limits and possibilities of laser speckle and white-light image-correlation methods: theory and...

Limits and possibilities of laser speckle andwhite-light image-correlation methods:theory and experiments

Jean Brillaud and Fabienne Lagattu

A laser-speckle method and a white-light image-correlation method are used for strain mapping. Aschematic model of the correlation function of two speckle patterns is proposed for investigation of straininfluence on displacement-measurement accuracy. A specific software has been developed to calculateby direct correlation the displacement values between two pictures with a grainy pattern at any point onan object’s surface. Its efficiency is demonstrated in several tests. Moreover, theoretical results arechecked through experimental measurements. The limitations and performances of both optical tech-niques are discussed. © 2002 Optical Society of America

OCIS codes: 120.0120, 120.6150.

1. Introduction

The mechanical analysis and design of structuralparts made of advanced materials require knowl-edge of the material’s constitutive laws. To obtainsuch laws, various mechanical tests have to be per-formed on specimens and are associated with accu-rate measurements of material strains. Severaltechniques are applicable. Strain gages are com-monly used, but they have an obvious drawbackthat prevents them from being a pointwise tech-nique: They hide an eventual nonhomogeneousstrain distribution. Therefore, in the case of non-uniform strain fields, such optical methods as pho-toelastic analysis, moire, holography, and speckleare of great interest. Their advantages are thatthey do not stick and are whole-field analysis meth-ods. But photoelastic analysis requires a birefrin-gent material that sticks to the sample beingstudied or replaces the actual prototype.1–4 Themoire method prints gratings on the surface of thetest specimen. Spatial resolution and experimen-tal difficulties are directly linked to the grid step.5,6

The authors are with Laboratoire de Mecanique et de Physiquedes Materiaux, Ecole Nationale Superieure de Mecanique etd’Aerotechnique, BP40109, 86961 Futuroscope, France. F.Lagattu’s e-mail address is [email protected].

Received 6 March 2002; revised manuscript received 12 June2002.

0003-6935�02�316603-11$15.00�0© 2002 Optical Society of America

The holographic technique is attractive because ofits high sensitivity but extreme environmental sta-bility is needed.7 Finally, speckle methods seem tobe more appropriate for engineering use. The useof the speckle effect for displacement analysis wasfirst proposed by Burch and Tokarski.8 Then dif-ferent speckle methods were developed.9–17 And adescription of the speckle-displacement propertiesin free-space geometry and a lens system was pro-posed by Yamaguchi and co-workers.18–20

In this paper we take particular interest in laserspeckle and the white-light image-correlation tech-niques. When an optical-scattering surface is illu-minated with coherent light, e.g., a laser beam,surface irregularities produce a random interferencepattern on a microscopic scale. When viewedthrough a lens, the surface appears grainy or speck-led. In the case of the white-light image-correlationmethod the illumination source is an incoherent lightand the grainy pattern has to be created on the sam-ple surface with black and white spray paint,21 orwith the chemical vapor deposition process,22 or byilluminating the object obliquely.23 In all these op-tical methods the in-plane displacement measure-ments are based on the same principle. The grainypattern image is recorded twice, before the sample isloaded and when the sample is deformed. Then, atevery point, by correlating the subimages in thesetwo pictures, it is possible to determine the in-planedisplacement vector resulting from the difference inloading. This correlation can be obtained either op-tically or numerically. When the complete displace-

1 November 2002 � Vol. 41, No. 31 � APPLIED OPTICS 6603

ment field is obtained, it can be differentiated toobtain an in-plane strain map.

In our laboratory we first developed a laser-specklemethod. A specific mechanical device was designedto realize in situ singly exposed speckle photographs.This optical method has been applied in various con-figurations24 and has also been developed by use ofdigital recording. However, an important drawbackwith this technique remains: the abrupt speckledecorrelation in the presence of out-of-plane displace-ment, light source variation, or excessive strain-ing of the object.25 Thus, using recent progress indigital cameras, we developed a white-light image-correlation method.

