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ACOUSTO-OPTIC IMAGING IN DIFFERENT FIELDS OF ACOUSTICS
W. Mayer
To cite this version:
W. Mayer. ACOUSTO-OPTIC IMAGING IN DIFFERENT FIELDS OF ACOUSTICS. Journal de
Physique Colloques, 1990, 51 (C2), pp.C2-641-C2-649. �10.1051/jphyscol:19902150�. �jpa-00230452�
Colloque C2, supplement au n02, Tome 51, Fevrier 1990
ACOUSTO-OPTIC IMAGING IN DIFFERENT FIELDS OF ACOUSTICS W.G. MAYER
Ultrasonics Research Laboratory, Physics Department GeOrgetaJn University, Washington DC 20057, U.S.A.
R e s u m e
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U n e introduction tr&s r a p i d e aux p r i n c i p e s d e la diffrac- tion d e la lumiere par les o n d e s u l t r a s o n i q u e s est s u i v i e par u n e discussion d e la technique d e m i s e e n image acousto-optique(schlieren). C e t t e m e t h o d e est souvent u t i l e A l'obtention d e r e s u l t a t s q u a l i t a t i f s ayant trait h d i v e r s ph&nom&nes d'acoustique
u l t r a s o n i q u e o u sous-marine,, A lY@talonnage d e transducteurs e t h d'autres d o m a i n e s d'acoustique. O n d o n n e d e s e x e m p l e s provenant d e
d i f f k r e n t s d o m a i n e s d'acoustique ainsi q u e q u e l q u e s e t u d e s d e m o d e l e s reduits, illustrant les c o n d i t i o n s s o u s lesquelles c e t t e
technique peut-Stre u t i l i s h e a f i n d'obtenir'des r e n s e i g n e m e n t s sur l e s c h a m p s a c o u s t i q u e s s a n s avoir a introduire d e sonde, d'hydro- p h o n e o u d'autre appareil.
Abstract
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A very short introduction of t h e p r i n c i p l e s o f light d i f f r a c t i o n by ultrasonic w a v e s is followed by a d i s c u s s i o n o f acousto-optic imaging ( s c h l i e r e n ) techniques. T h i s method is o f t e n useful to o b t a i n q u a l i t a t i v e r e s u l t s o f v a r i o u s acoustic phenomena in ultrasonics, underwater sound, material c h a r a c t e r i z a t i o n , trans- ducer p e r f o r m a n c e and other a r e a s o f acoustics. E x a m p l e s from different f i e l d s o f a c o u s t i c s and s o m e s c a l e model s t u d i e s will b egiven, illustrating under what c o n d i t i o n s t h i s method c a n b e used to o b t a i n information about sound fields, without having to intro- d u c e a probe, hydrophone or other devices.
1 - INTRODUCTION
Most p e o p l e who work in various f i e l d s o f a c o u s t i c s a r e very o f t e n interested in t h e shape, direction, intensity, a b s o r p t i o n and other p a r a m e t e r s o f t h e sound field with which t h e y work. T h i s i s particularly t r u e in t h e d o m a i n o f ultrasonics, underwater acoustics, medical acoustics, physical acoustics, material characterization, non-linear acoustics, mode analysis, interfacial w a v e s
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to n a m e only t h e most obvious. Reflectivity a s well a s transmission phenomena, t o n e burst and pulsed sonic s i g n a l s , all h a v e to b e analyzed if astudy o f t h e s e special sound f i e l d s and their propagation a r e to b e made.
These characteristics of sound f i e l d s c a n b e measured in most cases, usually by m e a n s o f scanning t h e field with probes, h y d r o p h o n e s or other recording d e v i c e s and gathering many numerical r e s u l t s from which t h e sound field c a n b e mapped. But t h e r e a r e many instances w h e r e t h e introduction o f a p r o b e into t h e s o n i c field d i s t u r b s t h e field ( b y possibly scattering or reflec- ting p a r t s o f t h e intercepted sound e n e r g y ) a n d t h i s invasion may c o n t r i b u t e to e r r o r s which may already exist b e c a u s e w e usually d o not know what c h a n g e s h a v e been introduced w h e n a mechanical v i b r a t i o n is "translated" into a n electrical signal f r o m t h e transducer to a n electronic display d e v i c e like a n osc i l loscope.
