electronispeckle interferometry speckle interferometry

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Electronic speckle interferometry, phase-mapping, and nondestructive testing techniques applied to real-time, thermal loading Jianmin Wang and Ian Grant A digital phase-mapping method has been developed for application in real-time electronic speckle interferometry studies. Its principles and application to a continuously deforming object are described. An efficient digital image-processing algorithm has been developed that permits quantitative interpreta- tion of the resulting phase maps. 1. Introduction Electronic speckle interferometry 1ESPI2 is a very powerful, whole-field, surface-displacement measure- ment technique. The deformation of a solid surface can be directly perceived by the observation of the motion of the contour fringes produced by real-time ESPI. These correlation fringes are composed of a variation in speckle contrast, and their interpretation provides only qualitative measurements. Although the fringes can be electronically smoothed and fil- tered, the noise level remains inherently high. A qualitative interpretation of fringe patterns is not sufficient when a complete description of an object deformation is required. Laser speckle, inherent in the interferometry process of fringe formation, also produces optical noise that results in a low fringe quality. This increases the difficulty of fringe process- ing and reduces the reliability of the measurement because of the low accuracy in the detection of the fringe peak and the inability of the simple method to determine the sign of the deformation. This is an inherent limitation in ESPI correlation fringes that have a sinusoidal intensity variation. 1 Phase-shifting techniques for the improvement of the measuring accuracy of ESPI have recently been developed by several authors. The essential feature of phase-shifting interferometry 1PSI2 is that the fringe signals formed are a map that represent phase rather than intensity. An accurate knowledge of the phase shifts in the fringe phase across the whole field may be used to extract quantitative body-deformation data efficiently and with high spatial resolution and accuracy. The basic principle of PSI relies on shifting the phase of one beam 1usually the reference beam2 in the speckle interferometer with respect to the other. Each phase step yields a new speckle pattern with its own intensity distribution. The intensity, I, in the speckle interferometry is given as I 5 I o 1 I r 1 2ΠI o I r cos1f2, 112 where I o and I r are the intensities of the object and reference beams, respectively, and f is the phase of the speckle pattern. Clearly, for phase f to be determined, three independent phase patterns, at least, are required. In other words, the phase should be shifted twice by a known value. This is the concept of three-phase stepping originally developed for holographic interferometry by Hariharan et al. 2 and extended into speckle interferometry by Robin- son and Williams. 3 A four-phase step method has also been used in speckle interferometry. 4,5 The use of this variation of phase shifting achieved higher accuracy. A single-phase stepping method was re- ported by Kerr et al. 6 All of the methods mentioned here are only suitable for double-exposure speckle interferometry with static loading. This is because the speckle patterns at each phase step must be taken under identical conditions apart from the phase When this research was performed the authors were with the Fluid Loading and Instrumentation Centre, Edinburgh, EH14 4AS, United Kingdom. J. Wang is now with the School of Environmen- tal Sciences, University of East Anglia, Norwich NR4 7TJ, United Kingdom. Received 12 July 1994; revised manuscript received 6 October 1994. 0003-6935@95@193620-08$06.00@0. r 1995 Optical Society of America. 3620 APPLIED OPTICS @ Vol. 34, No. 19 @ 1 July 1995

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Page 1: ElectroniSPECKLE INTERFEROMETRY Speckle Interferometry

Electronic speckle interferometry,phase-mapping, and nondestructive testingtechniques applied to real-time, thermal loading

Jianmin Wang and Ian Grant

A digital phase-mapping method has been developed for application in real-time electronic speckleinterferometry studies. Its principles and application to a continuously deforming object are described.An efficient digital image-processing algorithm has been developed that permits quantitative interpreta-tion of the resulting phase maps.

