ULTRASOUND WAVES QUANTITATIVE MONITORING BY DIGITAL LASER SPECKLE TECHNOLOGY. JCMB, The King s Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK

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1 International Conference on Methods of Aerophsical Research, ICMAR 2008 ULTRASOUND WAVES QUANTITATIVE MONITORING BY DIGITAL LASER SPECKLE TECHNOLOGY Nikolai Balev 1, Nikita Fomin 1, John Cosgrove 2,3, and Clive Greated 2 1 Phsical and Chemical Hdrodnamics Laborator, A.V.Luikov Heat and Mass Transfer Institute, P. Brovka 15, , Minsk, Belarus 2 School of Phsics, The Universit of Edinburgh, JCMB, The King s Buildings, Mafield Road, Edinburgh EH9 3JZ, UK 3 Profesional Scientific Ltd., ETTC Biospace, King s Buildings, Mafield Road, Edinburgh, EH9 3JF, UK Introduction 1 Introduction Flow visualiation of shock and sonic waves has a long histor starting from the work of E. Mach and P. Salcher and is reviewed in man fundamental issues [1-5]. Traditionall, flow visualiation techniques are used for qualitative flow analsis. Recent progress in the field is connected with the use of coherent optical methods of flow diagnostics and is based on the rapid development of laser techniques and modern digital recording and acquisition sstems, especiall with the high resolution CCD matrices. One of the first successful applications of advanced optical signal treatment for the quantitative analsis flow fields has been laser Doppler anemometr, see e.g. [6]. The development of cross-correlation analsis of optical signals has been started at that time with application to LDA and photon correlation spectroscop, see [7]. As soon as two dimensional digital image acquisition sstems appeared, particle image velocimetr (PIV) started to use the advantages of digital flowfield measurement [8, 9]. In spite of man efforts and successful applications of modern digital optical techniques, there still are man problems in ultrasound 2D mapping, and, especiall, in 3D sound fields imaging. Specific aspects and problems associated with appling these techniques to sound measurements in fluids are discussed in [10-13]. The present paper deals with the new application of digital speckle photograph (DSP) for quantitative monitoring of acoustical fields of wide dnamic range. This technique also belongs to the line-of-sight methods and is sensitive to densit variations in the fluid flow under stud. The information obtained from line-of- sight optical measurements consists of the averaged data along the optical path. The principles for measuring the light retardation and the light deflection angles b DSP are described in literature [14] and shortl illustrated below. An expanded collimated laser beam is transmitted through the test section. The distortion of the wave front due to refractions then evaluated quantitativel b auto- and cross-correlation analsis of the images before and after interactions with the media under stud. To facilitate the analsis, the images are modulated b a random speckle pattern, produced when the transmitted laser beam is directed onto the ground glass. With the use of the digital version of SP DSP, a huge amount of experimental data can be accumulated b computer-aided optical data acquisition sstems. This data can be further used for statistical flowfield analsis and quantitative flow parameter determination. As the result of the analsis, the quantitative measurement of the velocit and pressure fields in a standing acoustic wave is performed. The flow visualiation pattern is produced b the diffraction of laser light on the wave under stud, and the fine structure of the diffraction pattern, which is a speckle field, is evaluated using the DSP approach, described below. N. Balev, N. Fomin, J. Cosgrove, C. Greated. 2008

