Optics and Lasers in Engineering 51 (2013) 453–459

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Optics and Lasers in Engineering

0143-81

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n Corr

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borza@i1 N

journal homepage: www.elsevier.com/locate/optlaseng

High speed speckle interferometry for experimental analysis ofdynamic phenomena

Ioana Th. Nistea n,1, Dan N. Borza 1

Normandie University, INSA Rouen, LOFIMS, 13 av. de l’Universite, F-76801 Saint-Etienne du Rouvray, France

a r t i c l e i n f o

Article history:

Received 4 September 2012

Received in revised form

14 November 2012

Accepted 15 November 2012Available online 11 December 2012

Keywords:

High speed speckle interferometry

Phase stepping

Pixelwise temporal histories

Full-field measurement of non-periodical

deformations

66/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.optlaseng.2012.11.004

esponding author. Tel.: þ33 232 959 714.

ail addresses: ioana.nistea@insa-rouen.fr (I.Th

nsa-rouen.fr (D.N. Borza).

ormandie Univ, France.

a b s t r a c t

In this paper we present a high speed speckle interferometry system for the experimental analysis of

transient and dynamic phenomena. The system is based on an out-of-plane continuous wave speckle

interferometry setup and integrates a fast camera that allows acquisition rates of over 26,000 frames/s

in a reduced window (160�60 pixels). We obtain thus series of temporally sampled, full spatial data

fields of surface deformation during a given time interval. The data processing algorithms may concern

2D data fields or one-dimensional temporal histories of individual pixels.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Speckle interferometry (SI) is a non-contact, optical measurementtechnique applied in many research and industrial fields to measurethe deformations of an object under stress. The main interests of thetechnique are related to the non-intrusive nature of the measurementprocess and its high resolution and sensitivity. The standard measure-ment setup is based on a laser source, an interferometer and a camerathat records the intensity distribution of an interference field contain-ing the information on the displacements. Such measurementsystems use temporal phase stepping, usually done with the help ofa piezoelectric actuator, in order to estimate the displacement field.

The relatively low acquisition rates of the cameras and temporalphase stepping are limiting the possibilities of continuous wave SI tothe measurement of static and quasi-static deformation and sta-tionary vibration.

In order to apply SI to the full-field characterization of non-repetitive high speed deformation, the temporal sampling rate ofthe measurement system needs to be increased. Furthermore, theexposure times need to be short, so that the specimen may beconsidered still during the acquisition of each image frame.

SI systems using a pulsed laser source [1] allow obtainingalmost instantaneous phase maps in the case of fast deformationsby ‘‘freezing’’ the surface movement, but the dynamic phenomena

ll rights reserved.

. Nistea),

cannot be monitored with a sufficient temporal sampling ratebecause of the relatively low pulse repetition rates.

Other strategies are aimed at eliminating the need for tem-poral phase stepping in order to allow dynamic measurements:introduction of a spatial carrier [2,3]; multiple camera acquisition[4] or multiple images recorded simultaneously on the samedetector [5]. These approaches allow obtaining the displacementrelated phase maps at the cost of a more complicated measure-ment setup or reduced image resolution. The acquisition rate isstill limited by the performance capabilities of the camera.

Time resolved speckle interferometry (TRSI) [6,7] uses a highspeed camera with a continuous wave SI setup, which allowsobtaining increased acquisition rates and better temporal sam-pling of the deformation measurement. When used in measuringvibrations, TRSI allows obtaining directly the optical phase mapsrelated to surface displacement between any two instants of themeasurements [8], while in standard time average SI the dis-placement information, limited to the case of steady-state vibra-tions, is contained in the argument of the Bessel function of thefirst kind and zero order describing the fringe pattern.

This paper describes a TRSI system developed at the Photome-chanics Laboratory of INSA de Rouen. The system is based on acontinuous wave SI setup with out-of-plane sensitivity and uses ahigh speed CMOS camera in order to obtain increased acquisitionrates. The acquisition is made in a reduced window of 160�60pixels, which allows reaching acquisition rates of over 26,000 fps.In order to avoid phase errors due to damped oscillations accom-panying voltage steps applied to a piezoelectric transducer, thephase stepping device is an electro-optic phase modulator.

