акустика / gan_ws_acoustical_imaging_techniques_and_applications_for_en

13.2Optical Piezoelectric Transducers for Generation of

13.6Theory of Electron Inversion and Phonon Amplification Produced

14.2.2Gauge Invariance of Homogeneous Electromagnetic

14.2.5Gauge Invariance of Nonlinear Homogeneous Acoustic

14.2.6My Important Discovery of Negative Refraction is a Special

14.5Acoustic Metamaterial with Simultaneous Negative Mass Density

15.5Negative Refraction Derived from Gauge Invariance (Coordinates

15.5.1Gauge Invariance as a Unified Theory of Negative Refraction

15.6Reflection and Transmission of Sound Wave at Interface of Two Media

15.8Extension to Theory of Diffraction by Inclusion of General Form of Mass Density and Bulk Modulus Manipulated by Predetermined Direction of

15.9A New Approach to Diffraction Theory – A Rigorous Theory Based on the

15.14.2Nonlinear Acoustic Metamaterials for Sound Attenuation

About the Author

Woon Siong Gan obtained his BSc in physics in 1965, DIC in acoustics and vibration science in May 1967 and PhD in acoustics in February 1969, all from the Physics Department of Imperial College, London. He did his postdoctoral works in Imperial College London, Chelsea College London and the International Centre for Theoretical Physics, Trieste, Italy. He is a senior life member of the IEEE, a fellow of the Institute of Engineering and Technology, UK, a fellow of the Institute of Acoustics, UK, a fellow of the Southern African Acoustics Institute, a fellow of the Institution of Engineers, Singapore, a senior member of the American Institute of Ultrasound in Medicine and a member of the Acoustical Society of America since 1969.

He is a founding president of the Society of Acoustics (Singapore), founded in 1989, and a former director of the International Institute of Acoustics and Vibration (IIAV).

He is also a founder of the Signal Processing Singapore Chapter of the Institute of Electrical and Electronics Engineers, USA. He was an associate professor in the physics department of Nanyang University, Singapore, from 1970 to 1979. He was a practicing acoustical consultant from 1979 to 1989. He founded Acoustical Technologies Singapore Pte Ltd in 1989. It is an R&T company in ultrasonics technologies and has developed and patented the scanning acoustic microscope (SAM) and the surface acoustic wave (SAW) devices. So far, it is the only ultrasonic technologies company in Singapore, specializing in ultrasound imaging.

He is a theorist and has published several papers and book chapters on acoustical imaging, active noise cancellation and the application of gauge invariance to acoustics.

He published the paper Gauge Invariance of Acoustic Fields in 2007. This has been experimentally verified by the fabrication of acoustical metamaterials, which shows the invariance of the acoustic field equation to the simultaneously negative mass density and negative bulk modulus. This has been applied to negative refraction with the fabrication of perfect acoustical lens. He also made the important discovery that negative refraction is a special case of the coordinate transformations (gauge invariance) usually applied to cloaking, when the parity or the determinant of the direction cosines or transformation matrix equals –1. His current work is the development of the new field ‘New Acoustics’ based on acoustical metamaterials. This amounts to rewriting the solutions of the acoustic wave equations when the positive mass density and positive compressibility are replaced by negative mass density and negative compressibility and the solutions of the acoustic wave equations based on the bandgap properties of phononic crystals. This will involve refraction, diffraction and scattering, the three basic mechanisms of sound propagation in solids enabling the control and manipulation of direction of sound propagation in solids and give rise to several new phenomena and applications in the form of novel acoustical devices, and hence, the term ‘New Acoustics” coined by the author.

Foreword

Acoustic waves offer very different possibilities for imaging from light. Like X-rays, they can penetrate opaque media. This is why they are used for medical applications and for nondestructive testing. A wide frequency range is available. The human body can sense only one octave in the visible spectrum, but about eight octaves of sound, and ultrasound extends this range to much higher frequencies. Acoustic waves travel typically five orders of magnitude slower than electromagnetic wave, which means that submicron wavelengths can be achieved with frequencies of a few gigahertz. Transducers can be used to convert electrical signals to acoustic waves and vice versa, and the signals can be generated and processed using a full range of digital techniques.

The propagation of acoustic waves can be rich and subtle. In fluids, acoustic waves are longitudinal over all but the smallest distances. Solids can also support shear waves, with two orthogonal polarizations. In the proximity of a surface, combined shear and longitudinal waves can propagate, and they can couple into a fluid in contact with the surface. Solids that are anisotropic, such as crystals or composites, can exhibit rich phenomena, such as beam steering where the direction of propagation is not perpendicular to the wavefronts. The acoustic properties of different media can vary hugely, and this can lead to strong scattering, for example from fine cracks in solids. As well as imaging the geometry of objects, their mechanical properties can be probed. Many materials exhibit nonlinear properties at experimentally accessible acoustic amplitudes.