2 Section V 2 Theor of light interaction with acoustical field Let us consider a medium with standing acoustic wave located at 0. A monochromatic (laser) light beam with wavelength λ propagates this medium. Propagation of the sound wave through the water causes fluctuations in the refractive index, which produce the variation of the refractive index in an acoustic field. This variation is described b the equation: n(, t) = β p(, t). The variation n in acoustical wave is connected with variation of pressure and described b the pieo-optic coefficient. This coefficient, n β =, is a constant of p proportionalit relating refraction index with pressure. A simple formula has been given in [3] to enable the pieo-optic coefficient to be calculated at different water temperatures: n = T 1 10 T (1) p 10 1 For water, at λ = 633nm and T=17.0C, β = Pa. The instantaneous pressure distribution along the -axis for a standing wave is described b where k ( ) 0 ϕ0 p t, = 2 psin( k + )cosωt, (2) 2π is a component of the acoustic vector, k = Λ a and p0 is amplitude of the pressure variation in the acoustic wave. Thus, the spatial variation of the refractive index is described b n ( ) = 2β n p0( sin( k + ϕ 0 )), and the temporal variation b nt () = 2β n p0 cosωt. These variations in the refractive index cause diffraction and refraction of a probing laser beam passed through the acoustical flowfield. For opticall thin laer, the refraction effects are rather small and the diffraction can be described at the first approximation b Raman-Nath equations, see below. In spite of the refraction angles are small, the can be easil detected b DSP and then the acoustical parameters can be quantitativel determined, as it will be described below. 2.1 Raman - Nath diffraction Light diffraction after interaction with an ultrasonic wave has been described b Raman and Nath assuming the similarit of a sonic wave with a 2 D phase grating [15-17]. For such a grating, the direction of the diffracted light θ p in the p-th order of diffraction (p = 0, ± 1, ) is described b the formula θ = sin θ + pλ/ Λ n (3) p 0 a where θ 0 - is the angle of the incident light, Λa - is the wave length of the acoustic wave, and n the refraction index of the media. 2

3 A 2 rel. units x, mm, mm Fig. 1. Illustration of Raman Nath diffraction on the ultrasonic wave (upper part) and Rinkevichius, Evtikhieva and Raskovskaa model of the interaction (down). On the left the laser light intensit distribution after 2D Gaussian beam interaction with a standing acoustical wave obtained using the numerical model described in [18] The distribution of the diffracted light is described b the simple relation I p2 ± p = J ( ζ ) where ζ represents the Raman-Nath parameter, ζ = 2 π nl / λ, n is the maximal variation of the refractive index in the acoustic wave, L the optical path through the wave, and functions of the order of p. J p are Bessel 2.2 Analtical solution for the light refraction in the particular geometr of the experiments Let us consider refraction for the particular geometr of the present experiment. The acoustic standing wave has been generated in a circular glass tube filled with salt water submerged in a rectangular tank with the same salt water matched in refractive index with the glass of the internal tube as shown in Fig. 2. Thus the onl fluctuations in the refractive index within the circular glass tube due to the standing wave produce minute deflections of the collimated laser beam passing through the measurement volume. For such configuration, the line-of sight integral of refractive index disturbances is possible to solve analticall. Taking into account that there is no spatial dependence of the refractive index in x- plane and 2 the optical path l = r x 2, and that n ( t, ) = 2β pk 0 cos( k + ϕ0)cosω t, (4) the line-of-sight integral will be ε l 1 n n = d = 2l n n. (5) l 3

4 Section V Fig.2. Geometr of the acoustical field generation in a round glass tube submerged into the rectangular tank with salt water Taking into account that there is no spatial dependence of the refractive index in x- plane and 2 the optical path l = r x 2, and that n ( t, ) = 2β pk 0 cos( k + ϕ0)cosω t. (6) The line-of-sight integral will be ε l 1 n n = d = 2l n n l. (7) The (x, ) dependence of the light deflection along the axis is determined b ε n 4 β p k n n ( ) x, = 2 r x k 2 2 = r x cos( k + ϕ 0 ). (8) The model shows that the amplitude of the light deflection is a maximum at the acoustic nodes and is ero at the points with maximum acoustic intensit, as shown in Fig. 2(a). The deflection 4

