Microwave imaging of high-contrast objects [Elektronische Ressource] / Tobias Meyer

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• Publié par: otto-von-guericke-universitat_magdeburg
• Publié le: 01 janvier 2005
• Nombre de lectures: 11
• Langue: English
• Poids de l'ouvrage: 7 Mo

Extrait

Microwave Imaging of
High-Contrast Objects
Dissertation
zur Erlangung des akademischen Grades
Doktoringenieur
(Dr.-Ing.)
von Dipl.-Ing. Tobias Meyer
geb. am 6.10.1972 in Lauchhammer
genehmigt durch die Fakult¨at fur¨ Elektrotechnik und Informationstechnik
der Otto-von-Guericke Universit¨at Magdeburg
Gutachter:
Prof. Dr.-Ing. H. Chaloupka
Prof. Dr. rer. nat. habil. P. Hauptmann
Dr. I. L. Morrow
Prof. Dr.-Ing. A. S. Omar
Promotionskolloquium am 10.2.051
Preface
This work was performed at the Chair of Microwave and Communication Engineer-
ing of the O.-v.-Guericke University of Magdeburg. I would like to thank Prof. Dr.
A. Omar for drawing my attention to microwave engineering and the exciting field
of inverse electromagnetic problems as well as giving me the possibility to carry
out the research work and write this thesis with all the necessary support in every
aspect.
Thanks to the reviewers Prof. Chaloupka, Prof. Hauptmann and Dr. Morrow for
reviewing the somewhat lenghty thesis and their thoughtful comments.
I would like to thank Dr. A. J¨ostingmeier for the numerous discussions leading to
the major ideas presented in this work or solving one of the many little problems
occurring during the work on a complex project like a microwave imaging system.
The quality of the written thesis was also greatly enhanced by the suggestions of
Dr. J¨ostingmeier. I do thank Mr. Nick Spiliotis for the great contributions to the
development of the software for the multi-port VNA and the help in taking mea-
surements. I would like to thank all my colleagues at the Institute for Electronics,
Signal Processing and Communications for their assistance.
Tobias MeyerAbstract
Thisthesisdescribesanovelapproachtomicrowaveimaging. Theproposedmethods
arebasedonthespectralrepresentationoftheobject. Regularizationschemesforthe
solution of electromagnetic inverse problems are addressed. An iterative algorithm
for the solution of the nonlinear least-squares problem arising in iterative image re-
construction is developed. The application of this algorithm to one-dimensional and
three-dimensional imaging of high-contrast lossy objects is examined. The proper-
ties of the imaging systems designed to implement the algorithms are verified by
simulation and actual measurements. The algorithms proposed in this work are
computationally more expensive but accuracy and stability are superior compared
to other microwave imaging methods.
Zusammenfassung
Die vorliegende Dissertation beschreibt neuartige Verfahren zur Erzeugung tomo-
grafischer Bilder mittels Mikrowellen. Basis fur¨ diese Verfahren ist die spektrale
DarstellungdesUntersuchungsobjektsmittelsorthogonalerFunktionen. EineMeth-
odezuregularisiertenL¨osunginverserelektromagnetischerProblemewirdvorgestellt
und in die bekannten Standardverfahren eingeordnet. Das Untersuchungsobjekt
wird in einem iterativen Verfahren aus den Messdaten berechnet. Ein speziell fur¨
diesen Anwendungsfall entwickelter Algorithmus zur effizienten L¨osung des nicht-
linearen Problems der kleinsten Fehlerquadrate wird vorgestellt. Der Nachweis
der Funktionstuc¨ htigkeit dieser Ans¨atze erfolgt mittels Simulations- und Messdaten
von eindimensionalen Profilen und dreidimensionalen Untersuchungsobjekten mit
starkem Kontrast. Ein komplettes und weitgehend automatisiertes Messsystem,
welchesnachdenvorgeschlagenenAlgorithmenarbeitet,wirddetailliertbeschrieben
und die Testergebnisse werden vorgestellt. Das in dieser Arbeit entwickelte System
erfordert im Vergleich zu anderen Verfahren einen h¨oheren Rechenaufwand, kann
aber Untersuchungsobjekte mit hohem Kontrast stabil und mit ausgezeichneter Ab-
bildungsqualitt rekonstruieren.Contents
1 Introduction 7
1.1 Definition of Microwave Tomography . . . . . . . . . . . . . . . . . . 7
1.2 Electromagnetic Material Parameters . . . . . . . . . . . . . . . . . . 9
1.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 Inverse Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5 Outline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 State of the Art in Microwave Tomography and Imaging Methods 16
2.1 One-Dimensional Profile Inversion . . . . . . . . . . . . . . . . . . . . 16