Exciting applications are opened up by combining a deep understanding of the propagation of acoustic waves with sophisticated instrumentation for generating and detecting them. For example, an atomic force microscope can be used to probe acoustic fields with nanometre resolution by exploiting the nonlinear interaction between the tip and a surface. Scanned lenses and arrays can be used to form diffraction-limited images with resolution from a micrometre in an acoustic microscope to a millimetre or so in medical imaging and nondestructive testing, and greater scales still in sonar and geophysics.

All of this calls for a deep understanding of the propagation of acoustic waves in fluids and in solids, and a full appreciation of the instrumentation that has been developed. Dr Gan has written a book that aims to address this need comprehensively. My hope is that it will lead to better-informed and more widespread use of the rich resources of acoustic imaging.

G.A.D. Briggs

Oxford

14 May 2011

1

Introduction

Acoustical imaging is a multidisciplinary subject covering physics, mechanical engineering, electrical engineering, biology and chemistry. Imaging carries information; it is the procedure for recording information; and there is a saying that an image is worth a thousand equations. There are several forms of imaging modalities using various means of carrying information such as light waves, X-rays, γ -rays, electron beams, microwaves and sound waves. Of these, sound waves, like X-rays, have the capability of penetrating an opaque medium thus enabling the interior of structures to be imaged, due to the propagation of vibration to the interior of the material, and sound waves are generated by vibration. Compared with other imaging modalities, sound waves are safe with no radiation hazards.

This book is the only textbook and reference book that covers all engineering applications under one roof. It is also unique as it presents the latest developments and forefront research in acoustical imaging in the areas of elasticity imaging, time reversal acoustics applied to acoustical imaging, nonlinear acoustical imaging, stochastic and statistical treatments of multiple scattering effects in acoustical imaging, the application of negative refraction to acoustical imaging, and the new field of ‘new acoustics’ founded by the author. The book will therefore be of great interests to practising engineers and researchers. To reflect the engineering nature of the book, there are chapters on such topics as: signal processing and image processing, nondestructive evaluation, underwater acoustics and geophysical exploration.

Acoustical imaging is an old discipline. Various animals have the capability of acoustical imaging. Echo-locating bats, for example, can catch their prey in complete darkness. They utter twittering sounds, too high-pitched for human ears to detect, and process the echoes of this sound from nearby objects to avoid colliding with obstructions. This gives the bats an acoustical image of its surroundings. With a specialized larynx, unusually sensitive ears and a highly developed audio cortex, bats can quickly and safely navigate through the various potential obstructions in the darkness of a cave. Using the same principle of acoustical imaging, dolphins and whales can navigate the murky waters of the ocean. The acoustical imaging ability of animals is the basis of the principles of sonar – the use of pulse–echo technology for underwater viewing in the ocean. The significance and motivation for the development of sonar was: (1) the sinking of the Titanic, the world’s largest ship, by colliding with an iceberg

Acoustical Imaging: Techniques and Applications for Engineers, First Edition. Woon Siong Gan. © 2012 John Wiley & Sons, Ltd. Published 2012 by John Wiley & Sons, Ltd.

when moving at high speed about 1600 miles northeast of New York City on 15 April 1912; and (2) the German U-boat threat to French shipping in World War I.

Lord Rayleigh and O.P. Richardson had thought of using ultrasonic waves for underwater imaging, and the tragic shipwreck of the Titanic stimulated many new activities on how to prevent accidents of this kind in the future. In 1912, Hiram S. Maxim, an American engineer and inventor, was inspired by the techniques employed by bats. He proposed that ships could be protected from collisions with icebergs and other ships by generating underwater sound pulses and detecting their echoes. Shortly afterwards, L.F. Richardson filed a patent in 1912 for a device that would produce sound waves in either air or water and detect echoes from distant objects. R.A. Fessenden filed a patent in the United States early in 1913 for a similar invention. One year later an iceberg was successfully detected at a distance of 2 km using Fessenden’s invention.

Further momentum for the development of more advanced and sophisticated underwater detection equipment arose during World War I due to the immense destructive power of German submarines. Paul Langevin, an outstanding French physicist, was commissioned by his government to find an effective method of detecting the submarines. M.C. Chilowski, an engineer, had developed ultrasonic equipment for the French navy, but its acoustic intensity was much too weak to be effective. Heading a joint US, British and French venture, Langevin looked into the problem of how to increase the acoustic intensity in the water. Within three years, he succeeded in generating a higher acoustic intensity by means of piezoelectric transducers operating at resonance. By 1918, active systems for generating, receiving, and analyzing returned acoustic echoes were developed and proved useful in antisubmarine activities.

The above acoustical imaging systems are intended to image structures within the vast domains of the ocean. Extensive research programmes were needed before other acoustic systems could be applied to the imaging of small-scale systems, such as the tiny interior structures within regions of interest in industry, in hospitals and in laboratories. One of the most important of these programmes was that of the Russian scientist Sokolov [1] whose works started in the 1920s. He was one of the first to recognize and systematically explore the use of ultrasound to image the internal structures of optically opaque objects. Some of his systems were designed to image inhomogeneities, such as cracks, flaws and voids within manufacturing parts. In one of his systems, the inhomogeneities were made visible by reflecting collimated light from a liquid surface in a manner similar to that of liquid-surface acoustical holography [2]. The system provided a means of encoding image information to enable the image to be read out in real time by light diffracted from the sound. The method was a precursor of acoustical holography, and predated Denis Gabor’s invention of holography.