The aim of this paper is to study the limits andcapabilities of laser-speckle and white-light image-correlation methods. In Section 2 a schematicmodel of the correlation function of two grainy pat-terns allows an evaluation of the limits of these tech-niques. In Section 3 experimental tests show theadvantages and drawbacks of each method. In par-ticular, a white-light image-correlation techniquewith high accuracy and high correlation speed is pre-sented, and its performance in the measurement ofstrain is experimentally demonstrated.

2. Schematic Model of the Correlation Function ofTwo Speckle Patterns

Speckle techniques have been developed for strainmapping. Strain values are obtained by calculatingthe spatial derivative of the measured displacementvectors. These vectors are determined by correlat-ing two images before and after loading the sample.To investigate the theoretical limits of the specklemethods, it is necessary to study the correlation func-tion. A schematic model is proposed here, and as-sumptions and notations are described in detail.

A. Assumptions

�i� The sample studied has a grainy pattern on itssurface.

�ii� To simplify the model, a simulation is realizedwith a unidirectional model �� axis� �Fig. 1�. Theaim is to measure the strain ε at one point betweenthe first picture �the picture in the initial state� andthe second picture �the picture after deformation�.The first picture is divided into small subwindows.A point of measurement is the center of the subwin-dow being considered. In Fig. 1, subwindow 1 is oneof the subwindows in the first picture. It will becorrelated with subwindows of the same length in thesecond picture with different shift values x. For agiven shift value x the subwindow is called subwin-dow 2.

�iii� The real finite subwindow can be consideredas an infinite window because the average grain di-ameter is far less than the subwindow length.

�iv� The illuminating spot is supposed to be uni-formly bright.

�v� The grainy pattern is supposed to be a spectralrandom structure, to allow statistical field calcula-tions.26,27

B. Notations

L, initial subwindow length.�, coordinate of a point in the subwindow.x, shift between subwindow 1 and subwindow 2.ε, local strain at one point between the initial picture

and the strained picture. In the unidirectionalmodel, ε is defined as the ratio of the length vari-ation �L to length L. Thus the strain ε can evenbe a large strain.

�, average grain diameter.C� �, correlation function.Nt, total number of grains in the subwindow.Ne, number of efficient grains in the subwindow.� � Nt�Ne, ratio of the total number of grains to the

number of efficient grains in the subwindow.l, subwindow efficient length.

Note that the initial and efficient lengths of thesubwindow can be expressed by L � �Nt and l � �Ne.

Fig. 1. Schematic representation of undeformed subwindow 1 and deformed subwindow 2 �when a unidirectional model is used�.

6604 APPLIED OPTICS � Vol. 41, No. 31 � 1 November 2002

C. Basic Concepts

When the assumptions above are used, the correla-tion function of an infinite window with itself, for ashift factor x, is shown to have the following form27:

C� x� � 1 �

sin2��x��

��x��

2 . (1)

This function is called an autocorrelation functionand is plotted in Fig. 2. We can see in Fig. 2 that theshape of the autocorrelation function of an infinitewindow consists of a high central peak with very lowpeaks on both sides of it. The maximum value of thenormalized C�x� function, equal to 2, is reached forx � 0, that is, when the window is juxtaposed withitself. The total width of the correlation peak is ap-proximately two average grain diameters. Thus theexperimental subwindow, which is supposed to con-tain a very high number of grains, is far longer thanthe correlation peak width. Therefore Eq. �1�, whichis given for an infinite window, can be applied to theautocorrelation of a subwindow obtained by the laser-speckle method with a random diffuser.

For the white-light image-correlation method theautocorrelation function is obviously different fromthat of the laser-speckle method. To obtain an exactautocorrelation function for this method, a specificstudy �mostly numerical� is necessary because it de-pends on many parameters: the type of surfacepreparation, the optical system aperture, etc. How-ever, the autocorrelation functions for the two meth-ods have similar characteristics when the grains inthe white-light method are almost circular and witha diameter value as constant as possible. In thatcase we can consider that the correlation peak shapefor the white-light method is also symmetrical andwith a diameter width of two grains.

