Sound in flight: measurement of sound fields by use of TV holography

Sound in flight: measurement ofsound fields by use of TV holography

Ole J. L0kberg

The integrated amplitude and phase distribution of the sound field propagating from sinusoidallyvibrating objects in air have been recorded by time-averaged TV holography. The behavior of the soundfield is observed in real time by use of dynamic phase modulation. The magnitude and direction of thefield are found by acoustic phase stepping and image processing. The field is three dimensional, andrecordings of several cross sections are necessary for a complete description, but in many cases valuableinformation can be obtained by two-dimensional projections. The technique has been used to studysound propagation and details in the sound emission from extended sources.

Introduction

The refractive index of air is directly proportionalto the air pressure. Changes in the refractive indexas light passes through the medium can be measuredby optical techniques such as schlieren photography,classical interferometry, or holographic interferom-etry. Recording and analysis of strong pressurevariations, such as shock waves in air or water, bythese techniques have been commonplace for manyyears; see, for example, an excellent discussion in Ref.1. The mapping of weaker sound-pressure distribu-tion generated by sinusoidally vibrating objects atnormal sound levels is of practical interest, but noattempts to quantify the field directly in terms ofstrength and direction have been found in the litera-ture. The reason for this can be found mainly in thesmall fringe shifts introduced by these pressure varia-tions. In addition, to find the direction of the energypropagation, we need to quantify the acoustical phaseof the field.

TV holography (electronic speckle pattern recogni-tion) coupled with dynamic phase modulation hasbeen proved to possess the ability to detect a low levelof vibration amplitude and also to be phase sensitive.2Playing with this technique, we have observed effectsfrom sound pressure; however, the slow and cumber-some measuring analysis that is necessary when one

The author is with the Department of Physics, The NorwegianInstitute of Technology, 7034 Trondheim, Norway.

Received 21 May 1993; revised manuscript received 29 Septem-ber 1993.

0003-6935/94/132574-11$06.00/0.o 1994 Optical Society of America.

is using the pointwise lock-in technique did notencourage us to quantify the findings. Automaticdata acquisition followed by digital analysis as re-cently developed in our group measures amplitudeand phase distributions with high accuracy and sensi-tivity.3 In this paper I demonstrate how this tech-nique can be used to map the amplitude and the wavefronts of a propagating sinusoidal sound wave.

Theory

Sound Pressure versus Optical Fringe ShiftTo calculate the fringe shift resulting from the soundpressure, we use the Gladstone-Dale relation'

n - 1= const., (1)

where n is the refractive index and p is the density ofthe gas (air).

We assume nonadiabatic expansion and combineEq. (1) with the usual interference conditions to findthe fringe shift

Am =A(no -) (2)

where d is the distance traversed by the light, X is thewavelength, no is the refractive index at atmosphericpressurepo, andp, is the increased pressure caused bythe sound wave.

To get a feeling for the magnitude of the fringe shiftproduced by normal sound-pressure levels, we as-sume that A = 633 nm, no 1.0003, andpo 105 Pa(normal atmospheric pressure); 94 dB of sound level

2574 APPLIED OPTICS / Vol. 33, No. 13 / 1 May 1994

correspond to 1 Pa of increased air pressure (therms value for a sinusoidal pressure wave) relative tothe atmospheric pressure. We assume that the soundpressure is constant over 10 cm, which gives a fringeshift of 1/750 at 94 dB. This fringe shift repre-sents an equivalent vibration amplitude of 0.4 nm,which reconstructs far below the first dark fringe in atime-averaging recording. A change of 20 dB in thesound field corresponds to a 10-fold increase ordecrease in air pressure and fringe shift. We mustincrease the sound level to slightly more than 130 dB,which by the way represents an intolerable soundeven in this era of disco terror, to obtain a slightlydarkened reconstruction. It is therefore obviousthat if we want to record the sound-field distributionat sound levels acceptable to co-workers in the samebuilding, we must be able to record small fringe shifts.

