# Microwave detection and characterization of sub-surface defect properties in composites using an open ended rectangular waveguide

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D ISSE R T A T IO N MICROWAVE DETECTION AND CHARACTERIZATION OF SUB-SURFACE DEFECT PROPERTIES IN COMPOSITES USING AN OPEN ENDED RECTANGULAR WAVEGUIDE Submitted by Nasser Nidal Qaddoumi Department of Electrical Engineering In partial fulfillment of the requirements for the degree of Doctor of Philosophy Colorado State University Fort Collins, Colorado Spring 1998 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 9 835027 UMI Microform 9835027 Copyright 1998, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. COLORADO STATE UNIVERSITY February 17, 1998 WE THEREBY RECOMMEND THAT THE DISSERTATION PREPARED UNDER OUR SUPERVISION BY NASSER NIDAL QADDOUMI ENTITLED MICROWAVE DETECTION AND DEFECT PROPERTIES IN CHARACTERIZATION OF COMPOSITES USING AN SUB-SURFACE OPEN RECTANGULAR WAVEGUIDE BE ACCEPTED AS FULFILLING ENDED IN PART REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY. Committee on Graduate Work Adviser Department Head ii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT OF DISSERTATION MICROWAVE DETECTION AND CHARACTERIZATION OF SUB-SURFACE DEFECT PROPERTIES IN COMPOSITES USING AN OPEN ENDED RECTANGULAR WAVEGUIDE Near-field microwave imaging of dielectric composite structures, using open-ended rectangular waveguides, has shown to be a promising and powerful nondestructive testing (NDT) tool for the evaluation of these structures. Experimentally obtained raw images provide a great deal of detailed information about the properties of a specimen. To better interpret the information contained in such images it is important to develop theoretical models that explain the behavior of microwave energy inside a specimen under inspection. This will aid in the development of a methodology to obtain information about the shape and dimensions o f a defect or inclusion from such image. Near-field microwave imaging is based on transmitting a high frequency wave into a dielectric structure, which is located in the near-field of a sensor, and using a signal proportional to the magnitude or phase of the transmitted or reflected wave to create a two or three dimensional image of the structure under investigation. To analyze the features and properties of an image, it is important to understand the mechanism by which the incident electric and magnetic fields interact with the structure. In chapter 2 a theoretical study is conducted to expand on and demonstrate the ability of utilizing an open-ended rectangular waveguide probe to monitor the existence and iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. to determine the position of a disbond in a layered composite structure. The analyses and procedures applied in detecting and locating layers o f air (disbonds) can be applied to detect any defective dielectric layer. The transverse to the direction of propagation extent of the disbond was assumed to be large enough to consider the disbond a layer. In practice, the extent of a defect is not always larger than the aperture size in addition to the fact that large defects have edges which may significantly contribute to the scattering and diffraction from these defects. In chapter 3, near-field microwave imaging of dielectric composite structures using open-ended rectangular waveguides is studied experimentally. Experimental setups are presented and their operations are discussed. The utility of applying near-field microwave techniques to inspect a wide variety of composite structures with different types of defects is demonstrated, and several experimental results are presented. The experimentally obtained raw images provide a great deal of detailed information about the structure under inspection. A near-field microwave image is the result of several factors such as the probe type (for example a rectangular waveguide, a circular waveguide, a coaxial line, etc.), field properties (i.e. main lobe, sidelobes, and half-power beamwidth, etc.), geometrical and physical properties of both the defect and the material under inspection. Therefore, it is important to develop theoretical models that explain the behavior of microwave energy inside the structure under inspection. Chapter 4 will be devoted to study the field properties in the near-field region of an open-ended rectangular waveguide and its interaction with a dielectric material. This study will include investigating the influences of frequency and dielectric properties on the radiation pattern. In chapter 5 a study of the mechanism by which the fields interact with an inclusion will be presented. An effective dielectric constant formula will be used to model the reflection properties of dielectric structures. The influence of the non-uniformity associated with the electric field iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. distribution at the aperture of the waveguide will be investigated and incorporated in calculating the effective dielectric constant. Nasser Nidal Qaddoumi Department of Electrical Engineering Colorado State University Fort Collins, CO 80523 Spring 1998 V Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGMENTS First and foremost I would like to thank God for all that I am and all that I have. I would like to offer my sincere appreciation to those who supported me during this endeavor. I am very grateful for the patient guidance and the endless support and encouragement given by my advisor and mentor Dr. R. Zoughi. I would also like to express my gratitude to Dr. D. Lile, Dr. C. Menoni, and Dr. M. Peterson for their input and serving on my committee. I would like to thank in particular Dr. H. Abiri, Dr. S . Bakhtiari, Dr. S. Ganchev, Mr. K. Bois, Mr. E. Ranu, and everyone at the Applied Microwave NDT Laboratory for their help and encouragement during this work. I would also like to express my gratitude to the staff of the Electrical Engineering Department for their encouragement and support. I would like to thank my parents for their guidance and continuing support in every aspect of my life. To my wife Rania and my daughter Lana I must express my sincere appreciation for their continuing encouragement and love. vi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS CHAPTER I Introduction............................................................................................................. 1 1.1 Background................................................................................................ I 1.2 Motivation.................................................................................... 2 1.3 Previous Research Findings................................................................... 3 1.4 Potential Impact and Benefits............................................................... 4 15 Methodology............................................................................................. 5 CHAPTER II M icrow ave D isbond D etection an d D epth D eterm ination in Thick Layered Structures.............................................................................. 11.1 Variational Formulation o f Aperture Admittance............................ 8 10 11.2 Radiation From Rectangular Waveguide into Stratified Composite Media........................................................................................... 