adaptive systems in speckle-pattern interferometry

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Adaptive systems in speckle-pattern interferometry

Janos Kornis, Zoltan Fuzessy, and Attila Nemeth

The concept of adaptivity in television holography is discussed, and various realizations of adaptivity arepresented. In one possible variation, functions of the components of the optical arrangement may bechanged to adapt them to measurement conditions. An additional peculiarity of the technique is thatreference waves are produced by holographically reconstructed virtual images. A method, believed to benew, is introduced for synthesizing the phase front of the master object beam that is produced by a simpleholographic optical element and is used as a smooth or a speckled reference beam in the electronicspeckle-pattern interferometer. An adaptive interferometer is presented as a measuring device forvarious measuring tasks. Selected applications are shown, demonstrating different aspects of adaptiv-ity. © 2000 Optical Society of America

OCIS codes: 090.2890, 110.6150, 120.6160.

1. Introduction

Recent successes in the automatization of variousoptical measuring methods can assist in the creationof new knowledge-based systems. Such a systemcontinuously adapts itself to changing measuringconditions and environment.1–3 That is why it iscalled an adaptive system. On the one hand, one ofthe most powerful coherent optical methods to beimplemented successfully in the industry is television~TV! holography. On the other hand, with adaptiveystems more industrial measuring problems becomeolvable. So the applications of TV holography indaptive optical systems are expected to be fruitful.There are various realizations of adaptivity in mod-

rn optical measuring systems, for example, thedaptive optical arrangement, in which differenteasuring tasks can be carried out by simple modi-cation of the arrangement. One modification cane to change the modules of the measuring device byand, which makes the arrangement suitable foreasuring different displacement components,4 for

instance. Another modification may be the use ofone or two reference beams in a two-reference-beamsystem, with application of computer-controlledbeam stops to perform real-time or double-exposedholography.

The authors are with the Department of Physics, Technical Uni-versity of Budapest, Budafoki ut 8., Budapest, H-1111 Hungary.. Kornis’s e-mail address is [email protected] 22 November 1999.0003-6935y00y162620-08$15.00y0© 2000 Optical Society of America

2620 APPLIED OPTICS y Vol. 39, No. 16 y 1 June 2000

One peculiar realization of adaptivity worth men-tioning is the development of active interferometers.These interferometers can eliminate external distur-bances, e.g., unwanted vibrations of the arrangementor unwanted wavelength changes of the light source.A vibration-insensitive digital Twyman–Green inter-ferometer was developed5 to measure the quality ofoptical surfaces in a noisy environment. An activeinterferometer was realized with an optoelectronicfeedback loop that can stabilize any chosen phasedifference between the interfering beams in thephase-stepping interferometer.6 An adaptive holo-graphic interferometric system was presented inwhich time-averaged holograms were recorded on aBi12TiO20 crystal.3 Active interferometers were alsodeveloped for phase-shifting interferometry inspeckle metrology.2

The next possible realization of adaptability is theapplication of new adaptive methods.7,8 With thesenew methods the measuring system can change itssensitivity and its measuring range, for example.

Adaptability can be realized in the evaluationphase, too.9–11 Adaptive evaluation programs canchange parameters in the preprocessing and the post-processing phases of the evaluation.

In our paper a few applications of the adaptivespeckle-pattern interferometer is discussed. The ac-tual adaptive speckle-pattern interferometer is anadaptive optical arrangement in which a holographicoptical element is applied. A short overview of theapplication of the holographic optical elements~HOE’s! in speckle metrology can be found in Section2. The optical arrangement is presented in Section3. Two different realizations of adaptivity are

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shown in Sections 4 and 5. The adaptability of thepresented system is improved by computer-controlledbeam expanders and beam stops. Changing thefunctions of the optical arrangement with these de-vices, we successfully applied the system in compar-ative measurements and two-wavelength contouringas demonstrated in Section 4. Two methods, be-lieved to be novel, are suggested in Section 5; theyresult in an increase in the adaptivity, readability,and sensitivity of the measuring system.