Observation and Interpretation of the Sound Field

To calculate the pressure distribution according toEq. (2), we must assume that the distance d that thelight traverses is constant or has known variations.If we observe directly into the vibrating sound source,the fringe shift caused by changes in d (the vibrationamplitude) will in normal circumstances be far greaterthan the fringe shift caused by pressure changes inthe surrounding air.

We therefore must record the refractive-indexchanges in the light passing around the sound emitteras in the classical interferometry of shock waves, etc.This again leaves us with two options for the opticalsetups as shown in Fig. 1.

In Fig. 1(a) the light is transmitted once throughthe volume. The speckle wave is produced by adiffuser in either of the two positions shown in thefigure. Figure 1(b) shows a double-pass option inwhich a retroreflective screen can be used to improvethe light economy. The double pass has twice theinterferometric sensitivity compared with Fig. 1(a),which is definitely an advantage because of the smallfringe shifts generated by the sound field. Becauseof refraction in the air path, a ray might pass throughdifferent paths through the sound field to and fromthe recording unit. However, we have already found

diffuser diffuserpos.2 pos 1

interferometer

sound source(a)

imaging screeninterferometer beam splitter

illumination sound source

(b)

Fig. 1. Setups for recording the sound field: (a) single-passtransmission, (b) double-pass reflection.

that the fringe shifts to be measured are extremelysmall and the double-pass setup can be used withoutproblems since the rays are hardly influenced by thechanges in the refractive index.

In whatever configuration we use we measure theintegrated index change along the path length. Theabsolute value of this integrated change correspondsto the conventional vibration amplitude, whereas thetiming of the maximum change relative to a referencesinusoidal signal corresponds to the vibration phase.The measured amplitude thus indicates the strengthof the field, and the phase shows the wave fronts ofpropagation. The normal to the wave front indi-cates the direction of the energy flow.

We should not, however, forget that we are record-ing an integrated value of the field and we shouldinterpret our recordings with care. To illustrate thisproblem, we look at the field from an acoustical pointsource shown in Fig. 2. The semicircles representthe wave fronts of the sound field where the positive-negative air pressure is given by the pluses andminuses. From the normal 1/r falloff in the ampli-tude of a spherical wave, we should expect the samereduction in the recorded field strength. However,computer simulation tracing rays such as r and r2through the volume shows this falloff to be almostcompensated by the increase in the total path length.Integration along an infinite path yields a divergingcylindrical wave-amplitude falloff, 1/f, and aphase shift of iT/4. However, because we integratealong a finite path through positive and negativecontributions, the field amplitude is modulated by afringelike spherical pattern. The simulation alsoshows the integrated wave fronts to be correctlyrepresented as a first approximation. The inte-grated wave fronts are slightly retarded comparedwith a real wave front propagating straightforwardly,but this delay represents only an insignificant changein the absolute phase.

For a complete description of the three-dimen-sional field, we must determine three-dimensionaldistributions from two-dimensional projections. Theprojected field must be recorded from numerousdirections, and inversion mathematics is used toinvert the results.' We can achieve a change in theprojection angle by rotating the sound emitter ormoving the interferometer around it. In both caseswe must be extremely careful not to change theacoustical field.

In many cases, however, the two-dimensional pro-

J 4soundsource

Fig. 2. Integration of ray paths through the wave fronts of a pointsound source.

1 May 1994 / Vol. 33, No. 13 / APPLIED OPTICS 2575

jection can be useful and instructive for understand-ing the behavior of the sound field. Planar wavefields observed normal to the propagation is oneexample. It is also possible to localize the areas of anextended sound source making the largest contribu-tion to the sound emission by observing the field closeto the source surface before the field componentsoverlap. Note that in this sense the interferometricobservation is complementary to measurements byacoustical sensors, which are problematic to use inthe near field where their presence interferes with thesound field.

