Wave phase conjugation of high order harmonics for acoustic imaging in nonhomogeneous media

A.P. Brysev, F.V. Bunkin, L.M. Krutyansky, R.V. Klopotov Laboratoire Europeen associe en Magneto-Acoustique nonlineaire de la matiere condensee (LEMAC)

Wave Research Center, Prokhorov General Physics Institute, Russian Academy of Sciences, 38 Vavilov Street, Moscow 119991, Russia; (e-mail: brysev@orc.ru)

Abstract The possibility of acoustic imaging of objects was experimentally demonstrated for the practically important case when a phase-inhomogeneous medium is placed between a transducer and an object. In such configuration, focusing of the probing beam as a rule violated because of phase distortions introduced by a layer. This makes inefficient both conventional methods and the method using the phenomenon of ultrasonic phase conjugation (PC) to compensate for phase distortions. To overcome these difficulties, it is proposed to use parametric PC of one of the higher harmonics of the probing beam. In this case, focusing is provided due to small phase distortions at the fundamental frequency. At the same time, necessary resolution and compensation for introduced distortions can be achieved by PC of one of the higher harmonics generated by the probing beam in a nonlinear medium. The proposed method was experimentally tested at parametric PC of the fifth harmonic of the focused ultrasonic beam in the transmission mode. A comparative analysis of object images obtained by various acoustic methods showed that the proposed method in certain cases is unique opportunity to obtain reliable acoustic data on an object hidden inside an inhomogeneous medium.

Introduction Acoustic imaging of objects surrounded by a medium with a nonuniform distribution of the sound speed is still a rather difficult problem. In the commonly used C-scanning scheme, when an object moves at the focus of an acoustic system, an inhomogeneity in an acoustic path, for example, such as a phase layer, causes noise and geometrical distortions in images. As shown in [1,2], to compensate for distortions arising in the transmission mode, when the layer is between the object and conjugating system, the effect of parametric PC of ultrasonic beams can be efficiently used [3]. Since the reflection mode is most commonly utilized, for practical applications topical question is the case when the phase layer is between a transducer and the object. When the focusing of the probing beam is not strongly violated by a layer utilizing of PC can bring out some advantages in acoustic imaging [4]. However, if focusing of the probing beam is corrupted not only conventional methods, but even the use of PC become inefficient. In this situation, PC only reproduces the distorted probing beam in the focal plane, which is also inapplicable for C-scanning. To solve this problem, it is proposed to use a focused finite-amplitude probing beam and further PC of one of its higher harmonics. In this case, focusing can be provided due to smallness of inhomogeneities in comparison with the wavelength of the beam fundamental component. At the same time, necessary resolution and compensation for phase distortions can be achieved due to PC of one of the higher

harmonics generated by the probing beam propagating in a nonlinear medium. In this mode, the PC feature is that the conjugated harmonic field is not completely reproduced, since there is no coupling with the lower harmonics, necessary for perfect conjugation. Nevertheless, this circumstance is not an obstacle for retro-focusing of nonlinear ultrasonic beams using PC of harmonics, as it was shown for homogeneous and inhomogeneous media in [5] and [6], respectively. In [7], PC of the second harmonic of the focused beam was efficiently applied to acoustic imaging of test object, when the phase-inhomogeneous layer was between the object and the conjugating system. In this case, in addition to compensation for phase distortions, the resolution was improved in comparison with the image at the fundamental frequency of the probing beam. The mechanism of compensation for phase distortions during PC of the second harmonic followed by its propagation in an inhomogeneous nonlinear medium was theoretically developed in [8]. In practical implementation of the proposed method, the frequency of the first harmonic of the probing beam should be selected so low that to provide focusing of this component through the layer. Then, to compensate for phase distortions in obtained images, one should achieve PC of that higher harmonic of the probing beam, whose wavelength corresponds to the required system resolution. In this case, the probing beam intensity should be sufficiently high to efficiently generate such a harmonic at a distance not exceeding the transducer focal length. To focus all harmonics up to the conjugated one in a phase-inhomogeneous medium, it is also important that the layer could not dramatically affect the phase matching between these harmonics. It is clear that analysis of such conditions requires additional theoretical and experimental studies and is beyond the scope of this work. Its objective is narrower and consists in experimental demonstration of the operationability and advantages of the proposed method.

