dynamic holographic interferometry: devices and applications

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SVNY276-Gunter-v3 September 26, 2006 17:14

8

Dynamic HolographicInterferometry: Devices andApplications

Philippe Lemaire and Marc Georges

Centre Spatial de Liege, Avenue du Pre Aily, 4031 Angleur, [email protected]

This chapter is a review of photorefractive crystals used in holographic interfer-ometry, starting from the basics and early experiments up to devices achievement.

We first recall the basics of holographic interferometry and describe the mostimportant pioneering experiments that showed the tremendous potentialities ofphotorefractive crystals as dynamic recording media for this technique. We thenpresent the main requirements for the development of a holographic interferom-eter and we analyze the figures of merit and the properties of different photore-fractive crystals for that purpose. We emphasize the implementation of the phase-quantification techniques because they give access to displacement metrology.

The next sections are devoted to the presentation of metrological devicesbased on dynamic holographic interferometry with sillenite crystals. The firstsystem is a holographic camera with a continuous laser adapted to the study ofdisplacement of scattering objects. We present its main development steps andshow that it is highly versatile and can be used in the observation of different typesof phenomena. The second range of devices allows the observation of transparentobjects: one is especially studied for use in microgravity fluid experiments and thesecond is an adaptation of the first system for scattering objects to the observa-tion of transparent objects. The third system uses pulsed lasers with applicationsfocused on the study of structure vibrations.

8.1 Introduction: Historical Background

In order to have a clear understanding of the different works and approachesof holographic interferometry (HI) with photorefractive crystals (PRCs) carriedout by several groups, we will start this section by briefly recalling the differentholographic methods.

HI [1–3] is a technique working under coherent light that allows one to pro-duce the interference of two wavefronts (or more), at least one of which being

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224 Philippe Lemaire and Marc Georges

holographically stored. The interference pattern called an interferogram showsthe optical path difference (OPD) between the wavefronts as intensity variations(fringe patterns). In most cases, the OPDs come from the same object at two differ-ent instants. In the case of the opaque scattering objects, the variations arise fromthe displacement or deformation of the surface, while in the case of transparentobjects, they come from thickness or refractive-index variations.

Three main methods of HI exist. In real-time HI (RT-HI) only one hologram isrecorded. At the readout step, the object is still illuminated and one observes theinterferogram resulting from the superimposition of the wavefronts diffracted bythe hologram and the one coming directly from the object (transmitted throughthe hologram). Each object variation is then observed directly (live fringes). Thedouble-exposure HI (2E-HI) requires the recording of two holograms of the objectat different states. A further readout step (without the object beam) shows thesuperimposition of both stored wavefronts (frozen fringes). For both methods, theinterferogram is written at each point (x, y) of an observation plane as

I (x, y) = Iaverage(x, y), [1 + m(x, y) cos(φ(x, y))], (8.1)

with Iaverage(x, y) the average intensity and m(x, y) the contrast. The quantityφ(x, y) is the phase difference between the transmitted and the diffracted wave-fronts, and that has to be determined in order to calculate the OPDs.

A third technique can be applied to the case of vibrating objects: the time-average HI (TA-HI). The hologram is recorded during the modal vibration of theobject and over a time longer than the vibration period. Here the phase differenceis time dependent and written as φ(x, y, t) = φ0(x, y) sin(�t), where φ0 is theamplitude and � the pulsation of the vibration. The intensity pattern is givenby I (x, y) ∝ J 2

0 (φ0(x, y)), where J0 is the zero-order Bessel function whosemaximum is found at the vibration node and whose fringe modulation decreaseswhen φ0 increases.

A crucial element of HI is the photosensitive medium used for the hologramrecording. In earlier developments of this technique, one generally considersthat its principal figures of merit are the energetic sensitivity and the diffractionefficiency. However, with the further evolution of the necessary peripherals (suchas lasers, CCD cameras, computers, and frame grabbers), other features such asthe self-processing and the erasability/reusability of the medium will appear moreimportant in its practical applicability to HI.

Therefore, due to their self-developing in situ and indefinitely reusable proper-ties, the PRCs have been progressively considered interesting alternatives to otherrecording materials. Moreover, a large number of crystal families and species ex-ist, different charge transport mechanisms can be envisaged (diffusion, drift underexternal field, photovoltaic effect), different beam arrangements can be used (two-wave mixing, four-wave-mixing), different diffraction properties exist (diffractionanisotropy or energy transfer with diffraction isotropy), etc. As a consequence,even if the choice of a particular crystal and its working conditions is not a simplematter, it gives unique and smart optical schemes that cannot be envisaged withother recording media. In the following we will review different experiments asenvisaged by pioneer groups in the field as well as more recent studies. These

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8. Dynamic Holographic Interferometry: Devices and Applications 225

works show us the tremendous potentialities of PRCs for application to HI.They allowed us to select some particular combinations that we found the mostsuitable for the development of advanced tools for industrial and metrologicalapplications.

The first laboratory experiments of HI with PRCs were carried out by Huignardand Herriau [4] and employed a two-wave scheme whereby a BSO crystal wasused with an Argon laser at 488 nm and under an external electric field. Theyshowed the application of 2E-HI to transparent objects. They pointed out thatthe recording of the second hologram partially destroys the first one and then therecording time of the second has to be smaller than that of the first.

On the basis of the same crystal under an external field, the authors proposedthe use of the four-wave-mixing technique [5], yielding a permanent diffractedimage. The technique is applied to the study of vibrating objects under the TA-HI. The objects considered are transparent or reflecting membranes. The objectis continuously monitored during a scan of the sinusoidal excitation frequency.When resonant frequency is reached, mode shapes appear, while they disappearat nonresonant frequencies. Despite the alignment difficulties related to the four-wave-mixing arrangement, the authors note the extreme ease with which modeshapes are visualized. Later they proposed to use the same configuration to studya scattering object [6].

The same group proposed for the first time the use of the coupling effect appliedto a BSO crystal [7] when the grating wave vector is aligned along the crystalaxis 〈001〉. The goal is again the study of vibrating objects with the TA-HI. Theinterferogram contrast being too weak to be exploited, the authors introduce thetechnique of the mobile grating in order to reinforce the grating recorded.

In 1985, Kamshilin and Petrov [8] showed for the first time the application ofdiffraction anisotropy in HI. The principle is simple: only two waves are incidenton the crystal and simultaneously participate in the recording and the readout ofthe hologram, ensuring the automatic matching of the Bragg condition. Moreover,when the crystal is used under the diffusion regime and the grating wave vectororiented along the axis 〈110〉, they show that for a suitable orientation of the inputpolarization, the diffracted beam has a linear polarization perpendicular to thatof the transmitted beam. This allows one to filter out the diffracted beam fromthe other by placing an analyzer after the crystal. These authors show convincingresults of a vibrating object observed with the TA-HI method with a BSO crystal at514 nm. Later they used the same configuration with a BTO crystal at 633 nm [9].

