Detection and measurement of small vibrations usingelectronic speckle pattern interferometry

KAre H0gmoen and Ole J. L0kberg

We describe a new method for real-time detection and measurement of small vibrations, based on phasemodulation in time-average electronic speckle pattern interferometry. The modulation frequency is shiftedrelative to the vibration frequency, which makes the intensity of the reconstructed image vary at the differ-ence frequency. The amplitude detection limits are about 20 A by visual observation and 0.1 A8 by photo-electric measurement using a lockin technique. No auxiliary system for fringe stabilization is required. Athigher amplitude levels we can study the deformation of the object in slow motion. Measurements on differ-ent objects, including human ear preparation, are presented.

1. Introduction

By ordinary electronic speckle pattern interferometry(ESPI) we can detect vibration amplitudes down toabout A/12, while an amplitude of about X/5 is neededto give the first dark fringe for an absolute measure ofthe amplitude. Using a He-Ne laser (X = 6328 A), weget about 500 A and 1200 A as detectable and measur-able limits, respectively.

In many applications of optical vibration analysis, thedetection and measurement of amplitudes below theselimits are either required or desired. We have experi-enced this demand while working with biological objectslike human ear preparations, where excitation atphysiological sound pressure levels gives very small vi-bration amplitudes. Another example is testing ofsonar transducers in water, where large amplitudes andhigh frequencies result in deteriorating cavitation.From a more practical point of view, an increased sen-sitivity would reduce the demand for expensive poweramplifiers.

ESPI can be described as image holography with thefilm emulsion replaced by the TV target; therefore, itis natural to consider whether holographic methodswhich increase the sensitivity for small amplitude de-tection", 2 can be adapted to ESPI. By holography in-creased sensitivity is normally achieved by use of fringefunctions which give dark nodal areas, while small am-plitude antinodes reconstruct with larger intensity.The resulting increased contrast makes vibration am-

The authors are with University of Trondheim, Norwegian Instituteof Technology, Physics Department, N-7034 Trondheim-NTH,Norway.

Received 1 March 1977.

plitudes of the order of X/100 detectable,' a limit whichis highly dependent upon the background noise level.These methods are primarily used to increase the limitof visual detection, while absolute measurements are notreadily obtained. Transferred to ESPI, these methodscannot be expected to give satisfactory results due to thehigh background noise level and coarse image structureby ESPI.

It should also be noted that point measurements ofamplitudes down to 10-2 A have been reported by useof laser interferometric techniques. 3 -5 However, vi-brational noise and thermal instabilities representproblems by these techniques and have made vibrationisolation and stabilization systems necessary.

In this paper we describe a new method to increasethe sensitivity by ESPI, which provides both visualdetection and photoelectric measurement of small vi-brations without any additional system for stabilization.In a subsequent paper (Hogmoen and Pedersen, inpreparation) a theoretical analysis of this method forsmall amplitude measurement will be presented.

II. Description of the Method

Sinusoidal phase modulation of the reference wavein ESPI has been used to increase the amplitude rangetoward larger amplitudes and to separate the amplitudeand phase distributions of vibrating objects.6 7 Usingsubfringe interpolation,8 the same modulation tech-nique can be used to detect and measure smaller am-plitudes.

By time-average ESPI the reconstructed intensitydistribution across the object is given by J 2 [(47r/X)u(x,y)], where Jo is the zero order Bessel function offirst kind, and A is the wavelength of the laser light.With no additional phase modulation, u(x,y) is directlygiven by the amplitude distribution across the object.Figure 1 shows the J 0

2 function. The slope of this curve

July 1977 / Vol. 16, No. 7 / APPLIED OPTICS 1869

c0.5-Woking poi.t

00 500 Ur 1000Vibration amplitude A

Fig. 1. The intensity function J 02 (47ru/X) vs vibration amplitudeu, X = 6238 A. ur-working point by phase modulation.