Experimental setup The experimental setup of this prototype of acoustoscope with PC in general is little different from those used in [2,7], therefore, we present here its simplified scheme (Fig.1). The principal difference consists in the position of phase-inhomogeneous medium 3, which in this case is placed between transducer 1 and object 4, whereas it was between object 4 and conjugating system 5 in previous studies. To model the medium creating phase aberrations, we used a silicon polymer ring-shaped layer 4.8 cm in diameter (see Fig.2). The layer side faced to the object was plane; another side contained randomly arranged convexities and hollows with sizes from several fractions of millimeter to one millimeter.

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Figure 1: simplified schematic diagram of the experimental setup: 1 - two-frequency piezoelectric transducer, 2 - focusing lens, 3 - phase-inhomogeneous layer, 4 - test object, 5 - system of parametric ultrasonic PC, 6 - water tank.

Figure 2: photograph of the phase-inhomogeneous layer.

The distance between the plane layer surface and the object positioned in the focal plane was 15 mm. The layer material’s density was 850 kg/m3, value of sound speed was 1160 m/s, and attenuation at a frequency 5MHz was 6 dB/cm. The difference between phase progression for wave propagating in water and in the layer, for example, at a distance of 1.5 mm, was about 4π at 6.6 MHz. The acoustic impedance of the layer provided its good acoustic matching with water. Taking into account rather small layer thickness (not more than 2 mm), it can be assumed that distortions introduced by the layer to the acoustic beam were mostly phase-type, while the contribution of amplitude loss was rather small. The test object represented itself two crossed copper wires 0.2 mm in diameter (see Fig.3).

Figure 3: Photograph of the test object.

The object was moved in the focal Y-Z plane of the lens 2 using Velmex Inc positioning system. According to the concept of the proposed method, the ultrasonic transducer should be broadband or at least two-frequency. The latter version was chosen for these experiments, since the two-frequency transducer design is relatively simple and its fabrication was not too difficult. It consisted of two round silvered piezoceramic elements coaxially attached so that to provide both acoustic and electric contact between the attached surfaces. The low-frequency wave was emitted by a piezoelectric element with an effective diameter of 36 mm and resonant frequency of 1.3 MHz (the wavelength in water is 1.15 mm). The high-frequency wave was emitted and received by the piezoelectric element with effective diameter 18 mm and resonant frequency of 6.6 MHz (the wavelength in water is 0.27 mm). Thus, the resonant frequency of the high-frequency piezoelectric element was close to the fifth harmonic of the signal exciting the low-frequency piezoelectric element. Radiation of such combined transducer was focused by plexiglas lens 2 (see Fig.1) with a focal length 50 mm in water. Fig.4 shows the axial evolution in water without layer of the first six harmonics of the probing beam, emitted by the low-frequency element excited by a radio pulse with amplitude 50V.

Figure 4: axial distribution of harmonic pressure amplitudes in the finite-amplitude probing beam with fundamental frequency 1.3 MHz.

The acoustic pressure distribution was measured using a sound-transparent broadband membrane PVDF hydrophone. We can see that the probing beam propagation in water is accompanied by the higher harmonic generation especially efficient near the focus. It is important that the amplitude of the fifth harmonic which is of our interest is sufficiently high to noticeably exceed the noise level of the parametric PC system at the given frequency. Ultrasonic PC occurred due to the parametric phonon-magnon interaction in an active element 150 mm long and 36 mm in diameter, made from magnetostrictive Ni-Co ceramics (ferrite) [3]. The PC element was inside a coil fed by a 100 µs pulse of overthreshold pump of double acoustic frequency (13.24 MHz). The pump pulse was generated with a delay equal to the travel time of the probe pulse from the transducer to the PC system. To improve the PC focusing