Recording and Calculation of the Sound Field

We assume that our sound source vibrates with asingle, stable frequency f and that the correspondingamplitude and phase distributions in the vibrating airare given by a(x, y) and po(x, y). The x and ycoordinates are referred to the corresponding loca-tions in the image (detector) plane. As mentionedabove the amplitude ao(x, y) and phase po(x, y) in thiscase correspond to the integrated value of the refrac-tive index during the vibration cycle.

We make a TV-hologram recording of the vibratingpressure field. Normally the exposure time of thevideo system spans several vibration cycles, in whichcase the intensity distribution ITA(X, y) across themonitor image can be written as

ITA(X, A) J| g((+)ao(x, A)| (3)

where Jo is a Bessel function of the first kind and ofzero order and g(+) is the normal interference anglefactor, which can be set equal to 2 in our experiments.

From approximation (3) we find the equivalentamplitude distribution ao(x, y). The phase informa-tion is lost, however. In addition the interferometricsensitivity of the time-average function is not greatenough to reveal small fringe shifts as discussedabove. We can solve both of these problems byintroducing sinusoidal phase modulation into theinterferometer-usually by using a vibrating mirrorin the reference path. The modulation introducesan equivalent amplitude and phase, ar and (Pr, in theinterferometer, which modifies the intensity distribu-tion to read

ITA/PM(X, )

Jo2( A [g($)a0 (x, y)]2 + ar2 - 2g(,k)ao(x, y)ar

X cos[(po(x, y) - Pr]-/2 (4)

Comparing approximations (3) and (4), we see thatthe fringe function itself remains unchanged by theintroduction of the reference vibration. The argu-ment of the function does, however, now include theunknown phase distribution po(x, y) although it is

r:5S

S

Imil

- r -+ amplitudeFig. 3. Intensity of time-average fringe function J 2 at lowvibration amplitudes. Amplitude a, represents the working pointwhen sinusoidal PM is used.

encoded in the vectorial difference between the objectand reference vibrations.

For real-time observation the mirror is vibrated atan amplitude ar, which defines a working point on thesteepest part of the fringe function (see Fig. 3).Changing the phase Pr continuously gives a slow-motion display of the movement where the magni-tude is coded in the modulation of the gray levels,while the phase is dynamically coded as the timeprogression of the gray level.2 By optimizing therate of phase change and the monitor setting, we canvisually observe and to a certain degree interpretvibrations at amplitudes down to approximatelyX/250. This mode of observation has proved ex-tremely useful for finding interesting behavior in thesound field since the real-time display of TV hologra-phy permits us to scan continuously through thefrequency range.

In our data acquisition and fringe-analysis proce-dure3 we first vibrate the reference mirror at ampli-tudes corresponding to the extremal parts arma andar mi of the linear region of the fringe function, andthe corresponding Imae and Imin are recorded as thetwo first frames. The intensity values of these framesare used to calibrate the sensitivity of the system interms of an intensity-versus-amplitude factor k(x, y),which represents the slope at the working point.After the calibration the reference wave is vibratedwith an amplitude an. The object is vibrated at anexcitation level that keeps the vectorial amplitudesum within the linear part of the fringe function, that

__ __T] ; I (omput1Obj.Wave j I U I

I xcitation -k---_--_--

Fig. 4. Flow diagram of the TV holographic setup used forrecording sound fields. SA, speckle averaging.


- SI

(a)

(b)

Fig. 5. Recording of the sound field from the acoustical point source (dome tweeter) at 5000 Hz placed in the left part of the field: (a)real-time presentation of the TV monitor, (b) computed amplitude and phase values.

is, 30 nm. We step the vibration phase of thereference wave by 00, 900, 180°, and 2700 and recordthe corresponding intensities Io, Igo, I180, and I270.The four phase-shifted recordings are related by

Io(x, y) = Ib(X, y) - k(x, y)ao(x, y)cos p0(x, y), (5a)

s9o(x, y) = Ib(x, y) + k(x, y)ao(x, y)sin p0(x, y), (5b)

I180(x, y) = Ib(X, y) + k(x, y)ao(x, y)cos p0(x, y), (5c)

I270(X, y) = Ib(X, y) - k(x, y)ao(x, y)sin p0 (x, y), (5d)

where the (x, y) coordinates refer to pixel values inthe digitized video image and Ib(x, y) is an (unknown)bias intensity.