I.Th. Nistea, D.N. Borza / Optics and Lasers in Engineering 51 (2013) 453–459454

The paper presents experimental results obtained for the dynamicdeformation of a metallic blade. The displacement related opticalphase variation is calculated either over the image field, like inconventional SI, or pixelwise, by analyzing the temporal histories ofindividual pixels. Some of these results are closely related to the onespresented in [9] because they are parts of the same research work.While [9] is concentrated on post-acquisition data processing and thephase extraction algorithms, the present paper is aimed at testing andanalyzing the most important specific measurement capabilities —

transients, damped oscillations and multi-harmonic vibrations — ofthe TRSI system.

2. System description

2.1. Measurement setup and acquisition

The measurement setup is shown in Fig. 1. The main compo-nents of the measurement system are:

�

300 mW frequency-doubled Nd-YAG laser; � high speed CMOS camera, with a maximum acquisition speed

of 500 fps in full frame (1024�1280 pixels);

� electro-optic phase modulator (EOM), used as a phase stepping

device.

The beam emitted by the laser is separated by a beam splitter(BS1) into an object illumination beam and a reference beam thattravel along separate paths in the interferometer. The modulatoris placed in the reference path close to the laser, in order to avoidexpansion of the beam beyond the maximum diameter allowedby the EOM. A beam attenuator is used for adjusting the referencebeam intensity.

The wavefront scattered by the surface of the tested object isredirected onto the CMOS sensor of the camera, where it inter-feres with the reference wave. The beam splitter (BS2) is insertedbetween the camera and the camera lens, so as to obtain a zeroangle tilt between the two interfering wavefronts. This is neces-sary in order to allow the camera to resolve the interferencefringes. The relay lenses allow refocusing the object wave in theplane of the CMOS detector.

The instantaneous intensity of the interference field at anypixel (x,y) of the imaging sensor can be described by [10]:

I x,y,teð Þ ¼ I0 x,yð Þþ IM x,yð Þcos jx,y,teÞ ð1Þ

where te is the exposure time for the acquired specklegrams,I0(x,y) and IM(x,y) are the background and the modulation

Fig. 1. Time resolved speckle interferometry measurement setup.

intensities and j(x,y,te) is the optical phase difference betweenthe reference wavefront and the object wavefront.

Eq. (1) has three unknown variables. In order to find thesolution, a known variation is introduced in the optical path of thereference beam. The relative optical phase for each acquiredspecklegram will then be given by:

j x,y,tð Þ ¼DF0 x,y,teð ÞþDFRþcsp ð2Þ

where DF0 x,y,teð Þ describes the displacement field of the testsurface (our quantity of interest), DFR is the known phasevariation applied to the reference wave and csp is the randomphase component introduced by the speckle phenomenon. Due tothe fact that all of the phase extraction algorithms that were usedin this work require four phase-stepped images for the referencestate, the four-step phase shifting was applied during the entireseries of measurements, so as to be able to refresh the reference.

2.2. Data processing and phase extraction algorithms

In standard SI, when the number of temporally sampled datafields is low, a two-dimensional (2D) processing of the experi-mental data fields is usually applied. In TRSI, however, we usuallyhave to our disposal large series of specklegrams sampling themeasured dynamic deformation. There is an important volume ofexperimental data containing the information on the out-of-planedisplacement, w(x,y,t), that depends on both spatial coordinatesand time. This is well suited for the use of one-dimensional (1D)data processing, where the temporal evolution of the out-of-planedisplacement w(x0,y0,t) is followed for any selected pixel P(x0,y0)in the acquired data fields.

The choice of the approach to be used in processing thisvolume of information depends on the aspects of the dynamicdeformation to be emphasized.

In 2D data processing the displacement fields w(x,y) areobtained for the entire measured surface at different instants.This is the standard approach in classical SI and it allowsdetecting localized phenomena in the object surface (defects,local resonances, etc.). It also helps identifying the relevant pixelsin the image plane.

In 1D data processing (Fig. 2) the temporal evolution ofdisplacement w(t) is obtained pixelwise anywhere in the imageplane. The pixelwise temporal representation of surface out-of-planedeformation offers a valuable complement to two-dimensionaldata processing. It allows performing local temporal analysisof the dynamic displacement, calculating vibration parameters,frequencies, temporal propagation, etc.

Fig. 2. Illustration of 1D data processing.

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Furthermore, error propagation during phase unwrapping —

which is a common problem of 2D processing — can be avoidedby applying pixelwise unwrapping.