2. Use of Holographic Optical Elements in theElectronic Speckle-Pattern Interferometry System

The use of HOE’s in speckle metrology is well estab-lished. In speckle-shearing interferometry a full-aperture method has been reported that includes aholographic grating placed just before the holo-graphic plate.12 Transmission phase hololenses13

have been used to build shear interferometers forlens testing and phase-front investigations. Holo-shear lenses14 have also been also applied in speckle-shearing interferometry to measure in-planedisplacement, out-of-plane displacement, and slopedata.15

The application of HOE’s in electronic speckle-pattern interferometry ~ESPI! has also been de-scribed. The HOE under question is simply ahologram. HOE applications in ESPI systems are atwo-stage process as usual. In the first stage theHOE is recorded in a simple holographic arrange-ment. The developed HOE that is illuminated laterreconstructs the object wave, which serves as ESPIreference wave.16 In this way smooth or speckledreference waves can be generated. By storage of dif-ferent states of the reflected beam belonging to theundeformed and the deformed states of a master ob-ject in a HOE, comparative measurement can be per-formed.17 In this way the deformation of each testobject can be compared with the very same two statesof the master object. The application of a HOE indifference holographic interferometry has also beenreported.18

3. Optical Arrangement

The presented system is based on the application of aholographically recorded and reconstructed referencewave.16–18 The reference waves are produced by re-construction of the hologram recorded previously.The setup can be seen in Fig. 1. It contains the lightsource, the object-illuminating module, the reference-beam-forming optics, the holographic plate holder,and the CCD camera. In the first step of the mea-surement the hologram of the reference wave is re-corded. The scattered light from the master object~MO! is recorded on the holographic plate ~H! withone reference beam ~e.g., from BE1!.

In the second step the developed holographic plateis placed back in the setup. With the reference beam~from BE1! the reconstructed beam ~the virtual imagef the master object! is received by the CCD camera.he test object to be measured ~TO! is illuminatedimultaneously, and the scattered light is also re-

eived by the camera. The beams are interferingnd produce an interferometric speckle patternspecklegram!. After deformation of the test object,he second specklegram is recorded, and the correla-ion fringe pattern can be calculated corresponding tohe difference in displacement.

The arrangement distinguishes itself by simplicity.t may be easily adapted to different measuring tasksnd changes in measurement conditions.

4. Adapting the Optical Arrangement for DifferentMeasuring Tasks

Adaptivity of the experimental setup in Fig. 1 may beachieved by use of two simple types of computer-controlled device ~computer-controlled beam stopsand beam splitters!. With these devices the aper-ture and the variable density mirror are moved by acomputer-controlled stepping motor.

The arrangement can be used for recording a singlehologram and for making real-time holographic in-terferometry later on. In this case the other refer-ence beam is blocked by the beam stop.

By use of compensating measuring techniques, twonominally identical opaque objects can be comparedwith regard to their deformation and shape, even ona wide-scale level. Comparative TV holography19,20

is a sophisticated tool for this kind of investigation.The setup presented in Fig. 1 may easily be

adapted to perform comparative measurements. Asabove, we replace the master object in the compara-tive process by having its holograms belong to itsundeformed and deformed states. In addition to thesimplicity of the experimental arrangement, one ad-vantage is that, with the replacement, exactly thesame master object deformation is used for compari-son every time.

At the beginning the undeformed and the deformedstates of the master object are recorded with differentreference beams ~from BE1 and from BE2!. Afternstallation of the test object the sum of the speckleelds from the undeformed state of the illuminatedest object and the reconstructed speckle pattern ofhe undeformed master object is recorded and storedn the computer by use of a CCD camera ~C!. Next,he sum of the speckle fields from the deformed state

Fig. 1. Schematic diagram of the applied arrangement. BE,beam expander; BS, beam splitter; C, CCD camera; H, holographicplate; M, mirror; MO, master object; TO, test object.

1 June 2000 y Vol. 39, No. 16 y APPLIED OPTICS 2621

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of the illuminated test object and the reconstructedspeckle pattern of the deformed master object is re-corded and stored. Subtracting, the correlation im-age of the two stored images can be observed, whichcharacterizes the difference of the displacement ofthe master object and the test object. A differentialcorrelation fringe pattern can be seen in Fig. 2. Theobject was a 7-cm-diameter membrane fixed at itsboundaries. The loading was a concentrated forceacting at the center of the membrane. If a change ofthe order of overlapping speckle patterns takes place~e.g., we add the speckle pattern from the deformed

Fig. 2. Measurement of the difference and sum of two deformaeformation pattern, ~c! correlation fringes characterizing the dif

measure the sum of the deformations ~d!.


master object and the undeformed test object!, thesum of the deformations can be measured.