We find the vibration phase 0(x, y) simply bysubtracting Eq. (5a) from Eq. (5c) and Eq. (5b) fromEq. (5d) and dividing the results, which give

ll90(xX A - 270(X, ~yo(x, y) = arctan [9~ 2 0 x '] (6)

( I 180(, y) -Io(x, y)

Using the sensitivity factor k(x, y) found by thecalibration procedure, we give the unknown ampli-

tude as

ao(x, y)

={[18 0 (X, ) - o(X, y)]2 + [I90(X, y) - I2 7 0(X, y)]2J 1 /2

2k(x, y)

(7)

After the amplitude and phase distributions havebeen determined the information can be presented invarious ways, for example, two-dimensional contourplots or quasi-three-dimensional mesh plots of ampli-tudes and phases, color-encoded distributions, oreven animated computer displays that show thedisplacement during a vibration cycle.4

Experimental Instrumentation

The recording setup is based on the commercialRETRA 1000 TV-holography unit. Its basic layoutwith the associated electronics is shown in Fig. 4.For a more complete description of the TV-hologra-phy systems see Refs. 5 and 6.

A 5-mW He-Ne laser is built into our unit. Thelaser beam is divided into two paths by an opticalbeam splitter. One path is represented by theObj.Wave box. In this path the laser beam is ex-


(a)

(b)

(c)

(d)


(a)

(b)

(c)

Fig. 6. Two identical sound sources in the left part of the field atfrequencies that provide an acoustical Young's fringe pattern: (a)2500 Hz, (b) 5000 Hz, (c) 8000 Hz, (d) same sources as above butplaced in the extreme left and right parts of the field facing eachother; the frequency is 5000 Hz.

panded to illuminate the retroreflective screen behindthe sound emitter [see also Fig. 1(b)], and the reflectedlight is imaged onto the light-sensitive target of avideo camera. Here the object image is combinedwith the other wave passing through the second pathrepresented by the Ref.wave box in Fig. 4. Thereference wave is a diverging spherical wave that in


(d)Fig. 7. Amplitude and phase of the sound field generated by a midtone speaker at a frequency of 5000 Hz. The field is interrupted(diffracted) by (a) the acoustical edge (a brick), (b), (c) the acoustical slits made of two bricks separated by (b) 2.5 cm and (c) 8 cm, (d) theacoustical mirror at an angle (two bricks at an angle slanted to the field).

its path has been reflected from a (vibrating) mirrorto introduce phase modulation (PM) into the interfer-ometer. At high frequencies (higher than 20 kHz)the PM is obtained by transmission through anelectro-optic modulator.

The object and reference waves are combined in-line by means of an optical beam combiner. Theintensity distribution in this combined (speckle) pat-tern is transformed into a corresponding video signalby the photoelectronic process in the video camera.This signal is subsequently filtered and rectified bythe electronic processing unit to bring out the infor-mation contained in the modulation of the speckles.

Returning to the flow diagram in Fig. 4, we see thatthe data analysis takes place in the computer. Forthe data acquisition our system is equipped with adata translation frame grabber (with lookup tables) topermit us to digitize and store 16 consecutive framesand perform simple calculations, e.g., addition, sub-traction, multiplication, and division on the board.7Further image processing of the fringe data is per-formed by a personal computer. To reduce thecomputing time, the data arrays are reduced from512 x 512 to 100 x 100 pixels, which reduces thespatial resolution in the image but improves thesignal-to-noise ratio. The computer also controls aprocess called speckle averaging whereby the imagequality is improved by the addition of frames ofdifferent speckle structure. 8

In addition the digital generator used for excitationis controlled by the computer. The digital generatoris a two-channel synthesizer used in a two-phasemode for digital recording-one signal is to the soundsource, the other signal is to the PM. The generatoris used in a two-frequency mode for visual inspection.In the audio range its frequency resolution is 1 pIHz,and the relative phase between the source excitationand the PM can be set to an accuracy of 0.30. Thegenerator vibrates the sound source and the mirror inthe reference path. The amplitudes and phases of

the two excitations can be varied separately andrelative to each other.