Still in 1985, the group of Huignard [10] used benefits of polarization propertiesto improve interferograms, but instead of considering the energy transfer as in [7],the crystal was cut in order to exhibit diffraction anisotropy. They again appliedthe mobile grating technique to reinforce the space-charge field. They obtainedvery good results with a vibrating plate in TA-HI.

In 1991, Troth and Dainty [11] considered the diffraction anisotropy configu-ration and obtained excellent double-exposure and time-averaged interferogramswith a BSO crystal at 514 nm. They proposed a deep analysis of the signal-to-noise ratio (SNR) as a function of the ratio R between the beam intensities andfound that there is an optimum value of R. These works were the first attempt

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to optimize a holographic interferometer. They were followed by a photometricanalysis of the noise characteristics [12]. This approach allowed them to estimatethe size of observable objects on the basis of the SNR and the noise characteris-tics measured as a function of the fringe spacing. They showed that typically, onesquare-meter objects can be tested with 1-watt laser power. Another optimizationstudy was carried out by Miridonov et al. [13] and was similar to that of Trothand Dainty, although more theoretical. They used a BTO crystal at 633 nm andreached high SNR.

These pioneering experiments have paved the way for most of the recent studiestargeted at the development of metrological devices. They have all been importantfor an understanding of different principles that may be applied in more advancedsystems.

Our developments are based on a tradeoff that we made on the basis of theabove existing techniques with the aim of obtaining a device that satisfies somerequirements that are mandatory if one wishes to use such an instrument in a widevariety of industrial applications. For that purpose, the next section will reviewthe requirements of such instruments.

8.2 Requirements for Applicability of HI

8.2.1 The Ideal Holographic Measurement Device

Even if HI has been demonstrated as an interesting technique that can be ap-plied in full-field displacement metrology, in mode shape visualization or innondestructive testing, it has often failed to be accepted by industrial end users.The principal reason was that most of the experiments remained at the labo-ratory level, requiring large cumbersome lasers and specialists to interpret theinterferogram. Moreover, the holographic recording media generally necessitatecomplicated chemical processing (in the case of holoplates) or additional elec-trical charging and heating/cooling devices (in the case of photothermoplastics).These processes are time-consuming, and the hologram is not usable before sometens of seconds if not minutes.

A good example of how an industrial holographic interferometer must work interms of user friendliness is the Electronic Speckle Pattern Interferometer (ESPI)[2, 3]. These are attractive because the holographic recording is directly performedby the CCD camera. Despite the low resolution of the CCD cameras and the OPD’sresult, which shows an important speckle noise (requiring numerical filtering withthe risk of information loss), this technique is now well commercially established.

The above remarks helped us to understand what the potential user of a full-fieldtruly holographic measurement tool wishes:

(1) A compact system. Indeed, some measurement cases need a small lightweightdevice that can be placed in any position with respect to the object under test.

(2) A “cheap” system. This condition is mainly influenced by the laser source butalso by the quantity of consumables. The latter is generally important with

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holoplates and photothermoplastics. This also means that the measurementhead has to incorporate the least complicated and expensive componentspossible.

(3) A versatile system. Since such a device is an investment for the potential user,it may be useful if it can be adapted or adaptable to different applications.

(4) A simple “user-friendly” system. The measurement procedure has to be assimple as possible in order to not require an optics specialist for handling ameasurement. This means no adjustment, or at least the fewest possible.

(5) The largest observable area. This will have a positive impact in the durationof the inspection of a large object if different successive inspections have tobe operated to cover the entire area.

(6) Quantified data. This is probably one of the most important factors. The aim isto obtain the object displacement measurement from the interferogram. Dueto its importance, we will review some of the possible techniques in the nextsubsection.

8.2.2 Phase Quantification and Associated Techniques

The pioneering experiments presented in Section 8.1 did not consider the ap-plication of phase-quantification techniques. Such techniques aim to computeautomatically the value of φ(x, y) in expression (8.1), which in turn is used tocalculate the displacement of solid objects or refractive index variations in trans-parent objects. Most automated phase-quantification techniques are based onheterodyning, i.e., on the inclusion of an additional phase term in the argumentof the cosine of expression (8.1). Heterodyning can be envisaged temporally orspatially. We briefly present two ranges of methods that are frequently appliedand that have been considered in our developments.

First, the phase-shifting or phase-stepping (PS) [3,14], which consists in ac-quiring several interferograms with known phase steps introduced between theacquisitions (here we omit the (x, y) dependence of the variables) :

Ik = Iaverage[1 + m cos(φ + βk)], (8.2)

with k = 1, . . . , N (N an integer and greater than or equal to 3) and the phasestep βk . The computation of the phase φ is carried out following one or anotheralgorithm depending on the number N and the value of the additional constantphase βk at each step [3]. Generally, the latter is a fraction of 2π (calibrated phasesteps), but we can also use the algorithm of Carre (N = 4), which does not requirecalibrated steps, provided they are equal between consecutive interferograms.Equation (8.3) gives an example of phase computation when four images, phase-shifted by π/2, are captured:

φ = arctan

(I4 − I2

I1 − I3

). (8.3)

One distinguishes the temporal and the spatial PS. In the temporal version, theinterferograms (8.2) are acquired successively, with the phase shifts introduced

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between the acquisitions, by shifting the phase of one of the beams (generally thereference beam). In the spatial version, the interferograms are acquired simultane-ously in a multicamera system, with phase shifts introduced optically (generallythrough different polarization separation elements) [15].

The second technique, referred to as Fourier transform (FT) processing [15],consists in adding a spatial carrier to the phase difference φ; the interferogram isthen written

I = Iaverage[1 + m cos(φ + 2π f0x)], (8.4)

with f0 the carrier frequency. The Fourier spectrum of (8.4) shows a central peakwith two symmetric sidelobes. The latter contain the information on φ, which isextracted by proper filtering and taking the inverse Fourier transform of the result.

Contrarily to the PS, the FT requires only one interferogram for the calculationof φ, but it has to be noted that there are severe constraints on the spectra ofIaverage, m, and φ with respect to the carrier frequency f0 in order to have noambiguity in the final result. The FT technique is an alternative method to spatialPS adapted for the analysis of transient events, when it is not possible to have suf-ficiently stable interferograms to apply temporal PS. Nevertheless, FT generallygives less-accurate results than PS because of the filtering.

Following the pioneering experiments presented earlier, different groups devel-oping PRC-based holographic interferometers moved a step further by includingone of the above phase-quantification techniques.

The group of von Bally has developed a holographic camera that records se-quences of double exposures [16, 17]. It is based on a BTO crystal and works withan argon laser at 514 nm. They proposed the application of FT [16] but withoutaddition of a spatial carrier (this way to proceed strongly limits the amplitudeof the phase difference to measure). They later showed the application of the PS[17], which is applied by the technique of the double-reference beam [18]. Indeed,in the case of two frozen holograms, the phase between them can be shifted onlyif different reference beams are used for the recording, the phase being shiftedat the readout on one of these beams. This is clearly a disadvantage in terms ofsimplicity of the procedure. Later they considered the use of pulsed illuminationwith the FT technique for phase quantification [19]. In this case the spatial carrieris introduced between the two pulses by tilting the reference beam. This processis strongly limited by the important angular selectivity of the crystal which au-thorizes only a small number of carrier fringes, and therefore the amplitude ofφ(x, y) is also limited [15].