._

C

4E

.o-

0 Piot

Position

Fig. 2. Intensity distribution along a stiff bar, vibrating around acenter pivot. Reference modulation in phase with the left part of the

bar (fully drawn) and the right part (dotted).

a)Moulaingmi4ro-

-t

b) T.o,Modulating *

FromW Pit. ILock-in Detsctor-apItfier amplifier

gSi newnve _.rquencyl

Fig. 3. Experimental arrangement: (a) setup for visual detectionand photoelectric measurement; (b) calibration setup.

shows that the intensity variation, and thus the sensi-tivity, are poor at very small amplitudes.

Phase modulation is obtained by reflecting the ref-erence wave at normal incidence from a mirror, vi-brating at the same frequency as the object, but withamplitude ur and phase qr Assuming normal illumi-nation and observation, the intensity I(x,y) of the objectas reconstructed on the TV monitor can be written9

I(x,y) = Io(x,y)Jo2 ( lu 2 (x,y) + ur2

- 2U0 (X,y)ur cos[(x,y) -kr$]}12), (1)

where u(x,y) and f0 (x,y) are amplitude and phasedistributions across the object. I(x,y) is the recon-structed intensity distribution with the object and themodulating mirror at rest.

We now suppose the modulating mirror amplitudeu, to be adjusted so that nodal points on the object[where u0 (x,y) = 0] reconstruct with about half of theirmaximum intensity. This value of ur determines theworking point, which is indicated in Fig. 1. The vi-brating parts of the object will reconstruct with an in-tensity depending on the amplitude and phase of theobject relative to the modulating mirror, according toEq. (1). The resulting intensity distribution as givenby a single interferogram will generally be impossibleto interpret without additional information regardingthe object's vibration mode.

If we vary the phase r of the modulating mirrorcontinuously, the intensity of an object point will varybetween a maximum and a minimum value determinedby the vibration amplitude u, (x,y) at that point.Therefore, the range of intensity variation with varyingreference phase is a direct measure of the object's vi-bration amplitude. As an illustration we consider Fig.2, which gives the reconstructed intensity distributionof a stiff bar vibrating around a center pivot. Themaximum vibration amplitude of the bar is supposedto be small enough to keep the argument of the Jo2

function within the linear range, which is indicated inFig. 1. In Fig. 2 the fully drawn line gives the intensitydistribution when the reference phase equals the phaseof the left part of the bar, while the dotted line gives theintensity when the modulating mirror vibrates in phasewith the right part of the bar.

In practice, we obtain a continuous phase variationby driving the modulating mirror at a frequency fr

which is slightly different from the object's vibrationfrequency f The frequency difference f = fr - f ischosen small enough relative to the framing rate of theTV system to satisfy the sampling theorem. Thisimplies that the TV system can display an intensityvariation at the beat frequency f. The framing rateof our standard TV system is 25 Hz, and since f >> 25Hz, we essentially record time-average interferogramsof the corresponding exposure time, i.e., 1/25 sec.

This modulation technique results in an intensityvariation on the TV monitor at the beat frequency Af.The magnitude of the intensity variation is directlyrelated to the object's vibration amplitude u (x,y). By

1870 APPLIED OPTICS / Vol. 16, No. 7 / July 1977

appropriate choice of Af, we get an intensity flickerwhich increase the limit of visual detection. We usephotoelectric measurement of the intensity variationto obtain absolute amplitude and phase values on se-lected parts of the object.

III. Experimental Setup

The ESPI setup used for the experiments is shownin Fig. 3. The laser is a 10-mW He-Ne laser with X =6328 A, and the vibration amplitude values given in thispaper should be referred to this wavelength. The objectis imaged by two lenses onto the Si target of the TVcamera. The reference wave is reflected by two mirrors,filtered, expanded, and superimposed in line with theobject wave. The video signal from the TV camera isfiltered and rectified in the usual way, and the processedimage interferogram is displayed on the TV monitor.