16 11.2.1 Theoretical Formulation.......................................................... 16 11.2.2 Termination o f Layered Media into an Infinite II5 Half-Space.................................................................................. 19 Theoretical Results............................................................................... 21 II.3 .1 Sample Description.................................................................. 21 11.32 Standoff Distance and Frequency Analyses........................ 23 11.3.2.1 Ku-Band (12-18 GHz) Results....................................... vii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 24 11.3 .2 2 K-Band (18-265 GHz) Results..................................... 29 11.3 .2 3 Ka-Band (263-40 GHz) Results................................... 36 11.3.3 Potential o f Disbond Depth Determination....................... 45 11.33.1 Ka-band........................................................................... 45 11.33.2 K-band.............................................................................. 48 113.4 Real Part o f the Reflection Coefficient................................ 51 II.3 3 Ka-Band, 1 mm Thick Disbond............................................... 52 II.4 Summary and Remarks.......................................................................... 53 CHAPTER III N ear-F ield R ectan gu lar Waveguide Probes Used f o r Imaging.... 56 III.I Imaging Setups and Techniques......................................................... 58 111.2 Optimizing Scan Parameters............................................................. 64 111.3 Applications and Experimental Results.......................................... <56 III3 .1 Near-Field Imaging o f Thick Composites With Metallic Defects..................................................................... 66 111.3.1.1 Measurement Results and Discussion..................... 67 III.3.2 Near-Field Imaging o f Rust Under Paint and Dielectric Laminates............................................................. 71 111.3.2.1 Measurement Results and Discussion..................... 71 111.3.3 Near-Field Imaging o f Composites With Porosity Defects.................................................................................... 75 111.3.3.1 Measurement Results and Discussion...................... 76 111.3.4 Near-Field Imaging o f Fiberglass Composites With viii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Variable Binder Percentage and Cure State...................... 78 111.3.4.1 Measurement Results and Discussion.................. 79 III.3 5 Near-Field Imaging o f Composites With Impact Damage Defects................................................................................ 82 111.3 S . 1 Measurement Results and Discussion................... 82 III.4 Summary and Remarks................................................................................ 84 CHAPTER IV Analysis o f th e F ield Properties in the Near-Field o f Rectangular W aveguide Probes U sed f o r Imaging...................................... 86 IV. I Radiation Pattern Theoretical Modeling................................................... 86 IV.2 Fields in an Infinite Half-Space o f a Dielectric Material....................... 91 IV.3 Normalized Power Patterns in Different Planes..................................... 102 IV.3.1 Influence o f Frequency on the Radiation Pattern......................... 106 IV.3.1.1 Influence o f the Waveguide Dimensions............................. 106 IV.3 .1 2 Influence of The Frequency Within The Same Band 112 TV.3.2 Influence o f the Dielectric Properties on the Radiation Pattern............................................................................. 114 IV.3 2 .1 Influence o f Permitivitty...................................................... 114 IV.3.2 2 Influence o f Loss Factor..................................................... 116 IV.4 Summary and Remarks................................................................................. 720 CHAPTER V Influences o f The Effective D ielectric Constant and N onL in ear Probe A pertu re Field D istribu tion on Near-Field ix Reproduced with permission of the copyright owner. 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M icrowave Images................................................................................................... 122 V.l The Effective Dielectric Constant o f A Medium....................................... 123 V.2 Effective Dielectric Constant Formulae..................................................... 124 V 2.1 Far-Field vs. Near-Field............................................................... 124 V 2.2 Volume Fraction Calculation......................................................... 126 V.2.3 Effective Dielecrtic Constant Formulae....................................... 130 V.2.3.1 Simple Average Effective Dielectric Constant Formula........................................................... 130 V.2.3 2 Rayleigh Effective Dielectric Constant Formula 131 V .2 3 3 K.Wakin’s Effective Dielectric Constant Formula... 131 V2.3.4 Comparison..................................................................... 132 V 3 Results............................................................................................................ 138 V3 . 1 Two Infinite Half-Spaces............................................................... 139 V32 Surface Slab in An Infinite Half-Space......................................... 143 V33 Deep Slab in An Infinite Half-Space............................................ 146 V 3.4 Deep Slab in A Multi-Layered Structure..................................... 149 V.4 Summary and Remarks................................................................................. 152 CH APTER VI Conclusions............................................................................................................. 154 BIBLIOGRAPHY......................................................................................................... 160 x Reproduced with permission of the copyright owner. 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LIST OF TABLES 2.1 Phase differences at 25.3 GHz and at I mm standoff distance for all disbonds... 49 2.2 Phase differences at 30.3 GHz and at 1 mm standoff distance for all disbonds... 52 4.1 The ratios of the a-dimensions of x, ku- and k-bands and the half power widths associated with different frequencies in these bands.................. 4.2 108 The ratios of the a-dimensions of the x, ku- and k-bands and the half power widths associated with the same frequencies in these bands.................. 110 4.3 The half-power widths for materials with different permittivities at 24 GHz 4.4 The distances at which the power density drops to 32.8% of its original value for 115 materials with different permittivities at 24 GHz............................................. 116 4.5 The half-power widths for materials with different loss factors at24 GHz 4.6 The distances at which the power density drops to 32.8%of its original value for 117 materials with different loss factors at 24 GHz................................................ 117 xi Reproduced with permission of the copyright owner. 