The next step is to calculate the correlation be-tween subwindow 1 from the initial picture and sub-window 2 of the same length L from the strainedsample picture. Subwindow 2 is deformed with auniaxial strain ε. The strain value is supposed to beconstant all along the subwindow length L. It is

defined as the ratio of the length variation �L to thelength L. Each point in the subwindow has a coor-dinate �, varying between L�2 and L�2. For agiven shift value x the correlation of the two subwin-dows is the sum of elementary correlation functionsdC�x� for each elementary length d� �Fig. 1�. As-suming that the grain diameter is small comparedwith d�, the elementary correlation function, normal-ized by the subwindow length, can be deduced fromEq. �1�:

dC� x� � �1 �1L

sin2��ε � x�

� ��

��ε � x�

� �2 �d�. (2)

Using Eq. �2�, we obtain for the correlation function,normalized by the subwindow length, between theinitial and the strained subwindows

C� x� � 1 �1L �

L�2

L�2 �sin2��ε � x�

� ��

��ε � x�

� �2 �d�. (3)

When the total number of grains in the subwindow Ntare introduced into Eq. �3�, it is helpful to change thevariable � in the variable n � ��, which leads to

C� x� � 1 �1Nt �

Nt�2

Nt�2 �sin2��nε �x��

��nε �x��

2 �dn. (4)

D. Maximum Value of the Correlation Peak

The correlation function between both subwindowsreaches its maximum value when the initial subwin-dow coincides with the second subwindow, i.e., for x �0. Using Eq. �4�, we give this maximum value as

Cmax � C�0� � 1 �1Nt �

Nt�2

Nt�2 �sin2��nε�

��nε� 2 dn. (5)

Figure 3 presents the combined effect of factors εand Nt on the maximum value of the correlation peak.Note that results obtained with a small number ofgrains are not significant because the random as-sumption is then not valid. In Fig. 3 we point outthe decrease in the maximum value Cmax when thestrain ε between subwindow 1 and subwindow 2 in-creases. Moreover it shows that this decrease ismore important when the total number of grains Nt ishigher. To characterize this dependence thor-oughly, it is useful to introduce the subwindow effi-cient length l. The particular subwindow of totallength l is represented in Fig. 4. This configurationis obtained when the strain value ε leads to a dis-

Fig. 2. Autocorrelation function C�x� versus the shift x normal-ized by the average grain diameter �.


placement value on each subwindow side equal to onegrain diameter. It can be written

ε ��

l�2�

2Ne

, (6)

where Ne has been defined as the number of grains inthe efficient subwindow, i.e., Ne � l��.

Thus for a subwindow of length L only the efficientlength l can contribute to the correlation. To illus-trate this phenomenon, Fig. 5 presents for a givensubwindow area the influence of the strain value onthe efficient correlation area. Each part of Fig. 5was obtained by superposition of a grain field withitself after an isotropic dilatation. It can be seen inFig. 5 that the efficient correlation area is directlylinked with the strain value. As examples Table 1gives, for different subwindow lengths expressed interms of the total number of grains, the maximumstrain value εmax, above which only a partial length ofthe subwindow contributes to the correlation.

The results in Table 1 show that the correlationtechnique requires the use of small subwindowswhen the strain values are important. But thegrains in the subwindows must be numerous enough

to verify the random property. Thus in each case acompromise must be found by the user.

E. Shape of the Correlation Peak

It is also interesting to study the evolution of theshape of the correlation peak. Let us go back to Eq.�4� and introduce the variable v � nε. The result is

C� x� � 1 �1

2� ��

� �sin2��v �x��

��v �x��

2 �dv, (7)

where � is the ratio of the total number of grains tothe number of efficient grains in the subwindow, i.e.,� � Nt�Ne. In Eq. �7� the ratio x�� quantifies theshift value between the two subwindows, expressedin grain number. The shape of the correlation peak,that is, the evolution of C�x� versus x��, is shown inFig. 6. The curves show the different values of �.

