A Data Engineering Approach to Wave Scattering Analysis with Applications in Radar, Sonar, Medical Diagnostics, Structural Flaw Detection and Intelligent Robotics E-Book
Mark K. Hinders
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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
Comprehensive resource exploring how recent advancements in computational capabilities open doors to new applications in wave scattering
A Data Engineering Approach to Wave Scattering Analysis: with Applications in Radar, Sonar, Medical Diagnostics, Structural Flaw Detection and Intelligent Robotics applies scattering analysis to many applications including radar, sonar, medical diagnosis, intelligent robotics, and more, enabling readers to implement new and better measurements with both novel instrumentation and artificial intelligence that automates the interpretation of various (and multiple) imaging data streams. Composed of 10 chapters, this book brings together separate scientific topics that share a common basis of knowledge and their unchanged mathematical techniques to ensure successful results.
Through periodic exercises, this book reinforces the importance of revisiting derivations and reproducing established results. It also delves into the individuals who shaped scientific methods and technologies, exploring 81 notable names and providing insights into their professional journeys.
Classic results from scattering are included in each chapter, and rather than simply pasting in plots from classic papers, these results have largely been reproduced for a more coherent reader experience.
Written by an established academic in the field, A Data Engineering Approach to Wave Scattering Analysis: with Applications in Radar, Sonar, Medical Diagnostics, Structural Flaw Detection and Intelligent Robotics includes information on various topics:
- Field equations, covering strain as a dimensionless measure of deformation, generalized Hooke’s Law, and elastic and acoustic waves
- Reflection and refraction, covering reflection from a free surface and surface waves as well as the wave model of acoustic microscopy
- Guided waves, covering torsional modes, longitudinal waves, and flexural waves in rods, as well as data engineering for lamb wave tomography
- Inverse scattering, covering wavelet transforms and fingerprinting as well as applications of wavelet fingerprints such as roof fall detection
A Data Engineering Approach to Wave Scattering Analysis: with Applications in Radar, Sonar, Medical Diagnostics, Structural Flaw Detection and Intelligent Robotics is an essential up-to-date reference on the subject for researchers interested in radar, sonar, medical imaging, structural health monitoring, manufacturing process control, and autonomous vehicles, as well as upper-level undergraduates and graduate students in related programs of study.
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Table of Contents
Cover
Table of Contents
Title Page
Copyright
Dedication
About the Author
Preface
Acknowledgments
Introduction
1 Background
1.1 Some History
1.2 Ultrasound Immersion Tank Scans
1.3 A-, B-, C-Scans, M-Mode
1.4 Monostatic, Bistatic, Doppler
1.5 Didey Wagon vs. War Wagon
1.6 Acoustic Parametric Arrays
1.7 Forward to Scattering
References
Notes
2 Field Equations
2.1 Index Notation
2.2 Stress Is Force per Unit Area
2.3 Strain Is Dimensionless
2.4 Stress Is Proportional to Strain
2.5 Elastic Waves
2.6 Electromagnetic Waves
2.7 Acoustic Waves
2.8 Anisotropic Elastic Solids
2.9 Summary
Notes
3 Boundary Conditions: Continuous and Discretized
3.1 Boundary Conditions for E&M
3.2 Boundary Conditions for Acoustics
3.3 Boundary Conditions for Elastodynamics
3.4 Finite Difference Time Domain
3.5 Elastodynamic Simulations
3.6 The Acoustic Parametric Array
References
Notes
4 Reflection and Refraction
4.1 Reflection from a Free Surface
4.2 Surface Waves
4.3 Acoustic Microscopy
References
Notes
5 Guided Waves
5.1 Guided Waves in Plates
5.2 Cylindrical Guided Waves
5.3 Guided Waves in Pipes
5.4 Data Engineering for Tomography
References
Notes
6 Scattering from Spheres
6.1 Clebsch–Mie Scattering
6.2 Acoustic Scattering from a Sphere
6.3 Elastic Wave Sphere Scattering
6.4 Incident Transverse Wave
6.5 Scattering from Spherical Shells
References
Notes
7 Scattering from Cylinders
7.1 Electromagnetic Wave Scattering
7.2 Elastic Wave Scattering
7.3 Plate Wave Scattering
7.4 Thermal “Wave” Scattering
7.5 Scattering from a Semicircular Gap in a Ground Plane
References
Notes
8 Scattering from Spheroids and Elliptic Cylinders
8.1 Scalar Wave Equation in Elliptic Cylinder Coordinates
8.2 Scattering from a Perfectly-Conducting Elliptic Cylinder
8.3 Scattering from a Dielectric Elliptic Cylinder
8.4 Scattering of Elastic Waves by an Elliptic Cylindrical Inclusion
8.5 Scattering from Spheroids
References
Notes
9 Scattering from Parallelepipeds
9.1 Integral Equations
9.2 High Frequency Scattering and Diffraction Coefficients
9.3 Reflection/Transmission by a Slab
9.4 Reflection at Conducting Halfspace
9.5 Surface Plasmon Polaritons
References
Notes
10 Inverse Scattering
10.1 Wavelet Fingerprinting
10.2 Wavelet Fingerprints Applied
10.3 Conclusions
Notes
Index
End User License Agreement
List of Illustrations
Chapter 1
Figure 1.1 The infrasonic echo waves would be recorded by a stretched membra...
Figure 1.2 Aircraft engines produced unprecedented sound, so in order to hea...
Figure 1.3 We’ve grown used to wonders in this century. It’s hard to dazzle ...
Figure 1.4 Ultrasound immersion tank provides a convenient way to scan a spe...
Figure 1.5 Immersion tanks can be quite large, as in this one (a), which hol...
Figure 1.6 Consider an incident plane wave interacting with a slab of thickn...
Figure 1.7 Reflections from a flaw in the test specimen will give echoes in ...
Figure 1.8 In recent years, both the computers and the ultrasonic instrument...
Figure 1.9 Cutaway view of an ultrasound transducer. The PZT crystal has met...
Figure 1.10 A pulse-echo waveform is called an A-line, which shows amplitude...
Figure 1.11 A flaw in a sample will occur between the front-face and back-fa...