Phase modulation of the reference wave is providedby the modulating mirror, which is mounted on a pi-ezoelectric drive element. The mirror is acousticallyisolated to prevent coupling to the object.

The object is excited by a sine wave generator at fre-quency f,. From the same generator we get the inputsignal to a frequency translator, which provides theshifted modulation frequency fr = fo + Af. Af is ad-justable in the 0-± 10-Hz range. The frequencytranslator also provides a signal at Af, which can be usedas reference for a lockin amplifier. The reference andobject signal levels are controlled by amplifiers.

For photoelectric measurement of the intensityvariation we position a P-I-N photodiode, with a I-cm 2

active area, on the front of the TV monitor. We nor-mally use a lockin amplifier to measure the amplitudeand phase of the signal from the photodetector.

IV. Visual Detection

For visual detection of small amplitudes we adjust thebeat frequency to the range where the human eye ismost sensitive to flicker. According to the de Langecurves10 this should be in the range from 8 Hz to 12 Hz,where an intensity variation of less than 1% should beobservable under optimal conditions. The slope of theJ 0 2 function at the working point shown in Fig. 1 gives3.7-A vibration amplitude per 1% intensity change.Thus, we should have a theoretical detection limit ofabout 3.5 A. However, our experimental conditions aredifferent from those of de Lange. The coarse, speckledstructure of the image presented on the TV monitor,together with electronic noise, can be assumed to in-fluence the optimal frequency and the detection limit.We have experienced the optimal frequency range to be3-5 Hz and have found a detection limit of about 6%intensity variation, which corresponds to 20-25-A vi-bration amplitude. However, this limit also dependson the settings of the electronic processing elements ofthe ESPI system, which determine the contrast andbrightness of the presented image. Blurring of thespeckled image by, e.g., electronic low-pass filteringafter processing, has also been shown to have a favorableeffect.

At higher amplitude levels we get a valuable slow-motion presentation of the object's movement; we are

able to follow the deformation of the object during itsvibration cycle. Areas of the object with different vi-bration phases reach their intensity extrema at differenttimes. These time differences are directly proportionalto the phase differences, while different amplitudesresult in different values of the extrema. For the bestvisual impression of this effect, we should use a beatfrequency of 0.5-1 Hz, and the amplitudes should bewell above the detection limit.

A. Experimental Results

In the first example we consider a 10-cm circular steelplate. It was sprayed with retroreflective paint to im-prove the light economy. Since this object is very fa-vorable with regard to fringe contrast and stability, theresults described are assumed to represent an optimumfor our present system, which is based upon standardTV equipment. We found the limit of visual detectionto be about a 20-A peak vibration amplitude. This limitwas obtained by using very high contrast on the TVmonitor and by blurring the image speckles. Withoutthese precautions, the detection limit was about 30 A.Thus this technique increases the visual detection limitby an order of 25 compared to ordinary time-averageESPI. If we increased the amplitude to above 80 A, wegot an impression of the vibration phase distributionand could observe the vibration in slow motion.

Figures 4(a) and 4(b) show ordinary time-averageESPI recordings of the plate vibrating at 4600 Hz; thepeak amplitudes are about 0.27 ,4m in (a) and 200 A in(b). In Figs. 4(c) and 4(d) the excitation is the same asin (b), but they are recorded with modulated referencewave, ur = 575 A. In (c) the modulation is in phase withone set of antinodes; in (d) the modulation phase isshifted 1800 to the other set of antinodes. We want toemphasize that by direct observation of the flicker, theintensity variations are much easier detected than fromphotographs.

We have used the same method investigate a moredifficult object: the ossicular chain in fresh humantemporal bones. The preparation and excitation of thisobject are described in greater detail in Sec. V.B. Inthis case, the method was very valuable as a rapidscanning method before photoelectric measurement.On this unstable object, with gross variations in reflec-tivity, we experienced a visual detection limit of about50 A. By studying the vibration in slow motion, wecould readily detect differences in vibration mode,which we did not detect by ordinary time-average ESPI.This method also enabled us to use lower, more physi-ological sound pressure levels.