Figure 6 shows the disastrous evolution of the cor-relation peak shape when � increases. For a verysmall � value, i.e., a small strain value, the correla-tion peak shape between subwindows 1 and 2 is veryclose to the autocorrelation peak. But when � ismore important, the correlation peak flattens. Andfor � values higher than 1.5 the peak is nothing morethan a plane. That means that the higher the �value, the more difficult is localization of the correla-tion peak maximum. In that case, corresponding tohigh strain values, the uncertainties of the displace-ment values will be important.

The schematic model of the correlation functionthat has been studied here shows the theoretical lim-its of the laser-speckle technique. In the case of thewhite-light image-correlation method, if the grainshape and length are almost constant, we can con-sider that the same general trends would be obtainedwhen the sample is deformed: the decrease in thecorrelation peak maximum, the flatness of the corre-

Fig. 3. Combined effect of strain ε and total number of grains Nt on the maximum value of the correlation peak.

Fig. 4. Schematic representation of the l length subwindow.


lation peak shape, and the influence of the efficientsubwindow length.

Therefore experimental tests must be performed toconfirm these results. In Section 3 the white-lightimage-correlation technique developed in our labora-tory is described first.

3. Experimental Setup

The white-light image-correlation method can be di-vided into three steps: specimen preparation, dataacquisition, and data analysis. For each step we de-veloped a specific technique in order to optimize thefinal experimental performances.

A. Specimen Preparation

The aim is to create a random grainy aspect on thespecimen surface. The smaller the grains, thehigher the spatial resolution is. And the grain-diameter value must be as constant as possible.Moreover, the grain field has to be fixed firmly on thesurface, whatever the specimen material is. An-other condition is that the grain field must not dis-turb the strain field of the sample. Therefore aspray technique was perfected in our laboratory. Aspecial mixture composed of a solvent containingboth a white and a black powder is prepared. Thenthis mixture is sprayed on the plane surface of thesample with an airbrush set. It leads to a white andblack random grain field with an average grain di-ameter of 30 � 5 �m. The random grainy patternobtained allows us to compare the general trends ofthe theoretical results calculated for the laser-specklemethod with the experimental results measured bythe white-light image-correlation method.

B. Data Acquisition

In this paper our goal is to apply the white-lightimage-correlation method to determining the limita-tions and the performances of this technique forstrain measurements. Thus an elementary me-chanical setup has been developed; specimens aresubjected to tensile–flexural loading. This device ispresented in Fig. 7. It is made of two jointed rods,the extremities of which are displaced by micrometerscrews. Samples of a compliant polymer, 50 mmlong and 15 mm wide, have been studied.

The object surface is illuminated with a fluorescenttube, to take digital photography of the grain field.A digital camera with a focal length of 21 mm and aCCD matrix containing 1344 pixels � 1008 pixels isused. The focus distance is finely adjusted with amicrometer translator. The optical setup �Fig. 8� in-cludes a lens with a focal length of 40 mm in order toobtain a magnification of approximately 0.5. In thisexperimental configuration, one pixel of the CCD ma-trix corresponds to an area of approximately 9 �m �9 �m on the object. Thus one grain, with an average

Fig. 5. Visualization of the correlation area depending on thestrain value: �a� ε � 5%; �b� ε � 10%.

Fig. 6. Shape of the correlation peak for different values of � �Nt�Ne.

Table 1. Maximum Strain Value �max for a Different Total Number ofGrains in the Subwindow

Total number of grains inthe subwindow Nt εmax �%�

10 2020 1030 6.6


diameter of 30 �m, is defined by approximately 3pixels � 3 pixels on the CCD matrix.