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LIST OF FIGURES 2.1 Aperture of an arbitrary cross-section opening in a perfectly conducting ground plane of infinite extent radiating into an infinite half-space................................ 10 2.2a Cross-section o f a rectangular waveguide radiating into a layered media terminated into an infinite half-space................................................................................... 16 2.2b Cross-section of a rectangular waveguide radiating into a layered media terminated into a conducting sheet........................................................................................ 17 2.3 Schematic o f the sandwich com posite............................................................... 22 2.4 Phase of the reflection coefficient as a function of frequency at various standoff distances for the case of no disbond in the composite....................................... 2.5 Phase of the reflection coefficient as a function of frequency at various standoff distances for the case of a disbond under the skin laminate (1st disbond) 2.6 27 Phase difference between no disbond and the third disbond as a function of frequency at various standoff distances............................................................ 2.9 26 Phase difference between no disbond and the second disbond as a function of frequency at various standoff distances............................................................ 2.8 25 Phase difference between no disbond and the first disbond as a function of frequency at various standoff distances............................................................ 2.7 25 27 Phase difference between no disbond and the forth disbond as a function of frequency at various standoff distances.............................................................. 28 2.10 Phase difference between no disbond and the fifth disbond as a function of frequency at various standoff distances.............................................................. 28 2.11 Phase difference between no disbond and the sixth disbond as a function of frequency at various standoff distances.............................................................. xii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 29 2.12 Phase of the reflection coefficient as a function of frequency at various standoff distances for the case of no disbond in the composite........................... 31 2.13 Phase of the reflection coefficient as a function of frequency at various standoff distances for the case of a disbond under the skin laminate (1st disbond)............. 31 2.14 Phase difference between no disbond and the first disbond as a function o f frequency at various standoff distances.............................................................. 32 2.15 Phase difference between no disbond and the second disbond as a function of frequency at various standoff distances.............................................................. 32 2.16 Phase difference between no disbond and the third disbond as a function of frequency at various standoff distances.............................................................. 33 2.17 Phase difference between no disbond and the forth disbond as a function of frequency at various standoff distances............................................................ 33 2.18 Phase difference between no disbond and the fifth disbond as a function of frequency at various standoff distances............................................................ 34 2.19 Phase difference as a function of frequency at a standoff distance of 1 mm due to the first disbond...................................................................................... 35 2.20 Phase difference as a function of frequency at a standoff distance of 1 mm due to all other disbonds..................................................................................... 35 2.21 Phase of the reflection coefficient as a function of frequency at various standoff distances for the case of no disbond in the composite........................... 37 2.22 Phase of the reflection coefficient as a function of frequency at various standoff distances for the case of a disbond under the skin laminate (1st disbond)............. 38 2.23 Phase difference as a function of frequency at various standoff distances for the case o f a disbond under the skin laminate (1st disbond).................................... 38 2.24 Percent magnitude change as a function of frequency at various standoff distances for the case of a disbond under the skin laminate (1st disbond).......................... 2.25 Phase difference as a function of frequency at various standoff distances xiii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 39 for the second disbond......................................................................................... 39 2.26 Percent magnitude change as a function of frequency at various standoff distances for the second disbond....................................................................... 40 2.27 Phase difference as a function of frequency at various standoff distances for the third d isb o n d ............................................................................................ 40 2.28 Percent magnitude change as a function of frequency at various standoff distances for the third disbond........................................................................... 41 2.29 Phase difference as a function of frequency at various standoff distances for the forth d isb o n d ............................................................................................. 41 2.30 Percent magnitude change as a function of frequency at various standoff distances for the forth disbond........................................................................... 42 2.31 Phase difference as a function of frequency at various standoff distances for the fifth d isb o n d............................................................................................. 42 2.32 Percent magnitude change as a function of frequency at various standoff distances for the fifth disbond............................................................................ 43 2.33 Phase difference as a function of frequency at various standoff distances for the sixth d isb o n d ............................................................................................. 43 2.34 Percent magnitude change as a function of frequency at various standoff distances for the sixth disbond............................................................................ 44 2.35 Phase of the reflection coefficient as a function of frequency for all disbonds , in co n tact............................................................................................................... 46 2.36 Phase of the reflection coefficient as a function of frequency for all disbonds at 2 mm standoff distance.................................................................................. 47 2.37 Phase difference as a function of frequency for the second, third, forth, fifth and sixth disbond at 2mm standoff distance............................................. 47 2.38 Phase difference as a function of frequency at a standoff distance of 1 mm due to the first disbond....................................................................................... xiv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 50 2.39 Phase difference as a function of frequency at a standoff distance of 1 mm due to all other disbonds........................................................................................ 