V. Photoelectric MeasurementIf we want to detect amplitudes below the visual de-

tection limit and obtain absolute amplitude and phasevalues, we use photoelectric measurement of the in-tensity variations presented on the TV monitor. Thisis simply done by positioning the detector (e.g., a pho-todiode) in contact with the monitor at the object pointof interest. The detector area should be large enoughto average over a sufficient number of speckles. In thisway, we record the average intensity and avoid the in-

July 1977 / Vol. 16, No. 7 / APPLIED OPTICS 1871

(a) (b)

(c) (d)

Fig. 4. ESPI recordings of plate vibrating at 4600 Hz. (a) Ordinary time-average recording, peak amplitude about 0.27 Am. (b) Same as (a),but peak amplitude about 200 A. (c) As (b) with modulated reference wave, modulation in phase with one set of antinodes. (d) Same as (c),

but modulation phase is shifted 180°.

fluence of random intensity fluctuations of single spe-ckles. On the other hand, the detector should measurethe intensity at approximately one object point. Tofulfill these conflicting demands, we can use an aperturein front of the detector, alter the image magnification,and to a certain degree adjust the speckle size by varyingthe aperture of the ESPI imaging system.

The signal from the photodetector consists of currentpeaks due to the sampling of the TV system. The peaksare amplitude modulated by the intensity variation atthe beat frequency Af. Figure 5 gives examples of os-cilloscope traces of the photodetector signal. In orderto demodulate this signal and measure the amplitudeand phase of the frequency component at Af, we havefound it most appropriate to use a lockin technique.The beat signal at Af from the frequency translatorserves as a reference for the lockin amplifier. The longaveraging times and the corresponding narrow band-widths of the lockin amplifier make it possible to mea-sure low-level signals buried in noise.

In this connection, we would like to point out thatvarying image lag across the target of the TV camerallmight give erroneous phase values if we measure dif-ferent points on the monitor. We have measured animage lag difference of the order of 10 msec across ourmonitor under normal experimental conditions. At abeat frequency of 6.0 Hz, as normally used, this corre-sponds to a phase error of 220. However, we can avoidthe effect of this varying image lag by measuring at afixed point on the monitor and shifting the image of theobject. By visual observation, this effect is hardly de-tectable, since we then use a lower beat frequency.

A. Calibration

In order to calibrate the lockin amplifier readingsagainst vibration amplitude, we use the modulatingmirror, whose response is known, to simulate a knownobject movement. The object itself is at rest. In Fig.3(b) we have shown the electronic part of the calibrationsetup. At frequency fo we apply a signal to the mirror

1872 APPLIED OPTICS / Vol. 16, No. 7 / July 1977

(a)

(b)

Fig. 5. Oscilloscope traces of the signal from the photodetector.Af = 6.0 Hz. Vibration amplitudes about 60 A (a) and 15 A (b).

that makes it vibrate with an amplitude Ucal in the10-100-A range. We also add a signal at frequency f,= fo + f, with an amplitude which determines theworking point ur in Fig. 1. The added signals are ap-plied to the mirror, making the intensity of the imagevary uniformly at frequency Af. Using the photode-tector and the lockin amplifier, we record this intensityvariation (given as a voltage) as a function of Ucal. Thus,from knowledge of the mirror response, we have deter-mined the calibration factor in terms of mv/A.

This calibration factor is valid for the object point,working point, and beat frequency chosen. However,if we examine an object of about uniform intensity, wemay use the calibration factor from one object point bymeasurements across the whole object at the cost ofsome loss in accuracy. For instance, when scanning aturbine blade, we observed a variation in the value of thecalibration factor of 7%.