Figure 1.12 Since it’s the flaw that’s of interest, typically one gates the ...
Figure 1.13 As the transducer is scanned laterally, a number of A-scans can ...
Figure 1.14 The 3D volume of data can be sliced vertically to give a B-scan ...
Figure 1.15 In addition to A-, B-, and C-mode images, there’s also M-mode, w...
Figure 1.16 The portable, inexpensive, high-performance USRP is a scalable s...
Figure 1.17 You’d be pretty unlikely to get a speeding ticket in a pumpkin c...
Figure 1.18 The Horten [65] flying wing would have been quite stealthy even ...
Figure 1.19 Most people first became aware of stealth aircraft when the F117...
Figure 1.20 A simplified cartoon of an air vehicle allows us to consider wha...
Figure 1.21 The primary contribution to radar backscattering for a Volvo 240...
Figure 1.22 Step number one, get yourself a windshield with the Quickclear (...
Figure 1.23 The highly swept planform, carefully aligned facets, screened in...
Figure 1.24 Waveform synthesized via Matlab on laptop and sent via headphone...
Chapter 2
Figure 2.1 Stress is force per unit area. Normal stress on the left. Shear s...
Figure 2.2 The indices on the stress components indicate the direction of th...
Figure 2.3 Force is stress times area. The surface stresses in the -directi...
Figure 2.4 Moment is force times distance, so it’s then distance times stres...
Figure 2.5 Normal strain is change in length per unit length.
Figure 2.6 Shear strain is change from a rectangle to a parallelogram.
Figure 2.7 Shear strain in 3D is changed from a cube to a rhomboid, which ma...
Figure 2.8 Shear waves and longitudinal waves are propagating to the right. ...
Figure 2.9 Slowness curves for cubic anisotropy. Faster modes have smaller s...
Chapter 3
Figure 3.1 Pillbox that straddles the boundary between
Mediums 1
and
2
with ...
Figure 3.2 Here I am in my Air Force office about 1990 or so. It took me a c...
Figure 3.3 Forward (...
Figure 3.4 The physical space is divided up into a computational grid (left)...
Figure 3.5 The diamond stencil (a) uses the grid points to the left/right ...
Figure 3.6 Reproduction of Yee’s Fig 4 on right. The value of the field in...
Figure 3.7 Snapshots of simulations where mmWave signals interact with corne...
Figure 3.8 Lamb waves in an aluminum plate. Left image is an unflawed plate....
Figure 3.9 As the EFIT simulation steps through time, the guided waves inter...
Figure 3.10 Side and top views of acoustic waves scattering from a model tor...
Figure 3.11 A three-dimensional contour plot allows visualization of surface...
Chapter 4
Figure 4.1 Light entering the top of a diamond will be reflected back out th...
Figure 4.2 The amplitude ratios of the reflected and refracted vertically po...
Figure 4.3 Incident, reflected, and transmitted waves at an interface betwee...
Figure 4.4 Elastic wave in a steel block incident upon a brass wedge angled ...
Figure 4.5 Incident and reflected elastic waves at a free surface of a half-...
Figure 4.6 Elastic wave in a steel block scattering from an angled free surf...
Figure 4.7 Incident and reflected elastic waves at a free surface of a half-...
Figure 4.8 Incident and reflected SV elastic waves at a free surface of a ha...
Figure 4.9 Reflection at steel/air interface for incident L-wave (a) and inc...
Figure 4.10 The transducer is at the top of a delay line with a lens that fo...
Figure 4.11 The left lens at top is defocused by an amount as indicated by...
Figure 4.12 Rayleigh waves incident on the end of a quarterspace will reflec...
Figure 4.13 The transducer generates longitudinal waves in the delay line, w...
Figure 4.14 A right-angle delay line with a curved opening allows acoustic m...
Chapter 5
Figure 5.1 Dispersion curves for an aluminum plate. Solutions to the Rayleig...
Figure 5.2 Plate of thickness with propagation in the -direction.
Figure 5.3 Plate wave dispersion curves for SH modes. Note that the lowest o...
Figure 5.4 Infrared cameras can detect a person’s body heat entering a shipp...
Figure 5.5 Lamb wave detection of disbonds in a riveted lap joint. As the tr...
Figure 5.6 Cylindrical rod of radius with propagation in the -direction....
Figure 5.7 Torsional (a) and longitudinal (b) wave mode dispersion curves fo...
Figure 5.8 Phase velocities of extensional and flexural modes in a cylindric...
Figure 5.9 Pipe with inner radius and outer radius with propagation in t...
Figure 5.10 Fan beam tomography reconstruction for a 25-mm, 50% thickness fl...
Figure 5.11 Explanation of the ART algorithm for the double crosshole geomet...
Figure 5.12 Sequential ART reconstruction of two circular flat-bottom holes ...
Figure 5.13 Two investigational ultrasound devices we developed based on con...
Figure 5.14 Theoretical arrival times of the mode in a defect-free aluminu...
Figure 5.15 Wigner transform of the signal (top). The power spectrum and ori...
Figure 5.16 Aluminum plate with two circular thinnings (a), five through hol...
Figure 5.17 A sequence of tonebursts at increasing frequencies are transmitt...
Figure 5.18 A three-legged transducer array allows for tomographic reconstru...
Figure 5.19 Woman leans over scanner (left) with breast suspended into scann...
Chapter 6
Figure 6.1 Problem geometry for scattering from a sphere.
Figure 6.2 Absorption efficiency for various refractive indices vs. (a). E...
Figure 6.3 Backscatter gain for spheres with refractive index 1.61 (a) and 1...
Figure 6.4 Extinction efficiency of spheres for various values of refractive...
Figure 6.5 The total scattering from selected real refractive indexes (), s...
Figure 6.6 Anderson Figure 3. Reflectivity for direct backward scattering ...
Figure 6.7 Anderson Figure 5. Total scattering as a function of acoustic r...
Figure 6.8 Scattering cross sections for spherical cavities in various media...
Figure 6.9 Scattering cross sections: short dashed line is the SV-wave compo...
Figure 6.10 Elastic wave scattering from a two-layer spherical elastic inclu...
Chapter 7
Figure 7.1 Problem geometry for scattering from a cylinder.