50 2.40 Percentage change in the real part of the reflection coefficient as a function of frequency for the second through the sixth disbond......................................... 52 2.41 Phase difference as a function of frequency at various standoff distances for the second disbond with a thickness of 1 mm................................................ 3.1 53 Relative Geometry of an open-ended rectangular waveguide sensor and a thick composite panel with a defect: (a) side view, (b) plan view.................................. 59 3.2 A general near-field microwave imaging experimental setup................................ 60 3.3 A single reflectometer module used to produce magnitude and phase images 3.4 A single reflectometer module used to produce magnitude images........................ 63 3.5 A single reflectometer module used to produce phase images............................... 63 3.6 Standing wave patterns in a waveguide produced with and without a defect 62 65 3.7 Change in voltage across three separate diode detectors at 10 GHz with respect to 3.8 input power to the diode..................................................................... 66 Descriptive geometry of a thick composite panel with an aluminum inclusion embedded at the center of the panel...................................................... 68 3.9 An in contact phase scan of the composite shown in Figure 3.8 at a frequency of 10.5 G H z............................................................................................ 69 3.10 The voltage (related to the phase) with and without a defect as a function of the stan d o ff distance........................................................................................... 70 3.11 A phase scan of the composite shown in Figure 3.8 at a standoff distance of 9 mm and a frequency o f 10.5 GHz................................................................ 70 3.12 A 40 mm by 40 mm area of rust on a steel plate................................................ 72 3.13 Image of rust under 0.145 mm paint at 24 GHz and a standoff distance of 4 mm.... 3.14 Image o f rust under 0.60 mm paint at 24 GHz and a standoff distance of 4 mm 3.15 Image of rust under 25.4 mm laminate at 24 GHz and a standoff distance XV Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 73 73 of 4 74 mm 3.16 Image o f rust under 25.4 mm laminate at 10 GHz and a standoff distance of 4 m m .................................................................................................................... 75 3.17 The schematic of an epoxy resin sample with three different levels of local p o ro sity ........................................................................................................... 77 3.18 Image o f the sample shown in Figure 3.17 at a frequency of 34.8 GHz: (a) plan view, (b) signal intensity..................................................................... 78 3.19 Schematic o f the multibinder fiberglass sample................................................ 80 3.20 Voltage difference as a function of the standoff distance for all the local defects at 24 GHz.................................................................................... 81 3.21 Image o f the sample shown in Figure 3.19 at a frequency of 24 GHz and a standoff distance of 4 m m ........................................................................ 81 3.22 Image o f the 4 ply disk at a frequency of 34.8 GHz after 500 impact cycles 83 3.23 Image o f the 8 ply disk at a frequency of 34.8 GHz after 3000 impact cycles 83 3.24 Image o f the 8 ply disk at a frequency of 34.8 GHz after 4000 impact cycles 84 4.1 92 An open-ended rectangular waveguide aperture radiating into an infinite half-space. 4.2 The normalized power pattern in the xz-plane ( y = ^ plane) at 24 GHz inside a material with er = 2 J - j 0 J ........................................................................... 104 4.3 The normalized power pattern in the yz-plane ( x = j plane) at 24 GHz inside a material with £r = 2.5 - j 0 5 ........................................................................... 104 4.4 The normalized power pattern in the xy-plane (z=l mm plane) at 24 GHz inside a material with £r = 2.5 - j 0 5 ........................................................................... 4.5 105 Plan view image of a phase scan at a standoff distance of 3.8 mm at 9.2 GHz, a) E-field is parallel to vertical axis, b) E-field is parallel to the horizontal axis 4.6 The normalized power patterns in the x-direction at 10, 14 and 22 GHz xv i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 105 inside a material with e r = 5 - jO .l............................................................................... 4.7 The normalized power patterns in the x-direction at 12.4 GHz in the xand ku-bands inside a material with er =5 —jO .l....................................................... 4.8 109 The normalized power patterns in the x-direction at 18 GHz in the ku- and k-bands inside a material with er = 5 - jO .l................................................................ 4.9 108 109 The normalized power patterns in the z-direction at 10, 14 and 22 GHz inside a material with eT — 5 - jO .l............................................................................... Ill 4.10 The normalized power patterns in the z-direction at 12.4 GHz in the x- and ku-bands inside a material with er = 5 - jO .l................................................... Ill 4.11 The normalized power patterns in the z-direction at 18 GHz in the ku- and k-bands inside a material with er = 5 —jO .l................................................... 112 4.12 The normalized power patterns in the x-direction at 18, 22 and 26 GHz inside a material with er = 5 - jO .l............................................................................... 113 4.13 The normalized power patterns in the z-direction 18, 22 and 26 GHz inside a material with er = 5 —jO .l............................................................................... 114 4.14 The normalized power patterns in the x-direction at 24 GHz inside dielectric materials with constant loss factor..................................................... 115 4.15 The normalized power patterns in the z-direction at 24 GHz in side dielectric materials with constant loss factor....................................................... 116 4.16 The normalized power patterns in the x-direction at 24 GHz inside dielectric materials with constant permittivity..................................................... 117 4.17 The normalized power patterns in the z-direction at 24 GHz inside dielectric materials with constant permittivity.................................................... 118 4.18 The normalized power patterns in the x-direction at 24 GHz inside dielectric materials with constant loss tangent................................................... 4.19 The normalized power patterns in the z-direction at 24 GHz inside xvii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 119 dielectric m aterials with constant loss tangent.................................................... 