This calibration procedure presumes that we knowthe response of the modulating mirror. Our mirror hasbeen tested in a Michelson interferometer and has aconstant response of 40 A/V in the 0-34-kHz frequencyrange. We may also calibrate the mirror in the ESPIitself. This is done by recording the intensity of a sta-tionary object as a function of excitation voltage to themirror at a single frequency. A typical recording isshown in Fig. 6. We know that the voltage which givesthe first minimum of the intensity corresponds to about1200-A effective vibration amplitude, according to Fig.1. Effective implies here that we have taken into ac-count the angles of incidence and reflection to themirror. For more accurate calibration we can also usehigher order maxima and minima of the intensityfunction.

We also use this intensity recording to optimize theparameters of the ESPI system, such as camera settings,filter/rectifier, monitor, and object wave to referencewave intensity ratio. Ideally, the intensity recordingshould resemble the J 0 2 function in Fig. 1.

50

Modulation voltageV

Fig. 6. The intensity of a stationary object point recorded as functionof modulation voltage; vibration frequency, 1000 Hz. Fig. 7. Photodetector (arrow) positioned on the TV monitor.

July 1977 / Vol. 16, No. 7 / APPLIED OPTICS 1873

100

I

ioo_~

TC=3s

10_

TC-10,

1.0--

TC=30s

TC =00r/

0.1 L _0.01 0.1 1.0 10

Excitation voltage, V

Fig. 8. Vibration amplitude of the plate measured as a function ofexcitation voltage. TC-required output time constants of the lockin

amplifier.

Fig. 9. Ordinary time-average ESPI recording of turbine blade, vi-brating at 2200 Hz.

B. Experimental Results

As the first example, we consider the 10-cm circularsteel plate from Sec. Iv.A. We used an electromagnetictransducer for excitation. For photoelectric measure-ments, we increased the magnification and placed thedetector as shown in Fig. 7. Figure 8 gives measuredvibration amplitude as a function of excitation voltage

to the electromagnetic transducer. In Fig. 8 we havealso included the output time constants of the lockinamplifier (with 18-dB/octave output filter), requiredfor stable readings at the different amplitude levels.This measurement was carried out in rather noisy sur-roundings with traffic passing just outside the window5 m away, but still a detection limit of 0.1 A could bereached, although at the somewhat uncomfortable timeconstant of 100 sec.

The next example of application is a 4 X 11-cm2 tur-bine blade, excited with a ceramic drive element.Figure 9 shows an ordinary time-average ESPI record-ing of the blade, vibrating at a high amplitude level at2200 Hz in its second torsional mode. By shifting thecamera, we scanned across the blade and measured thevibration amplitude and phase at nine different pointsat three low excitation levels. The monitor image wasmagnified 3X in order to approximate point measure-ments. The results are shown in Fig. 10. The phasemeasurements showed that the blade was vibrating ina pure mode, with opposite phase on each side of thenodal line. In this case, we made separate calibrationat each point, because there was some intensity varia-tion across the blade. About 1Y2 h was required for thisscanning measurement; we used lockin amplifier timeconstants of 3 sec or 10 sec.

As an example of a more adverse object, we againconsider the human temporal bone preparation. Thepreparation was opened from the medial side, whichgave us access to malleus and incus of the ossicularchain. A closed sound system was used to excite the

20 /--

.4 0

.<ow

.0

> 20t-

10

Position

-rI I

Fig. 10. Vibration amplitudes measured at different points (0) onthe turbine blade, vibrating at 2200 Hz. Negative amplitudes imply

phase reversals. Excitation voltages: , 2.0 V; A 1.0 V; * 0.5 V.

1874 APPLIED OPTICS / Vol. 16, No. 7 / July 1977

._aE

.0

100

E.E

.0

.0 10

1L0.1 1.0 10

Frequency, kHz

Fig. 11. Vibration amplitude vs. frequency, measured at the malleushead in a human temporal bone preparation. Sound pressure

level-90 dB.

