Electromagnetic and acoustic wave tomography : direct and inverse problems in practical applications

381 Pages·2019·45.36 MB·English

by  Blaunstein

Electromagnetic and
Acoustic Wave Tomography
Direct and Inverse Problems
in Practical Applications

Electromagnetic and
Acoustic Wave Tomography
Direct and Inverse Problems
in Practical Applications
Edited by
Nathan Blaunstein and Vladimir Yakubov
CRC Press
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Library of Congress Cataloging-in-Publication Data
Names: Blaunstein, Nathan, editor. | Yakubov, Vladimir, editor.
Title: Electromagnetic and acoustic wave tomography : direct and inverse
problems in practical applications / editors, Nathan Blaunstein, Vladimir
Yakubov.
Description: Boca Raton, FL : CRC Press/Taylor & Francis Group, 2018. | “A
CRC title, part of the Taylor & Francis imprint, a member of the Taylor &
Francis Group, the academic division of T&F Informa plc.” | Includes
bibliographical references and index.
Identifiers: LCCN 2018006943| ISBN 9781138490734 (hb : acid-free paper) |
ISBN 9780429488276 (ebook)
Subjects: LCSH: Three-dimensional imaging--Mathematics. | Tomography. |
Acoustic emission testing. | Electromagnetic waves--Mathematical models. |
Remote sensing. | Radar.
Classification: LCC TA1560 .E44 2018 | DDC 681/.2--dc23
LC record available at https://lccn.loc.gov/2018006943
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
Contents
Contents
Contents
Preface ...............................................................................................................vii
Acknowledgments .............................................................................................xv
Editors .............................................................................................................xvii
Contributors .....................................................................................................xix
SeCtion i tHeoRetiCAL FUnDAMentALS
oF WAVe toMoGRAPHY
1 Mathematical Fundamentals to Inverse Problems .................................3
VLADIMIR YAKUBOV, SERGEY SHIPILOV, AND NATHAN BLAUNSTEIN
2 Theoretical Overview of Wave Tomography .........................................17
VLADIMIR YAKUBOV, SERGEY SHIPILOV, DMITRY SUKHANOV, AND
ANDREY KLOKOV
3 Special Theoretical Approaches in Wave Tomography .........................47
VLADIMIR YAKUBOV, SERGEY SHIPILOV, DMITRY SUKHANOV,
ANDREY KLOKOV, AND NATHAN BLAUNSTEIN
4 Low-Frequency Magnetic and Electrostatic Tomography ....................79
VLADIMIR YAKUBOV, SERGEY SHIPILOV, DMITRY SUKHANOV, AND
ANDREY KLOKOV
5 Eddy Current Tomography ..................................................................89
NATHAN BLAUNSTEIN AND ALEXEY VERTIY
SeCtion ii eXPeRiMentAL VeRiFiCAtion oF
WAVe toMoGRAPHY tHeoRetiCAL FRAMeWoRK
6 Radio Tomography of Various Objects Hidden in Clutter
Conditions ..........................................................................................121
VLADIMIR YAKUBOV, SERGEY SHIPILOV, DMITRY SUKHANOV,
AND ANDREY KLOKOV
v
vi ◾ Contents
7 Proof of Specific Radio Tomography Methods ...................................167
VLADIMIR YAKUBOV, SERGEY SHIPILOV, DMITRY SUKHANOV, AND
ANDREY KLOKOV
SeCtion iii RADio toMoGRAPHY
PRACtiCAL APPLiCAtionS
8 Ground-Penetrating and Geo-Radars ................................................203
VLADIMIR YAKUBOV, SERGEY SHIPILOV, ANDREY KLOKOV, AND
NATHAN BLAUNSTEIN
9 Sub-Surface Tomography Applications ..............................................225
VLADIMIR YAKUBOV, SERGEY SHIPILOV, ANDREY KLOKOV, AND
NATHAN BLAUNSTEIN
10 UWB Tomography of Forested and Rural Environments ..................265
VLADIMIR YAKUBOV, SERGEY SHIPILOV, AND ANDREY KLOKOV
11 Detection of Live People in Clutter Conditions .................................281
NATHAN BLAUNSTEIN, FELIX YANOVSKY, VLADIMIR YAKUBOV, AND
SERGEY SHIPILOV
SeCtion iV non-ContACtinG ACoUStiC AnD
CoMBineD RADio-ACoUStiC toMoGRAPHY
12 Applications of Radio-Acoustic Tomography ....................................293
VLADIMIR YAKUBOV, SERGEY SHIPILOV, DMITRY SUKHANOV, AND
ANDREY KLOKOV
SeCtion V APPLiCAtionS oF LoW-FReQUenCY
MAGnetiC AnD eDDY CURRent toMoGRAPHY
13 Applications of Low-Frequency Magnetic Tomography .....................313
VLADIMIR YAKUBOV AND DMITRY SUKHANOV