Experiments

We used a setup as indicated in Figs. 1(b) and 4 exceptthat the illuminating wave front was not collimated.The sound emitters were placed in the vicinity of a70-cm-thick solid concrete wall that acted as thebackground screen. There was no indication thatthe sound induced measurable vibration in the wall.However, at certain frequencies the retroreflectivetape covering the wall showed small pockets of vibra-tion. Because of the small size of these vibrationcells the main features of the sound-field pattern arenot disturbed, but the cells show up as noise specks insome recordings. The floor was covered with soundabsorbers to avoid direct reflections, and the wallsand ceilings were hard reflectors.

The distance from the interferometer to the objectswas varied from 1 to 3.5 m for the different recordings.Note that we do not need to worry about the interfero-metric stability of the sound emitter as long as itsmovements do not substantially change the soundfield. In principle the sound emitter could be sus-pended freely in the room.

All the recordings shown here represent soundlevels where the fringes could be clearly seen in realtime by dynamic PM. However, none of the patterncould be observed by ordinary time-average recording.The recordings to be shown have not been improvedby image postprocessing but represent the raw dataas photographed from the monitor screen. The com-puted values are presented as gray-tone pictureswhere the increasing amplitude or phase is coded ascorresponding increasing brightness.

As a first sound source we used a small loudspeaker(dome tweeter), which in the midfrequency rangecould be considered an acoustical point emitter.Figure 5(a) shows the fringe pattern caused by theemitted sound field as seen directly on the monitor


(a)

(b)

Fig. 8. Steel plate (9 cm x 12 cm) vibrating at 2660 Hz: (a) the ordinary time-average vibration pattern of the plate surface showing twoantinodes separated by a central nodal line, (b) the sound field in a direction parallel to the nodal line.

screen when PM is used. By dynamic PM the fringepattern expands in slow motion, giving a greatlyincreased detection compared with still pictures.Note that this fringe pattern depends on both theamplitude and phase distributions, which makes itdifficult to give an exact interpretation of the field.

The (integrated) amplitude and phase distributionsof the acoustical wave fronts are, however, separatedon the computed values shown on Fig. 5(b). Thephase is constantly increasing out from the source asexpected in traveling waves. The shape of the wavefront is clearly outlined by the black lines where thephase values cross 2Nr. Measurements of the wave-length defined as the distance between the wave frontsgive agreement with the theoretical values within themeasuring accuracy. The envelope of the amplitudedistribution is reasonably constant but modulated bythe fringelike structure because of integration throughthe positive and negative regions as discussed above.Note that this artificial variation of the apparentamplitude causes problems when we are recording atlow sound levels since the amplitude in the minimamay be below the detection limit of the system and weare not able to record the wave fronts there.

In the next experiments we added another identicalloudspeaker to perform some experiments that arewell known from classical optics.

First the loudspeakers are placed 20 cm apart onthe left part of the imaged area to simulate Young'sfringe experiment. Figures 6(a), 6(b), and 6(c) repre-sent the sound fields recorded at frequencies of 2500,5000, and 8000 Hz, respectively. If we disregard themodulation structure on the amplitude maps, weclearly see paths of zero energy. From the wavefronts we see that the field changes polarity goingfrom one fringe to another. This effect is demon-strated particularly well in the near field of thesources.

In Fig. 6(d) the loudspeakers face each other withthe speakers in the left and right corners of the image.Between the speakers the amplitude and phase distri-butions alike show the existence of a standing-wavepattern. The spacing between the wave fronts ishalf of that of the traveling wave, and the phase isshifted by 1800 when we cross the nodes. As wemove away from the symmetry line the phase frontsof the traveling waves appear.