Figure 7.2 Backscattering from a perfectly electrically conducting (PEC) cyl...
Figure 7.3 Normalized scattering cross sections for a dielectric cylinder wi...
Figure 7.4 Backscattering from elastic cylinders. (a) is for an air-filled h...
Figure 7.5 Scattering patterns for 0.093 in diameter brass (a) 0.09375 in di...
Figure 7.6 Scattering patterns for 0.032 in diameter brass (a) 0.032 in diam...
Figure 7.7 A mobile robot which we named rWilliam has a forward-looking 50 k...
Figure 7.8 Differential scattering cross sections for boron cylinders in alu...
Figure 7.9 Differential scattering cross sections for boron cylinders in alu...
Figure 7.10 White’s Figure 4 reproduced from [12] showing normalized angular...
Figure 7.11 Figures 5, 6, and 7 from [12] showing angular scattering of elas...
Figure 7.12 Differential scattering cross sections for cylindrical holes in ...
Figure 7.13 Dynamic stress concentrations for a boron fiber in epoxy. The th...
Figure 7.14 Solving the similar but more algebraically involved problem of s...
Figure 7.15 Polar plots of the magnitude of the scattered amplitude of a pla...
Figure 7.16 Angular far-field scattering for in-plane steel disk in aluminum...
Figure 7.17 Angular far-field scattering for in-plane titanium disk in alumi...
Figure 7.18 An incident TM plane wave at angle to a semicircular channel o...
Figure 7.19 Amplitude parameter plotted vs. for TM and TE cases. Note th...
Chapter 8
Figure 8.1 Elliptical coordinates with the radial lines (ellipses) shown f...
Figure 8.2 Polar plots of normalized bistatic scattering cross section for a...
Figure 8.3 Polar plots of EM scattering from a long PEC ribbon of width . A...
Figure 8.4 Polar plots of sound scattering from a long rigid ribbon of width...
Figure 8.5 Polar plots of scattering of from a dielectric ribbon with . T...
Figure 8.6 Polar plots of scattering of from a dielectric ribbon with . T...
Figure 8.7 Polar plots of scattering of from a dielectric ribbon with . T...
Figure 8.8 Polar plots of scattering of from a dielectric ribbon with . T...
Figure 8.9 Scattering for acoustic wave incident along the axis of a rigid s...
Figure 8.10 Scattering cross sections for prolate (dots) and oblate (dashes)...
Chapter 9
Figure 9.1 Source term is in the volume while passive scatterer is in volu...
Figure 9.2 Scattering cross section for a perfectly conducting cube with a p...
Figure 9.3 Angle of reflection is equal to angle of incidence for a curved s...
Figure 9.4 Front view of the F117 stealth fighter (a) from which you can see...
Figure 9.5 Opaque body with source at point 0 and observation at point , wh...
Figure 9.6 Diffraction at a curved edge. The source is shown coming in from ...
Figure 9.7 Geometry for magnetic line current illuminating a truncated wedge...
Figure 9.8 The radar cross sections of simple shapes in the high-frequency a...
Figure 9.9 My advisor, Asim Yildiz (right) talking with his advisor, Julian ...
Figure 9.10 The RCS of wires, rods, cylinders, and discs depend on and the...
Figure 9.11 Creeping waves are generated at the shadow boundary for any rays...
Figure 9.12 Creeping waves will scatter from any discontinuity of surface-to...
Figure 9.13 A Rayleigh wave incident on the boundary of two adjoining quarte...
Figure 9.14 Plane wave reflection and transmission by a slab of thickness ....
Figure 9.15 Incident TE plane wave reflection and refraction at a halfspace....
Figure 9.16 Incident TM plane wave reflection and refraction at a halfspace....
Figure 9.17 Incident TE plane wave reflection and diffraction by a defect.
Chapter 10
Figure 10.1 For inverse scattering, we know the source and measure the scatt...
Figure 10.2 A visual summary of the DWFP algorithm. A time-domain signal (a)...
Figure 10.3 The top fingerprint, labeled as a fracture event, shows the kind...
Figure 10.4 (Top) The time domain plot of a pulse in the received signal for...
Figure 10.5 Wavelet fingerprints from TDR waveforms. The top fingerprint (a)...
Figure 10.6 The 100 MHz ultrasonic pulse-echo instrument detects delaminatio...
Figure 10.7 Typical ultrasound backscattering results for full (left) and em...
Figure 10.8 Fingerprints of the pulse, demodulated from a 5 GHz center frequ...
Guide
Cover
Table of Contents
Series Page
Title Page
Copyright
Dedication
About the Author
Preface
Acknowledgments
Introduction
Begin Reading
Index
WILEY END USER LICENSE AGREEMENT
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IEEE Press445 Hoes LanePiscataway, NJ 08854
IEEE Press Editorial BoardSarah Spurgeon, Editor-in-Chief
Moeness Amin
Jón Atli Benediktsson
Adam Drobot
James Duncan
Ekram Hossain
Brian Johnson
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James Lyke
Joydeep Mitra
Desineni Subbaram Naidu
Tony Q. S. Quek
Behzad Razavi
Thomas Robertazzi
Diomidis Spinellis
A Data Engineering Approach to Wave Scattering Analysis
with Applications in Radar, Sonar, Medical Diagnostics, Structural Flaw Detection and Intelligent Robotics
Mark K. Hinders
William & Mary, Williamsburg
USA
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To my former and future students.
About the Author
Mark K. Hinders holds BS, MS, and PhD in Aerospace and Mechanical Engineering from Boston University and is Professor of Applied Science at the College of William & Mary in Virginia. Before coming to Williamsburg in 1993, Professor Hinders was senior scientist at Massachusetts Technological Laboratory, Inc., and research assistant professor at Boston University. Before that Dr. Hinders was an electromagnetics research engineer at the USAF Rome Laboratory located at Hanscom AFB, MA. Professor Hinders conducts research in wave propagation and scattering phenomena, applied to medical imaging, intelligent robotics, security screening, remote sensing, and nondestructive evaluation. He and his students study the interaction of acoustic, ultrasonic, elastic, thermal, electromagnetic, and optical waves with materials, tissues, and structures.