119 5.1 Dominant mode electric field distribution at a waveguide aperture....................... 125 5.2 The volume fraction as a function of scan position as a slab of 10 % the area of the aperture is being seen by the aperture............................................... 5.3 The volume fraction as a function of scan position as a slab o f 30 % the area of the aperture is being seen by the aperture......................................... 5.4 The volume 128 129 fraction as a function of scan position as a slab o f 50 % the area o f the aperture is being seen by the aperture......................................... 129 5.5 Two infinite half-spaces of cement paste and EPDM arranged side-by-side to model a large defect........................................................................................ 134 5.6 Real part o f the effective dielectric constant obtained using the K.Wakin formula... 134 5.7 Real part o f the effective dielectric constant obtained using the Rayleigh formula... 135 5.8 Real part o f the effective dielectric constant obtained using the average formula 135 5.9 Imaginary part of the effective dielectric constant obtained using the K .W akin form ula............................................................................................ 136 5.10 Imaginary part of the effective dielectric constant obtained using the R ayleigh form ula........................................................................................... 136 5.11 Imaginary part of the effective dielectric constant obtained using the average fo rm u la ......................................................................................................... 137 5.12 Real part o f the effective dielectric constant obtained using the three formulae with the non-linear approach....................................................... 137 5.13 Imaginary part of the effective dielectric constant obtained using the three formulae with the non-linear approach.............................................................. 138 5.14 a) The phase and b) magnitude of the reflection coefficient at the aperture of the waveguide using the linear modelfor the specimen shown in Figure 5.5..... 5.15 a) The phase and b) magnitude of the reflection coefficient at the aperture o f the waveguide using the non-linear model for the specimen x v ii i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 141 shown in Figure 5.5................................................................................................. 142 5.16 A thin Plexiglas slab inserted in between an infinite half-space of cement paste to m odel a one dimensional defect.............................................................. 144 5.17 The magnitude of the reflection coefficient for 4 mm-thick Plexiglas in an infinite half-space of cement paste................................................................... 145 5.18 The magnitude of the reflection coefficient for 5.8 mm-thick Plexiglas in an infinite half-space of cem ent paste................................................................... 145 5.19 A thin Plexiglas slab inserted at depth d in an infinite half-space of cement paste to model a one dimensional defect under a layer of material.......................... 5.20 The normalized YZ-plane field pattern at 7 GHz in an infinite half space of cement. 147 147 5.21 The magnitude of the reflection coefficient for a 5.8 mm-thick Plexiglas slab 8 mm deep in an infinite half-space of cement paste...................................... 148 5.22 The magnitude of the reflection coefficient for a 5.8 mm-thick Plexiglas slab 4.8 mm deep in an infinite half-space of cement paste................................... 148 5.23 The magnitude of the reflection coefficient for a 8.8 mm-thick Plexiglas slab 4.8 mm deep in an infinite half-space of cement paste................................... 149 5.24 A thin Plexiglas slab inserted at depth d in an infinite half-space of cement paste under a 3.17 mm thick layer of synthetic rubber to model a one dim ensional defect in a multi-layered structure.................................................... 150 5.25 The magnitude of the reflection coefficient for a 5.8 mm-thick Plexiglas slab 8 mm deep in an infinite half-space of cement paste...................................... 150 5.26 The magnitude of the reflection coefficient for a 5.8 mm-thick Plexiglas slab 4.8 mm deep in an infinite half-space of cement paste................................... 151 5.27 The magnitude of the reflection coefficient for a 8.8 mm-thick Plexiglas slab 4.8 mm deep in an infinite half-space of cement paste................................... xix Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 151 CHAPTER I In tro d u ctio n 1.1 Background Nondestructive inspection methods utilizing microwave radiators for the purpose of material examination, either in a contact or a non-contact manner, began years ago and have been applied to various media [Alt.63] [Arc.88] [Ash.81] [Bah.82] [Bak.94] [Bel.90] [Dec.74] [Gho.89] [Lun.72] [Qad.95] [Ven.86] [Zou.90]. The increased use of composite materials both for industrial and military applications presents quite a challenge to the standard nondestructive testing (NDT) methods [Car.94]. Difficulties arise from the inherent anisotropy and physical property inhomogeneities of these materials, as well as the relative high absorption and scattering of the radiated signals. The ability of microwaves to penetrate deeply inside dielectric materials makes microwave nondestructive testing and evaluation (NDT&E) techniques very attractive for interrogating such materials [Lav.67] [Bah.82] [Zou.94]. The same applies to structures made of dielectric composites. The sensitivity of microwaves to the presence of dissimilar layers in these materials allows for accurate thickness variation measurement in the range of a few micrometers at 10 GHz [Zou.90] [Bak.94] [Edw.93]. Microwave NDT techniques, applied to composites, are performed on a contact or non-contact basis. In addition, these measurements may be conducted from only one side o f the sample (reflection techniques). Microwave NDT techniques are also capable of material characteristic identification and classification [Gan.94], It has also been shown that microwaves have the ability to detect voids, t Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. delaminations and porosity variations in a variety of dielectric materials and composite structures. The polarizability of microwave signals enables the study of fiber bundle orientation or misalignment during manufacturing [Qad.95]. This same feature may also provide information about cut or broken fiber bundles inside a thick composite member. Microwave NDT techniques have also shown tremendous potential for detecting impact fatigue/damage in composites. This is shown to be true for both non-graphite and graphite composites [Rad.94]. 