1. Introduction

Electronic speckle interferometry 1ESPI2 is a verypowerful, whole-field, surface-displacement measure-ment technique. The deformation of a solid surfacecan be directly perceived by the observation of themotion of the contour fringes produced by real-timeESPI. These correlation fringes are composed of avariation in speckle contrast, and their interpretationprovides only qualitative measurements. Althoughthe fringes can be electronically smoothed and fil-tered, the noise level remains inherently high. Aqualitative interpretation of fringe patterns is notsufficient when a complete description of an objectdeformation is required. Laser speckle, inherent inthe interferometry process of fringe formation, alsoproduces optical noise that results in a low fringequality. This increases the difficulty of fringe process-ing and reduces the reliability of the measurementbecause of the low accuracy in the detection of thefringe peak and the inability of the simple method todetermine the sign of the deformation. This is aninherent limitation in ESPI correlation fringes thathave a sinusoidal intensity variation.1Phase-shifting techniques for the improvement of

the measuring accuracy of ESPI have recently been

When this research was performed the authors were with theFluid Loading and Instrumentation Centre, Edinburgh, EH14 4AS,United Kingdom. J. Wang is now with the School of Environmen-tal Sciences, University of East Anglia, Norwich NR4 7TJ, UnitedKingdom.Received 12 July 1994; revised manuscript received 6 October

1994.0003-6935@95@193620-08$06.00@0.

r 1995 Optical Society of America.

3620 APPLIED OPTICS @ Vol. 34, No. 19 @ 1 July 1995

developed by several authors. The essential featureof phase-shifting interferometry 1PSI2 is that thefringe signals formed are a map that represent phaserather than intensity. An accurate knowledge of thephase shifts in the fringe phase across the whole fieldmay be used to extract quantitative body-deformationdata efficiently and with high spatial resolution andaccuracy.The basic principle of PSI relies on shifting the

phase of one beam 1usually the reference beam2 in thespeckle interferometer with respect to the other.Each phase step yields a new speckle pattern with itsown intensity distribution. The intensity, I, in thespeckle interferometry is given as

I 5 Io1 Ir 1 2ŒIoIr cos1f2, 112

where I o and Ir are the intensities of the object andreference beams, respectively, and f is the phase ofthe speckle pattern. Clearly, for phase f to bedetermined, three independent phase patterns, atleast, are required. In other words, the phase shouldbe shifted twice by a known value. This is theconcept of three-phase stepping originally developedfor holographic interferometry by Hariharan et al.2and extended into speckle interferometry by Robin-son and Williams.3 A four-phase step method hasalso been used in speckle interferometry.4,5 The useof this variation of phase shifting achieved higheraccuracy. A single-phase stepping method was re-ported by Kerr et al.6 All of the methods mentionedhere are only suitable for double-exposure speckleinterferometry with static loading. This is becausethe speckle patterns at each phase step must be takenunder identical conditions apart from the phase

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change caused by phase shifting. This represents amajor obstacle in the application of PSI to manypractical situations in which the object is continu-ously deforming under load. In the present study,thermal loading was considered where the objectsurface was continuously changing. A further cat-egory of the phase-shifting technique was reported byVikhagen,7 i.e., the scanning phase-shift method thatuses a piezoelectric transducer. This variation of theprocess provided the possibility ofmeasuring deforma-tion in slowly changing objects. It was still neces-sary, however, to obtain two fringe patterns, one ofwhich was phase shifted, for each deformed state ofthe test object. This requirement and the subse-quent image processing meant that the method couldnot operate in real time.We describe a system, based on a scanning phase-

shift technique, that can be used for creating phasemaps in real-time ESPI. The principal differencebetween this method and other PSI variants is thatthis technique does not require the phase shifting tobe carried out under object conditions. In the pres-ent real-time PSI technique, each pixel on the elec-tronic image seen by the video camera is treated as anindividual interferometer; the light in the specklefield has a particular amplitude and phase relative tothe reference beam. This amplitude and phase isencoded as intensity variations that can be detectedby a TV camera. By the recording and processing ofthe values of the light intensity before and after thesurface moves, the phase of the light at each point canbe retrieved. Furthermore, an estimate of surfacedeformation can be calculated by subtraction of thephase measured before and after loading. Althougheach point will have a different intensity, which variessinusoidally according to its initial phase, the phasechange at different points will be the same as long asthe surface displacement is the same. The result ofthe subtraction of patterns obtained at different in-stants should be a continuous map of phase differ-ences representing object deformation. Wheneverthe phase difference exceeds a multiple of 2p rad adiscontinuity will occur, and the image of the objectwill be contoured by a set of sawtooth fringes thatmay be interpreted quantitatively to a high accuracy.Applied to, for example, composite materials, thisgives an image with high contract and resolution thatis well suited for defect detection.A typical optical setup used in the experiments was