Preface
I like to work on real-world problems that matter. I also like that there are new problems all the time, with the caveat that the basic math and physics doesn’t change so we get to continue to exploit our hard-won mastery of difficult subjects. In my lab I have a Monty Python poster. It’s John Cleese in a suit and tie sitting at a desk on a beach. It’s not captioned, but he would be saying, “And now for something completely different.”
20 September 2024
Mark K. Hinders
Williamsburg, Virginia
Acknowledgments
The author would especially like to thank his research mentors, the late Profs. Asim Yildiz and Guido Sandri, and their research mentors, Prof. Julian Schwinger and Dr. J. Robert Oppenheimer. Asim Yildiz (DEng, Yale) was already a Professor of Engineering at the University of New Hampshire (UNH) when Prof. Schwinger at Harvard told him that he was “doing good physics” already so he should “get a union card.” Schwinger meant that Yildiz should get a PhD in theoretical physics with him at Harvard, which Yildiz did while still keeping his faculty position at UNH and mentoring his own engineering graduate students, running his own research program, and so on. He also taught Schwinger to play tennis, having been a member of the Turkish national team and all the best tennis clubs in the Boston area.
When Prof. Yildiz died at age 58, his genial and irrepressibly jolly Boston University (BU) colleague took on his orphaned doctoral students, including yours truly, even though the students’ research areas were all quite distant from his own. Prof. Sandri had done postdoctoral research with Oppenheimer at the Princeton Institute for Advanced Study and then was a senior scientist at Aeronautical Research Associates of Princeton for many years before spending a year in Milan at Instituto Di Mathematica del Politecnico and then joining BU. In retirement, he helped found Wavelet Technologies, Inc. to exploit mathematical applications of novel wavelets in digital signal processing, image processing, data compression, and problems in convolution algebra.
Introduction
In this book, scattering analysis is applied to many seemingly different things, including but not in any way limited to:
Radar
: The atomic bomb may have ended WWII, but radar won it. Radar kept Britain in the war long enough for the arsenal of democracy to get fully into the game. After the Cold War ended, radar-scattering folks ended up making video games realistic and cell phones reliable.
Sonar
: For decades, humans have been hard at work trying to duplicate the innate abilities of echolocating mammals like dolphins, whales, and bats. Acoustic scattering is more than just a scalar version of electromagnetics.
Medical diagnostics
: Ultrasound images, mammograms, etc. are 2D “cuts” of three-dimensional anatomy. Doctors are expert at interpreting them, but the diagnosis is still quite subjective. Machine learning can assist doctors by highlighting suspicious features in signals.
Structural flaw detection
: Technicians are not as highly trained at diagnosis as are doctors, plus there is no standard “anatomy” and the structure can’t tell where it hurts. For many applications, machine learning can take the lead by automatically identifying flaws that could lead to structural failure.
On-line inspection
: Process engineers don’t want to interpret images. They want the instrumentation to give a green light if the process is OK, and a red light if it’s out of spec. Automatic, real-time interpretation of complex process-monitoring signals is now doable.
Intelligent robotics
: The key to useful robots is a combination of imaging sensors and the on-board intelligence to interpret them in real time. You want to simply tell the robot to turn left at the big tree, not feed it GPS coordinates.
The modeling techniques, and applications of them, we’ll be discussing allow one to implement new and better measurements with both novel instrumentation and artificial intelligence that automates the interpretation of the various (and multiple) imaging data streams. There’s rather a lot of high-level math, of course, but that’s good for us because we’re not the sort of laymen who Einstein said “have a secret grudge against arithmetic.”
The underlying mathematical and computational methods we’ll discuss transcend any particular application(s). If you can do radar, you can do sonar, seismology, nondestructive evaluation, and so on. That turns out to be pretty important because lifequakes come along about every six to eight years, and any particular thing that you happen to be expert at might go from hot to not in an instant. That has happened to me repeatedly since 1986 and so all these years later, I’ve accumulated a seemingly diverse set of subject matter expertise with a mindset of always being on the lookout for new applications of what I know and can do.
It has recently come to my attention that the current cohort of graduate students are Gen Z, who did at least some college via Zoom and are fundamentally different from the generations that came before them. They’ve never not had all the world’s knowledge in a portable, semidisposable device that they carry with them at all times. One goal of this book is to help connect this generation with the vast scientific literature that has long existed in musty libraries but now is available for download at places like Internet Archive, but only if you know what sources to seek out and use as the basis for your personal reference library. It’s also important to pay homage to those scientists and mathematicians who spent their professional lives developing tools that you can now use to solve problems. Tea will be spilled; the index is designed to allow a quick Hollywood read.
This book is based on a multisemester sequence of graduate classes that I’ve been giving for three decades now. I started by typing up my own hand-written notes, and as I was going along, many of my students made plots for this book as exercises in class. Thanks for that, BTW. I’ve also drawn examples whenever possible from the dissertation research of my graduate students, with discussion of the real-world problems that motivated their research. I’ve deliberately included anecdotes of the sorts of issues that can arise in collaborative research that includes multiple investigators and multiple institutions. Much of our work is done in close collaboration with small companies, several of whom I’ve shepherded from de novo startups on through VC investment or M&A, but I’ve always avoided taking any equity stake so I’d be at arm’s length and could focus on doing what’s best for my students’ career progression.
This isn’t intended to be a comprehensive reference work on scattering for radar, sonar, etc. Indeed, I’ve deliberately downplayed techniques that aren’t all that important now that ubiquitous computing of sufficient power means we can simulate realistic 3D scattering scenarios. I do try to point the reader to classic texts where those mature areas of research are discussed in great detail by those notables who developed the methods, doing the best they could with the computational power they had available. Once upon a time, of course, computer was a job title.
1Background
1.1 Some History
As a child you probably played the swimming pool game of tag where you close your eyes and then repeatedly call out “Marco” with the response “Polo” each time from the other players by which you’re supposed to locate them and tag someone who is then it. Biurnal hearing allowed you to tell which direction to lunge, and you could guesstimate who was nearby and who was farther away. The game is a little trickier to play at indoor pools because the acoustic scattering from walls and such can be confounding.
