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Generality of wave phase conjugation and air-coupled ultrasound
The first chapter presents description of different nature concepts of wave phase conjugation, properties and applications of phase conjugate ultrasonic beams; description of non-contact ultrasonic techniques and air-coupled transducers. Various ultrasonic techniques are presented for velocity measuring.
Acoustic phase conjugation
The problem of the ultrasonic phase conjugation (PC) has long attracted attention because of the unusual physical properties of phase conjugate wave beams and the unique possibilities offered by the PC technique in physical research, nondestructive testing, technology, and medicine. Phase conjugation means the transformation of a wave field resulting in the reversal of propagation of the waves conserving the initial spatial distribution of amplitudes and phases [1]. Unlike the usual specular reflection corresponding to the inversion of one of the spatial coordinates, PC represents the time inversion transformation.
The phenomenon of PC was first observed in a stimulated scattering of light [2]. After this discovery in 1972, phase conjugation has been extensively studied in optics [1, 3].
Studies in acoustics started in 1980’s and several kinds of methods to generate phase conjugate waves have been proposed. It was found that some already known physical phenomena contain the process of phase conjugation. Since then, a considerable number of studies on this matter have been reported. The range of study extends from the basic study to the application to practical ultrasonic instruments. The considerable progress in experiments on acoustic PC during the last decade has made these studies into a field of physical acoustics in its own right.
Despite the generality of the concept of phase conjugation for waves of different nature, PC in acoustics is characterized by silent features related to the wave properties of acoustic media, interactions involved in the PC process, the space-time structure of the acoustic beams being conjugate, and finally, to practical problems that can be solved using the PC phenomenon.
Phase conjugation in the time domain
The phase conjugation of sound waves at relatively low frequencies can be achieved by purely electrical methods [4 – 6] – using multichannel transmitting-receiving antenna arrays. Electronic channel control of the time delay of the received signal allows one to simulate on the array the amplitude-phase distribution corresponding to the phase conjugate wave. Recently, this approach was technically implemented [7, 8]. Modern microprocessors and the technology of matrix piezoelectric transducers permit the realization of PC schemes with hundreds of array elements and an operating frequency of about 5 MHz [9]. Among their advantages are the absence of fundamental restrictions on the shape of the pulse signals being processed and the possibility of deliberate correction of the synthesized amplitude-phase distribution. However, such electronic systems are still extremely complicated to control, cumbersome, and expensive.
Multichannel parametric systems provide some simplification of control and the possibility of operation in real time [4]. The principle of operation is analogous to the wave phase conjugation from a reflecting surface oscillating at double frequency [10 – 12]. The amplitudes of the phase conjugate acoustic waves generated upon such reflection are usually small because of the absence of accumulating parametric effects. A quasi-harmonic signal from a separate receiving transducer in the electronic parametric system is electronically mixed with the double-frequency pump, resulting in the generation of the phase conjugate signal in each channel. In this case, the spatial phase distribution over the array reflects that in the incident wave. The input and output signals are decoupled by means of two closely spaced piezoelectric transducers placed in each channel, operating as a receiver and a transmitter, respectively. This principle has been used in a one-dimensional 300-kHz PC mirror consisting of 20 elements [4]. However, devices of this type have not gained wide acceptance because of the drastic complexity of construction of the parametric array with increasing operating frequency and the passage to two-dimensional arrays.
Purely acoustic phase conjugation methods and acoustic holography
Alternative physical principles of wave phase conjugation in acoustics were analyzed [13, 14]. Attention was devoted to processes in which the generation of phase conjugate sound waves was accompanied by amplification. Similarly to nonlinear optics [15, 3], mechanisms of phase conjugation based on the intrinsic nonlinearity of an acoustic medium were considered. It is known that four-wave mixing of holographic and parametric types can produce PC in a nonlinear medium. In the case of the holographic mechanism, information on the amplitude-phase distribution in the signal wave is recorded during its interaction with the pump wave of the same frequency. The recording occurs as the spatially inhomogeneous quasi-static perturbation of the medium. The conjugate wave is generated during reading the dynamic hologram by the second pump wave propagating toward the recording wave. In the parametric mechanism, the counter-propagating pump waves produce a spatially uniform modulation of parameters of the medium at double frequency. The conjugate wave is generated during parametric interaction of the variable perturbation of the medium with the signal wave. Both holographic and parametric mechanisms principally allow one to generate a phase conjugate wave which is amplified relative to the incident wave.