S o t h e r e a r e different potential e r r o r s in making a measurement. Therefore, o n e might wish to u s e a method which is non-invasive, d o e s not disturb t h e sound field, and d o e s not depend o n a c o n v e r s i o n from mechanical vibration energy to a n electronic signal which c a n t h e n b e processed.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19902150
C2-642 COLLOQUE DE PHYSIQUE
Fortunately, such a method exists. In its usual application it is limited to frequencies in the inaudible range, starting at about 100 kHz and ending, in principle, in the gigahertz region. This method is based on phonon-photon
interactions, and is referred to as acoqsto-optics. If it is used the sound field never knows that it is being measured, so the method is non-invasive.
The method is not new, it was first suggested as a possibility in 1922 by Brillouin / l / . However, it was not successfully tried until the 1930s.
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PRINCIPLES OF ACOUSTO-OPTIC INTERACTIONA sound wave is a pressure wave. As it travels through a transparent medium, it changes the index of refraction of the medium in a periodic fashion, determined by the sound wavelength S*. If a beam of monochromatic light with wavelength S travels through the sound.wave, the originally plane wave fronts of the light beam will emerge with a very slight corrugation. The sound wave has acted as a phase grating for the light beam; constructive end destructive interference will create a light diffraction pattern where the angle between the orders, 8 , is given by
sine = S/&*.
Since diffraction patterns usually have angular spacing5 of a few degrees or less, it is evident that the sound frequency must be rather high (short S*) if visible light is to be used and the interaction is to take place in a transparent liquid where the velocity is around 1500 m / s or in a transparent solid where the longitudinal velocity may be 10 km/s or higher.
The principle of the interaction is shown in Fig. 1 together with the basic setup for the experiment where light is collimated b y a lens into a beam of a few cm diameter to cover many ultrasonic wavelengths and a second lens focu- ses focus the resulting diffraction orders onto a screen for visual inspec- tion as indicated in Fig. lb. Similar basic setups were first
used b y Lucas and Biquard / 2 / and by Debye and Sears / 3 / to measure sound velocities in various liquids. The complete theory for low-intensity and low-MHz waves transversed b y visible light was first worked out correctly b y Sir Raman and N. Nath / 4 / , resulting in an expression which also gives an
indication of the sound pressure which determines the light intensity in the various diffr-action pattern orders. Accordingly, the light intensity I , in the nth order (for progressive waves) is given by
where 3 , is the nth order Bessel function and the parameter v is directly proportional to the sound pressure.
It is obvious that only those parts of the light beam which travel through the sound field will be affected by the sound field. This means that any light which is present in the diffraction orders outside the zero order has gone through a portion in the liquid which is a part of the sound field.
This is indicated schematically in Fig. 2a which sketches a cross-section of the light beam going through an ultrasonic beam which is incident on a solid plate, is partially reflected and partially transmitted. The incident and
transmitted beam have the same k-vector direction which is different from the direction of the reflected beam k-vector. So two diffraction patterns are produced, as shown in Fig 2b, where the alignment of the pattern corresponds
to the sound travel direction.
If we now block the light in the zero order but let the light of the other orders continue and use another lens behind the diffraction plane (Fig.3) we create a light image of the entire sound field which was illuminated by the expanded light beam. The amount of illumination in such an image ( o r , as it is sometimes called, the schlieren image) is related .to the local sound pressure via the parameter v in the Raman-Nath equation shown above.
This then is the basic idea behind the visualization of an entire ultrasonic field. We should, however, be aware of the fact that one does not necessa- rily obtain an accurate picture of the exact pressure levels which exist in the field at any point (after all, the light integrates over a depth of the field and the diffraction order light intensity is not p'roportional to the pressure, as is seen from the Bessel function formulation above).
obtained where the brightest portions generally correspond to the highest intensities in the field and the dark portions clearly are the locations where no sound energy is present. One thus produces an integrated quantita- tive intensity map of the ultrasonic field in the planes perpendicular to the light propagation direction.
W e will now discuss some application in different fields of acoustics where a knowledge of the sound field configuration is of interest and value. From above it is evident that a visual image (schlieren image) cannot be produced unless a sufficiently strong light diffraction pattern has been formed. Much can be learned about the sound field from the diffraction pattern all by
itself, without investigating the schlieren image.