Following a similar reasoning, the volume of data may bepresented either as w(x,y) tables, images, surfaces, at arbitrarymeasurement instants, or as one-dimensional graphs describingw(t) for arbitrary (x0,y0) points. When it is possible, the volume ofdata can also be displayed as a multimedia-type presentation, (forinstance ‘‘avi’’ files) showing the temporal evolution of the surfacedeformation.

Several phase extraction algorithms were used in order tocalculate the displacement related phase:

�

the standard four-step algorithm (Section 2.2.1), � two-step algorithm (Section 2.2.2), � one-step algorithm based on a least squares approximation of

displacement, described in [11],

� two- and four-step least squares based algorithms, described

in [9].

2.2.1. Four-step algorithm

The standard four-bucket algorithm requires four phase stepsof p/2 applied to the reference wave, resulting into groups of fourrecorded intensities, given by:

I1 ¼ I0þ IM cos jI2 ¼ I0�IM sin jI3 ¼ I0�IM cos jI4 ¼ I0þ IM sin j

8>>>><>>>>:

ð3Þ

For the sake of clarity, the (x,y) and (x,y,te) notations areremoved from the equations.

In Eq. (3), the phase j is constant during the acquisition ofI1...I4. Small phase variations between two consecutive intensityfields may occur, due to measured dynamic deformation. For thisstudy, a phase variation of up to p/100 was considered negligible,since in this case the phase error is not greater than 5%.

The reference state, IREF_i, i¼1,2,3,4 is described by a similarset of equations. The wrapped phase variation, Dj, can beobtained by applying:

Dj¼ arctanSREF C�SCREF

CREF CþSREFS

� �ð4Þ

where C, S, CREF and SREF are the orthogonal phase componentscalculated from:

C ¼ I1�I3 ¼ 2IMcos jS¼ I4�I2 ¼ 2IMsin j

(

CREF ¼ IREF_1�IREF_3 ¼ 2IMcosjREF

SREF ¼ IREF_4�IREF_2 ¼ 2IMsinjREF

(ð5Þ

The wrapped phase distribution contains the informationrelated to the out-of-plane component of the surface deformationand needs to be processed and unwrapped in order to obtain aquantitative estimation.

The relative phase Dj can be calculated either from separategroups of four specklegrams (I1...I4, I5...I9) or with each newacquired specklegram (I1...I4, I2...I5).

2.2.2. Two-step algorithm

By implementing a two-step algorithm deformations occurringat higher speeds can be measured. The procedure requires a groupof four phase-stepped reference images, IREF_i, i¼1,2,3,4, in order

to evaluate the background intensity, I0:

I0 ¼1

4

X4

i ¼ 1

IREF_i ð6Þ

The orthogonal phase components Ck, Sk at any moment tk

during the acquisition are obtained from:

C ¼ Ik�I0 ¼ IMcosjk

S¼ Ikþ1�I0 ¼ IMsinjkþ1

(ð7Þ

where Ik and Ikþ1 are the intensity fields of two consecutivespecklegrams, recorded at instant tk¼kte, where k¼2nþ1. As forthe four-step algorithm, the difference between jk and jkþ1 isconsidered negligible if it is smaller than p/100. The phase stepbetween any two consecutive specklegrams is DFR¼p/2.

The orthogonal components of the reference phase aregiven by:

CREF ¼IREF_1�IREF_3

2 ¼ IM cosjREF

SREF ¼IREF_4�IREF_2

2 ¼ IM sinjREF

8<: ð8Þ

The wrapped optical phase variation relative to the referencestate is then obtained by applying Eq. (4).

3. Experimental results

The tests presented in this paper concern dynamic loadingtests that are well beyond the measurement capabilities of aclassical SI system.

The most important loading scenarios leading to dynamicstressing are:

�

Arbitrary waveform excitation, presented in Section 3.2; � Step voltage excitation, presented in Section 3.3; � High amplitude step voltage excitation, presented in

Section 3.4.

The experimental results will demonstrate the ability of theTRSI system to measure rapid dynamic deformations containingtransients, damped oscillations and multi-harmonic vibrations.The most important limitations are also shown.

3.1. Test specimen

The test specimen was a 3�10 mm metallic contact bladehaving a variable section, clamped on the left border. The blade ispart of a group of 3 blades belonging to a contact relay. The wholegroup of blades can be seen in Fig. 7, and the tested blade, towhich the excitation was applied (the lower position in thegroup) in Figs. 7, 9 and 10. In Fig. 7, A is a point on the lowerblade and B is a point on the upper blade.