C. Data Analysis

With this experimental setup, two pictures of thespecimen surface are recorded, the first before thesample is loaded and the second when the sample isdeformed. Then the first picture is divided intosmall subwindows. The discrete matrix of the val-ues of the pixel gray level in each subwindow forms aunique fingerprint identification within the image.Therefore at every point, i.e., at every subwindowcenter, it is possible to determine the in-plane dis-placement vector resulting from the difference inloading between the two pictures. The displace-ment value can be obtained several ways: by anoptical method using an analysis of Young’sfringes,23,28–31 by a fast Fourier Transform,24,32 or bydirect correlation.9,21

In our laboratory we have developed a computerprogram, called GRANU.EXE, to correlate directly thesubwindow matrices of the two pictures and to givehorizontal and vertical displacements of the centralpoint of each subwindow. This program has beenwritten in the C programming language that al-lows a very high execution speed. Our program isable to determine displacement values for 1000points on the sample surface in 40 s by using a 200-MHz PC. Moreover our program can be usedequally well on OS Windows or Linux and is easy toupgrade by change or introduction of new subrou-

tines. This program is based on calculation of thedirect correlation of the two subwindows. The inter-correlation factor is the pixel-by-pixel multiplicationof two subwindows, normalized by the average pixelintensity. It corresponds to one value of the corre-lation function. This method avoids the problem ofpartial subwindows recovery that remains with thecalculation solution of the fast Fourier Transformand thus allows a high-displacement measurement,even in presence of a discontinuous phenomenon.

Because the pictures are digitally recorded, the re-sulting accuracy of the displacement components isalways limited by the pixel size of the sensor array.For a more accurate characterization a subpixel in-vestigation of the crest position is realized. We em-ploy as usual a biparabolic least-squares fitting nearthe correlation peak. This fitting is realized in alocal region of 5 pixels � 5 pixels or 7 pixels � 7 pixelsaround the peak crest. With this technique we ob-tain subpixel accuracy. The accuracy value is obvi-ously not characterized by the number of digits afterthe decimal point in the displacement value result.It is given by the real experimental accuracy esti-mated on measured displacement values. As dem-onstrated below, several tests have shown that thismethod leads to an accuracy of around 1�10 pixel, i.e.,1�60 of the autocorrelation peak width.

The simplified flow chart of the GRANU.EXE softwareis in Fig. 9. At first, the user must choose

• the points Gk on the picture where the displace-ment values are calculated,

• the subwindow size �from 20 pixels � 20 pixelsto 95 pixels � 95 pixels�,

• the correlation threshold value �depending onpicture contrast�.

To calculate the displacement value at the chosenpoint, Gk, a subwindow of the given size centered atGk is cut out from the first picture. Note subwindow1 in Fig. 10. Then with the software one calculatesthe correlation value of this subwindow with a sub-window of the same size, taken in the second picture,and centered at point Pi �Fig. 10�. This point, Pi, israndomly chosen in the second picture near the cor-responding point, Gk. If the calculated correlationvalue is less than the threshold value, the program

Fig. 7. Mechanical device for applying a tensile–flexural loading.

Fig. 8. Optical setup used to record digital pictures.


will go to the next randomly chosen point, Pi1. If itis higher, the program will realize systematic calcu-lations of correlation values in a region of 5 pixels �5 pixels or 7 pixels � 7 pixels around Pi. That givesthe shape of the correlation function in this region.Different numerical tests are then performed on thecorrelation peak shape to detect what would be due toan erratic point. If the software detects an erraticpoint, it will try to correlate subwindow 1 with an-other subwindow in picture 2 centered at a neighbor-ing point of Pi. If the tested point is correct, thebiparabolic fitting is performed and the displacementvalue dk of point Gk is calculated as being the vectorfrom Gk to Pi.

To determine the displacement value at Gk1, thesoftware starts its research with a subwindow in thesecond picture shifted by the previous computed dis-placement value dk. It allows a reduction in thesearching time for the new location of subwindow 1 inpicture 2. When this shift value is unknown, thesearching is also efficient but more time-consuming.

The GRANU.EXE software has been successfully usedfor several experiments with a very high executionspeed.