Marco Polo may or may not have traveled from Venice to China, although he did spend a couple of decades travelling and trading along the Silk Road, where he would certainly have picked up a lot of information, such as how to make power smoothies, and trade goods like yak hair [1]. He mistook rhinos for chubby unicorns, which is now a meme. In his book, he also claimed to have been besties with the emperor Kublai Khan. Christopher Columbus brought a copy of that book along with him on his 1492 trip to the Orient, but it turned out to be unhelpful. Navigating the world based on maps pieced together from stories of other travelers is always going to be a bit iffy. Fortunately, over the last century or so there has been a rapid development of navigation technologies.
The Submarine Signal Company, established in 1901 in Boston, was the first commercial enterprise organized to conduct underwater sound research and to develop equipment to be used for increasing the safety of navigation [2]. “Our invention relates to a method of ringing or sounding a bell and also to a system and apparatus for transmitting intelligence between ships at sea and between the shore and any ship by means of sound-signals made in the water at the transmitting-station by electrical means. These sounds are picked up from the water at the receiving-station by means of electrical or mechanical devices.” The initial product line included underwater bells for shore-based stations, buoys, and lightships as well as encased microphones for sound detection on the ships [3, 4].
1.1.1 The Titanic Disaster
In 1912, the unsinkable Titanic struck an iceberg and sank [5]. Not long after, Sir Hiram Maxim self-published a short book and submitted a letter to Scientific American [6] in which he asked, “Has Science reached the end of its tether? Is there no possible means of avoiding such a deplorable loss of life and property? Thousands of ships have been lost by running ashore in a fog, hundreds by collisions with other ships or with icebergs, nearly all resulting in great loss of life and property.” Maxim noted that collisions often take place in a fog at night when a searchlight is worse than useless because it just illuminates the haze. It was (becoming) known that bats used some form of sound that was outside the range of human hearing in order to echolocate and feed, but he thought it was infrasound rather than ultrasound [7, 8]. Maxim described a concept for a very low-frequency directional steam whistle or siren that could be used to (echo)locate icebergs during foggy nights when collisions were most likely to occur. Whether Maxim’s patented apparatus would have been effective at preventing collisions at sea is a question that’s a little like whether Da Vinci’s contraptions would have flown. He got the general idea right, and can be credited with stimulating the imaginations of those who subsequently worked out all the engineering details.
His sketch, reproduced as Figure 1.1, is quite remarkable. The key idea is that the time delay of the echoes determines distance because the speed of sound is known, but more importantly, the shape of the echoes gives information about the object that is returning those echoes. Analysis of those echo waveforms can, in principle, tell the difference between a ship and an iceberg, and even differentiate large and small icebergs. He even illustrates how clutter affects the echoes differently from backscattering targets. Science has not, in fact, reached the end of its tether, even after a century of further development. This is exactly how radar, sonar, and ultrasound work [9, 10].
Maxim’s suggested apparatus embodies a modified form of “siren,” through which high-pressure steam can be made to flow in order to produce sound-waves with about 14–15 vibrations per second, and consequently not coming within the range of the human ear. These waves, it is asserted, would be capable of traveling great distances, and if they struck against a body ahead of the ship, they would be reflected toward their source, “echo waves” being formed [11]. This self-published pamphlet was discussed in [12].
1.1.2 Das Unterseeboot
The first submarine to successfully dive, cruise below the water surface, and emerge to the surface again on its own was the Sub Marine Explorer of the German American engineer Julius H. Kroehl, which already comprised many technologies that are still essential to modern submarines [13]. The first submarine built in Germany, the three-man Brandtaucher, sank to the bottom of Kiel harbor on 1 February 1851 during a test dive [14]. The Confederate States of America fielded several human-powered submarines, including CSS H. L. Hunley. The first Confederate submarine was the 30-foot-long Pioneer, which sank a target schooner using a towed mine during tests on Lake Pontchartrain, but it was not used in combat. It was scuttled after New Orleans was captured and in 1868 was sold for scrap, but the similar Bayou St. John submarine is preserved in the Louisiana State Museum. CSS Hunley was intended for attacking Union ships that were blockading Confederate seaports. The submarine had a long pole with an explosive charge in the bow called a spar torpedo. The sub had to approach an enemy vessel, attach the explosive, move away, and then detonate it. It was extremely hazardous to operate, and had no air supply other than what was contained inside the main compartment. On two occasions, the sub sank; on the first occasion, half the crew died, and on the second, the entire eight-man crew (including Hunley himself) drowned. On 17 February 1864, CSS Hunley sank USS Housatonic off the Charleston Harbor, the first time a submarine successfully sank another ship, although it sank in the same engagement shortly after signaling its success. Submarines did not have a major impact on the outcome of the American War Between the States,1 but did portend their coming importance to naval warfare and increased interest in their use in naval warfare.2
Figure 1.1 The infrasonic echo waves would be recorded by a stretched membrane that the infrasound waves would vibrate, and those membrane vibrations could jingle attached bells or wiggle pens tracing lines on paper as Maxim illustrated. Maxim’s concept was discussed in Nature, a leading scientific journal yet today.
You almost certainly know Captain Nemo’s submarine Nautilus from Jules Verne’s Twenty Thousand Leagues Under the Sea (1870), but you may not have read The Mysterious Island (1874) or know that Nemo’s fictional craft was named after Robert Fulton’s real-life submarine Nautilus (1800). Verne was inspired by the French Navy submarine Plongeur, a model of which he saw at the 1867 Exposition Universelle. The fictional Nautilus was battery powered, not nuclear like today’s boomers that can travel way more than 20,000 leagues (not quite three laps around the earth) under the sea, sneaking around for six months at a time just in case they need to destroy the world because reasons.