5 angle is directl proportional to the local amplitude of the acoustic wave. The experiment described below is based on such a behavior. When the probing beam propagates through the acoustic pressure node during several acoustic ccles, the speckles generated b the beam are smeared and have less contrast as compared to the speckles generated b the beams passing through the maxima. 5 For the acoustic pressure P = 10 Pa, the deflection angles are about 10 5, and could be easil recorded b defocused speckle photograph. 3 Quantitative acoustic flow visualiation 3.1 Experimental technique Laser speckle interferometr enables the direct non-intrusive measurement of densit gradients for opticall transparent media with non-uniform refractive index distributions [19, 20]. Fig. 3 presents the general principles of laser probing of a test medium. An expanded parallel beam of laser light is transmitted through the test section. The wave front of the transmitted laser light is disturbed due to refraction of the beam on the densit gradients. In speckle interferometr, the test object is placed in front (on the left side) of the ground glass, and it is imaged b means of a lens onto the plane of the ground glass, as shown in the Fig. 3, top. Space behind it the laser light consists of the smallest granules of light speckles. The speckles are recorded b a digital CCD camera of high resolution. The ground glass works as a speckle-field generator and the camera is focused onto a plane at distance L from the ground glass. In the double exposure mode, (DEM), two speckle patterns are superimposed b recording two exposures on the same CCD matrices, like in PIV. B digital specklegram processing as described below, it is possible to determine two components of the speckle displacement at each specklegram interrogation point. These values can be easil converted into the components of the deflection angle of the light passing through the flow under stud. In the single exposure mode (SEM), a speckle pattern is recorded during a prolonged, as compared to DEM, time. During this time the speckles could be in movement due to changes in the refractive field distribution in a test object. This results in a relativel large speckle sie and in decreasing of the speckle contrast in the time-integrated speckle image. The speckle blurring and enlargement is correlated to the intensit of densit fluctuations in a flow under stud and can be reconstructed through the autocorrelation analsis of the specklegram described below. Fig. 3 illustrates application of these principles to acoustic standing wave monitoring, bottom. The laser light is passed through the standing wave and is recorded during several acoustic ccles. This results in a relativel large speckle sie and low contrast in the regions between the acoustic pressure nodes. Along the nodes the light is not deflected and the speckle pattern is not disturbed. For quantitative determination of the refractive index fluctuation, an experimental validation of SEM has been performed using a rotating ground glass. A linear calibration curves have been obtained both for contrast measurements and for speckle elongations measurements b autocorrelation specklegramm analsis, see below. 5

6 Section V Fig.3. Schematic optical configuration for laser speckle interferometr (top) and acoustic standing wave probing b collimated laser beam with Gaussian intensit distribution (bottom). The obtained diffraction pattern record is shown on the right. 3.2 Results & Discussion The diffraction patterns obtained for different acoustic waves are shown in Fig. 4. The patterns themselves provide a qualitative visualiation of the acoustic standing waves. However, in order to extract quantitative data on the sound amplitude, the microstructure of the images must be evaluated at each small interrogation one. It is possible to use this data for quantitative analsis b comparing the intensit distributions with the calculated ones. Fig. 5 contains the results of the quantitative speckle pattern microstructure contrast analsis. This speckle contrast can be used to evaluate the speckle elongation and then the pressure amplitude at each sound field one. As the calibration results show, this contrast is linearl related to the sound pressure amplitude providing the possibilit of the quantitative measurement of the sound wave intensit. The pressure distribution enables the velocit field in the acoustic wave to be constructed. The results of such a reconstruction are shown on Fig It is seen that the present technique allows quantitative pressure amplitudes in the range kpa to be measured simultaneousl over the whole acoustic field. The scale of the measurements can be changed and adapted to the amplitude of the wave b choosing different defocusing distances L, see Fig.3 (top). 6

7 Fig. 4. Recorded diffraction patterns for collimated laser probing of acoustic standing waves Fig. 5 Light intensit distribution in diffraction pattern ( up) and contrast variation of microstructure of the speckle pattern recorded (down) 7