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INFORMATION CONTAINED IN DIFFRACTION PATTERNThe first evaluations of sound fields, in this case the velocity of sound in various liquids, were made in 1932. An example of these early efforts is shown in Fig. 4, taken from Lucas and Biquard / S / . No lasers were available then, and the light sources were mercury or sodium arc lamps, focused o n a slit and then the light was collimated. These were some of the first measure- ments of sound velocity in liquids. One should note that the diffraction pattern is not symmetric with respect to the central order
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which, as w e now know, is an indication that the liquid is nonlinear. However, a discussion of this rather complex field of acoustics is beyond the scope of this paper.6 calculation was made by Biquard / 6 / , in his doctoral theses, of the wave deformation for high-power sound waves
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but the calculated effect was not considered too important-
at that time.The velocities in the liquids investigated by Lucas and Biquard and by Debye and Sears yielded very satisfactory results. The investigators at that time used continuous waves to drive their quartz transducers. Many years later esst7rttially the same techniques were used to determine longitudinal and shear wave velocities in transparent solids, particularly for single crystalL. where the sound velocities are dependent o n crystal orientation. Equation 1 1 ) is still valid, except the quantity 6* varies with direction, and 3 waves (two shear and one longitudinal) can exist simultaneously in the crystal, all of whom will contribute to the formation of individual diffraction patterns.
An example is shown in Fig. 5, for NaCI. The interpretation of the spacing in the various directions enables one to find the elastic constants of the crystal under investigation. Usually, two or three direction-dependent measurements are sufficient to find all the elastic constants, provided the crystal symmetry is not too complex.
In this age of digitalization, much work is done with pulses, and perhaps the most obvious area is that of underwater sound and sonar. It is comparatively easy to characterize a continuous wave by the diffraction pattern it produces but when the wave is pulsed, the repetition frequency is the lowest frequency component in the wave trains ( a Fourier analysis quite readily shows this).
Now, rather than having a simple diffraction pattern with the spacing given by Eq.(l) we have a multitude of frequencies, all of them making their con- tribution to the light diffraction. An example is shown in Fig. 6 which compares a continuous wave pattern (top) with a pulsed wave pattern (bottom).
The reproduction here is severely reduced so that much of the spectral detail is not discernible. However, an interpretation of the satellite orders can yield valuable information about repetition rate, pulse shape, even about the
influence of nonlinearity in the liquid o n the propagation of the pulse and its changes over distance. But since this type of pulse evaluation can only be done effectively by interpreting diffraction patterns and the purpose of this contribution is to discuss visualizations, we will not go into details of this particular branch of acousto-optics.
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VISUALIZATION OF SOUND FIELDSWe have just mentioned pulsed waves, which are used in sonar and other appli- cations in medicine and many other fields like nondestructive testing, qua- lity control, material characterization and more. In most of these cases one is interested in an echo or more specifically, in reflection and transmission
C2-644 COLLOQUE DE PHYSIQUE
and the changes in the sound pattern which such diScontinu'ities mlght eai~se.
In the following w e will look at bounded beam continuous waves and some o f the beam changes which are caused by impedance mismatches such a 5 reflection, material boundaries and other discontinuities. We will now no longer inspect the diffraction pattern but will concentrate on the imaae, the picture, the visualization, of the sound beam before and after it encounters a disconti- nuity in the medium through which it propagates. We will look at some prob-
lems in physical acoustics, mode conversion, scale model studies o f reflec- tion from an ice cover in the Arctic and other phenomena which are usually extremely difficult to measure with hydrophone or transducer-pickup methods.
Beam Visualization
The first question one might want to ask concerns the type o f beam a given transducer produces. Putting the transducer into a transparent Piquid and using the schlieren apparatus (Fig. 3) will show the beam structure with side-lobes and the near-field structure a s shown in Figs. 7 and 8, which were taken from an early book on Ultrasonics /7/. Clearly, shape and size a s well a s frequency determine the particular form of the output, the number of lobes and the extent of the near-field.
Another example of beam configuration is shown in Fig. 9 where a 2 MHz beam is focused by a Plexiglas lens. Regions of the lens with regions o f trans- missions and np transmission are clearly spaced (depending o n the thickness of the focusing lens compared to the wavelength of the ultrasound in the lens material). The focal point and with it the local intensity of sound clearly depends also on the velocity in the medium. Knowledge of these parameters are important in medical ultrasound, and, to some extent, in nondestructive testing.
Visual inspection of transducer performance clearly is a great help so that possible peculiarities of transducers or focusing devices c a n be avoided.
Moreover, knowled'ge of the output of the sound source wi'll make it possible to use the far-field of the transducer which no longer is influenced greatly by side lobes or near-field effects.