The pointwise excitation was applied on the lower blade inFig. 7 by means of a PZT transducer driven by a frequencygenerator or, alternatively, by an analogue voltage output gener-ated by the acquisition board of the system computer.

The control and synchronization between the main compo-nents of our measurement system was performed by softwaredeveloped in our laboratory. Most of the data processing wascarried out in Matlab environment.

3.2. Arbitrary waveform loading

The object was submitted to a dynamic loading provided by anarbitrary periodic waveform shown in Fig. 3, having a maximumamplitude of 8 V and a frequency of 1 Hz.

I.Th. Nistea, D.N. Borza / Optics and Lasers in Engineering 51 (2013) 453–459456

A first group of tests was run using dynamic loading of thecontact blade provided by an arbitrary periodic waveform, withan acquisition window of 60�160 pixels (in our case, approxi-mately 5.5�13.5 mm). The framerate was set at 26,007 fps, witha sampling time of tech¼38.6 ms and an exposure time oftexp ¼ 32 ms.

The volume of acquired data was processed pixelwise and as2D data fields, by applying the 4-step and 2-step algorithmsdescribed in Sections 2.2.1 and 2.2.2. In Fig. 4 the wrapped phasehistory (Fig. 4a) as well as the unwrapped phase history (Fig. 4b)for a selected pixel on the surface of the object is presented. The

Fig. 3. Arbitrary waveform used as excitation signal and measurement period.

Fig. 4. Temporal histories for a selected point of the tested surface: (a) wrapped

phase; (b) unwrapped phase.

Fig. 5. (a) Wrapped phase map; (b) unwrapped phase map; (c) horizontal cross sectio

phase map.

wrapped and unwrapped temporal phase histories correspond tothe interval marked on Fig. 3.

By applying a 2D approach, for each instant t, a wrapped phaseinterferogram can be obtained, like the one presented in Fig. 5a.The corresponding unwrapped phase map is shown in Fig. 5b asgray-coded image and in Fig. 5d as 3D surface.

3.3. Incremental voltage step excitation

This group of tests used an excitation consisting of series offour incremental steps of voltage applied to the PZT transducer.The excitation signal is similar to the one classically applied inorder to produce the phase stepping.

Fig. 6a shows the out-of-plane displacement, expressed inradians, of a point on the surface during a full cycle of fourvoltage steps and obtained by applying a one-step phase extrac-tion algorithm presented in [9]. The graphic shows the dampedoscillations following each voltage step. For the first three steps,each of DV1,2,3¼V0, the response time is about 0.3 ms, while forthe forth variation DV4¼3V0, the response time of 1.3 ms presentssignificantly higher oscillation amplitudes.

Fig. 6b shows the wrapped phase maps corresponding to thefour steps, as obtained through 2D processing. The referencephase is obtained from four phase-stepped frames acquiredduring a stationary state of the object.

Due to the high temporal resolution of the measurements, asecondary vibration was detected taking place in a different partof the tested structure. As shown in Fig. 7, the upper contactblade, marked by a dotted line rectangle, although not having adirect mechanical contact with the PZT transducer, was also setinto vibration. Its position is oscillating between the twoextremes corresponding to the unwrapped phase maps presentedin Fig. 7a. Point B is situated on this upper contact blade.

The temporal histories presented in Fig. 7b describe the out-of-plane displacement during a voltage step for two points (markedA and B) placed on the two contact blades.

3.4. High amplitude voltage step excitation

The last group of tests investigated the response of the testobject to a dynamic loading by a high amplitude voltage step.The testing conditions were the same as described at Section 3.2.

The wrapped phase interferograms were computed from thespecklegrams acquired during deformation, by applying a sliding4-bucket algorithm (Section 2.2.1). This allows having 26,007phase measurements per second. Several of these interferograms,

ns of the wrapped and unwrapped phase maps; (d) 3D surface of the unwrapped

Fig. 6. (a) Temporal evolution of the unwrapped phase variation for one pixel; (b) wrapped phase maps for every level of the applied voltage—interferograms

A (index 500), B (index 2000), C (index 4000) and D (index 5500).

Fig. 7. (a) Unwrapped phase maps corresponding to the maximum amplitudes of vibration for the upper contact blade (the region of interest is inside the white, dotted

line rectangles); (b) temporal evolution of two points situated on the two vibrating contact blades—before and after a voltage step.