When the complete displacement field is obtained,the data file is automatically transferred to a finite-element code. The finite-element-method softwareis used to calculate the spatial derivative of theexperimental data in order to obtain the in-planestrain values. Each point, Gk, becomes a node of thefinite-element mesh, and the measured displacementvectors are imposed as boundary conditions. Visu-

alization facilities of the finite-element-method soft-ware are used to present strain maps.

4. Results and Discussion

Several experimental tests have been performed withthe laser-speckle method or the white-light image-correlation method. They have allowed us to deter-mine the limitations and the performances of the twotechniques. The laser-speckle method24,28 is inter-esting in terms of displacement measurement accu-racy, 0.5 �m, and spatial resolution, a point on theobject covers 128 �m � 128 �m. But this methodhas an important drawback: the speckle decorrela-tion that abruptly occurs in the presence of out-of-plane displacement, or light variation, or excessivestraining of the object, even for small displacementvalues. With this technique we were not able tomeasure strain values higher than 2%. Moreoverthis optical technique remains quite difficult andtime consuming to apply, and for an efficient numer-ical acquisition it needs specific monochromatic cam-eras. For all these reasons we now use the white-light image-correlation method, and in the followingsubsections we relate in detail the experimental re-sults.

A. Maximum Measurable Displacement Values

Several experimental tests using the white-lightimage-correlation method have been performed to de-termine the maximum measurable displacement val-

Fig. 9. Simplified flow chart of the GRANU.EXE software designedfor displacement calculations by direct correlation.

Fig. 10. Schematic representation of different steps executed bythe GRANU.EXE software.


ues. First, note that the phenomenon due to thefocusing faults occurs progressively when the out-of-plane displacement increases, without preventing cor-relation calculations, up to the total focusing loss. Itis easier to manage than the abrupt decorrelation phe-nomenon that occurs with the laser-speckle technique.

Rigid-body displacement values of 550 pixels, i.e.,around 5 mm, have been successfully measured in anundeformed field. And, when studying a deformedfield with strain values as great as 12%, we have beenable to measure displacement values of 110 pixels,�1 mm. In fact, as long as the displacement valuesare smaller than the total picture length, there is notechnical limitation to measuring it with this method.

B. Maximum Measurable Strain Values

The first batch in the experiment was devoted to thecapability evaluation of the method with reference toa subwindow dimension and a sample strain level.The tensile–flexural device was used on polymersamples. For each experiment the displacementmeasurement was realized in 25 points on the samplesurface. Each point is the center of a subwindow.The percentage of a successful correlation calculation,the maximum correlation value, and the calculationtime with GRANU.EXE software are reported in Table 2.

The results in Table 2 show that the maximumcorrelation value decreases as the strain value in-creases and as the subwindow size increases. Thisis in accordance with the theoretical results in Fig. 3.As expected, the experimental values are differentfrom the theoretical ones, calculated for the laser-speckle method, but general trends remain compara-ble. In this experimental configuration we havebeen able to measure strain values to as great as 12%.For higher strain values the percentage of successfulcalculation is so small that we consider the measure-ments unreliable. It means that for strain valueshigher than 12% the strained subwindow becomesunrecognizable. Thus, to measure strain valueshigher than 12%, it is necessary to realize an inter-mediate picture, 1�. The displacement values aremeasured between picture 1 and picture 1� and be-tween picture 1� and picture 2. Then the measure-ments are added and differentiated. Note that theinterest in the white-light image-correlation methoddeveloped here is its capacity to measure in each

point strain values as great as 12% between two con-secutive pictures. Thus it allows important hetero-geneities in the studied field, even unforeseen ones, tobe characterized.