However, as was noted [14, 16], a practical implementation of wave phase conjugation on the hydrodynamic nonlinearity in common liquids is hindered by the silent feature related to the absence of ultrasound dispersion, which is typical of nonlinear acoustics as a whole [17]. When the pump-wave intensity is sufficient for producing noticeable PC effect, the processes of energy transfer ‘upward’ over the spectrum firstly develop, resulting in the generation of saw-tooth waves. To introduce dispersion and enhance nonlinearity, it was suggested to use liquids containing air bubbles [18]. In a system of such type, the nondegenerate three-wave generation of the phase conjugate wave was experimentally examined with an efficiency of about 1% [19]. The use of temperature nonlinearity was considered, which can only be applied for PC in special cases of highly viscous liquids [20]. The holographic mechanism of wave phase conjugation in liquids containing suspended particles or gas bubbles capable of ordering under the action of acoustic pondermotive forces was discussed [14, 21]. PC of this type was experimentally realized with an efficiency of about 1% [26]. The holographic mechanism of PC based on the nonlinearity of the radiative pressure of sound on the liquid – gas interface was suggested and experimentally realized [22 – 24]. In this case, the PC efficiency in water was about 5% and was limited by side nonlinear effects of surface distortion caused by self-focusing of the sound. By changing the experimental conditions, the PC efficiency was increased almost to unity, which made it possible to observe active suppression of the sound field with the help of the wave phase conjugation considered earlier [25].
A cardinal change in the approach to the problem of the sound wave phase conjugation was associated with abandoning the acoustic pump for modulation of the parameters of a medium. The outlook for the development of parametric PC amplifiers using uniform modulation of the sound velocity by alternating fields of a nonacoustic nature was discussed [13]. However, the search for appropriate mechanisms in real liquids has not led to the desired practical result. Studies of the methods of ultrasonic wave phase conjugation produced in solid-state electro- and magneto-acoustic active media proved to be significantly more efficient.
Parametric wave phase conjugation
The first observations of the generation of phase conjugate sound waves in a solid were reported about thirty years ago [26]. Later, the effects of acoustic PC in crystals were often discussed, mainly in phonon-echo studies. Comprehensive references on this subject can be found in reviews and monographs [27 – 29].
Acoustic phase conjugation in nonlinear piezoelectric media
The simplest way of obtaining acoustic PC in a solid is by modulation of the sound velocity by an alternating electromagnetic field. Nonlinear piezoelectric method is based on the parametric interaction between acoustic waves at a frequency ω and an electric field at a frequency 2ω. Svaasand is reported on this effect [30] about forty years ago.
Thompson and Quate [31] studied this phenomenon extensively, with special interest in the generation of an electric field at 2ω as a result of the mixing of two acoustic waves at ω. In their work, and in the following studies in this field, the main interest was in the ‘‘convolving effect’’ of two acoustic waves. The phase conjugate effect involved in this phenomenon seems to have been paid little attention at that time.
In the 1980’s, after the prosperous research of optical phase conjugation, this nonlinear piezoelectric interaction attracted the attention of researchers with special interest in the wavefront of acoustic waves. It was pointed out that two acoustic fields in this interaction were in the relation of phase conjugation, and this phenomenon was nothing but a method of generating acoustic phase conjugate waves with the help of electrical field [32, 33]. Papers on phase conjugation using nonlinear piezoelectric materials such as LiNbO3 [34], CdS, BK7 glass [35] and PZT ceramics [36, 37] have been presented.
Magneto-acoustic phase conjugation
The use of the interaction of sound with soft modes of collective excitations of different physical nature substantially extends the possibilities of applications of solids for acoustic PC. The strong influence of the magnetic field on the sound velocity is observed in magnetostriction ferrites [38], a number of rare-earth compounds with giant magnetostriction [39, 40], and in some amorphous alloys [41].
It was reported that an acoustic phase conjugate wave at a frequency ω was generated as a result of the parametric interaction between the incident acoustic wave at a frequency ω and a magnetic field at 2ω in nonlinear magneto-acoustic media such as a-Fe2O3 and hematites. An outstanding feature of this method is that the conversion ratio from the incident wave to the phase conjugate wave is extremely high. Preobrazhensky et al. have reported on this method extensively [42 – 44].
Substantial parametric amplification of the bulk phase conjugate ultrasonic wave amounting to 35 dB at a frequency of 30 MHz was achieved in an antiferromagnetic hematite single crystal [45]. Earlier, parametric excitation of standing sound waves by an alternating magnetic field [46] and nondegenerate generation of the backward travelling ultrasonic wave in the acoustic pump field [47] were observed in this crystal. In the latter case, the generation was caused by the anomalous strong three-wave interaction of coupled magnetoelastic excitations [48].