2.2 Diffraction Tomography . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Iterative Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4 Confocal Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3 Regularization and Iterative Algorithm for Imaging of Strongly
Scattering and Lossy Objects 29
3.1 Regularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1.1 Iterative Regularization Methods . . . . . . . . . . . . . . . . 29
3.1.2 Regularization and Bandlimiting . . . . . . . . . . . . . . . . 32
3.1.3 Spectral Expansion of the Object Function . . . . . . . . . . . 36
3.1.4 Formulation of the Smoothness Constraint . . . . . . . . . . . 38
3.1.5 The Successively Relaxed Smoothness Constraint . . . . . . . 40
3.2 Iterative Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.1 Nonlinear Least-Squares . . . . . . . . . . . . . . . . . . . . . 42
3.2.2 Hybrid Jacobian Approximation . . . . . . . . . . . . . . . . . 44
3.2.3 Step Acceptance and Line Search . . . . . . . . . . . . . . . . 49
4 Reconstruction of Lossy One-Dimensional Permittivity Profiles 51
4.1 Imaging System Design . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.1.1 Measuring System . . . . . . . . . . . . . . . . . . . . . . . . 51
4.1.2 Design of Dielectrically Loaded Waveguide to Coax Transitions 53
4.1.3 Design of Dielectrically Loaded TRL Calibration Kits . . . . . 55
4.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2.1 Noise Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2.2 Feasibility of Tumor detection . . . . . . . . . . . . . . . . . . 61
12
4.2.3 Measuring Results . . . . . . . . . . . . . . . . . . . . . . . . 62
5 Three-Dimensional Microwave Resonator Tomography 66
5.1 Microwave Resonator Tomography System . . . . . . . . . . . . . . . 66
5.1.1 System Concept . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.1.2 Resonator Design . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.1.3 Absorber Materials for Resonator Wall Coating . . . . . . . . 71
5.1.4 Automated Multi-Port S-Parameter Measurement System . . 76
5.1.5 Software Architecture . . . . . . . . . . . . . . . . . . . . . . . 85
5.2 Imaging System Operation . . . . . . . . . . . . . . . . . . . . . . . . 87
5.2.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . 87
5.2.2 Avoiding Undesired Constraints . . . . . . . . . . . . . . . . . 88
5.2.3 Initial Guess . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.2.4 Imaging Process . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.3.1 Sensitivity Distribution within the Cavity . . . . . . . . . . . 91
5.3.2 Effect of measuring Frequency Range . . . . . . . . . . . . . . 91
5.3.3 Effect of cavity wall coating . . . . . . . . . . . . . . . . . . . 93
5.3.4 FDTD model accuracy . . . . . . . . . . . . . . . . . . . . . . 93
5.3.5 Error functions . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.3.6 Imaging results . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.3.7 Measuring Results . . . . . . . . . . . . . . . . . . . . . . . . 102
6 Summary and Conclusion 104
A Proof of the Tikhonov Reconstruction Formula 106
B Calculation of the Gradient, Jacobian and Hessian for Nonlinear
Least-Squares 108
C Derivatives of a Series Expansion 110List of Figures
1.1 Active microwave imaging system . . . . . . . . . . . . . . . . . . . . 8
1.2 Well-posed direct problem . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3 Ill-posed inverse problem . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1 One-dimensional profile inversion problem . . . . . . . . . . . . . . . 17
2.2 Diffraction tomography measuring schemes: receiver line (left), cir-
cular receiver array (right) . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 Confocal microwave imaging system . . . . . . . . . . . . . . . . . . 27
3.1 Unregularized solution of a layered media problem. . . . . . . . . . . 30
3.2 Magnitude of input reflection (measured, simulated, start and recon-
structed) for the layered media problem in figure 3.1. . . . . . . . . . 30
3.3 TSVD and Tikhonov regularization image reconstruction example . . 33
3.4 Reconstructed objects from data with 80 dB SNR . . . . . . . . . . . 35
3.5 Permittivity functions and corresponding magnitude of reflection . . . 39
3.6 Number of required FDTD solver runs using the full finite difference
Jacobian or the hybrid Jacobian approximation . . . . . . . . . . . . 48
4.1 Measuring set-up for the one-dimensional layered media reconstruction 52
4.2 Model and photo of the dielectrically loaded waveguide to coax tran-
sition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3 Simulatedandmeasuredinputmatchforadielectricallyloadedwave-
guide t