Moreover Table 2 shows the importance of the sub-window size. For a strain value higher than 6% thelarge subwindow �95 pixels � 95 pixels� is no moreefficient. The optimum subwindow size for measur-ing the strain value at around 12% appears to be 35pixels � 35 pixels. In our experimental configura-tion, one pixel of the CCD matrix corresponds to anarea of approximately 9 �m � 9 �m on the object.Thus a 35 pixel � 35 pixel subwindow corresponds toa point area of 315 �m � 315 �m on the specimensurface. This gives the spatial resolution of thetechnique. With the magnification used here, onegrain is defined by approximately 3 pixels � 3 pixels.It means that the efficient length in this configura-tion is �10 grains. These results correspond to thetheoretical results in Table 1. It should be possibleto measure higher strain values by using smallersubwindows. But in fact experiments show that the23 pixel � 23 pixel subwindow is not able to giveresults for strain values higher than 10%. This isprobably due to the insufficient grain number in thesubwindow, which makes statistical assumptions un-true. Therefore for each experiment the choice ofthe subwindow size must be optimized.

Note in Table 2 that the calculation time can bereduced to a few seconds for 25 points of measure-ment when the subwindow size fits the experimentalproblem well. This is one of the GRANU.EXE softwarequalities. The calculation time is at a minimum foran optimum choice of parameters.

C. Accuracy and Strain Value

Another experiment batch was performed to deter-mine the accuracy of the measured displacementwhen the strain value increases. The tensile–flexural device was used again with the polymer sam-ples. For each experiment the displacement valueswere measured along the longitudinal axis of thespecimen close to the sample center. The distancebetween two points was 25 pixels. Two subwindowsizes were used measuring 40 pixels � 40 pixels and60 pixels � 60 pixels. The biparabolic fitting hasbeen interpolated either in a 5 pixel � 5 pixel region

Table 2. Experimental Results for Different Strain Values Depending on the Correlation Subwindow Size

ε �%�

23 � 23 35 � 35 47 � 47 95 � 95

%OKa Cmaxb Time �s�c %OKa Cmax

b Time �s�c %OKa Cmaxb Time �s�c %OKa Cmax

b Time �s�c

0 100 1.813 1 100 1.804 2 100 1.80 3 100 1.792 193 90 1.479 4 100 1.451 4 100 1.42 8 100 1.301 406 100 1.381 3 100 1.321 9 100 1.275 6 88 1.102 909 92 1.307 25 100 1.228 6 96 1.168 11 — — —

12 56 1.282 52 88 1.166 22 40 1.129 300 — — —15 — — — 36 1.161 117 — — — — — —

aPercentage of successful correlation calculation.bMaximum value of the correlation calculation.cCalculation time with GRANU.EXE software used on a 200-MHz PC.


around the crest or in a 7 pixel � 7 pixel region.Several strain levels have been applied to the sample.For each level a longitudinal strain value was calcu-lated as being the slope of the straight line plottedthrough the set of the measured displacement values.A linear regression has been performed with theleast-squares method to fit a line through the popu-lation of values. The standard deviation, calculatedwith the longitudinal component of the displacementvector, is expressed in pixels. It corresponds to thedispersion of the measured displacement values.Results are in Fig. 11. In Fig. 11 the method’s ac-curacy when the displacement measurement de-creases quasi-linearly when the strain value on thesample surface increases is pointed out. The stan-dard deviation varies from 2 � 102 to 2 � 101

pixels. This means that in the measurable strainrange the average accuracy of the displacement valuesis approximately 1�10 pixel, i.e., approximately 1 �m.

So, we can obtain in a few seconds the strain mapbetween two consecutive pictures with both smalland high strain values in the field studied, whichcovers an area of 12 mm � 9 mm on the specimensurface. The accuracy of the strain measurements

is better when the distance between two measure-ment points is larger. But, if it is too large, it couldhide heterogeneities in the field studied. Thus, oncemore, the user must choose a good compromise be-tween the different influential parameters of thisstrain-mapping technique.

It is interesting to compare the accuracy evolutionwith degradation of the correlation-peak shape.Figure 12 shows examples of the correlation peakexperimentally obtained for different strain values.The peak flattens when the strain value increases.This leads to difficulties in determining the locationof the peak maximum value, that is, the displacementvalue. It can explain the decrease in the accuracywhen the strain value increases. As expected, theexperimental results present the same generaltrends as the theoretical ones calculated for the laser-speckle method �Fig. 6�.