as shown in Fig. 1, in which the object is illuminatedby the object beam and recorded by the CCD array ofthe video camera. The parameters of the opticalsetup were carefully chosen to match the conditionsrequired by the speckle-pattern correlation interfer-ometer8 as closely as possible. The reference beamwas combined in line with the object beam, resultingin an interference speckle pattern at the plane of theCCD array. In this case a JVC CCD camera wasused with a spatial resolution of horizontal andvertical pixels of 767 3 581, respectively. The aper-ture of object lens L3 was used to control the speckle

size to match the digital camera resolution. Anexact theoretical matching of speckle visibility andlens aperture is difficult.8 However, the optimumvalue can be readily formed in practice simply by theadjustment of the aperture size until maximumspeckle contrast is obtained.

2. Real-time Electronic Speckle InterferometryPhase-Map Formation

A. Principles

From Eq. 112 it can be seen that each individual pixelin the CCD array will have a particular intensity thatvaries sinusoidally according to the initial phase ofthe point. Equation 112may be abbreviated to

I 5 Id1 Ie cos1f2, 122

where Id 5 Io 1 Ir and Ie 5 2ŒIoIr. In principle, if theoptical system is kept stable, Id and Ie are constants.For this case, light intensity I is a function of f only.Because f is given by the scalar productK · DL, whereK is a sensitivity vector and DL is the optical path-length difference between Io and Ir, a change in DLwill result in a change of f. If one assumes that thereference beam optical path is constant and that anyvariation of DL is due to the changing optical pathlength of the object wave as the object is deformed,then, if the change of DL is great enough 1more than2p2, intensity I will lie somewhere between Imax andImin as in Fig. 2.In real-time ESPI with thermal loading, the object

shape was found to change continuously, causingvariations in the optical path length of the objectbeam. This in turn produced a continuous change inthe phase angle as defined in Eq. 112. The objectdeformation was big enough to make the phasechange greater than 2p. The recording of the varia-tion in intensity, sequentially over a series of images,during the object deformation then permitted Imaxand Imin to be obtained by computer comparison of aseries of images. From Eq. 122 and Fig. 2, therefore,

Fig. 1. Experimental setup for the application of phase-mappingESPI to a continuously deforming object: L’s, lenses; M’s, mir-rors; BS’s, beam splitters.

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one has

Imax 5 Id 1 Ie 1f 5 2pn, n 5 0, 1, 2, . . . 2, 132

Imin 5 Id 2 Ie 1f 5 12n 1 12p, n 5 0, 1, 2, . . . 2.142

Substituting Eq. 122with Eqs. 132 and 142 gives

f 5 cos2112I 2 Imax 2 IminImax 2 Imin 2 . 152

Through the use of Eq. 152 the phase of each pixel on arecorded speckle patternwas calculated, and deforma-tion of the object was deduced.It is assumed that before and after object deforma-

Fig. 2. Flow diagram that shows the algorithm for obtaining Imaxand Imin.

3622 APPLIED OPTICS @ Vol. 34, No. 19 @ 1 July 1995

tion the phase angles at a point are f1 and f2,respectively, with corresponding intensities I1 and I2.Then from Eqs. 122–152, at each pixel position thechange in phase angle, Df 1caused by the objectdeformation2, is given by

Df 5 f1 2 f2 5 cos2112I2 2 Imax 2 IminImax 2 Imin 2

2 cos2112I1 2 Imax 2 IminImax 2 Imin 2 . 162

The use of Eq. 162 to calculate the value of Dfcorresponding to each pixel on the whole imagepermitted the formation of the phase map. The mapwas then effectively a fringe image on the monitor,with the value of Df, varied with a period of 2p,represented by gray-scale levels.Once the phase map was formed, the relative

deformation, DL, at a pixel position could be obtainedquantitatively from a typical equation,8

Df 52p

l3cos1u1) 1 cos1u224DL, 172

where l is the laser light wavelength, u1 is the angle ofthe object illumination to the surface normal, and u2 isthe angle of viewing direction to the surface normal.An optical setup of the interferometric system such asthat shown in Fig. 1 permits both u1 and u2 to be zero.The accuracy of the phase calculation depended

mainly on the validity of Imax and Imin. In principle,better estimates for Imax and Imin could be obtained byan increase of the number of images in the series anda decrease of the time interval between image capture.In practice, the number of images that could berecorded in a set was limited by the memory capabil-ity of the computer 1or image-grabbing board2. It canbe seen from Eq. 122 that intensity I varied cosinusoi-dally. Thus if the angle varies linearly, for themajor-ity of the time the intensity is close to the value of Imaxand Imin, where the phase angles are equal to 2np and12n 1 12p, and the variation in the intensity is rathersmall. The true value of Imax and Imin could thereforebe obtained with high accuracy from just a fewimages. This was verified in the experiments de-scribed.