For the remaining acousto-optical experiments we


I-;

i5

I :T

I -l :~ ] AOr Z I Ad

1. tSt~;U I a i

(a)

Fig. 9. Same object as in Fig. 8 but vibrating at 6474 Hz: (a)

used a larger midtone loudspeaker as an illuminator.This speaker gave an approximately plane wave overits active aperture at the frequency, 5500 Hz, thatwas used. In Fig. 7(a) we observe acoustical diffrac-tion around a edge made by a single brick. We seethe wave propagating in the geometrical shadow andalso can observe the presence of a creep wave with itswave front normal to the brick surface. In Figs. 7(b)and 7(c) the sound from the speaker is forced todiffract through a slit. We made the slit by balanc-ing two bricks on top of each other with two smallsteel blocks between.

In Fig. 7(b) the slit opening (2.5 cm) is less than thewavelength used (- 5.3 cm). A standing-wave pat-tern forms in front of the bricks because of reflec-tions, whereas a diffracted spherical wave propagatesbehind the brick. Note how the illuminating wavefront is hardly influenced by the opening.

In Fig. 7(c) the opening (8 cm) is larger than thewavelength. The diffracted wave front has less cur-vature as expected. Note how the illumination waveis clearly influenced by the energy leakage throughthe slit.

Finally Fig. 7(d) shows the acoustical equivalent toLloyd's mirror experiment where the loudspeaker is

(b)

time-averaging vibration pattern, (b) sound field along nodal lines.

placed at an angle to the brick. We observe the inter-ference between the direct wave and the reflectedwave, which gives a combination between a standingwave and a traveling wave depending on the overlap.

So far we have considered the sound source to be ahomogeneous emitter for which we have made noattempts to relate the sound field to the vibrationbehavior of the source. The final experiments dem-onstrate how the technique can be used to diagnosethe source and obtain information not readily obviousfrom the recording of normal vibration patterns.

A 9 cm x 12 cm steel plate excited by a piezoelectrictransducer is used as the first object. Figure 8(a)shows the vibration mode of the plate at 2660 Hz.The plate vibrates in a 3.2 mode with the antinodesout of phase with one another-a fact verified by dataanalysis of the vibration pattern. The emitted soundfield along the direction of the nodal line is shown inFig. 8(b). From the amplitude plot we see clearlythat the field has a zero value in a direction from thenodal line and upward. The main energy propagatesin directions 450 to the surface. The wave frontsas represented by the phase map show the expected1800 phase shift from waves emerging from theantinodes.


(a)

(b)

(c)Fig. 10. Wave fronts emitted from a violin excited by piezoelectrictransducers fastened on the back plate. The front plate facesleft. The figures cover the entire body of the violin and half of theneck: (a) 1250 Hz, (b) 2200 Hz, (c) 3500 Hz.

The vibration pattern of the steel plate at 6474 Hzis shown in Fig. 9(a) where we have four antinodes.The resulting sound field is shown in Fig. 9(b).From the amplitude map we see that the energypropagates with four lobes as expected, but the twooutermost lobes are much stronger than expected

from the vibration pattern. The emitted wave frontis represented by a wave centered at the strongestlobe at the right.

The final example is the sound emission from amusical instrument. In memory of my late father Ichose to use his beloved violin. To obtain suffi-ciently strong excitation of the violin, four smalltransducers were fastened close to one another on theback of the violin. The transducers represented anextremely small load compared with the mass of theviolin. In the recordings the violin was placed up-right with the bridge and sound holes pointed to theleft. Here we show only the phase recordings or thewave fronts propagating from the violin body.

The sound field from the violin could be observed atsome frequencies below 1 kHz but it was weak, and nodetails of interest were detected. The first record-ing, Fig. 10(a), shows the sound field at 1250 Hz.Most sound is generated in the bridge area and theupper part of the back plate. The two contributionsare in phase, giving rise to a common wave front asshown by the phase recording. Little sound is emit-ted from the lower part of the back plate.