The Battle of Hampton Roads was the most important naval battle of the American Civil War. It was fought over two days in March 1862, where the Elizabeth and Nansemond rivers meet the James River just before it enters the Chesapeake Bay adjacent to the city of Norfolk, Virginia. The battle was a part of the effort of the Confederacy to break the Union blockade, which had cut off Virginia’s largest cities and major industrial centers, Norfolk and Richmond, from international trade. The battle was the first meeting in combat of ironclad warships: USS Monitor and CSS Virginia. USS Monitor was a semisubmersed, iron-hulled steamship and was the first ironclad warship commissioned by the Union Navy. Her remains were found upside down 16 miles off Cape Hatteras in 1973 at a depth of about 240 ft. In 1987, the site was declared a National Marine Sanctuary, the first shipwreck to receive this distinction. Because of Monitor’s advanced state of deterioration, recovery of any remaining significant artifacts and ship components was quite urgent. Numerous fragile artifacts, including the innovative turret and its two Dahlgren guns, an anchor, steam engine, and propeller, were recovered. They were transported to the Mariners’ Museum in Newport News, where a full-scale copy of USS Monitor, the original recovered turret, and a variety of artifacts and related items are on display.3 Also in Newport News is the largest military shipbuilder in the United States and sole designer, builder, and refueler of nuclear-powered aircraft carriers. HII is responsible for building more current aircraft carriers than the rest of the world’s navies put together. Virginia would be a superpower if they seceded today.
Most consider French physicist Pierre Curie’s discovery of piezoelectricity in 1877 to be the moment that sonar was conceived. Thirty-five years later, also inspired by the sinking of the Titanic, Physicist Paul Langevin was commissioned to invent a device that detected objects at the bottom of the sea. Langevin invented a hydrophone –what the World Congress of Ultrasound in Medical Education refers to as the “first transducer” in 1915. Langevin built an echo-ranging system using quartz crystals placed between two steel plates to generate sound. In 1918, for the first time, echoes were received from a submarine at distances as great as 1500 m. WWI came to an end, however, before underwater echo ranging could meet the German U-boat threat (See http://rsnr.royalsocietypublishing.org/content/66/2/141, https://phys.org/news/2008-02-inventor-sonar-history.html and http://journals.sagepub.com/doi/pdf/10.1177/0968344516651308).
1.1.3 Aircraft Detection
Acoustic location was used until the early years of WW2 for detection of aircraft by picking up the noise of their engines (Marco!), which was then analyzed to determine the direction of the aircraft (Polo!). Horns give both acoustic gain and directionality; the increased interhorn spacing compared with human ears increases the listener’s ability to localize the direction of a sound. Acoustic techniques had the advantage that they could “see” around corners and over hills, due to sound refraction. The technology, shown in Figure 1.2, was rendered obsolete by the introduction of radar, which travels at the speed of light instead of the speed of sound. Japanese acoustic locators were colloquially known as “war tubas,” which I hope sounds as funny in Japanese as it does in English.
Figure 1.2 Aircraft engines produced unprecedented sound, so in order to hear them at a distance, the war efforts developed listening devices. A two-horn system at Bolling Field, USA, 1921. Sound location equipment sometimes had four acoustic horns, a horizontal pair and a vertical pair, connected by rubber tubes to stethoscope type earphones worn by two technicians that enabled one to determine the direction and the other the elevation of the aircraft.
Source: Unknown author/Wikimedia Commons/Public Domain.
Practical radar technology was ready just in time to turn the tide during the Battle of Britain, thanks to the cavity magnetron [16] and amateur scientist and Wall Street tycoon Alfred Lee Loomis, who personally funded an enormous amount of scientific research at his private estate before leading radar research efforts during WW2 [17, 18]. The atomic bomb may have ended the war, but radar and sonar won it. Then, during the entirety of the Cold War, uncounted billions were spent continuing to refine radar and sonar technology, countermeasures, counter-countermeasures, etc. with much of that high-level and mathematically esoteric scientific work quite highly classified. The result is virtually undetectable submarines that patrol the world’s oceans and stand ready to assure mutual destruction as a deterrent to sneak attack. More visibly, but highly stealthy, radar-evading fighters and bombers carrying satellite-guided precision weapons can destroy any fixed target anywhere on the planet with impunity while minimizing collateral damage. It’s both comforting and horrifying at the same time.
What humans have been trying to figure out since Maxim’s pamphlet, is how to interpret the various radar blips, sonar pings, and ultrasound images [9]. The fundamental issue is that the shape, size, orientation, and composition of the object determines the character of the scattered signal, so an enormous amount of mental effort has gone into mathematical modeling and computer simulation to try to understand enough about that exceedingly complex physics in order to detect navigation hazards, enemy aircraft and submarines, tumors, structural flaws, etc. Much of that work has been what is called by mathematical physics forward scattering, wherein I know what I transmit, and I know the size and shape and materials and location and orientation of the scattering object. I then want to predict the scattered field so I’ll know what to look for in my data. The true problem is mathematically much more difficult, called inverse scattering, wherein I know what I transmit, and I measure some of the scattered field. I then want to estimate the size and shape and materials and location and orientation of the scatterer. Many scientific generations have been spent trying to solve inverse scattering problems in radar, sonar, and ultrasound. There has been a fair amount of success [19–23].
1.1.4 Medical Ultrasonography and NDE
X-rays were discovered entirely by accident. Professor Roentgen was messing around in his laboratory with some new-fangled cathode ray tubes and he noticed that photographic plates were being fogged even though they were still wrapped tightly in paper and had never been exposed to light. He shut himself into his laboratory and worked tirelessly to explore the behavior of these unknown rays (which he gave the symbol “X”) before announcing his discovery to the world and winning the first Nobel Prize. His first X-ray image is still used in textbooks today. It’s his wife’s hand with her large ring. Presumably she was bringing him a sandwich or something and he said, “Put your hand here, bitte.”
Getting the occasional X-ray isn’t a problem, but if you X-ray your hand each time you tune up the machine, you’re going to lose that hand. Edison recognized the adverse health effects of X-rays pretty early on, and personally stepped back from the development efforts in his laboratory. He ended up losing his head X-ray technician bit by bit, starting with fingers and then hands.
It’s a little hard to overstate how quickly X-rays became important; it took a matter of several weeks. In those days, doctors made house calls, of course, but they couldn’t really do all that much. They would often do their diagnosis without even having their female patients disrobe, so it’s not all that surprising that a common mansplainy diagnosis was “women’s troubles.” X-rays were a revelation. Some considered them shockingly improper in that they could see through clothing and make photographs of bones and other private things.