B. Algorithm for Obtaining Imax and IminThe variation in the intensity of the scattered lightproduced by speckle meant that Io and Ir varied frompixel to pixel, and in general all pixels had their ownImax and Imin values. In images containing 512 3 512pixels, it would take an unacceptably long time to findall of the Imax and Imin. The present algorithm, whichsolved this problem, was based on the real-timefeatures of the DT 2862@2861 image-processing board.The board could perform processing on 512 3 512images with 8-bit 1256 gray-level2 accuracy in realtime 11@25 s, video rate2.The two images, A and B, were stored on board in

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separate frame buffers, and a subtraction functionwas set to operate in the following ways. When thevalue of A 2B for any individual pixel was negative, azero value was stored for that pixel. The subtractionhad a nonzero result only when the pixel value of Awas greater than that of B.

A 2 B 5 5T · · · 1A s B2

0 · · · 1A # B26 , 182

where 5T 06 is the resulting image and T is a valuegreater than zero. Let those pixel values in A, whichare greater than their corresponding pixels in B, bedefined as GA, and let those pixel values in B, whichare greater than their corresponding pixels in A, bedefined as GB; then a new image, 5GA GB6, containingthe larger element from either A or B, can be obtainedby the addition

B 1 5T0 6 5 5GA

GB6 . 192

Similarly, an image 5SA SB6 containing the smallerelement of A and B can be obtained by

A 2 5T0 6 5 5SA

SB6 . 1102

Using this basis, one finds that the algorithm forsorting Imax and Imin values from a group of n imagesoperates as follows. First, assume that I1, I2,. . . Ii, . . . In are a group of speckle pattern images,and that IT, Imaxi, and Imini are the images as variables.Then its operation is as illustrated in the flow dia-gram shown in Fig. 2. Finally, the values of Imax andImin are stored in Imaxn and Iminn, respectively.

C. Determination of the Phase-Angle Sign

Because angle f in Eq. 152 was the principal param-eter in the arccos calculation, having possible valuesfrom 0 to p rad, it was necessary to determine the truevalue of the angle by the determination of its sign.A few methods to determine the sign of the phaseangle have been reported.5,7 The method used herewas based on the sign-image method.7 For example,for the sign of the phase angle of image Ii to bedetermined, an image Is, the sign image, should bestored just after image Ii has been recorded. Be-tween the recording of these images the phase of onebeam in the interferometer has to be shifted by asmall value.The sign image had to satisfy the following condi-

tions. First, between images Ii and Is the phaseangle at any one of the pixels was shifted by a smallvalue, df, which lay in the range 10, p@22. Second,the sign of df had to be the same for every pixel, sothat the sign of the quantity

Ii 2 Is 5 Ie3cos1f2 2 cos1f 2 df24

5 2Ie3sin1f 1df

2 2sin1df

2 24 1112

determined in which quadrant the phase angle, f, lay.The value of intensity Ie was always positive; there-fore

2Ie sin1df@22 s 0, 1122

Ii 2 Is ~ sin1f 1 df@22. 1132

Providing df was small enough, relation 1132 could besimplified as

Ii 2 Is ~ sin1f2. 1142

When the value of Ii 2 Is was positive, from relation1142 phase angle f should have been positive andplaced in quadrant 1 or 2. Otherwise, if Ii 2 Is wasnegative, f should have been subtracted from 2p toplace it in quadrant 3 or 4.Because a small value, df, was omitted from the

procedure of determining the sign of the phase angle,there was a calculation error in the angle when it wasclose to p or 2p. Relation 1132 shows that the range ofthis error was directly related to the value of the shiftangle. When df was located in the interval12df@2, 02, it was transferred to the first quadrantrather than the fourth quadrant as shown in Fig. 3.