Pouet and Krishnaswamy [20] proposed the use of 2E-HI associated with astroboscopic technique for the visualization of vibration patterns with a BSO at514 nm. Once again short response times are needed, so relatively small objectsare observed. The measurement is operated three times with the same resonantmodes but with different phase offsets introduced by an electrooptic modulator(“piston” effect), yielding three phase-shifted interferograms. This instrumentgives convincing results but can be applied only in the case of small vibratingobjects.

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The group of G. Roosen proposed the use of a special polarization separationtechnique to obtain, simultaneously, two phase-shifted images of the same objectdisplacement acquired by two separate CCD cameras [21]. They can performquantitative phase measurement with high accuracy based on a single shot, par-ticularly well adapted to pulse lasers. Their holographic camera is breadboardedand has been successfully used with an argon laser at 514 nm and was furtherused in pulsed illumination with a ruby laser (694 nm) [22]. In the last case,the wavelength is badly adapted to the sensitivity range of the sillenite crystal.For that reason, a BGO-doped copper crystal has been especially developed toincrease the response at these wavelengths. Though the response is weak in theseconditions, the quality of the results is acceptable. This is the first use of pulsedillumination with a PRC on an industrial example (turbine blade under vibration).

All these works show that it is possible to perform quantified measurementsof displacements adapted to a photorefractive crystal-based holographic interfer-ometer, some of the works being adapted to a very specific range of application.

With the basic target to achieve a lightweight and portable holographic camerafor industrial purposes, we chose, ten years ago, an original approach by combin-ing the use of a sillenite PRC in anisotropy configuration with the RT-HI method.Indeed, with regard to the existing knowledge and also the criteria mentionedabove, it appears the most promising, in terms of performance, flexibility, andadaptability, to cover a wide area of applications. The different devices and theirapplications that will be shown later confirm the opportunity of this approach.

8.3 Potentialities of Photorefractive Crystals forHolographic Interferometry

We will give the main figures of merit that are important for HI. Moreover, aspointed out before, crystal optics allow original optical schemes, and thereforewe will briefly review different photorefractive properties, configurations, andrecording geometries.

8.3.1 Figures of Merit

The photorefractive effect is characterized by the variation of the photoinducedrefractive index variation �n, which is proportional to the local space chargefield Esc. The latter is a replica of the incident interference pattern created bythe superimposition of the reference and the object beams. In order to find thebehavior of Esc with respect to the temporal and spatial characteristics of theincident pattern, one has to solve a system of four equations (charge generationand recombination, conduction, continuity (or charge conservation) and Gaussequations) by injecting a Fourier series of Esc in terms of spatial frequency. Thesystem can be solved analytically if it is linearized in the spatial frequency com-ponents, which is the case of small modulation of the incident pattern M(M � 1)

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[23, 24]. The more appropriate solution is found in the case of quasi-continuousluminous excitation and with low modulation of the incident pattern, which isgenerally the case in HI (Iref � Iobj ).

For these cases and if we consider the practical case in which we do not use anyexternal electric field (diffusive charge transport), the refractive index variationis given by

�n = �nsat (1 − exp(−t/τ )) (8.5)

in the case that two beams start to interact at time t = 0. Here �nsat is therefractive index at saturation of the process and τ is the response time. Thesaturation value of �n depends on many parameters but mainly on the charge-transport mechanism (presence of external field or not), as well as the electroopticcoefficient (depending on the crystal and its cutting orientation).

The first important figure of merit is the diffraction efficiency, which is definedas the ratio between the diffracted beam and the readout beam intensities. Fol-lowing Kogelnik’s coupled waves theory [25] applied to the case of thick phaseholograms, it is given by

η = exp

(− αd

cos(θ )

)sin2

(π �n dλ cos(θ )

), (8.6)

where α is the absorption, d the crystal thickness, θ the half-angle between beams,and λ the wavelength. The diffraction efficiency depends on different material andexperimental parameters. Therefore it is impossible to indicate a value for a givencrystal; one generally prefers to give a range of values. An important fact to notefor the application to HI is the effect of the ratio R = Iref /Iobj between beams onthe recording/readout properties of PRCs.

Since the variations �n are weak, the efficiency is proportional to �n2. Since�n is proportional to the space-charge field, itself a replica of the light pattern,it transpires that the efficiency is proportional to M2. If one expresses it in termsof R, one obtains

η ∝ M2 ∝ Iref Iobj(Iref + Iobj )2

= R

(1 + R)2, (8.7)

which is inversely proportional to R for R � 1.Consequently, the diffracted intensity Idiff , given by the product of η and Iref ,

is proportional to only the incident object beam intensity Iobj . In contrast to otherholographic recording media, PRCs are not affected by a low modulation M , andmore practically, we can set the recording time by bringing the major part of lightby way of the reference beam, while the object beam is adjusted to have lightintensity on the imaging detector after the crystal.

Another important figure of merit in practice is the temporal characteristics ofhologram recording. Instead of considering the response time, which depends onthe intensity of the beams, or the sensitivity (which can be defined in differentways), it is preferable to use the writing fluence given by the product of the

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response time τ and the total intensity of the beams (Iref + Iobj ). It representsthe quantity of light necessary to reach (1 − 1/e) of the saturation value of �n.

Another interesting parameter is the storage time. Indeed, for some applicationsin which slow phenomena have to be monitored, it could be interesting to keepthe hologram for a long time in the dark.

At last, the spectral sensitivity is important because it has to be high at wave-lengths at which the main commercial lasers emit.

8.3.2 Crystal Families and Choice of the Crystal

The three main families of crystals are the ferroelectrics, the sillenites, and thesemiconductors. The first two have sensitivities mainly in the visible spectrum, thelast one in the near infrared. The main laser sources that are nowadays availablewith a long coherence length and a high power are the Nd:YAG emitting at1064 nm and 532 nm after frequency doubling and their pulse version the YAGQ-switch. Gas lasers such as Ar3+ (488, 514 nm), Kr+ (647 nm), and He-Ne(633 nm) and the pulsed ruby laser (694 nm) are progressively disappearing ininterferometric applications. Consequently, it is more interesting to consider thechoice of a crystal for the two wavelengths of the YAG lasers.

The first family is that of the ferroelectric crystals. They generally are con-sidered efficient crystals but with a poor sensitivity. In that family one finds theLiNbO3, the KNbO3, and BaTiO3, among the principal ones. The transport mech-anism is generally the photovoltaic regime, but both the diffusion and the drift canbe used. The variations of refractive index �nsat are on the order of 10−3 to 10−5,the efficiencies can be ranged from a few percent to 100% under some conditions,and the writing fluences are on the order of 1 to 0.1 J/cm2 [26]. Some species, suchas BaTiO3, have a range extending to the near infrared with suitable dopants [27].