Two-dimensional shape measurement or contour-ing by ESPI is one of the most difficult measuringtasks. The requirement for the position alignmentof the master object and the test object with inter-ferometric accuracy complicates application of thismethod for quality control. The alignment can beperformed easily in the setup in Fig. 1, because thesame mounting device can be used for positioning themaster object and the test object. The measurementis performed by use of a multiple-wavelength light

patterns. ~a! Master object deformation pattern, ~b! test objectce between the deformations, ~d! correlation fringe pattern if we

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source. As at the differential speckle interferome-ter, the holograms of the master object are recordedin the first step. But for the two reference beams adifferent wavelength was used ~e.g., l1 for BE1 and l2for BE2!. After we remove the master object, theest object is placed on the object holder, and twoxposures are made. At the first exposure the objects illuminated with the first wavelength. The mas-er object is reconstructed with the beam that corre-ponds to this wavelength. For the second exposurehe other wavelength and the other reference beamre used. Examples from measurements can beeen in Fig. 3.

5. New Adaptive Methods

A. Varying the Intensity of the Reconstructed MasterObject

The use of a holographically stored reference wave forTV holography has a nice adaptive feature. It is wellknown that the quality of the resultant correlationfringes in a measurement is best when the meanintensities of the object beam and the speckled refer-ence beam are equal. When we change the intensityof the reconstructed reference beam in Fig. 1, equaltest object and master object ~reference! intensitiesre easily achieved. When computer-controlledeam splitter and beam stops are applied, the equal-zation process can be performed automatically.he results can be seen in Fig. 4. Before the mea-urements, half of each object surface was paintedith two different colors. The ratio of the reflected

ntensities was greater than 100 @Fig. 4~a!#. Thevaluation program can produce mask areas withredefined intensity threshold levels, in which theveraged intensity distribution is uniform. With

Fig. 3. Two-wavelength contour map of a ceramic plate. The di-mension of the plate was 50 mm 3 50 mm. The contouring depthwas 5 mm.

ne intensity-threshold value ~150 on the 0–255 graycale in our measurement! the program defined twoask areas corresponding to the two halves. Theseere on the left- and on the right-hand sides of the

mage, as expected. The intensity measurementsere made from the pictures of the CCD camera byse of computer-controlled beam stops. First, the

ntensity of the reference beam was adjusted auto-atically to the intensity along the first mask area

the left-hand side of the image!. Correlation fringesith good visibility can be obtained on this side only

Fig. 4~b!#. Next, the program increased the illumi-ation of the object by use of a computer-controlledeam splitter to reach an equal intensity ratio for theeference beam and for the second mask area ~theight-hand side of the image!. The correspondingorrelation fringe system can be seen in Fig. 4~c!.sing the mask areas, the evaluation program auto-atically edited the final image @in Fig. 4~d!# with

niform visibility on the whole object surface.

B. Application of Synthesized Reference Phase-FrontInterferometer for Wide-Scale Displacement Measurement

Slight modification of the optical arrangement pre-sented in Section 1 furnishes the basis for introducinga new method, which can be applied successfully forcompensating the fringe pattern at a wide-scale dis-placement measurement. The reference wave ~vir-tual image of the master object! in the system is stillproduced by the HOE, but a phase-shifting device isinserted into one of the reconstructing paths of theinterferometer in Fig. 1 by means of replacing themirror M1, for example, with a piezoelectricallymoved mirror.

The phase-shifted reconstructions of the master ob-ject can be used for synthesizing the wave front of thereference wave in ESPI. In our case the wave frontbelonging to the undeformed master object was usedfor synthesizing.

Both the HOE and the test object are illuminatedin a proper way, and the interferometric speckle pat-tern is received by the CCD camera ~Fig. 1!.Multiple-intensity maps are recorded by means ofshifting the phase of the reconstructed beam by equalvalues.

So, contrary to the usual ESPI measurement inwhich there is one image before and one after thedeformation in the computer memory, in this casethere are multiple ~typically eight! images before andone image after the deformation in the memory.