The extremely high efficiency of the parametric PC of a travelling ultrasonic wave was found experimentally in a magnetostriction ceramics based on nickel ferrite [49]. The amplification coefficient of the backward wave at a frequency of 30 MHz exceeded 80 dB, its estimated intensity being hundreds of 100 W/cm2. The possibility of generation of highly intense phase conjugate ultrasonic waves by means of polycrystalline materials is of special interest because modern ceramic technology allows one to manufacture active elements for PC devices of any size and shape, which may be required for specific applications.
Ultrasound uses in the majority of practical applications are imposed by the obligation of use of ultrasound in low MHz range. Therefore development of ultrasonic PC methods has led to reduce working frequencies of WPC systems 5-10 MHz
In time of ultrasonic waves conjugation in the most of practical uses of WPC effect the liquid became the medium of wave propagation or became plays a role of immersion layer between conjugator, object of testing and transducer.
Development of the supercritical parametric technique of acoustic wave phase conjugation and interest in the implementation of nonlinear wave phenomena in acoustic imaging systems for medical purposes and nondestructive testing has noticeably quickened in the last few years.
The possible application of ultrasonic PCWs that are targets themselves to a scatterer for measuring the scatterer velocity is demonstrated [50, 51]. When PCWs of similar frequencies collided near a scatterer in experiments [52], they produced ultrasound of a low difference frequency, with its phase being anomalously sensitive to the movements of the scatterer.
The possibility of the giant amplification of PCWs in the above-threshold parametric mode permitted the natural expansion of the PCW technique to nonlinear acoustic imaging. The PCW technique has been combined with harmonic imaging [53, 54].
Properties and applications of phase conjugate ultrasonic beams
Despite the generality of the concept of phase conjugation for waves of different nature, PC in acoustics is characterized by silent features related to the wave properties of acoustic media, interactions involved in the PC process, the space-time structure of the acoustic beams being conjugate, and finally, to practical problems that can be solved using the PC phenomenon.
Almost all known manifestations of the acoustic PC are of interest for applications. The most important among them are the compensation for phase distortions in an inhomogeneous, acoustically transparent medium, including the compensation for acoustic losses in elastic scattering, autofocusing or `self-targeting’ of ultrasonic beams on scatterers, and the lensless formation of acoustic images. Figures 1.1 and Figures 1.2 illustrate these effects.
Table of contents :
Introduction
Chapter 1: Generality of wave phase conjugation and air-coupled ultrasound
1.1. Acoustic phase conjugation
1.1.1. Phase conjugation in the time domain
1.1.2. Purely acoustic phase conjugation methods and acoustic holography
1.2. Parametric wave phase conjugation
1.2.1. Acoustic phase conjugation in nonlinear piezoelectric media
1.2.2. Magneto-acoustic phase conjugation
1.2.3. Properties and applications of phase conjugate ultrasonic beams
1.3. Ultrasonic velocimetry
1.3.1. Ultrasonic velocimetry
1.3.2. Ultrasonic velocimetry by Ultrasonic Phase Conjugation
1.4. Ultrasonic nondestructive testing in air
1.4.1. Non-contact ultrasonic techniques
1.4.2. Air-coupled transducers
Conclusion
Chapter 2: Features of ultrasonic wave phase conjugation system operating with weak signals
2.1. Introduction
2.2. Operating modes of wave conjugation system
2.3. Linear and saturation modes of parametrical PCW generation
2.4. Coded excitation
2.4.1. Codes
2.4.2. Code choice and realization
Conclusion
Chapter 3: Numerical simulations of propagation of ultrasonic phase conjugate wave in con-focal system
3.1. Transmission angular characteristics
3.2. Evolution of an amplitude and phase of PC wave in con-focal ultrasonic system in the framework of ray acoustics
3.3. Results of numerical modeling
Conclusion
Chapter 4: Acoustical matching of the ultrasonic wave phase conjugation system
4.1. Introduction
4.2. Resonant λ/4 acoustical matching
4.3. Acoustical matching of wave phase conjugation system
4.4. Experimental results
Conclusion
Chapter 5: Examples of applications of air-coupled phase conjugate waves
5.1. Experimental setup for demonstration the applications of PC waves in air
5.2. Air-coupled acoustic C-scan imaging (acoustic microscopy) by means of supercritical parametric wave phase conjugation
5.3. Air flowmeter based on wave phase conjugation phenomena
5.4. Velocimetry of air flow by means of wave phase conjugation
Conclusion
General conclusion
Bibliography