The second family is that of the sillenite crystals. This family includes threecompounds: Bi12SiO20 (BSO), Bi12GeO20 (BGO), and Bi12TiO20 (BTO). Theirspectral sensitivity is important in the blue-green spectrum but is extended to thered for the BTO and doped species of BGO. Their photoinduced refractive indexvariations �nsat are smaller than in the case of ferroelectrics, typically 10−6

to 5.10−6[16, 28]; the efficiencies are on the order of 0.05% in diffusive regime[11], whereas they can reach 25% in drift regime [29]. The writing fluences areon the order of a few mJ/cm2 in diffusive regime depending on experimentalparameters [28].

The last family is that of the semiconductors (CdTe, AsGa, etc.), whose sensi-tivities are around 1 micron. They are more sensitive than the sillenites but at thesame time are equally or more efficient. Values of writing fluences of 14 μJ/cm2

for CdTe and 110 μJ/cm2 for AsGa have been reported as well as values for �nsat

larger than 10−6 [30].For application in holographic interferometry, we have the choice among the

different crystals species. It seems obvious to consider the crystals that are themost sensitive. Indeed, even the faster crystals are still less sensitive than classicalholographic media with recording energy densities on the order of a few μJ/cm2.

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Most of the experiments presented in the above sections considered sillenitecrystals. A very few examples can be found in the literature that make use offerroelectrics [31–33]. Even if the quality of the results obtained with the latteris excellent, the writing fluences are quite important, which implies either longresponse times or a concentration of the beams in order to have fast responsetimes. All the experiments showing good results in LiNbO3 consider transparentobjects because there is little loss of light, in contrast to the case of scatteringobjects.

Therefore we consider sillenites as the best candidates for operation in the blue-green spectrum. The problem with these crystals is their low efficiency. If oneconsiders the RT-HI method, the interferogram observed after the crystal duringthe readout with the illuminated object has a contrast m given by

m = 2

√Itrans Idiff

Itrans + Idiff, (8.8)

where Itrans and Idiff are the intensities of the transmitted and diffracted beamsrespectively. It is easily understandable that the contrast cannot be good with verysmall values of the diffraction efficiency.

Nevertheless, this problem is overcome if one considers special diffractionproperties (beam coupling, anisotropy of diffraction) that are exhibited by thephotorefractive crystals, and which are presented in the next subsection.

8.3.3 Photorefractive Configurations

“Beam coupling” [34] arises for a crystal cut along 〈001〉, 〈110〉, and 〈−110〉and with the grating wave vector parallel to 〈001〉. It can be explained by thefact that the recording beams interact with the grating they are recording insidethe material. This modifies the amplitude and phase of the beams inside thecrystal. One can show that energy can be totally transferred from the referencebeam into the diffracted beam (in the direction of the transmitted object beam),reinforcing the transmitted object beam. The photorefractive gain γ , which is theratio between the object beam intensities at the crystal output and input, is given byγ = exp[(− − α/ cos θ )d], where is the coupling constant. The latter dependson material parameters, on the value of the external field, and on the orientation ofthe polarization, among other factors. These beam-coupling properties are usedin applications such as image amplification and novelty filtering [26]. It can beused also in HI, with the feature that the diffracted and transmitted beams havethe same polarization state [22]. It is also interesting to know the evolution of thecontrast as a function of the product d [22, 28]: if the latter is smaller than unity,it is equal to the contrast of the interferograms (m ≈ d) and m = 1 is obtainedfor d ≈ 1.4. For example, for sillenite crystals having a coupling constant oftypically 0.5 cm−1 in the green, the useful crystal thickness is about 2 cm.

The “anisotropy of diffraction” or “polarization transfer” arises for the samecrystal cut as in the case of beam coupling but for the grating wave vector parallel

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to 〈110〉 or 〈−110〉[8, 11, 35, 36]. It can be explained by the fact that two gratingsare recorded at the same time in the crystal. These are phase-shifted by π/2, andafter diffraction, the two components of the diffracted wave recombine with thisshift. Therefore the crystal acts as a half-wave plate on the diffracted beam, whichis rotated with respect to the transmitted object beam. It is sufficient to place ananalyzer after the crystal to observe the interference between both waves. Also,due to the fact that the intensity of the diffracted beam is small compared to thatof the transmitted beam, a correct orientation of the analyzer axis allows oneto obtain an interferogram with contrast equal to unity if no background noiseis present. Strictly speaking, the anisotropy of diffraction can be obtained onlywithout applied electric field.

Concerning the sillenite crystals, the application of anisotropy of diffraction issomewhat limited by the presence of optical activity. In contrast to other crystalssuch as the semiconductors AsGa and CdTe, one cannot increase the thickness inorder to optimize the diffraction efficiency. For example, in BSO, the presence ofnatural optical activity yields a first maximum of the efficiency for thicknessesaround 2.5 to 3 mm.

8.3.4 Recording Geometries

An interesting feature exhibited by PRCs is due to their important thickness, com-pared to other holographic media, which allows one to consider a reference beamentering by a lateral side of the crystal, whereas the object beam enters throughthe front window. This 90◦ geometry of beams was first considered by Tontchevet al. in a holographic microscope [37] and can be interesting compared to theclassical copropagating geometry, where the two beams enter the crystal from thesame window. Indeed, copropagating geometries generally lead to noise enteringthe CCD cameras and coming from the scattering by dust or scratches located onthe crystal optical windows. This is no longer true with the 90◦ geometry. More-over, short-focal-length objective lenses can be used close to the crystal withoutbeing disturbed by the reference.

8.4 Holographic Camera with Continuous LaserIllumination for Scattering Objects

8.4.1 Main Developments and Achievements

The different steps in the development of a breadboard holographic camera us-ing a sillenite PRC has already been presented [38–40]. The aim was to build atransportable device that satisfies as largely as possible the criteria of an “ideal”holographic system, as listed in Section 8.2. For that, the RT-HI technique as-sociated with the crystal configuration exhibiting anisotropy of diffraction waschosen, and we showed that this choice best satisfies the system requirements.This choice is motivated by the following facts.

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First, the choice of the RT-HI technique is justified by the fact that it is a pri-ori open to more applications than other techniques (2E-HI and TA-HI). Indeed,static, dynamic, and vibratory displacements can be examined in RT-HI. In thecase of vibrations, a stroboscopic technique such as that described by Nakadate etal. can be associated [41]. The 2E-HI technique can also be used in all cases but ismore complicated in the case of dynamic (continuously evolving) displacementsbecause sequences of double-exposed holograms must be related one to another,which necessitates multiplexing procedures. Finally, phase-quantification tech-niques are more complicated to introduce with 2E-HI, the PS process requiringthe use of a double-reference scheme [18]. TA-HI is applicable only with vibratingobjects, so basically it is much too limited. Also, phase-quantification techniquesare generally addressed to sinusoidal fringe patterns, and this is not the case inTA-HI (Bessel function fringe profiles).