Personally, I find X-rays kind of boring. All they do is go in a straight line getting absorbed along the way according to the tissue density. CT scans are cool, of course, but the radiation dose is a concern. They’re also expensive.
I like diagnostic ultrasound quite a lot. It’s so safe we use it on pregnant women. It’s cheap. It’s portable. It’s real time. The physics is really complicated. It works for medical imaging and structural health monitoring, with surprisingly few differences. The same equations also describe underwater sound and bat echolocation. Medical ultrasonography dates from the early 1950s4 although ultrasound for structural inspection is just a bit older.
In my research group, we do both medical imaging and structural health monitoring using ultrasound. We also do quite a lot of other things because every so often the world changes dramatically and unpredictably. For example, when the Space Shuttle Challenger exploded in January 1986 (Figure 1.3). I was a second-semester senior, aerospace engineering major, about to be commissioned as an officer in the US Air Force with orders to go to Space Command. I was in my apartment in Boston doing propulsion homework when the anomaly happened and the entire space program imploded.
Figure 1.3 We’ve grown used to wonders in this century. It’s hard to dazzle us. But for 25 years, the United States space program has been doing just that. We’ve grown used to the idea of space, and perhaps we forget that we’ve only just begun. We’re still pioneers. They, the members of the Challenger crew, were pioneers. We’ll continue our quest in space. There will be more shuttle flights and more shuttle crews and, yes, more volunteers, more civilians, and more teachers in space. Nothing ends here; our hopes and our journeys continue [24]. The loss of the Space Shuttle Challenger may have effectively ended a generation’s hopes of going to space, but it did cause an explosion of R&D.
Source: NASA/Public Domain.
Since the Air Force suddenly didn’t have anything for me to do, they let me stay at the university for a year and get a master’s degree. I wrote a thesis on elastic wave attenuation due to scattering from inhomogeneities, with applications in seismology. That went well enough that I requested to delay my active duty service commitment for three more years and get a PhD. The Air Force didn’t need second lieutenants with doctorates, so they issued me orders to report to San Bernadino, CA where, for four years, I would do something or other entirely unrelated to either of my freshly minted engineering degrees.
From his hospital bed where he was recovering from colon cancer surgery, my advisor phoned a three-star general and got my orders changed so that I would be assigned to the Air Force base outside of Boston and could then continue on with graduate school in my spare time. Even back then, I knew how unusual that was. So, I cut my hair, put on my uniform, and reported for duty on 21 July 1987. They had more lieutenants than they knew what to do with because this was just about at the peak of the Reagan military buildup. In modern terms, it was a lieutenant bubble.
The commanding general had a policy of making the various program offices on base compete for the new talent, so I was told to take two weeks and interview around base and then come back and tell them where I wanted to be assigned. It was an easy choice because I had just finished a master’s thesis with applications in seismology, and the one place in the Air Force where that kind of research was done was the Air Force Geophysical Laboratory up on the Hill with an excellent library and grass and trees and such. Recall that the whole point of getting my orders changed was so that I could both serve on active duty and finish my PhD.
It turned out that AFGL was a tenant organization on the base, and so I could choose to be assigned anywhere except there. If you’re familiar with the way bureaucracies function, that outcome should give you comfort because my story was going far too well to be believable. So, there was a little cinder-block building up on the Hill near the library, where a small group of people were doing electromagnetic scattering for counter low-observables, that is, stealth. They didn’t need me or have anything for me to do, but I had myself assigned there and they gave me a big gray steel desk in a corner where I could try to come up with something for myself to do related to electromagnetic scattering.
It worked out reasonably well. I finished my PhD on schedule, despite my advisor dying from colon cancer. Along the way, I taught myself quite a lot about electromagnetic scattering for stealth at a time when the big aerospace companies were paying enormous salaries to anybody who could recognize Maxwell’s equations in neon lights. If you’re doing the math in your head, you may have calculated that the Cold War ended just before my four years in the Air Force were up. I learned early on in my career to focus on the fundamental mathematics and physics that can be applied to a variety of applications so that you can reinvent yourself as needed. You’ll need to.
Meanwhile, the Challenger disaster and a sequence of aircraft accidents caused by structural flaws (Aloha Airlines Flight 243 and United Flight 232) caused the field of nondestructive evaluation5 to explode, in a good way.
Flight 243 was caused by cracks around rivets in fuselage lap joints, which developed due to metal fatigue after many years of pressurization for innumerable short hops between islands. Flight 232 was caused by a crack in the titanium engine rotor hub that developed due to a hard alpha inclusion in the titanium billet the rotor hub was forged from. Both tragedies should have been prevented by proper inspections. In 232, only 100 people died; in 243, only one person died. Only is the key word, except that nobody should have died dammit!
At NASA Langley Research Center in Hampton, VA, the Nondestructive Evaluation Sciences Branch grew much faster than their allotment of civil service slots would allow. The answer was to bring on board most of the scientific researchers as contractors rather than government employees, and The College of William & Mary in Virginia was one of those contractors. I was excited to come to Williamsburg to help build the Applied Science Department and oversee the NDE graduate program, with very close ties to NASA LaRC because we had a number of graduate students and research scientists who worked on the Center. We also often work with the people building aircraft carriers, just across the peninsula from NASA. There seems to be a never-ending sequence of scientifically interesting and technically challenging NDE problems both places. I’ve been at W&M for 62 semesters and counting. I plan to stay here for an even 100 semesters, so I guess you could count down: T-minus 38 semesters. You may note that many of the notables who developed the scattering we’ll be discussing had quite long and productive scientific careers.
1.2 Ultrasound Immersion Tank Scans
So I ended up doing radar scattering for a living by accident, and then ended up doing ultrasound scattering for NDE by accident. I am also accidentally a leading expert in dental ultrasonography and developed a sequence of prototype machine-learning-based prostate cancer diagnosis systems that used both trans-rectal and trans-urethral ultrasound scanners. It’s new things all the time, which is part of the fun, especially since the math and physics we’ve worked hard to master doesn’t change. We’ll get to all that, but first I think it would be helpful to describe some of the ways that the data we’ll be modeling with those equations is acquired. We’ll start with ultrasound, which is a subset of acoustics.