In Langevin’s system, the ultrasonic transmitter emitted a pulse, and the amplitude of the echo, or reflected pulse, was used to produce the acoustical image. In Sokolov’s system, the ultrasonic transmitter emitted continuous waves and the amplitude and phase of the transmitted waves were both used to produce the image. Since Langevin and Sokolov several acoustical imaging systems have been invented with various features and certain degrees of success.

Presently, the acoustical imaging systems can be classified into three main types: pulse–echo, phase–amplitude and amplitude mapping. Examples of pulse–echo systems are B-scan and C-scan systems for medical imaging and nondestructive evaluation, linear array systems for geophysical exploration and seismology, and sonar systems for underwater acoustics. Acoustical holography is an example of a phase–amplitude system. A typical example of an

amplitude-mapping system is acoustical microscopy [3] for nondestructive evaluation, failure analysis, material studies, and biomedical imaging and analysis.

Pulse–echo techniques [4] will involve knowhow in transducer technology, both single element and array types for the generation of ultrasound, electronics such as pulser–receiver for the transmission and receiving of ultrasonic signals, data acquisition card for the capturing and digitization of analogue ultrasonic signals for computation, and software for interfacing the hardware parts. The advance in electronics and digital-processing techniques over the last few decades has given rise to major improvements in the systems available and permitted the development of new and significant scanning and processing methods. This book reviews the latest technology improvements and describes new concepts and approaches that have emerged from the research laboratories where work is being done in this segment.

An example of phase–amplitude acoustical imaging is the acoustical holographic system [2], which originated from Denis Gabor’s Nobel prize works in holography in 1948 [5]. Gabor’s original purpose was in the improvement of the resolution of the electron microscope to 1 A˚ to view the atom. He invented holography as a lensless two-step imaging process in which a hologram would be generated by a scattered electron beam and reconstruction would take place by means of an optical beam. Holographic techniques, however, are not limited to electron or optical beams. Coherence beams are the critical requirement. Holographic systems record both the amplitude and the phase of the scattered beam, and the phase information gives rise to three-dimensional images.

Acoustical microscopic [3] systems were invented in 1974. Unlike the previous two systems, in which the frequencies were typically well below 10 MHz, the acoustic microscopes use much higher frequencies, ranging from tens of megahertz to gigahertz.

As a unique feature, this book includes all the latest inventions in acoustical imaging systems and the forefront research in acoustical imaging systems after the three main types of imaging systems described previously. These will include elasticity imaging, nonlinear acoustical imaging for nondestructive evaluation, time reversal acoustics in acoustical imaging, stochastic and statistical treatment of acoustical imaging, the application of chaos theory to acoustical imaging, and the application of negative refraction to acoustical imaging.

Acoustical imaging is the study of sound propagation in solids, making use of the mechanical and elastic properties to image the interior structure of solids. It will build on the theory of elasticity, the theory of diffraction, the theory of single and multiple scattering, time reversal acoustics, and gauge invariance approach to acoustic fields. Recently, I have pioneered the application of gauge theory and symmetries as a framework to describe sound propagation in solids, and an introduction to this new subject will be given in Chapter 15 of this book.

Signal processing and image processing are important topics of engineering interest. They can be applied to all three of the main engineering applications of acoustical imaging: (1) nondestructive evaluation, (2) underwater acoustics, and (3) geophysical exploration. Examples of some techniques of signal processing are spatial deconvolution, histogram-based amplitude mapping, operator construction, quantization errors and wavefield orthogonalization. Imageprocessing techniques will help in image understanding, which covers texture analysis and tissue characterization. Some topics of image processing are image sampling and quantization, image transforms, image representations by stochastic models, image enhancement, image filtering and restoration, and image reconstruction from projections.

This book is particularly intended for practising engineers and researchers. The reader will study all the key areas of the engineering applications of acoustical imaging under one cover.

Looking forward to the prospects of acoustical imaging, its share of the global market is already catching up with X-rays. It also has the advantages of no radiation hazards and is safe to use regularly with long exposure over a period of time. It also has the capability of viewing minute cracks in the texture of materials, which is outside the ability of an X-ray. With the explosive advancement and application of nanotechnology, acoustical imaging will play an even more important role in the forthcoming decades.

References

[1]Sokolov, S. USSR Patent no. 49 (31 August 1936); British Patent no. 477 139, 1937; US Patent no. 21 64 125, 1939.

[2]Mueller, R.K. and Sheridon, N.K. (1966) Sound holograms and optical reconstruction. Appl. Phys. Lett., 9, 328.

[3]Korpel, A. (1974) Acoustic Microscopy in Ultrasonic Imaging and Holography (eds G.W. Stroke et al.), Plenum Press, New York.

[4]Wells, P.N.T. (1977) Biomedical Ultrasonics, Academic Press, New York.

[5]Gabor, D. (1948) A new microscopic principle. Nature, 161, 777.