I Harm II Harm

III Harm IV HarmV Harm

VI Harm

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quality, a system of concentric grooves was made at the working surface of the active element, faced to the emitter [9]. The distance between this surface and the transducer was 225 mm. We shall demonstrate the acoustoscope prototype operation by the example of a single measurement cycle, which yields one point of an acoustic image. The setup operation was triggered using a pulse generated by a computer. Simultaneously with the trigger pulse, burst was generated, which excited one of the piezoelectric elements of the transducer. In the case of a powerful wave emission by the low-frequency element, a signal to it was fed through an additional 30W RF-amplifier. The focused ultrasonic pulse 10-30 µs in duration propagated along the X-axis through the phase-inhomogeneous layer toward an object. The test object was placed into one of the positions corresponding to a certain point of an acoustic image. To obtain images in the conventional reflection mode, one and the same (low- or high-frequency) element of the transducer was used for both ultrasound emission and for reception. The signal reflected from the object came to Tektronix TDS 340A digital oscilloscope input and then to the computer where the image was constructed. In the proposed method, the probing beam that had been passed through the focus and enriched with the higher harmonics arrived at the parametric PC system. The conjugate wave pulse highly amplified with respect to the incident pulse, having five times higher frequency than the excitation frequency of the low-frequency transducer, passed the entire path of the probing beam in the backward direction. As a result, it was received by the high-frequency transducer element whose signal was recorded by the oscilloscope. Then acoustic imaging was similar to that as is described above for the reflection mode. With the next triggering pulse, the positioning system moved the object to a new position, and the entire process was repeated. Thus, the image was formed in the line-by-line sweep mode.

Results The sizes of the geometrical region corresponding to obtained images were 4 mm and 9 mm along Y and Z axes with steps of 0.2 mm and 0.3 mm, respectively. Images were constructed on the scale of 256 gray levels, where brighter areas correspond to more intense received signals. The signal value at each image point was obtained by averaging over eight readings. Fig.5 shows the acoustic images of the wire cross region, obtained at 6.6 MHz in the conventional reflection mode with-out (Fig.5a) and with (Fig.5b) the phase-inhomogeneous layer. Images in Fig.6 were obtained under similar conditions but at 1.3 MHz. We can see that double passage of the high-frequency beam through the phase layer results in image distortion, while the layer has no such dramatic effect on the low-frequency beam but only slightly broadens the wire image (cf. Figs.6b and 6a). However, we can see in Fig.6 that the system resolution at low frequency is unsatisfactory for adequate visual perception of an object. Fig.7 shows the object image obtained during emission and conjugation of the high-frequency wave.

a b

Figure 5: Acoustic images of the test object, obtained at the frequency 6.6 MHz in the reflection mode (a) with-out and (b) with a phase-inhomogeneous layer.

a b

Figure 6: The same as in Fig.5 but at the frequency 1.3 MHz.

a b

Figure 7: Acoustic images of the test object, obtained during parametric PC of the probing beam with the frequency 6.6 MHz (a) without and (b) with the phase-inhomogeneous layer.

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In the absence of the layer (Fig.7a), the image quality and resolution are comparable to that in Fig.6a, i.e., without PC. However, the image is distorted in the presence of a phase-inhomogeneous layer (Fig.7b) because of defocusing of the high-frequency probing beam, i.e., direct application of PC does not offer advantages under these conditions. Fig.8b shows the main result of this study.

a b

Figure 8: Acoustic images of the test object, obtained during parametric PC of the fifth harmonic of the finite-amplitude probing beam with the fundamental frequency 1.3 MHz (a) without and (b) with the phase-inhomogeneous layer.