14 Eddy Current Tomography Applications ..........................................323
ALEXEY VERTIY AND NATHAN BLAUNSTEIN
SeCtion Vi MetHoDS oF ViSUALiZAtion
AnD ReConStRUCtion oF oBJeCtS
15 Visualization and Reconstruction of Objects .....................................335
VLADIMIR YAKUBOV, SERGEY SHIPILOV, DMITRY SUKHANOV, AND
ANDREY KLOKOV
Symbols and Abbreviations .........................................................................347
Index ...........................................................................................................353
Preface
This monograph is intended for any researcher, practical engineer, or designer who
is concerned with the operation and service of radio and acoustic radar systems of
various frequency bands to resolve both direct and inverse problems of radio and
acoustic location, with practical applications for the reconstruction and visualiza-
tion of different elements and objects embedded and hidden in sub-surface clutter
environments and structures.
The main goal of this monograph is to introduce the main aspects of novel
methods and theoretical frameworks, as well as of advanced technologies and the
corresponding radar systems, developed by three groups of researchers, that have
separately and jointly been presented during the last three decades. These methods,
frameworks, and technologies are based not only on pure research activity, but also
on the authors’ experience during more than 40 years’ teaching of the correspond-
ing courses in these areas for undergraduate and postgraduate students.
The main subject of research presented in this monograph is how to develop
radio and acoustic wave tomography methods as a means of remote non-destructive
testing, diagnostics of the internal structure of semitransparent media, and recon-
struction of the shapes of opaque objects based on multi-angle sounding, presented
in such a way that has been covered before in the literature (see references [1–7] and
the bibliography therein).
Historically, in the corresponding literature (see bibliography in [1]), tomogra-
phy means “to write a layer”; that is, to investigate a structure layer by layer. The dif-
ference between tomography and other computational diagnostic methods is that
information from the same test element is recorded in multiple integral projections,
that is, many times from different angles relative to the embedded inhomogeneities.
Since about 50 years ago up until the present day, researchers in this field have
learned how to “clean up” these projections and recover the structure of inhomoge-
neities layer by layer. For the most part, this became possible due to the development
of new computational methods and computer technologies. Huge data flows were
“smoothly” layered as images of “crosscuts” of the internal structure of objects in
a non-destructive fashion. At the present time, computed tomography is rightfully
considered as an “absolute” diagnostic technique in medicine. Radio and acoustic
wave tomography is similar to X-ray and magnetic resonance tomography, but it
vii
viii ◾ Preface
deals with electromagnetic radiation in the radio-frequency band and ultrasound
waves in the acoustic band. In this case, the wave length is comparable to the size of
the inhomogeneities, and diffraction effects and the effects of multiple interactions
hold much significance. For that reason, this form of tomography is sometimes
called diffraction tomography . Without dwelling on all the different methods of and
approaches to geometric optics and wave diffraction tomography that are currently
available, we focus on active location (detection) wave tomography, which is of vital
importance, for example, for security systems applications.
During recent decades, the use of manufactured and homemade improvised
explosive devices in acts of terrorism and local armed conflicts has become more
frequent. There have been numerous reported cases of the transportation of such
devices and other prohibited items in hand luggage and under clothes in airports,
and also in stadiums and other crowded places. Put very simply, the problem of
designing a highly efficient means for remote detection of prohibited devices and
articles is of urgent interest. It is of particular importance in view of different public
events being held across the world.