Fig. 4. Timing diagram for ESPI image capture.

Fig. 3. Graphical representation of the phase-angle calculationerror.

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36

(d) (h)

Fig. 5. continued.

24 APPLIED OPTICS @ Vol. 34, No. 19 @ 1 July 1995

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(j) (l)

Fig. 5. Real-time ESPI interferograms: 1a2–1d2, main images A1–A4, respectively; 1e2–1h2, sign images A18–A48, respectively; 1i2–1l2,phase maps of main images B1–B4, respectively.

The same erroneous determination was made withinthe interval 1p 2 df@2, p2, with the difference that thephase would be transferred to the third quadrant andnot the second. Obviously the sign ambiguity onlyoccurred if intensity Ii was close to Imax and Imin.That is, the phase was close to p or 2p and relation1142 was positive. Therefore, a further calculationwas carried out for those pixels with a sign ambiguity,after sign-determination processing had been per-formed on the image by the use of relation 1142.The calculation was implemented in the following

way. First, phase angles fs of the sign-ambiguouspixels within the sign image were calculated by theuse of Eq. 152, and each fs was then compared with itscorresponding fi. When fi was close to zero, iffs 2 fi $ df 1where df is the average of the df’s of theneighboring pixels2, then fi had a positive sign; other-wise, fi was taken to be negative 1transferred toquadrant 42. If fi was close to p and fs 2 fi # df,then fi had a positive sign and was located inquadrant 2; otherwise, fiwas subtracted from 2p andtransferred to quadrant 3.

3. Experiments

The experiments used to demonstrate the methoddescribed above were performed on a 245 mm 3 185mm aluminium honeycomb sandwich having 0.3-mm

aluminium facing sheets. It was demonstrated else-where that there are eight debonded flaws inside thetest datum specimen.9,10 The specimen was ther-mally loaded from the rear by the use of a heat gun.The heat source was removed and the speckle pat-terns for nondestructive testing were recorded duringcooling.A series of speckle patterns with good fringe visibil-

ity is essential for the efficient performance of themethod. The decorrelation of the speckle patternsbetween the exposures taken before and after deforma-tion can seriously affect the visibility of the fringes.This is likely to happen when a relatively largesurface displacement or tilt occurs.9 In this experi-ment the sample was fixed, by the edges, on a rigidframe and was loaded centrally. The maximum pos-sible deformation was therefore around the center.Because the operation was carried out under real-time ESPI conditions, a good initial condition could bedetermined from observation of the visibility of thefringe pattern.Initially a series of speckle patterns was recorded in

real-time. The timing table shown in Fig. 4 docu-ments the method of acquisition of speckle patternsthat can be used for obtaining the values of Imax andImin, meeting the requirement of the algorithm de-scribed above. Each main image had to have an

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individual sign image for phase calculation. For thisreason, two images were grabbed sequentially andstored. The second image was used as the signimage of the first image. The phase angle, df, in thesign image was created by object deformation underthermal loading. The phase angle in the first signimage was produced by the transducer shifting ofmirror M2 in the reference beam path. This wasnecessary because in real-time ESPI the first imagewas taken before object deformation. For the firstsign image, phase angle df could in principle becreated by object deformation, but in practice thiscould be inconsistent because the thermal loadingcould cause the object to deform so suddenly andrapidly that the phase angle could not be containedwithin an appropriate range.There are two time parameters in Fig. 4, both of

which could be adjusted under the software control.Parameter t1 controlled the value of angle df in Eq.1112. When the rate of object deformation underloading was low, then time interval t1 between themain image and sign image could be set sufficientlylong to generate a large enough df to meet thecondition of the algorithm mentioned above. Other-wise, t1 should be shortened. The shortest accept-able value was 1@25 s, so that real-time conditionscould be maintained.The second time parameter, t2, was used to control

the time interval between the two main images. Theshorter the t2, the greater the detail of the objectdeformation. This value could not, however, be asshort as t1. Because there are only four framebuffers on the DT 2862 board, the extendedmemory ofthe computer had to be used as frame buffers tomaintain acquired images. After two successive im-ages were captured, they were transferred and storedin extended memory. Thus, time t2 was limited bythe minimum time over which the image transfercould take place. For t2 to be minimized with thecurrent hardware, an image transfer function wasdevised and encoded. Through the use of this func-

3626 APPLIED OPTICS @ Vol. 34, No. 19 @ 1 July 1995

tion, the implementation of an image transfer1256 kbytes2 required only 0.2 s.As an example a set of images are presented in Fig.