8 Section V Fig.6. Results of validation of the technique and pressure distribution in a standing acoustical wave at different positions 1-5 Fig. 7. Velocit distribution at different positions of the 3 M acoustic waves with the wavelength The arrow on the right side shows the velocit value equal to 5 cm/s. Conclusions λ = 0.5cm. The line-in-sight DSP technique allows quantitative measurements of sound intensit of an acoustical field in liquids. The technique is sensitive to fluctuations in refractive index and, unlike PIV, does not require seeding particles. An analsis has been presented that allows pressure and velocit fields to be calculated from the recorded speckle images. It is shown, that the deflection angles of a probing laser light passed through an acoustical field due to refraction are determined and directl proportional to local acoustical pressure amplitudes. The refraction cause local speckles elongation what can be quantitativel measured b DSP. B using the obtained values of speckles elongation, pressure and velocit fields in acoustical wave has been constructed. The whole 3D acoustic field can be reconstructed b multi-projectional measurements with proposed technique and computeried reconstruction b using Radon inversion for speckle photograph. 8

9 Acknowledgement The research described in this publication was supported partl b the Roal Societ of Edinburgh and INTAS (Innovation grant Ref. No ), as well as b Belarus Foundation for Fundamental Research (grants #Т and T07Ф-005). REFERENCES 1. Merkirch W. Flow Visualiation (2nd edition). Orlando: Academic Press, Takaama K. Application of holographic interferometr to shock wave research. Proc. SPIE Vol P Ben-Dor G., Igra O., Elperin T. (eds.) Handbook of Shock Waves. New York: Academic Press, Vol. 1, Chapt Settles G. S. Schlieren and Shadowgraph Techniques. Visualiing Phenomena in Transparent Media. New York: Springer, Molin N-E., Zipser L. Optical methods of toda for visualiing sound fields in musical acoustics. Acta Acustica & Acustica Vol. 90, P Durrani T.S., Greated C.A. Laser Sstems in Flow Measurements. New York: Plenum Press, Durrani T.S., Greated C.A. Spectral analsis and cross-correlation techniques for the photon correlarion technique. Appl. Opt Vol. 14, P Adrian R. J. Particle imaging technique for experimental fluid mechanics. Ann. Rev. Fluid Mech Vol. 23. P Raffel M, Willert C., Kompenhans J. Particle Image Velocimetr: A Practical Guide. Berlin: Springer, Sharpe J. P., Greated C.A. The measurement of periodic acoustic field using photon correlation spectroscop. J. Phs. D: Appl. Phs Vol. 20, P Hann D.B., Greated C.A. Acoustic measurements in flows using photon correlation spectroscop. Meas. Sci. Technol Vol. 4, P Hann D.B., Greated C.A. The measurement of flow velocit and acoustic particle velocit using particle-image velocimetr. Meas. Sci. Technol Vol. 8, P Campbell M., Cosgrove J.A., Greated C.A., Jack S., Rockliff D. Review of LDA and PIV applied to the measurement of sound and acoustic streaming. Opt. and Laser Techn Vol. 32, P Fomin N. Speckle Photograph for Fluid Mechanics Measurements. Berlin: Springer, Kuliasko F., Mertens R., Lero O. Diffraction of light b supersonic waves: the solution of the Raman- Nath Equations. Proc. Ind. Acad. Sci Vol. 67A. P Lero C.C. Development of simple equations for accurate and more realistic calculation of the speed of sound in seawater. JOSA Vol. 46, P Ko H.S., Ikeda K., Okamoto K. Combination of holographic interferometr and digital speckle sstem for measurement of densit distributions. Meas. Sci. Technol Vol. 13, P Rinkevichius B.S., Evtikhieva O.A., Raskovskaa I.L. Propagation of a Gaussian laser beam with elliptical cross-section through a medium in the presence of a standing acoustic wave. In Book Phsics of Shock Waves, Combustion, Detonation and Non-Equilibrium Processes. N. Fomin, O.Penakov and S. Zhdanok, Eds, Minsk, ISBN , P Fomin N., Lavinskaa E., Vitkin D. Speckle tomograph of turbulent flows with densit fluctuations. Exp. Fluids Vol. 33, P Fomin N., Lavinskaa E., Takaama K. Limited projections laser speckle tomograph of complex flows. Optics and Lasers in Engn Vol. 44. P