. The accuracy

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can be further improved by using deep beams coupled with high optical magnification while preparing the calibration tables.

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Acknowledgements 12.Ajovalasit,A.,Barone, S. andPetrucci,G., “Automated This resew& was sponsored in part (Project No.786) by the Aeronautics Research and Development Board of the Government of India and the Department of Mechanical Engineering IIT Kanpur. The authors thank Prof. B. Dattaguru, Prof. K. Rajaiah and Prof. N.K. Gupta for their interest in this work.

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