.4

CLc.E

100-

50-

0 200 400

Time, s600

Fig. 12. Time variation of lockin amplifier output at constant ex-citation (1600 Hz, 90-dB SPL) of the temporal bone. Measuringpoint: malleus head. Output time constant of the lockin amplifier,

TC = 3 sec.

drum membrane, and we used a probe microphone tomeasure the input sound signal at the membrane.Figure 11 shows vibration amplitude recorded at themalleus head as a function of frequency at 90-dB SPL(sound pressure level re 2 X 10-5 N/M2 ). We usedlockin amplifier time constants of 3 sec below 2500 Hzand 10 sec at higher frequencies. To illustrate the effectof the over-all noise, Fig. 12 shows the output of thelockin amplifier, recorded as a function of time. Theexcitation (1600-Hz, 90-dB SPL) was turned on at thebeginning and off at the end of this recording. We findan equivalent noise displacement of 10 A peak to peakat 95-A peak vibration amplitude. The output timeconstant was 3 sec.

VI. Conclusion

We have described a new method for real-time de-tection and measurement of the amplitude and phaseof small vibrations, based on ESPI with phase modu-lated reference wave. The modulation frequency isslightly shifted relative to the vibration frequency of theobject, and we detect the beat between the two motions.The method has a visual detection limit of the order of20 A and a limit of 0.1 A by photoelectric measurement.This represents a major increase in sensitivity comparedto ordinary ESPI techniques.

The method makes use of the favorable characteris-tics of ESPI: high sampling rate and short exposuretime, which make it possible to examine unstableobjects in rather noisy surroundings. We also get avivid visual impression of the object's vibration in slowmotion at low amplitude levels. These propertiesoutweigh the disadvantages of the poor image qualityby ESPI.

By use of photoelectric measurement of the intensityflicker, there are two additional averaging processes thatcome to our benefit. First, the detector averages overa representative number of speckles; and, second, thelockin amplifier averages over a large number of TVframes, i.e., over many beat periods. Altogether, thesecharacteristics of the system make it possible to measurevery small vibration amplitudes on relatively unfavor-able objects. Unlike other comparable optical inter-ferometric techniques,3-5 our method does not requireany additional system for fringe stabilization. An ab-solute in situ calibration of the system is readily per-formed, and its spatial resolution is adjustable byvariation of image magnification and/or detector size.We may also store the information by use of a videorecorder, which enables us to select different objectpoints and analyze their motions at a later processingstage. This should prove very convenient when weexamine objects like biological preparations, whereaging effects influence the object's behavior. Finallywe mention that it should be possible to perform thevibration measurement on the video signal directly in-stead of using photoelectric measurement on the TVmonitor.

Thanks are due to T. Gundersen for preparing thetemporal bones, 0. M. Holje for valuable assistanceduring the experiments, and H. M. Pedersen for stim-ulating discussions of this paper.

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(1968).4. H. A. Deferrari, R. A. Darby, and F. A. Andrews, J. Acoust. Soc. Am. 42, 982

(1967).5. P. R. Dragsten, W. W. Webb, J. A. Paton, and R. R. Capranica, J. Acoust.

Soc. Am. 60, 665 (1976).6. 0. J. Loikberg and K. Hgmoen, J. Phys. E. 9,847 (1976).7. 0. J. Lokberg and K. Hogmoen, Appl. Opt. 15, 2701 (1976).8. A. F. Metherell, S. Spinak, and E. J. Pisa, J. Opt. Soc. Am. 59, 1534

(1969).9. C. C. Aleksoff, Appl. Phys. Lett. 14, 23 (1969).

10. W. A. van de Grind, 0.-J. Grusser, and H.-U. Lunkenheimer, in Handbookof Sensory Physiology, R. Jung, Ed. (Springer-Verlag, Berlin, 1973), Vol.7/3 A, p. 447.

11. A. D. Cope, S. Gray, and E. C. Hutter, in Photoelectronic Imaging Devices:Devices and Their Evaluation, L. M. Biberman and S. Nudelman, Eds.(Plenum, New York, 1971), Vol. 2, p. 47.

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