1.2 Motivation The accumulation of flaws or defects (and damage) in a composite structure is closely tied to its loaded physical and mechanical properties such as strength, durability, stiffness, etc. It is imperative to have a good knowledge of the integrity of a composite structure before and during use. In composite media, defects may be divided into two groups (depending on the size with respect to the footprint, sensing area, of the microwave sensor), namely: large and small defects. A large defect, is a defect whose area is several times larger than the footprint (e.g. a disbond or a delamination), and it can be considered as an extra layer in a structure. This layer can be detected and characterized using the measured reflection coefficient. If the defect is small (i.e. its extent is smaller than the footprint) it will have a different interaction with the fields, due to the boundaries and edges, and this interaction will influence the refection coefficient and consequently the signal measured by the microwave sensor. Characterization of defects (determining their sizes, locations and properties), after they are detected, is a very important part of any nondestructive testing technique. That is why it is of great importance to understand the interaction of the measurement probe with the structure under inspection. 2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.3 P revious Research F indings Since 1990, several approaches of applying microwaves for NDT purposes of sub surface defect detection have been conducted at the Applied Microwave Nondestructive Testing Laboratory at the Electrical Engineering Department at Colorado State University. It has been established that an open-ended waveguide probe operating at a certain frequency, polarization and excitation mode can be effectively used for defect detection and classification. A homogeneous dielectric panel without a defect provides a certain reflection coefficient at the aperture of the waveguide. The presence of a defect (i.e. inhomogenity) will cause the reflection coefficient to change. Thus, the study of the reflection properties, as a defective structure is being scanned by an open-ended waveguide, renders information about the existence of a defect (detection) and its characteristics (dimensions, type, etc.). The ability of microwaves to penetrate inside dielectric materials and interact with their inner structure makes them an excellent candidate for nondestructively inspecting dielectric media for defects and material property characterization. Microwave nondestructive evaluation techniques offer novel solutions when inspecting composites for the purpose of detecting various types of defects such as inclusions, voids, delaminations, etc. [Qad.95]. Microwave techniques do not require a couplant, and can effectively scan samples in contact and non-contact fashions (i.e. at some stand-off distance) [Bak.93] [Zou.90] [Zou.94], Furthermore, the use of standoff distance has been theoretically and experimentally shown to significantly improve measurement resolution when detecting coating thickness variations and delaminations [Zou.94]. Real-time imaging systems using battery operated, simple and inexpensive hardware used in an on-line fashion can be relatively easily designed and built. Several of these systems have been built and employed 3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. at the Applied Microwaves Nondestructive Testing Laboratory during the past few years, yielding impressive results [Qad.95] [Gra.95]. The use of an open-ended rectangular waveguide as a sensor for measuring material properties at microwave frequencies has received considerable attention [Com.64] [Bov.89] [Nik.89] [Zou.90] [Bak.95] [Gan.95]. The use of an open-ended rectangular waveguide is very attractive, since it offers advantages such as a relatively small footprint (sensing area) compared with an antenna operating from the far-field. The problem of open-ended rectangular waveguides radiating into a layered dielectric composite media has been addressed by many investigators, including investigators at the Applied Microwaves Nondestructive Testing Laboratory. 1.4 P oten tia l Im pact an d Benefits As mentioned earlier, microwave NDT techniques offer several unique advantages over other techniques for inspecting thick composites. Microwave imaging is a way by which a composite structure can be interrogated. Microwave imaging is based on transmitting a microwave signal into a dielectric material and using the magnitude and/or phase information of the transmitted and/or the reflected signal to create a two or three dimensional image of the object. This can be done in contact, non-contact and either in the near- or the far-field. Near-field imaging uses simple probes such as open-ended waveguides and coaxial lines, whereas far-field imaging requires an antenna for focusing the microwave energy. Furthermore, far-field imaging approaches do not offer good spatial resolution since the footprint is relatively large. Therefore, focusing lenses are often used to remedy this problem [Gop.941. Images can be obtained using either phase or amplitude information. Far-field techniques generally use amplitude information. Near- 4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. field imaging is more versatile since phase images are easily produced and often contain more or complimentary information to amplitude imaging. Transmission type microwave approaches require access to both sides of the sample [Gop.94] [d’Amb.93]. Near-field approaches have recently been used to image a variety of thick composites with defects and other types of anomalies [Gra.95] [Qad.95]. These investigations have shown the potential of obtaining high spatial resolutions without using any special antenna or image processing of any kind. Near-field microwave imaging systems can be made simple, handheld, and battery operated at a relatively low cost. The output signals of these microwave sensors are easy to interpret and minimal operator skills are required. 1.5 Methodology A rigorous study o f the interaction of microwave signals radiating out of an openended rectangular waveguide with stratified dielectric media has resulted in optimization techniques with which dielectric slab thickness variation detection, in the order of a few microns has become possible at a relatively low frequency (10 GHz, wavelength of 3 cm). Therefore, an extensive theoretical code for this purpose has been developed in a previous research [Bak.94], This code can be used to optimize the measurement parameters (frequency of operation and standoff distance) to monitor variations in any layer in a stratified dielectric media made of up to 5 layers. Recently, we have been faced with the problem of detecting disbonds in a 16 or more layers composite structures (generally n layers). That is why it was of great importance to upgrade the existing code to analyze structures made of any number of layers. Near-field microwave imaging of composite structures with small defects has received considerable attention recently. The success achieved on the experimental level 5 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. motivated the development of a theoretical model to describe the high quality images obtained using near-field microwave imaging, and to explain some of the features associated with these images [Qad.951 [Rad.94], This theoretical model should also help in building an intuitive understanding of the behavior of the fields inside dielectric materials in the near-field o f an open-ended rectangular waveguide probe. As mentioned earlier near field microwave image is the result of several factors such as probe type (example rectangular waveguide, circular waveguide or coaxial