The next recording is at 2.2 kHz as shown in Fig.10(b). The front plate sends out a reasonably uni-form wave front. This wave front is continuouslyconnected to the strong sound waves emitted fromthe upper and lower parts of the back plate. Themiddle part of the back plate emits a strong wave outof phase with the remaining parts.

An even more complex sound-emission pattern isshown in Fig. 10(c) where the violin is excited at 3.5kHz. We observe clearly how both the front and theback plates send out sharply defined waves, whichespecially in the front are clearly out of phase withone another. It is also interesting to note how someof the wave fronts are emitted at rather steep anglesto the surface, which may indicate that the vibrationvector receives a considerable contribution from in-plane components. (A final sentimental note: Al-though the author has spent a major part of the last25 years observing live vibration patterns of numer-ous strange objects including his own eardrum, thesight of the old violin emitting sound waves in alldirections was a most memorable experience.)

Conclusion

We have discussed how the small fringe shifts in-duced by normal sound field can be observed by TVholography with dynamic PM. Using acousticalphase stepping and image processing, we can quantifythe amplitude and phase part of the sound field. Inboth cases the quantities measured represent theintegrated values along the light paths, and a tomo-graphic approach is necessary to provide a completerepresentation of the field. Valuable informationmay, however, also be obtained by the two-dimen-sional projection provided by TV holography.

The usual question remains: Will the techniqueor application suggested ever be of practical value?Apart from the pedagogical value of actually seeing


the propagation of the sound field, we believe that thetechnique offers complementary information to ordi-nary vibration analysis by TV holography. For acous-tical diagnosis, locating the main contributions to thesound field may be as valuable as detailed vibrationpatterns of the sound emitter itself.

There are two main drawbacks to the method. Wehave already commented on the problem of recordingintegrated values of amplitude and phase. The sec-ond problem is the high sound pressure needed forobtaining recordings of sufficient quality. Most ofthe experiments were done at a sound pressure wellover 110 dB at 30 cm from the source and 90 dB inthe room and left in their wake burned out speakersand transducers. We have been able to record thewave front at sound pressures as low as 85 dB at 30cm by using a long integration line. The use ofshorter wavelengths from, e.g., a He-Cd laser andmore efficient averaging and sophisticated imageprocessing may enable us to record at acceptablesound levels below 80 dB.

The author thanks Hans M. Pedersen and EiolfVikhagen for stimulating discussions and advice and

J. Paus, SEAS Loudspeaker Company, for furnishingsome of the sound sources.

References

1. C. M. Vest, Holographic Interferometry (Wiley, New York,1979), Chaps. 5 and 6.

2. K. H0gmoen and 0. J. L0kberg, "Detection and measurement ofsmall vibrations using electronic speckle pattern interferom-etry," Appl. Opt. 16, 1869-1875 (1977).

3. S. Ellingsrud and G. 0. Rosvold, "Analysis of a data-basedTV-holography system used to measure small vibration ampli-tudes," J. Opt. Soc. Am. A 9, 237-251 (1992).

4. S. Ellingsrud and 0. J. L0kberg, "Full field amplitude and phasemeasurement of loudspeakers using TV holography and digitalimage processing," J. Sound Vib. 168, 193-208 (1993).

5. R. Jones and C. Wykeds, Holographic and Speckle Interferom-etry (Cambridge U. Press, London, 1983).

6. 0. J. L0kberg and G. A. Slettemoen, "Basic electronic specklepattern interferometry," in Applied Optics and Optical Engi-neering, J. C. Wyant and R. Shannon, eds. (Academic, SanDiego, Calif., 1987), Vol. 10, pp. 455-504.

7. G. 0. Rosvold, "Fast measurements of phase using a PC-basedframe grabber and phase stepping technique," Appl. Opt. 29,237-241 (1990).

8. G. A. Slettemoen, "Electronic speckle pattern interferometricsystem based on a speckle reference beam," Appl. Opt. 19,616-623 (1980).


Sound in flight: measurement of sound fields by use of TV holography

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