Reflections and Wave Modes Analysis
Reflection coefficients of different materials had been known for a long time and early work on sonsic wave reflections and mode conversions was done a s far back a s the last century when seismologists defined wave modes (like shear waves, Lamb modes, Rayleigh waves, etc). These were of great importance in identifying seismographic record of earthquakes
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except o n e had to wait until nature provided the data.Ultrasonic scale model studies, o n the other hand, can b e done in laborato- ries and much can be learned about vibrational modes and reflectians. For a long time, sound reflectibn theories from an interface of two dissimilar media was based on the early calculations by Knott /E/ who assumed that we are dealing with infinite plane waves. This very often is almost true and his formulism is useful in many applications. However, there are more and more cases where one must replace the plane wave approach by a bounded beam approach; one way of describing a bounded beam is to consider it a s the sum of infinite plane waves /9,10/ by using Fourier transforms.
The plane-wave reflection coefficient for an infinite plane wave from a liquid-solid interface, a s given by Knott, can be written a s
( R / I ) = Ccosa
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A cose(1-
B)3/Ccosa + A cose(1-
B)3,where A is the ratio of acoustic impedance of the solid to that of the liquid and the angles 8, a, and fi are the angle of incidence in the liquid, the angle of refraction of the longitudinal and the shear wave, respectively, in the solid> all being connected via B, which is given by
The quantities Vs and V1 are the velocities of the shear and longitudinal waves in the solid, respectively. The fact that a bounded beam consists o f many plane waves impinging at different angles 8 , the reflected beam may vary
one often does not have an "infinite half-space". All this may result in what is called "nonspecular reflection";' and the first examples were given by Schoch / 1 1 / . A complete analysis for the relation of reflection, beam pro- file and the excitation of special modes of vibration of the solid was given many years later b y Pitts et al. /12/.
Experimental examples are shown in Fig. 10 on the left. The right side of this figure shows the calculated velocity dispersion curves of Lamb waves on a brass plate immersed in water, giving the necessary angle of incidence to excite a mode, as a function of plate thickness,d and frequency f where the units of the product fd has the dimensions (meter-kilohertz). If the beam is
incident at an angle not corresponding to a point on any of the curves, the beam will simply be reflected specularly. But when the incident angle is such that a mode can be excited, the reflected beam may widen, show a trai- ling field, show displaced transmissions or exhibit a zero-intensity portion partitioning the reflected (or reradiated) beam into two portions. The left side of the figure shows some examples of this phenomenon., The beam is
incident from the top right, strikes the plate (the horizontal dark line in the picture) and then is reflected, showing the predicted pattern. Photo ( d ) shows the incidence at the Rayleigh angle, and a simple lateral "displace- ment" of the beam is seen, with no transmission through the plate.
This indicates that one can determine visually what type of plate vibration is produced by incident sound, how sound is reflected, what mode (Rayleigh or Lamb) is excited. No other measurement is needed for this type of identifi- cat ion.
It is evident that one can make a thickness measurement of a plate without having to touch the plate at all (or not being able to reach the inside of a metal pipe or container)
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simply by matchinng the angles of incidence where plate modes are excited to the appropriate dispersion curve. This is often a great help in material characterization or nondestructive testing.Scale Model Studies
In principle, the technique described above can be used for scale model studies whenever it is possible to reduce the dimensions and wavelengths involved so that an initial light diffraction pattern can be obtained. As an example consider the Arctic ice cover, which is usually on the order of 2.5 m thick, and a sonar signal of frequency 3 k H z . The product fd is 7 , the same as for an ice plate of 2.5 mm thickness and a frequency of 3 MHz. This makes it possible to conduct laboratory studies of Lamb or Rayleigh modes, reflec- tivity, or variations in ice thickness in precisely the same manner as was indicated above for the brass plate immersed in water. Unfortunatley, now one has a three-layer system (water-ice-air) which complicates the theoreti- cal analysis significantly. Nevertheless, modes can be excited and observed
and interesting results can be obtained. Again, an evaluation of reflec- tivity patterns does go beyond the scope of this contribution.
To illustrate the complexity of the problem consider that the Arctic ice cover frequently has large half-round or triangular ridges on the water side and ice plates often have cracks and complete breaks. These present formi- dable irregularities for thg periodicity of the propagation of any mode established in the ice or on the ice/water interface
In order to have a qualitative look to see what happens when a geometric structure like a ridge is in the pathe of a Lamb wave we excited a Lamb mode on a metal plate near a triangular ridge. A nonspecular reflection and a
transmission is seen shortly on the up-stream side of the plate and then a series of very strong radiation filaments leave the area of the ridge, as is seen in Fig. 1 1 . The pattern changes with the Lamb mode used and the dis- tance of incidence point to the location of the wedge.