It is easily seen that the object can be recognized in the presence of the layer during phase conjugation of one of the higher (fifth in this case) harmonics of the probing beam. For comparison, Fig.8a shows the image obtained using the same technique as for the image in Fig.8b but without layer. The image contrast in Fig.8b is lower and noisiness is higher than in images obtained in the absence of layer. Moreover, the width of wires in Fig.8 is although smaller than in Fig.6, but is larger than in Fig.5a. Such broadening can be caused by a certain distortion of the front of the fifth harmonic when the probing beam passes through the phase-inhomogeneous layer. One the one hand, the short distance of the layer from the object (15 mm) allows the harmonic to be focused. On the other hand, information on phase inhomogeneities is transmitted to the conjugate beam due to distortions of the front of the fifth harmonic. This makes it possible their compensation during the backward passage through the layer. Thus, this method allows recognition of an object inside a phase-inhomogeneous medium. Under these conditions, the method provides slightly poorer resolution and lower image contrast than conventional methods in the absence of layer. We note one more advantage of this scheme with PC over the conventional transmission mode. Namely, the use of the PC effect, in addition to compensation for phase distortions, necessarily provides the system's confocality condition. In the conventional method, this is hardly achieved or impossible at all in the case of visualization of the internal structure of complex-shaped objects [4]. Comparison of Fig.8b with images obtained by other methods in the presence of the layer (Figs.5b, 6b, 7b) shows that, under

certain conditions, only the proposed method makes it possible to obtain images of an object with a quality satisfactory for adequate visual perception.

Conclusion The use of PC of harmonics allows development of acoustic imaging systems with improved resolution in media with inhomogeneities. At the same frequency of the conjugate wave, systems with PC of higher harmonics can offer advantages over PC of the fundamental component. These advantages are achieved among other due to better conservation of focusing of the higher harmonics at a given frequency compared to routine focusing of the probing wave in the discussed conditions. The results obtained give sufficient grounding to methodical basis for further development of nonlinear acoustic imaging with PC. First of all, this is related to realization of an acoustoscope prototype with PC, operating in the reflection mode. Implementation of this scheme, which is even more important for applications, requires consideration of the same problems of probing beam focusing to an object through a phase-inhomogeneous medium and compensations for phase distortions.

Acknowledgements The work was supported by RFBR Projects 05-02-17530, OFI 05-02-08311, 05-02-19640-CNRS, the Federal Program of Support for Leading Scientific Schools (Project NSh-8108.2006.2), Federal Program “Coherent Acoustic Fields and Signals”, French Foundation Programmes Internationaux de Cooperation Scientifique CNRS-RAS (Project 1573), French Embassy in Moscow, and Russian French Program PAI-RUSSIER (dossier 04585TK).

References [1] Yamamoto K., Ohno M., Kokubo A., Sakai K., Takagi K. J. Acoust. Soc. Am. 1999, 106 (3), 1339. [2] Brysev A., Krutyansky L., Pernod P., Preobrazhensky V. Appl. Phys. Lett. 2000, 76, 3133. [3] Brysev A.P., Krutyansky L.M., Preobrazhensky V.L. Phys. Usp. 1998, 41 (8), 793. [4] L.M. Krutyansky, К. Yamomoto, F. Pernod. Physics of Wave Phenomena, 2005, 13, 87-90. [5] Brysev A.P., Bunkin F.V., Hamilton M.F., Klopotov R.V., Krutyanski L.M., Yan K. Acoust. Phys. 2003, 49 (1), 19. [6] Brysev A.P., Klopotov R.V., Krutyansky L.M., Preobrazhensky V.L. Phys. Wave Phenom. 2003, 11 (1), 10. [7] Brysev A., Bunkin F., Krutyansky L., Pernod P., Preobrazhensky V. IEEE TUFFC 2002, 49 (4), 409. [8] Preobrazhensky V., Pernod P. Proc. 17th Int. Congress on Acoustics. Rome, 2001, 1, Phys. Acoust. A, 25. [9] Brysev A., Krutyansky L. Acoust. Phys. 2000, 46 (4), 382.

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