Second, at the level of the crystal configuration we considered the diffractionanisotropy by self-diffraction, as used by Kamshilin et al. [8] and Troth et al.[11]. Indeed, this technique automatically satisfies the Bragg condition, and oncethe output polarizer is well oriented, the interferogram contrast doesn’t need tobe readjusted. This satisfies the criteria of the ideal system of ease and userfriendliness.

The study and optimization of this first device included several ways of working.A tradeoff between two optical systems has been carried out in order to optimizethe ratio between the available laser power and the object area observed. Theresponses of several sillenite species were compared and a sample was chosen.Finally, two phase-quantification techniques were considered, the PS and the FT.For both of them, our aim was to analyze the difficulties appearing in applyingthem with regard to the particularities of PRCs. Figure 8.1 shows the schemeof the first prototype. The gray line surrounds all the elements present on thebreadboard, which includes all the components necessary for the holographicinterferometer: the laser, the beamsplitter, the reference-beam-forming elements,a mirror mounted on a piezotranslator (to apply the phase-shifting technique), and

Camera SH2L2L3 PRC

M2

L1SH1 SF

MO

OB

M3

RB

M1PZT

VBS

Display

Object

SU

DPSS

YAG laser

490 mW

L1, L2, L3 : lenses

M1, M2, M3 : mirrors

SH1, SH2 : shutters

MO : microscope objective

VBS : variable beamsplitter

PZT : piezo translator

SF : spatial filter

SU : stimulation unit

OB : object beam

RB : reference beam

PRC : photorefractive crystal

between polarizers

Frame GrabberDriving interface CPU

F I G U R E 8.1. Scheme of the first holographic camera using a sillenite crystal.

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the imaging system, which incorporates a sillenite crystal sandwiched betweentwo polarizers. The imagery is composed of two objective lenses with the crystalin the vicinity of the intermediate image plane. The crystal is a BGO (windowsize typically 3 × 3 cm2); the angle between beams is 50◦.

The working principle is the following. Both recording beams (reference andobject) are continuously incident on the crystal. The recording of the hologramtakes place under the response time of the photorefractive effect. This responsetime being the same at the recording and at the readout, it must not be too shortin order to allow a proper use of the PS process during interferogram capture.Once the hologram of the first state is recorded, the object undergoes a stimulationthat modifies its surface shape or position. When the stimulation is stopped, thereadout process starts and gives an interference image between the stored imageand the direct one corresponding to the stimulated object. Depending on thetime to achieve the stimulation, the laser beam is shut down or not. Once thereadout is complete and the first hologram erased, the instrument is ready for anew measurement. The repetition rate of the measurement sequence obviouslydepends on the response time, which depends on the total intensity incident on thecrystal. In the case of scattering objects, most of the light is sent to the object buta small amount comes back to the crystal, so that the ratio R is much larger thanunity. Owing to the property described by equation (8.7), the diffracted intensityis directly proportional to the object beam intensity and is unaffected by thereference beam intensity (without considering scattering noise). Consequently,the first operation consists in sending a sufficient quantity of light to the object inorder to have a diffracted signal detectable by the CCD camera placed after thesecond polarizer. The remaining light is used for the reference beam, which canthen define the limits of the response time. These are the only adjustments to bemade when the object is changed.

One can tune the light intensity and distribution between the reference andobject beam by a variable beamsplitter and also a half-wave plate working in thereference arm in combination with the polarizer in front of the crystal.

The response time to use depends mainly on the external conditions underwhich the holographic camera is utilized, but generally its value ranges from 5to 10 seconds if a moderately stable environment is considered (few externalvibrations and air turbulence, no need of a vibration-compensated optical table).The size of the observable area depends on the object-illuminating power. Weshowed that with 340 mW one can observe a 55 × 37 cm2 object coated withremovable white powder [40].

Applications of the system were presented: measurement of static displace-ments (with examples in defect detection), dynamic displacements, and vibrationmodes. It was clearly observed that the instrument allows one to obtain high-quality results on large objects and with a high degree of versatility as a functionof the application. In the case of the study of vibrating objects, a stroboscopictechnique has been implemented to supplement the basic technique [42].

Despite the good performance of the first prototype, the fact remains that thisinstrument is not compact and lightweight enough to render it really flexible in use

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FI G U R E 8.2. Compact holographiccamera using a sillenite crystal.

(e.g., it cannot be set to observe an object from the top, it has to lie on a table andobserve horizontally). Consequently, we have carried on the development towarda more compact head [43]. Mainly, the laser is removed from the optical headand the light is brought through an optical fiber, the latter acting as a spatial filter.The variable beamsplitter, an electromechanical shutter, and the piezotranslatorfor the phase-shifting have been reduced and confined in a small compartmentattached to the imaging system, the latter remaining unchanged. The result is acylinder of typically 25-cm length and 8-cm diameter with a typical weight of1 kg (Figure 8.2). The performance is exactly the same as that of the previousprototype.

8.4.2 Applications

8.4.2.1 Quasi-static Displacements

The first range of applications is that of static displacements, when the object isin a final state that does not evolve (or very slowly) with time. This is the simplestcase of applications, and the PS can be easily applied.

An interesting example is that of nondestructive testing (defect detection) ofaeronautical composite structures with internal defects or surface impacts. Theoperating mode is the following. First, record the hologram of the object at rest.Second, shut down the laser beam so that the hologram is not erased and theobject is adequately stimulated during this blind period. The stimulation must beappropriate to the type of structure studied, as well as to the defects searched;here we heat the structure with a halogen lamp, stop the heating, and let theobject relax a few seconds. Afterward, the readout is performed showing aninterferogram of the residual deformation, which is sufficiently stable for the PSprocess. This residual deformation depends on the structure and on the boundaryconditions. The defects appear as important local variations in the smoother globaldeformation. The residual deformation then disappears slowly, and the objectslightly returns to its initial state.

Figure 8.3(a) shows one of the interferograms of the PS sequence obtainedwith a 60 × 40 cm2 composite structure with impact defects. Figure 8.3(b) showsthe phase interferogram modulo 2π resulting from the phase calculation. These

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FI G U R E 8.3. (a) Interferogram, (b) phase image after phase-shifting, (c) image of thedefects after differentiation of (b).

images illustrate the interest in calculating the phase. Indeed, in the interferogram(a), the average intensity and the contrast are weak at the edges of the field, withthe consequence that the defects in the bottom of the images are not clearly visible.This problem no longer appears in the phase interferogram. In the rest of the paperwe will mostly show phase results. A subsequent phase derivation suppresses thebackground deformation and puts the defects in evidence (Figure 8.3(c)).

Other examples of defect detection were presented in [40, 43, 45]. Figure8.4(b) shows recent results obtained on an entire car door (Figure 8.4(a)) in orderto observe abnormal behavior under mechanical load.

Another important application is pure full-field displacement metrology. A firstgoal was a comparison of measurements with finite-element models of honey-comb structures undergoing thermal loading [44]. Another example, depicted inFigure 8.5(a), is the calibration of piezosheets bonded to the rear side of a metal-lic plate that return an electric signal proportional to the surface displacement.Figures 8.5(b) and (c) show the interferograms obtained for different mechanicalloads applied in the middle of the rear side of the panel. We note the extremeresolution in the fringes, allowing a very large range-displacement measurement.