Radio-wave systems are preferable in the development of contactless detection
devices for a variety of reasons. In the first place, radio waves are practically harm-
less to human health. This is their crucial difference from ionizing X-rays. Second,
the potential range of application of these systems is quite wide: in crowded public
places, in special forces raids for detection and tracking of people hiding behind
walls, detection of injured persons after emergency events, and so on. There is also
a great demand for contactless and computer-aided systems for quality control in
building construction, timber processing, avionics, electronic devices construction,
and other industries.
The variety of physical processes involved in radio-wave detection, taking place
in natural and simulated complex environments and involving complex objects,
underlies the complexity of the mathematical descriptions of such processes and the
urgency of solutions of the tomography problem as well.
The main object of this monograph is to describe physical–mathematical models
of systems designed to reconstruct images of hidden objects, based on tomographic
processing of multi-angle remote measurements of scattered radio and acoustic
(ultrasonic) wave radiation. This class of problems is related to so-called inverse prob-
lems , the mathematical fundamentals of which are briefly described in Chapter 1.
One way or another, radio-wave tomography is based on the ray-focusing effect,
which enables the inverse transformation of wave projections of test objects and the
propagation medium. Multiple effects (scattering and diffraction) of interactions of
the wave fields with inhomogeneities of the propagation medium can be consider-
ably reduced by the use of spatiotemporal radiation focusing. The corresponding
mathematical and physical theoretical approaches based on the single-scattering
(Born) approximation with different ray-focusing and refocusing techniques, and
then on multiple-scattering approximations (Rytov and that based on Feynman’s
path integral), are the subjects of Chapters 2 and 3 of the proposed monograph.
Preface ◾ ix
In the course of research on this problem, a number of working laboratory and
“Demo” tomography systems have been developed together with the associated
software that assist in the assessment of the potential of the system and its key
parameters such as resolution, range of action, and response time. The fact that the
development of a radio-location tomography is possible is not in doubt—it has been
demonstrated by numerous published results and by the co-authors’ own research
[1–7]. The drawbacks of most current safety systems designed for crowded places
and areas with heavy human traffic are as follows:
◾ Microwave systems are very time consuming as things stand; it takes a lot of
time to screen people, as the antennas are moved mechanically.
◾ The subject being screened must remain motionless for several seconds.
Therefore, a doorway or a cabin is required that interrupts the constant
human stream.
◾ It is not difficult to obstruct such a system, for example, by wetting your outer
garments with mineral water because the system operates in the millimeter
wave length band.
It should be noted that this interference is neutralized in ultra-wide band (UWB)
systems where the working frequency spectrum lies within the range from a few
MHz to tens of GHz. The use of UWB signals is considered to be the most promis-
ing approach from the standpoint of applications. The development of a domestic
radio-detection UWB tomography requires the solution of a number of problems.
However, this does not exhaust all of the currently available possibilities. The
development of an optimal antenna array configuration is, of necessity, the first
step in this process. This development would include the relative placement of
the receiving and transmitting antennas and a determination of their minimum
number required for tomographic imaging. The solution of this problem is one of
the objectives of ongoing research. This includes a determination of the optimal
sequence of radar measurements to provide the required data digitization in a short
period of time. Moreover, considerable attention must be paid to the development
of fast algorithms for real-time 3-D image restoration of scanned objects based on
radio sounding data.
To overcome the drawbacks of the existing systems mentioned above, in
Chapters 3–5 the theoretical background of 3-D diffraction tomography for high-
frequency wave (Chapter 3) and millimeter wave (Chapter 4) tomography were
presented, as well as for low-frequency electric and magnetic wave tomography
(Chapter 5), generalized by the use of eddy current tomography (Chapter 5). The
results obtained from such approaches have then been proven experimentally by use
of prototypes performed by the authors of this monograph in Chapters 7, 8, and 14.
Another important subject reflected in Chapters 7 and 8 is the antenna array
optimization problem, which we have already alluded to and which also arises
from the need to minimize the number of antennas to reduce antenna array costs