line), field properties (i.e. main lobe, sidelobes and half power beam width, etc.), geometrical and physical properties o f both the defect and the material under inspection. Thus, in order to characterize a defect, the effect of all non-defect factors needs to be taken out of an image. This requires understanding the interaction of the fields with the structure and the defects. In chapter 2 a theoretical study is conducted to expand on and demonstrate the ability of utilizing an open-ended rectangular waveguide probe to monitor the existence and to determine the position of a disbond in a layered composite structure. In chapter 3, nearfield microwave imaging of dielectric composite structures using open-ended rectangular waveguides is studied experimentally. operations are discussed. Experimental setups are presented and their The utility of applying near-field microwave techniques to inspect a wide variety of composite structures with different types of defects is demonstrated, and several experimental results are presented in this chapter. Chapter 4 will be devoted to study the field properties in the near-field region of an open-ended rectangular waveguide and its interaction with a dielectric material. This study will include investigating the influences of frequency and dielectric properties on the radiation pattern. In chapter 5 a study of the mechanism by which the fields, radiated out of an open-ended rectangular waveguide probe, interact with an inclusion will be presented. An effective dielectric constant formula will be used to model the reflection properties of dielectric structures. The influence of the non-uniformity associated with the electric field 6 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. distribution at the aperture of the waveguide will be investigated and incorporated calculating the effective dielectric constant. 7 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER II M icrowave D isb o n d Detection a n d Depth D eterm ination in Thick L ayered S tructures Rectangular waveguides were one of the earliest types of transmission lines used to transport microwave signals. Because o f recent trend toward minimization and integration, most microwave circuitry is currently fabricated using planner transmission lines, such as microstrip and striplines, rather than waveguides. But there is still a need for waveguides in many applications such as high-power systems, millimeter wave systems, and in some precision test applications. Open-ended rectangular waveguides are by far the most commonly used transducers in microwave NDT applications. A large variety of waveguide components such as couplers, detectors, isolators, attenuators, and slotted lines are commercially available for various standard waveguide bands from 1 GHz to over 220 GHz. One o f the most important features of utilizing waveguides as measurement sensors is that for the dominant TEi0 mode of propagation, the field throughout the guide may be conveniently monitored, using a small probe, with minimum perturbation of the field distribution inside the waveguide. This fact is utilized in making slotted lines where a slot, cut axially in the center of the guide, is used for inserting a probe to accurately monitor variations of the standing wave in the guide. 8 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The problem of radiation out of a waveguide has been addressed by many investigators. Most of the earlier research have addressed the problem of plasma covered aperture antennas [Gal.64] [Vil.65] [Com.64][Cro.67,68]. More recent analyses o f the problem have been in conjunction with applications such as the measurements of dielectric properties of materials [Teo.85] [Jam.77] [Dec.74] [Mac.80] and field interactions with biological tissue layers [Nik.89], The foundation of the theoretical implementation adopted here is parallel with the work done by Compton in application to radiation from plasma covered aperture antennas [Com.64], Bakhtiari expanded and modified Compton’s formulation for application to microwave nondestructive examination o f layered lossy dielectric composite media [Bak.92] (structures made of 5 layers were analyzed). The formulation is further expanded to analyze any layered composite structure (up to n-layers). To construct a stationary expression o f the aperture admittance of general cylindrical waveguides of arbitrary cross-section radiating into an infinite half-space, a variational formulation was evoked [Bak 92], This result was then used for the analysis of multi-layered composite structures backed by free-space or a conductor. Fourier transform boundary matching technique is applied in the medium in front o f the waveguide aperture to solve for the appropriate set of field components pertaining to the inspected geometry. This solution is then coupled with the admittance expression to calculate the reflection coefficient at the aperture of the waveguide. 9 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. //./ Variational Form ulation o f A perture Adm ittance The theoretical derivations of this part of the work were originated by S. Bakhtiari as part of his Ph.D. dissertation [Bak.92]. The limitation of Bakhtiari’s work was that althoughthe modeling was for an n layered medium, the numerical simulation was limited to structures made of up to 5 layers. So, I repeated the work and expanded it to be able to analyze structures made o f any number of layers. The basis of his formulations are given here. The geometry of an open-ended cylindrical waveguide o f arbitrary cross section, opening onto a perfectly conducting infinite ground plane is shown in Figure 2.1. To construct a general expression for the admittance at the waveguide aperture, variational formulation is implemented first. Figure 2.1: Aperture of an arbitrary cross-section opening in a perfectly conducting ground plane of infinite extent radiating into an infinite half-space [Bak.93]. Figure 2.1 shows the waveguide’s cross-sectional symmetry orthogonal to the direction of propagation, z. In the waveguide the electric field (E ) and the magnetic field 10 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. iff) components arc orthogonal, similarly we may introduce transverse mode functions e(x,y) and h(x,y), along with the mode currents and voltages V(z) and f(z), respectively [Bak.93] [Col.66] [Har.61]. Then one may write the following simple relations E(x,y,z) = e(x, y) V(z) (2.1) H(x,y, z) = h(x,y)I (z) where the orthogonality and normalization properties over the waveguide cross-section and the transverse aperture plane of the vector mode functions are as follows ei =hi '<at (2.2a) ^ = a, x ^ (2 .2b) \ \ ^ d S = \ j ] ^ d S = \ 0t \* J . (2.2d) Each mode vector is orthogonal to all the other mode vectors. To verify this, one can use Green’s first and second identities and the divergence theorem [Har.61]. The construction of the aperture admittance for the geometry of Figure 2.1 will be conducted by evoking a variational formulation method [Bak.93]. In the waveguide, the 11 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. electric and magnetic fields may be written as a summation of infinite number of discrete modes. With the dominant TEi0 mode being incident on the aperture, these fields can be constructed in terms o f the vector mode functions as E(x,y,0) = V ^ i x . y ) + Vr en(x,y) (2.3a) *=0 <2 -3b) H{x,y,0) = YytJ ^ { x , y ) - ^ Y RVrM x^ «=0 where V and V are the magnitudes of n* incident and reflected modes respectively, and Yn is the admittance of the ntb mode. The normalized aperture admittance in terms of these mode voltages may be written as Y Y= /- £ ^ vT ( 2 -4> where Yq is the characteristic admittance of the fundamental mode. The above expression (2.4) may be rewritten as Y.