FI G U R E 8.4. (a) Car door. (b) Phase image obtained after mechanical loading showingabnormal displacement of one part of the door (courtesy of Optrion).

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aluminium plate(back side)

piezosheets

point where the force is applied

clamping points of the plate

(a) (b)

F I G U R E 8.5. Calibration of piezosheet’s electric signal. (a) Drawing of a clamped metallicplate on which are glued piezosheets. In the center of the plate is located the mechanicalloading point. (b) Phase image after mechanical load.

Another example is the determination of the coefficient of thermal expansion(CTE) using the measurement of small displacements between the top of a spec-imen and a baseplate on which it is standing [43].

8.4.2.2 Dynamic Displacements

The second range of applications consists in studying phenomena that are notstationary. On the basis of RT-HI, an easy possibility to implement is to performa sequential readout during the object displacement or deformation. The factthat the object is evolving prevents the use of the phase-shifting technique as itis applied in the above case of quasi-static displacements. Therefore we use asingle-frame analysis technique based on Fourier transform filtering as explainedin a previous section. Consequently, we need to introduce a spatial carrier in theinterferograms. This is done just after the holographic recording, prior to the objectdisplacement and the holographic readout. The classical technique of tilting thereference beam to introduce the carrier cannot be applied due to the high angularselectivity of the thick hologram recorded in the crystal. We have shown the use ofa simple technique consisting of displacing transversally the object illuminationlens between the recording and the readout [40]. This in fact generates fringeslocated on hyperboloidal equiphase sheets that are intersected by the object. Thecarrier is then not an ideal rectilinear fringe pattern but is very close to one.Once the spatial carrier has been introduced, the object can be stimulated andthe readout can start. Figure 8.6 shows the complete sequence of a wooden panelundergoing heating. After the processing explained in Section 9.2.2, one obtainsphase images such as those of Figures 6(a) to (h). The time after hologram captureis indicated for each image. Between the image-capture instants, the shutter afterthe laser has been shut in order not to erase the hologram in the crystal. This way,

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FI G U R E 8.6. Phase images obtained after processing by the FT technique on interfer-ograms with carrier fringes. The readout has been performed on the basis of a singlereference hologram and with a sequential readout during the continuous heating of awooden panel. The time indicated above each image is the time of interferogram captureafter the heating has been initiated.

one can use the same hologram for all the successive readouts and then followthe evolution of the object.

The above technique has its limit: the number of recordable interferogramsdepends on the response time of the photorefractive effect and the time used torecord each separate interferogram. Theoretically, with a perfect synchronizationbetween the shutter and the CCD acquisition, it is possible to obtain 100 inter-ferograms. Finally, the dark conductivity of the crystal gives the ultimate limit ofthe storage time of the hologram in the crystal. With our BSO and BGO crystal,we observed a few days of dark storage time.

8.4.2.3 Vibratory Displacements

We have applied the stroboscopic technique in combination with the RT-HI forthe measurement of vibrations. We were the first to apply it to a PRC-basedreal-time holographic interferometer [42]. The operating mode is simple: thehologram of the object is recorded at the rest, and when the object is vibrating at agiven frequency, a stroboscopic readout is operated in synchrony with the objectexcitation signal. When the object reaches a resonant frequency, the stroboscopedelay is adjusted in order to let the light enter the holographic camera at the instantwhen the object is at its maximum of modal displacement, say when its speedtends to zero. We have pointed out the experimental particularities related to thistechnique. In practice, the opening time has to be long enough to obtain a sufficientimage intensity at the CCD camera. The duty cycle measures the ratio between

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FI G U R E 8.7. Phase images of different mode shapes of a compressor blade excited by ashaker (courtesy of Optrion).

the opening time and the vibration period. The quantity of light is proportional tothis parameter. If the duty cycle is increased, a higher luminous level reaches theCCD, but in contrast, one integrates interferograms of the moving object beforeand after its maximum displacement. As a consequence, the contrast of the fringesdecreases because the object is partly seen moving. We have analyzed the errorscoming from the phase calculation as a function of the duty cycle. Also, we haveshown an original technique to remove this error from the measurements. Aftercorrection, the final accuracy is limited by the external perturbations, as for thestatic displacement measurements, say λ/40 RMS. In practice, duty cycles of 12to 16% are used.

The first objects to which the technique was applied were academic cases(metallic plates excited by loudspeakers) [42]. With a YAG laser (532 nm) emit-ting 490 mW, we were able to observe very good interferograms on a 23 × 23cm2 aluminium plate. Later we showed application to the detection of turbineblade mode shapes [40]. The examples shown in Figure 8.7 are recent results ob-tained with a holographic camera made available commercially by the OPTRIONcompany [46]. They show some mode shapes obtained for different compressorblades of a new aircraft engine. The aim of the test campaign was to comparethe frequencies at which the resonance appears and the shape of the modes to thesame information derived from mechanical simulation by the compressor bladeconceptor.

Another interesting example is searching for abnormal behavior of a microelec-tronic chip soldered on an electronic board. Figure 8.8 shows the phase imagesobtained at two resonant frequencies of the electronic board, which show that thechip is not properly attached to the board. Indeed, the fringes are not correctlyconnected between the chip and the board.

8.4.3 Extension to Tridimensional Displacements

The phase difference φ calculated by phase-quantification techniques allow oneto compute the displacement L of each point of the surface observed. Theirrelationship is the following:

φ(x, y) = S(x, y) • L(x, y), (8.9)

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FI G U R E 8.8. Vibration patterns of an electronic board on which is soldered a microelec-tronic chip. The pattern shows abnormal behavior of the chip caused by bad soldering tothe board (courtesy of Optrion).

where S is the sensitivity vector, defined as the difference between theillumination-vector (traveling from the illumination source to a given object point)and the observation vector (traveling from the object point to the observationplane). The vector S can be determined if one knows the geometry of the setupand the object. Equation (8.9) suggests that if one wishes to determine the threecomponents of vector L, three independent measurements of φ have to be per-formed. In order to do this, one needs different sensitivity vectors, obtained forexample by considering different illumination points and a single observationdirection. Another possibility is to have one illumination with three directionsof visualization (three cameras). Numerous examples exist in the literature, andreferences [2] and [3] summarize different approaches.

In all the applications presented above, we consider only single measurementswith one observation direction and one illumination point close to the observationcamera. Therefore the sensitivity vector is almost directed along the line of sightof the holographic camera. If the object is observed perpendicularly, one measuresmainly the “out-of-plane” displacement component.

In order to access the complete vector displacement, we have studied the possi-bility of recording different holograms in the same crystal with a single referencebeam or to use a stack of different crystals [47]. This is the first time to ourknowledge that such multiple recording in a sillenite crystal has been used onlarge objects for interferometric purposes. When the object is displaced, the read-out is performed sequentially very fast with one illumination at a time, and theinterferograms allow one to compute the displacements with each of the sensitivityvectors. Equation (8.9) is inverted in order to retrieve vector L.