The effect of the phase shifting in the speckle pat-tern is periodic by 2p, as is usual. If this period isdivided into n parts, the images in the computer be-longing to the phase-stepped reference waves can beused cyclically. This means that the ith phase-shifted wave can be used whenever the necessaryreference phase value is

k2p

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where k is an integer and i 5 1, 2, . . . , n.


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To simplify and accelerate the whole measurementprocedure, multiple images corresponding to thephase-shifted reference waves are recorded duringthe measurement, and the necessary phase front canbe built after the measurement by use of the recordedimages in the computer memory. Usually 8–16phase-stepped images are recorded in one measure-ment. By variation of the synthesized referencephase front in the memory, when a suitable fringepattern is obtained ~e.g., fringe pattern with desirablefringe density for automatic evaluation!, the evalua-

Fig. 4. Deformation measurement when the illumination of the ohe two intensities was greater than 100. ~b! and ~c! When the

presented only on halves of the object. The adaptive feature of theon the whole object surface with uniform visibility ~d!.


tion of the compensated fringe pattern takes place.The actual deformation of the test object is the sum ofthe synthesized deformation and the compensateddeformation.

An additional feature of this method is that thesensitivity of the measurement can be changed afterthe recording. This fact is extremely valuable in in-dustrial measurements, in which the measurementcan rarely be repeated under the same conditions.When we evaluate the correlogram, the fringe densityat highly deformed points can be decreased, or differ-

is not uniform. ~a! Scattered light from the object The ratio ofnsity of the reference beam is adjusted, correlation fringes areuation–controlling program can help to get the correlation fringes

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ent components of the complicated fringe pattern canbe removed, and so the evaluation of the fringe sys-tem can be performed more easily.

In the actual experiment a 35 mm 3 35 mm bronzeplate was slightly rotated and deformed by concen-trated force acting at the middle of the plate betweenthe exposures. The corresponding fringe patterncan be seen in Fig. 5~a!. In the undeformed stateeight phase-stepped images were recorded. By useof the evaluation program, fringes from the rotation@Fig. 5~b!# and from the deformation @Fig. 5~c!# aresuccessfully separated.

Phase-shifting techniques are successfully applied

Fig. 5. Application of the synthesized reference beam method.Separated displacement components: ~b! rotation, ~c! deformatio

in comparative methods20 because of the higher pre-cision. Using the redundant data set, the compen-sated phase map can be calculated by this method,too. With eight phase-shifted pictures in the mea-surement the phase difference between two succes-sive pictures is 2py8. If the cycle of the applied

hase-shifted images starts not from the first, butrom the third or the fifth image, the resulting fringeatterns are phase shifted by 90 or 180 deg, respec-ively. So the three-frame phase-stepping techniquean be applied. One example can be seen in Fig. 6.he original fringe pattern was the same as in Fig.~a!, but the fringe system was only partially com-

Original fringe pattern built from two types of displacement.
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pensated. From three phase-stepped intensitymaps the phase map for the compensated measure-ment can be calculated.

6. Conclusions

It has been shown that the presented simple TV ho-lographic arrangement may be adapted to differentmeasuring tasks and conditions. Various realiza-tions of adaptivity were presented. Application ofsimple computer-controlled optical devices ~e.g.,computer-controlled beam stops and computer-

Fig. 6. Application of phase-stepping method in synthesized ref-erence beam technique. ~a! Original partially compensated cor-relation fringe pattern, ~b! calculated phase map.


controlled beam splitters! enhances the adaptabilityof the system. A method, believed to new, has beenintroduced in which the virtual images of the masterobject—produced by a simple HOE—can be used fora phase-synthesized reference wave in electronicspeckle-pattern interferometers. The wave front ofthe reference wave is synthesized with phase-steppedreconstructions of the master object. By use of thistechnique the fringe density at highly deformedpoints can be decreased, or different components ofthe complicated fringe pattern can be removed, whichresults in an increase of the sensitivity and leads toeasier evaluation of the fringe pattern. The sug-gested method has been applied successfully for pro-ducing intensity maps as well as phase maps.

This research was supported by Hungarian Na-tional Scientific Research Foundation ~OTKA! project

032911.

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adaptive systems in speckle-pattern interferometry

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