At the free ednd of a plate in a liquid, the Lamb mode is partly reflected in the plate but a great deal of energy leaves the plate in rather intricate patterns, again, depending on the mode as is seen, as an example without an attempt of analysis, in Fig. 12.
COLLOQUE DE PHYSIQUE
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CONCLUSIONIt i s evident f r o m all t h e e x a m p l e s g i v e n a b o v e that t h e a c o u s t o ~ . o p t i c image c a n p r o v i d e a ery detailed q u a l i t a t i v e p i c t u r e o f very complex radiation patterns, w h o s e interpretation is not a l w a y s easy, o f t e n imposssible.
Nevertheless, it,would appear that any attempt to map out a radiation field a s complex a s s o m e s h o w n in t h i s c o n t r i b u t i o n would b e inconvenient and n o doubt very t i m e c o n s u m i n g and p e r h a p s f a r f r o m being a s detailed, i f a hydro- p h o n e or a p r o b e w e r e introduced; more t h a n likely, t h e p r o b e would act a s a
scatterer itself and t h e r e s u l t s would not correspond to t h e sound field a s it e x i s t s in i t s undisturbed form.
Acknowledgement:
Much o f t h i s paper is based o n work supported by t h e O f f i c e o f Naval Research, U.S. Navy. S o m e p o r t i o n s o f t h e work w e r e m a d e p o s s i b l e through a s s i s t a n c e from t h e S c i e n t i f i c A f f a i r s D i v i s i o n o f NATO.
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Light i n
Sound
t
Light
I-.-
Fig. 1.
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S c h e m a t i c o f interaction p r o c e s s and a p p a r a t u s o u t l i n e where lens L c o l l i m a t e s t h e light f r o m t h e laser, L' f o c u s e s t h e o r d e r s around the central o r d e r C o n t h e screen. T h e sound wave may travel in either direction.Fig. 2. - ( a ) Schematic of a c r o s s s e c t i o n through a sound field impinging o n a plate, t h e c i r c l e indicates t h e c r o s s s e c t i o n o f t h e collimated light, I, R and T signify the incidence, r e f l e c t i o n and transmission. ( b ) Schematic o f a diffraction p a t t e r n formed ( t w o o r d e r s indicated) o f t h e s i t u a t i o n in (a).
Fig. 3.
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Schematic o f t h e s c h l i e r e n ( v i s u a l i z a t i o n ) system.T h e single line appears to be the reference zero order, the series o f lines below it are the diffraction orders.
Fig. 5.
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Multiple diffraction patterns in a four-fold symmetric crystal.Fig. 6.
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Diffraction pattern from continuous wave (top) and from pulsed wave (bottom).Fig. 7.
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Schlieren image o f beam from a transducer, eleven wavelength wide.C2-648 COLLOQUE DE PHYSIQUE
. .am=--m?%v
Fig. 8
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Sound intensity distribution in the near field o f a transducer.Fig. 9.
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Schlieren picture of a 2-MHz beam focused by a Plexiglas lens.Experimental points
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90
Fig. 10.
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Dispersion curve for Lamb modes (brass/water) and experimental results of reflection at mode excitations ( a through c ) and at the Rayleigh mode, (d). The latter only shows displacement of the beam.Fig. 12. - Radiation from the end of a plate when Lamb mode is excited near the boundary of the plate.
REFERENCES
/l/ Brillouin, L., Ann. Physique (9)
1 7
(1922) 88./2/ Lucas, R. and Biquard, F., J. Physique Radium (7) 3_ (1932) 464.
/3/ Debye, P. and Sears, F., Proc. Nat. Acad. Sci. Washington
18
(1932) 409 /4/ Sir Raman. C.V. and Nath, N.S., Proc. Indian Acad. Sci A 2 (1936) 75./5/ Lucas, R. and Biquard, P., Compt. Rend.
194
(1932) 2132./6/ Biquard, P., These de Doctorat, Universitk Paris, Octobre 1935.
/7/ Hiedemann, E. "Ultraschallforschung", d e Gruyter, Berlin 1939.
/ 8 / Knott, C.G., Philosoph. Mag. 41 (1899) 64.
/9/ Brekhovskikh, L.M., "Waves in Layered Media", Academic, New York (1960).
/10/ Bertoni, H.L. and Tamir, T., Appl. Phys.
2
(1973) 157./11/ Schoch, A., Acustica 2_ 11952) 1.
/12/ Pitts, L.E., Plona, T.J., and Mayer, W . G . , IEEE-SU 24 (1977) 101.