This technique has been applied with two point sources illuminating the objectlaterally and symmetrically located with respect to the holographic camera [48].

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FI G U R E 8.9. Image showing the result of the determination of in-plane and out-of-planedisplacement. On the left, the phase images obtained with two different illuminationsources; on the right, in-plane (black line) and out-of-plane (gray line) computed from thephase images (courtesy of Optrion).

This arrangement allows one to access the “in-plane” displacement componentalong one transverse direction, as well as the out-of-plane component. This kindof measurement is of major importance in the determination of strain and stressin materials. Figure 8.9 displays the results of the elongation of a metallic sample.The phase images on the left show the displacements measured with two differentillumination points; the diagram on the bottom right shows the in-plane (blackline) and the out-of-plane (gray line) displacements, computed on the basis of thephase images.

8.5 Holographic Cameras with Continuous LaserIllumination for Transparent Objects

8.5.1 Study of a Microgravity Fluid-MonitoringHolographic Camera

Holographic interferometry allows the measurement of refractive index variationsof transparent objects [1]. The basic configuration for fluid holographic measure-ment is that the object illumination beam is collimated and passes through thecomplete experimental cell. Since the eighties, this technique has gained the atten-tion of space agencies as a diagnostic tool for microgravity experiments. Most ofthem use holoplates with liquid bridges or photothermoplastics. Some feasibilitystudies have been performed in the past with LiNbO3 crystals with long storagetimes [33]. These crystals are difficult to apply in the space environment because

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FI G U R E 8.10. (a): Sketch of the cell containing silicon oil sandwiched between two heatedplates. The figure shows also the convection rolls appearing above a threshold gradient(T2-T1). (b) and (c): Phase images respectively for gradient under and above the threshold.

they require powerful lasers. For that reason we proposed to consider more sen-sitive crystals, such as the sillenites [49]. We have studied the implementationof a BSO crystal in the future multidiagnostics Fluid Science Laboratory (FSL)of the European Space Agency, to be placed on board the International SpaceStation (ISS). A first demonstration experiment was to observe convection rollsappearing in a parallelepipedic cell filled with silicon oil and undergoing an in-creasing temperature gradient (T2-T1) between the bottom and the upper heatingplates (Figure 8.10(a)). Figures 8.10(b) and (c) show interferograms arising fromrefractive index variation between the two plates and integrated along the line ofsight. In Figure 8.10(c), the temperature gradient is higher than a threshold abovewhich the convection process is initiated.

The final goal of the FSL is to follow the variations over a long time. Theprocedure to be implemented is to record a single reference hologram, with aresponse time smaller than 50 ms, and to be able to capture more than 1000 real-time interferograms on the basis of this hologram [50]. The consequence of this isthat we have to change strongly the response time between the recording and thereadout, e.g., by means of orientable polarization-sensitive elements. The objectbeam intensity is then reduced for the readout, but this is not critical in the caseof transparent objects because there is no light loss from the object.

In [50], we have shown some interferograms obtained with such a system. Forslowly varying fluid phenomena, the phase-shifting can be applied for quantifi-cation purposes.

In order to implement such crystals on spaceborne facilities, the change ofholographic performance due to the radiation doses aboard ISS has to be measured,mainly with respect to gamma rays and protons [51]. No significant damage orlosses were observed that could prevent the use of sillenite crystals aboard ISS.

8.5.2 Extension of the Holographic Camerato Transparent Objects

It would be interesting if one could slightly modify the holographic camera in or-der to allow visualization of fluids instead of scattering objects. The idea is to placean additional device in front of the camera, which produces a collimated beam

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optical fiber

CCDcamera relay

lenscrystal +polarizers

front lens

mirror

lens

beamsplitter collimatinglens

cellmirror

Holographic camera for scattering objects Additional optics for transparent objects

collimated beam

FI G U R E 8.11. Scheme of the adaptation of the holographic camera to transparent objects.

F I G U R E 8.12. Phase images of air variations due to heating by a flame. The flame itselfis overexposed in image (a), resulting in a uniform phase.

passing through the object and traveling toward the holographic camera. One pos-sibility is shown in the figure, where a mirror is placed after the transparent cell andreflects the light back to the holographic camera. A beamsplitter is necessary toinject light in the line of sight. The other possibility is to avoid the beamsplitter anddirectly expand and collimate the beam before two folding mirrors, which allowone to inject the light through the cell. The system depicted in Figure 8.11 has beendesigned for a test bed in which folding mirrors cannot be placed behind the cell.

Figure 8.12 shows two phase interferograms obtained with the RT-HI techniqueand phase-shifting in the case of air variations around the flame of a candle.

8.6 Holographic Camera with Pulsed Lasers

8.6.1 Early Experiments

The Laboratoire Charles Fabry de l’Institut d’Optique (LCFIO) has developeda photorefractive holographic camera operating in the pulse regime [22]. The

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object

beam dump

delayline

M1

M2

PBS2PBS1

Pockels 2

Pockels 3

Pockels 1

M3

laser

HWP1

O3

O3'

O2

PRCrystal O1 P

M4

M5

M6

HWP2CL

DL DL

PBS3

Cam 2

Cam 1

F I G U R E 8.13. Scheme of the pulse holographic camera adapted to the single-pulse laser.HWPx: half-wave plates, Mx: mirrors, PBSx: polarizing beamsplitter cubes, DL: divergentlenses, CL: convergent lenses, Ox: objective lenses, P: polarizer, Cam x: CCD cameras.

phase-shifting system has been briefly explained in Section 9.2.2; it allows si-multaneous acquisition of two phase-shifted images. A preliminary measurementof the average intensity of the images without interference fringes is, however,necessary to calculate the phase. Initially, this camera was designed for vibrationanalysis using a ruby laser. The main drawback is that the laser wavelength (694nm) does not match the sensitivity range of BSO and BGO crystals. A copper-doped BGO sample was specially grown to increase the sensitivity at 694 nm.

Since then, the Centre Spatial de Liege group and LCFIO have carried onthis work together to adapt the developed system to a frequency-doubled Q-switched YAG laser (COHERENT Infinity) whose wavelength is naturally adaptedto sillenite crystals [52, 53]. For these new experiments, the photorefractivecrystal is a nominally undoped BGO sample, cut along the beam-couplingconfiguration.