Figure 11 also shows that in this range of strainvalues results obtained with the 40 pixel � 40 pixelsubimage or 60 pixel � 60 pixel subimage are similar.Thus in that case it would be better to use the smallersubimage to reduce the calculation time.

We have also studied the influence of the size of thebiparabolic fitting region by using two fitting-regionsizes, 5 pixels � 5 pixels and 7 pixels � 7 pixels. Wecan see in Fig. 11 that the two sizes lead to a system-atic shift of several hundredths of a pixel of displace-ment accuracy. It is due to the real correlation peakwidth, which is around 2 grains � 2 grains �see Fig.6�, i.e., 6 pixels � 6 pixels in our experiment. Whenthe biparabolic fit is performed on 7 pixels � 7 pixelsthe calculation uses some pixels outside the correla-tion peak, which gives noisy signals. That is whythe accuracy is worse with this fitting-region size.These results show an important link between thegrain diameter and the calculation parameters.

5. Conclusion

We have studied the capabilities and limits of laser-speckle and white-light image-correlation methods.

Fig. 11. Standard deviation, i.e., the dispersion of displacementmeasurement versus longitudinal strain values.

Fig. 12. Examples of correlation peaks experimentally obtained for different strain values: The calculation is performed in the 7 pixel �7 pixel region around the correlation peak crest with a subwindow size of 35 pixels � 35 pixels.


The schematic theoretical model showed the straininfluence on both the maximum value and the shapeof the correlation peak. With the introduction of theefficient subwindow length notion, we have shownthe determining role of the subwindow size in strainmeasurements. These theoretical results have beenconfirmed by several experimental tests. In previ-ous research we showed that the laser-specklemethod is interesting in terms of displacement-measurement accuracy, 0.5 �m, and spatial resolu-tion; a point covers an area of 128 �m � 128 �m onthe object. But this technique presents importantdrawbacks that prevent displacement measurementfor strain values higher than 2%. Thus we devel-oped the white-light image-correlation method in ourlaboratory, as described in this paper. With thistechnique, using a standard digital camera, becauseof the very fine grainy pattern that was deposited onthe specimen surface �the diameter of each grain isaround 30 �m�, we obtained a fine spatial resolution.A point of measurement is an area of 315 �m � 315�m on the specimen surface. Moreover the softwareGRANU.EXE that used the direct-correlation calculationhas been shown to be very efficient. The software isable to quickly determine displacement values �0.04 sfor each point when a 200-MHz PC is used�, and itallows measurement of the displacement value at anypoint on the object surface, even in the presence oflarge discontinuities, with an accuracy varying from0.5 to 3 �m, depending on strain values. This studyhas also demonstrated the necessity of choosing agood compromise between the influential parametersof this optical technique: the grain diameter, thesubwindow size, the correlation threshold value, thefitting region size, and the measurable strain range.With our experimental configuration we have beenable to measure in each point strain values as greatas 12% between two consecutive pictures. To mea-sure such a strain value with the laser-specklemethod, it would be necessary to realize five inter-mediate pictures. Another advantage of the white-light image-correlation method is that the abruptdecorrelation phenomenon that occurs with the laser-speckle technique is replaced by a progressive focus-ing loss, which is easier to cope with.

This study has shown that the white-light image-correlation method developed in our laboratory al-lows one to obtain good measurement accuracy witha fine spatial resolution and a wide range of measur-able strains. With this technique it is possible tocharacterize important heterogeneities and disconti-nuities in the field studied. Thus it can be appliedfor strain mapping at a crack tip, in a necked region,or in the presence of faults or near geometric singu-larities. Work is in progress in our laboratory touse, develop, and enhance these capabilities of thewhite-light image-correlation method.

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limits and possibilities of laser speckle and white-light image-correlation methods: theory and...

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