Acoustics describes the phenomenon of mechanical vibrations and their propagation in solid, liquid, or gaseous materials. Sound waves above 20 kHz or so are inaudible and are referred to as ultrasonic or ultrasound. Ultrasound is useful for medical imaging and structural flaw detection because it propagates well in many solids and liquids, and because it is sensitive to local changes in material properties. Ultrasonic wavelengths are of the same order as flaw sizes that are often of interest.
Here’s a simple question for you: What are ultrasonic wavelengths at 100 kHz, 1 MHz, 10 MHz, 100 MHz, and 1 GHz for several common structural materials? This question is going to come up again throughout the book, so I’d suggest taking a few minutes and tabulating the numbers. More importantly, keep in mind about what the answers turn out to be.
Here’s another question: What can I do to keep the sound from my neighbor’s stereo from coming through the wall of my apartment? The Straight Dope explains nicely a few key concepts that are in play in response to apartment-dweller-Derek’s question, so I think I’ll just include three paragraphs here from Cecil Adams’ overnight staff reporters6:
Everyone knows intuitively – it barely counts as an observation – that sounds get weaker (i.e. become attenuated) as they travel farther from their source. But why? Much of it is scattering and absorption. A sound wave passing through any medium – air, say, or drywall – does so by causing the medium’s molecules to vibrate. Scattering is the extent to which the wave gets fragmented and redirected upon striking an obstacle in its path. (Picture ripples on the surface of a pond breaking into subripples when they encounter a rock or stick poking out of the water.) Absorption is the drop in volume caused by energy loss in the form of heat – the result of making all those molecules move around. And the effects of both scattering and absorption increase with the frequency of the wave – the higher the frequency, the greater its tendency to die out. Thus, the treble and midrange sounds coming from your neighbor’s apartment get scattered and absorbed more thoroughly as they pass through the various matter surrounding it, leaving the big, dumb low-end waves to lumber along till they find you.
If the frequency and volume are right, sound waves can cause entire objects to vibrate sympathetically – surely you’ve heard of those souped-up car stereos that turn their host vehicles into gigantic joy buzzers. Because of their relatively large mass, things like walls and floors resonate more at low frequencies than at high ones, and thus can help to pass the bass notes along, particularly if the speaker is touching the potentially resonant surface. Long-term resonance can be pretty destructive: Thanks in part to vibrations caused by the wind that regularly swept over it, in 1940, the old Tacoma Narrows Bridge7 shook itself to pieces and collapsed into Puget Sound.
Low-frequency noise is weird stuff. Years back, I noted that infrasound – sound pitched below the hearing range of most humans, which stops at around 20 Hz – can cause dizziness. Some recent research suggests it may do more than that. After taking spectrum analysis readings at a couple of UK sites repeatedly described by visitors as “haunted,” Vic Tandy and Tony Lawrence of Coventry University have argued that the presence of 18.9 Hz infrasound is responsible for the creepy feelings described. (In one case, they concluded that a terrifying, seemingly paranormal experience of Tandy’s had likely resulted from the whirring of a laboratory extractor fan causing his eyeballs to resonate.) And in 2003, the use of 17 Hz infrasound at London concerts of experimental electronic music correlated with audience reports of “unusual experiences” including nausea, momentary anxiety, tingling, and a sense of coldness. Ideally, Derek, by the time your neighbor has traded his bass for an ultra-low-end tone generator, one of you will have found someplace else to live.
Here’s another question: Is there some sort of semiaudible acoustic weapon causing concussion-like symptoms among US diplomats around the world? Havana Syndrome caused quite a lot of noise a few years ago, although it turned out to be a fairly typical case of mass psychogenic illness. The sounds that diplomats were hearing were crickets and cicadas, but it’s not true that the ill effects were all in their heads. Psychogenic illnesses can, in fact, result in physiological symptoms [25]. To be clear, infrasound generated by wind turbines does not manifest ghosts in your basement or bats in your belfry [26]. Bats do use ultrasound to echolocate, though. Typical frequencies are around 50 kHz and it’s a good thing that those frequencies are inaudible to us because bats are really loud and they screech COVID into the miasma while I’m trying to sleep.8
The last time I went to the eye doctor to get my prescription updated, I was very excited to have him scan my eyeball via Optical Coherence Tomography. He was equally excited to have a patient who knew the technology and how to interpret the images. We may have chatted for a while and backed up his other appointments. My bad.
OCT uses low-coherence interferometry to produce a two-dimensional image of optical scattering from internal tissue microstructures in a way that is analogous to ultrasonic pulse-echo imaging. Indeed, the display looks rather a lot like ultrasound B-mode, but OCT has longitudinal and lateral spatial resolutions of a few micrometers and can detect reflected signals as small as of the incident optical power. I’ve been following this technology development from the earliest day. The first NSF review panel I ever served on, back in the 1990s, was for OCT. The most unwieldy review panel I ever served on was when NIH was pushing hard to get this technology out of the laboratory and into clinical usage. That panel had 50-ish reviewers on it, and we were trying to do the premeeting streamlining of the noncompetitive proposals via an old-fashioned conference call. The problem was that the panel chair was on his cell phone driving in his car, and when his call would drop, we’d all have to wait on the phone until he dialed back in.
Because OCT uses near-IR wavelengths, there’s sufficient penetration of opaque soft tissues to use it for a variety of superficial applications. Many are being developed in dentistry these days. Since the light can be delivered via fiber optics, there are all manner of endoscopic applications of OCT. You’d be surprised to know what urologists will jam where and still call it noninvasive.
Ultrasonic frequencies used for medical imaging and NDT of structural materials tend to be in the low MHz range. At these frequencies, the wavelengths are quite small and attenuation is usually a concern. The trade-off is that you’d like to go to higher frequencies in order to get better resolution, but attenuation often scales like the square of frequency, so doubling the frequency quarters the depth of penetration. As a personal aside, I think all this is pretty interesting because it requires a fair amount of understanding of the propagation properties of the ultrasound in order to design sensible measurement schemes. The first ultrasound measurement scheme we should talk about is immersion tank scanning.
Figure 1.4