Figure 8.13 shows a scheme of the complete experiment. Real-time HI is per-formed: a first pulse records the hologram of the object at some instant; the objectis then visualized through the crystal while the hologram is reconstructed by thesecond pulse. The energy of the incident beams has to be decreased in order toavoid erasure of the hologram and CCD blooming with the object beam duringthe readout. This forced us to add an energy balance: a half-wave plate (HWP1)defines the ratio between reference and object beam energies for the first pulse,through the use of a first polarizing beamsplitter cube (PBS1). At the second pulse,two Pockels cells are supplied with a half-wave voltage. The beam polarizationis rotated in such a way that the object beam energy is reduced, all of the lighttraveling into the reference beam, but most of it deviated in the beam dump soas not to erase the hologram. The delay line constituted by two moving mirrors(M1, M2) is present to equalize the paths of the reference and object beams (thecoherence length depends on the pulse duration, here 90 cm). The third Pockels

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FI G U R E 8.14. (a) Interferogram recorded by one of the two CCDs, (b) correspondingphase image.

cell is used to circularize the reference beam polarization at the readout step, inorder to provide the polarization separation through the polarizing beamsplitterPBS3. Here the crystal is orientated in the beam-coupling configuration, so thatthe polarization state of the diffracted beam is the same as the transmitted one.

An optimization experiment has been carried out first in order to evaluatethe correct energies for the recording and the readout. Figure 8.14(a) shows theinterferogram obtained by one of the cameras, (b) the phase calculated, and (c)the displacement.

A method for vibration measurement has been implemented with the pulsesystem [52, 53]. It is adapted to the sinusoidal vibration. It consists of a firstdisplacement measurement at a given time in the vibration period. A quarter ofperiod later, a new pair of pulses allows the determination of a new displacement.By combining both displacement measurements together with the known vibra-tion frequency and inter pulse delay, one can find the amplitude and phase ofvibration. The same procedure is applied over a range of excitation frequencies.At the end, one can obtain the frequency response in all points of the vibratingobject. Figure 8.15 shows a series of interferograms appearing when the excitationfrequency is progressively increased around a resonance frequency. The object isa metallic plate excited by a loudspeaker.

The four-pulse vibration measurement technique described in [52] and [53]allows one to compute the amplitude and phase of the vibration in every pixel.

F I G U R E 8.15. Interferograms of a metallic plate during a frequency scan, passing by aresonance.

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00

50 100 200150 250 300 350 400

frequency (Hz)

1

2

3

4

5

Am

plit

ude (

μm)

FI G U R E 8.16. Amplitude response of themetallic plate as a function of the excita-tion frequency.

Figure 8.16 shows the frequency spectrum of the plate above at one pixel. Theresonances are clearly seen. The same kind of information can be recovered forall the image points.

8.6.2 Recent Developments

8.6.2.1 Simplifications of the Pulse System

The system above suffers from some limitations or complexities of utilization.First, the laser emits a single pulse, which requires complicated synchronizationif one wishes to study vibrations. Second, the energy balance system requiresthe use of active polarization-changing devices such as a Pockels cell. Third, thetechnique of phase quantification requires an additional Pockels cell to circularizethe polarization at the readout.

The first drawback can be eliminated if one uses a double-pulse laser withdelay between pulses that can be adjusted. The second can be eliminated if thesecond pulse of such a laser has a lower energy than the first pulse. Presently theuse of such lasers is under investigation. Doing so, we avoid the two first Pockelscells.

Concerning the simplification of the two-phase shifting technique, we havefound an easy way to do it. Instead of considering the beam-coupling configura-tion, and consequently the isotropy of diffraction, we consider the anisotropy ofdiffraction configuration. In that case the diffracted and the transmitted waves haveorthogonal polarizations after the crystal. It is sufficient to place a nonpolarizingbeamsplitter cube after the latter in order to observe with two cameras. In front ofthe first camera, we place a polarizer (as with the holographic camera presentedin Section 8.4.) and in front of the second camera, we place a quarter-wave plate(QWP) followed by a polarizer. If one of the principal axes of the QWP is alignedalong the polarization of, e.g., the diffracted beam, the latter will be phase-shiftedby π/2, while the other components will not undergo any phase shift. Both com-ponents will then be phase-shifted by π/2, for this camera, and consequently, theinterferograms observed by the two cameras will be phase-shifted by the same

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FI G U R E 8.17. (a), (b): Interferograms observed by the each of the two cameras with aπ/2 phase-shifting. (c) Phase image obtained with the two former.

quantity one to the other. This is clearly observable in the interferograms shownin Figures 17(a) and (b) obtained with such a system.

Figure 17(c) is the phase calculated using the following algorithm. The generalexpression of phase-shifted images (equation (8.2)) is written here for both imagesas

I1 = Iav1[1 + m1 cos(φ)], (8.10)

I2 = Iav2[1 + m2 sin(φ)]. (8.11)

The computation of phase φ is obtained if one captures preliminary averageimages (without fringes) Iav1 and Iav2. Supposing m1 and m2 equal (which canbe set by correct orientation of the polarizers in each arm), the phase is given by

φ = arctan

[(I2

Iav2

− 1

)/(I1

Iav1

− 1

)]. (8.12)

8.6.2.2 New Crystals and Geometries

Developments have also been performed on the basis of semiconductor crystalsworking in the near infrared. Mainly, one uses AsGa crystals, which can be adaptedto the pulse regime because they exhibit small storage times. They are moreefficient and sensitive in the near infrared than are sillenites in the green (seeSection 8.3.2).

The 90◦ geometry of the recording beam has also been studied with both theBSO and the AsGa crystals [54]. This can be of great interest in limiting thescattering noise observed in the copropagating geometry (see Section 8.3.4).Due to the presence of optical activity in BSO, one needs to place QWP in theinput and output beams, in order to avoid a periodic spatial inhomogeneity ofthe diffraction efficiency. The quality of polarization in such arrangements limitsthe quality of the results. This is no longer the case with AsGa crystals, which donot exhibit optical activity. Figure 8.18 shows the interferogram obtained with anAsGa crystal under the 90◦ geometry of beams.

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FI G U R E 8.18. Interferogramobtained with a 90◦ geometryof beams (image by CSL andLCFIO).

8.7 Conclusion

In this contribution, we have reviewed the possibilities of photorefractive crystalsin the field of dynamic holographic interferometry. For this purpose we made asurvey of different possibilities already envisaged by different groups. We havehighlighted the criteria that are important for the development of an ideal de-vice in order to justify the choice of the configuration and the method that weconsidered in our developments. The technique is real-time holographic interfer-ometry with sillenite crystals using self-diffraction in the anisotropy of diffractionconfiguration.

We have then presented the study of different devices adapted to different cat-egories of object and illumination regime that are based on the mentioned tech-nique: continuous illumination with scattering objects, continuous illuminationwith transparent objects, and finally, pulsed illumination.

Acknowledgments. The authors would like to express their thanks to Dr. Jean-Claude Launay, of the Institut de Chimie de la Matiere Condensee of the Universitede Bordeaux (France), for his efforts and cooperation in crystal growth; to Dr.Gilles Pauliat and Dr. Gerald Roosen, of the MANOLIA group of the Labora-toire Charles Fabry de l’Institut d’Optique of Orsay (France), for their fruitfuldiscussions and collaboration in common research projects.

The results presented have been obtained throughout different research projectsfunded by the General Directorate of Research, Technology and Energy ofWalloon Region of Belgium, by the Research General Directorate of the Eu-ropean Commission, and by the European Space Agency.

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dynamic holographic interferometry: devices and applications

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