Fig. 8. Series of interferograms measured at different instants during the dynamic

deformation, with a time interval of dt¼38.45 ms between any two consecutive

phase maps.

Fig. 9. Temporal histories for two points illustrating the multi-frequency move-

ment of the contact blade.

I.Th. Nistea, D.N. Borza / Optics and Lasers in Engineering 51 (2013) 453–459 457

filtered with the windowed Fourier algorithm described in [12],are shown in Fig. 8, where the numbers represent the indexes ofthe corresponding wrapped interferograms.

For the maximum slopes of deformation, towards the free endof the contact blade, the phase variation between two consecutiveinterferograms introduces errors in the phase extraction algo-rithm and the interferograms are locally degraded. Therefore, dueto the acquisition rate limitation of the measurement system thewrapped phase for the entire measurement period cannot beobtained.

At a closer examination of the interferogram series, one maynotice that in addition to the out-of-plane deflection (the response

Fig. 10. Points A, B, C and D along the upper side of blade and temporal histories of the out-of-plane displacement at these points, spanning 4.6 ms.

I.Th. Nistea, D.N. Borza / Optics and Lasers in Engineering 51 (2013) 453–459458

to the step force applied by the PZT actuator), the contact bladewas also vibrating freely at several frequencies. The alternatinginclination of the fringes between the upper and the lower side ofthe blade (Fig. 8) and, more clearly, the temporal histories in Fig. 9show that the vibration amplitudes as well as the dominantfrequencies are different on the two sides of the blade.

The analysis of the two temporal histories spanning 38.5 ms(1000 samples), presented in Fig. 9, shows that during thedynamic deformation due to the applied voltage step the objectperforms a multi-frequency vibration. As calculated by using theFourier transform of the one-dimensional datasets, the dominat-ing frequency for points A, B and C is f1¼111.6 Hz (which is thefundamental frequency). For the point B, on the upper side, asecond frequency is also visible, f2¼1228 Hz. For points A and Cthe contribution from the second frequency f2 is not visible. Thisshows the existence of a second, torsional vibration, with a nodalline running along the lower side, where the blade is in contactwith the piezoelectric actuator, and with the highest amplitudeson the upper side.The local structural differences between(B, C—thin plate) and (A—concentrated mass) are also visible in theblade different curvatures in the two regions, Fig. 5d. The Fouriertransform of the signals shows that the out-of-plane displacementcontains several other harmonics of smaller amplitudes.

The quantitative evaluation of the unwrapped displacementfields yields a maximum surface speed of 20.8 rad/ms during thestep variation of the excitation signal corresponding to a phasevariation of about 0.8 rad between two consecutive interfero-grams. These values exceed the measurement capabilities of oursystem, as shown in Fig. 10. The temporal histories shown herecorrespond to the four points, A–D, on the upper side of thecontact blade. Other temporal histories obtained during ourstudies show that the detection sensitivity is better than 0.5 nm.These data may help in establishing the system’s measurementcapability.

4. Conclusion

In this paper we presented a time resolved SI system devel-oped at our laboratory and based on a high-speed CMOS camera.The experimental setup, the measurement principle as well as thedata processing are presented in the first part of the paper. In the

second part, several experimental results obtained by temporal SIfor the measurement of vibration and transient phenomena areshown and discussed. The tests were aimed at demonstrating theperformance of our system in dynamic regime and consist ofarbitrary and step excitation. Acceptable limits of the error due toobject-induced phase variation have been estimated in the pre-sent study at p/100 rad. The detection sensitivity of the system isbetter than 0.5 nm.

The results show that the measurements provide experimentalinformation that allows for the characterization in the case ofdifferent types of dynamic phenomena: periodic deformation pro-duced by arbitrary waveform, damped vibration, transient responseor multi-frequency vibration. This is a major point of improvementover the classical continuous wave SI systems, which are restricted toquasi-static or harmonic vibration measurement.

In case of a harmonic excitation, an important achievement ofthe measurement system is the possibility of retrieving the fullfields of relative vibration phases. If, as a future prospect, theapplied force is measured, for example with a force sensor, wecould obtain the frequency responses for most of the points onthe surface and thus, perform a modal analysis.

Acknowledgements

The authors acknowledge the creative collaboration andinspiring discussions with many specialists in related fields,mostly in the frame of the PREDIT-REBECA project, financed byADEME (French Environment and Energy Management Agency).

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