5, showing the results of the measurement on thehoneycomb structure plate with thermal loading.The figures in row A, shown in Figs. 51a2–51h2, areordinary ESPI fringe patterns. They were obtainedby absolute subtraction of the two speckle patternsacquired before and after object heating in a real-timeESPI test. The fringes from these figures graduallymoved out from the central, thermal loading point.The movement of the fringes was helpful in discover-ing the flaws, which made the fringes deform whilethey moved across the flaws. This kind of informa-tion can be used for qualitative analysis.Further quantitative analysis was carried out by

means of phase maps generated from these real-timeESPI fringe patterns. From these, the speckle pat-terns that formed images A18 to A48 3Figs. 51e2–51h24were used as the sign images for the main imagescorresponding to the speckle patterns formed inimages A1–A4 3Figs. 51a2–51d24 in the phase calcula-tion. The images in row B, shown in Figs. 51i2–51l2,are calculated phase maps corresponding to the mainimages. As expected, the phase maps give a moredetailed and accurate description of the object defor-mation compared with normal ESPI fringe patterns.In phase-map representations, the layout 1blurred2 ofthe honeycomb cells is seen within the fringes. 1It ismore visible at the center of the map, where thevariation in the gray level is less rapid. This struc-ture can easily be detected in holographic nondestruc-tive testing9 but is less evident in ESPI because of itslower resolution and sensitivity.2 The randomspeckle noise, originating in the speckle fringe pat-terns, was still contained in the phase maps. So thatthis speckle noise was reduced, these pictures wereprocessed with a fast median filter.11,12 The digitaldata from these pictures permitted the deformationto be obtained quantitatively by the use of Eq. 172.For instance, the data within the window shown as

Fig. 6. Quantitative three-dimensional representation of the detected debonded areas within the window shown in Fig. 51l2.

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Fig. 51l2 was first processed with a integration 1orunwrapping2method4 to remove multiple 2p disconti-nuities, and then the deformations were calculated bythe use of Eq. 172. The detection of a debonded arearequired only the calculation of relative displacement.In this example the bottom right corner of the windowwas chosen as reference point, where the relativedisplacement was zero. The displacement at otherpoints within the window was then calculated byreferral to this reference point. The resulting con-tour map of the window area is shown in Fig. 6. Thedebonded area can clearly be seen in this illustration1although it is less evident in the raw ESPI image2,and the abnormal deformation is evaluated as ,0.1µm.In this example only ten speckle patterns were

taken to obtain the values of Imax and Imin, includingthe pattern before loading the object. For verifica-tion of the reliability of the Imax and Imin values,another two experiments were carried out; 19 and 29images were taken, respectively. The results showedno obvious improvement. In this case ten imageswere sufficient to obtain representative values of Imaxand Imin, and the memory requirement was only 2.56Mbytes.

4. Conclusion

The method for calculation of the phase map inreal-time ESPI presented here extends the applicabil-ity of ESPI in dynamic measurement and the analysisof engineering structures. It permits quantitativemeasurements of a slowly deforming object to bemade, by the interpretation of fringe patterns ob-tained in real time. No high-accuracy piezoelectrictransducer was required to implement the presenttechnique, because the phase-shifting angle was usedonly for sign determination of the phase angle. Inother phase-calculation techniques, such as single- orthree-phase stepping interferometry, the phase anglemust be shifted by an exactly constant value.6,13 Infour-phase stepping techniques the accuracy of thephase-shifting angle was not as strict, but a piezoelec-tric transducer was still required to ensure that, ineach step, the phase was shifted by the same angle.4In addition, the accuracy of phase shifting was easilyinfluenced by the disturbance of surrounding air flow

and the environmental vibration. These disadvan-tages do not exist in the method presented here. Thepresent technique is clearly suitable for studies ofstructural deformation. Through the use of the DT2862 frame grabber, which has four on-board framebuffers, interval t2 has been decreased to 0.4 s.Through the use of DT 2861, with its ability to acquireand store 16 frames in real time by using on-boardframe buffers, time t2 could be shortened to 0.08 s.

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