(V,-V,) N Y = - llJ z sr l = 1 _ (2 .5) D where N and D denote the numerator and denominator of the admittance function respectively, and will be evaluated separately [Bak.93]. In order to construct D, both sides of (2.3a) are dot producted by eQand integrated over the aperture area as 12 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. JJ E(x,y,0).etdxdy = V0j j e o.eod x d y + j j ^ V r eH.e0dxdy s S (2.6) S «=0 which with the aid of (2.2a) simplifies to Vio + VTm= \ \ E (x , y, 0).e0(x, y)dxdy (2.7) s Equation (2.7) represents the denominator of the admittance function. To construct N, (2.3b) is first rearranged by taking the dominant mode out of the summation and rewriting the equation as Yo { \ - K.)R(x,y) = H (x,y , 0 ) + J Y X M x ^ n-i (2-8) which may be written as Nh0(x,y) = W (2.9) So, to extract N from this equation the aperture electric field is cross producted by both sides of (2.9) and the z-component is integrated over the aperture surface resulting in ^ N [ E ( x , y , 0 ) x h o(x,yj\.dt = ^ [ E ( x , y , 0 ) x W ( x , y ) \ d t dxdy s (2.10) s Substituting (2.3a) in the left hand side of the above equation and using the orthogonal properties of the vector mode functions in the following manner 13 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. results in the above simplified relation and leads to the following form of (2.10) +K.) \l[E(.x,y,0)xWU,y)\a,dxdy=Y,{v,' (212) S The complete expression for W may be simply expanded by dot producting both sides of (2.3a) by an orthogonal vector mode function em and integrating over the aperture cross section, resulting in V% = ^ E ( x , y , 0 ) . e n(x,y)dxdy s (2.13) Once the above is substituted back into (2.8) it results in the following W(x,y)= H(x,y,0)+ j ^ A C ^ J j Edi,Z,0).en(Ti,£)dridZ n~o (2.14) 5 To be able to incorporate the above results in the admittance expression, (2.5) can be manipulated to take the following form 14 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (2.15) Y=— D which can be constructed using the results of (2.7) and (2.12). Consequently, substituting the former equation for the denominator and the later for numerator respectively, renders the variational form of the complex admittance function which can be expressed as JJ [E (x, y, 0 ) x W (x, y, 0)].az dxdy (2.16) Y = G + jB = - ~ JJ E(x,y,0).ea(x,y)dxdy where W is given by (2.14). The conductance G and susceptance B represent the real and imaginary parts of the admittance, respectively. The above expression is stationary since small variations of the approximate aperture electric field distribution about its exact value would not effect the determined parameter Y. A typical stationary expression may be recognized from its general form of containing the square of the trial function in both the numerator and denominator. This in effect implies that, for a reasonable estimate of this function the resulting calculated parameter will not deviate form its actual value. Proof of stationarity of such an admittance expression of (2.16) has been established by several authors [Sax.68] [Har.61] [Com.64] [Bak.93]. 15 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. II.2 Radiation From Rectangular W aveguide into S tra tifie d C o m p o site M e d ia The general problem of aperture admittance radiating into a stratified dielectric media is addressed in this section. Fourier transform boundary matching procedure is used to construct a complete set of solutions for the external medium, z > 0. Consequently, the solutions are used in the stationary admittance expression to achieve the desired solution. The versatility o f such a model for near-field in-situ interrogation of stratified composite media arises from the fact that it allows addressing non-contact as well as contact type measurements. 11.2.1 T h eoretical Formulation The cross section of an open-ended rectangular waveguide radiating into a layered medium which is terminated into an infinite half-space and a perfectly conducting sheet are shown in Figures 2.2a and 2.2b, respectively. Each layer is assumed to be homogeneous and nonmagnetic with relative complex dielectric constant of em. Waveguide Figure 2.2a: Cross-section of a rectangular waveguide radiating into a layered media terminated into an infinite half-space [Bak.93]. 16 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Waveguide Figure 2.2b : Cross-section of a rectangular waveguide radiating into a layered media terminated into a conducting sheet [Bak.93]. With the TE10 mode incident on the aperture, a symmetrical electric field distribution over the large dimension can be written as Over Aperture (2.17) Elsewhere where a and b are the broad and small dimensions of the waveguide cross-section, respectively. The electric field distribution is normalized so that a Fourier transform boundary matching technique is used to construct the field solutions in an N-layer stratified generally lossy dielectric medium. The transverse field components are expanded in each layer in terms of Fourier integrals. Subsequently, appropriate boundary conditions across each interface are enforced to solve for the unknown field coefficients in each medium. The fields outside the waveguide may be constructed using a single vector potential. In each layer, denoted by layer number n, fields must satisfy the source-free wave equation En(x,y,z) = - V x n„ (2.18) 17 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The vector potential II satisfies the field conditions for 0 < z < d and can be decomposed into two orthogonal components n = O al + 4 'a y (2.20) General solutions of (2.17) and (2.18) may be expressed in terms of integrations over the entire mode space as A E n (x,y ,z) = — A - f f j*Jv ' (2;r)2 J J -+Aa* e ~ikznZj.An ±A ft! . ft! xe -j(kxx+kyy) t H n (x,y,z) = {;} j J hJ<Wo - k xky A — e jk 7 e jkZnz (2.21 ) . dkxdky \ + A' k2 n-k 2 0 , Z Jk z z n +A J kZnZ •„r >e J(kxX+kyy)>dkzdky (2.22) •-J where kn is the complex propagation constant in each layer, and 18 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. which is chosen such that R e{^}>0, lm { ^ } < 0 (2.23b) to comply with the appropriate direction of propagation. [1.2.2 Termination o f L ayered M edia into an Infinite Half-Space Referring to Figure 2.2a, only positively traveling waves exist in the last (N ^ ) layer which is unbounded in the +z direction. Thus, for the field components in this region only those terms in (2.21 and 2.22) which are associated with positive direction o f propagation remain. Using Fourier properties of the field components in (2.21 and 2.22) and enforcing the continuity o f the tangential field components at each interface, the unknown field coefficients for each layer can be determined. The admittance expression normalized with respect to the guide admittance, can be expressed as 19 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. x j J ||^£r<—(%.cosfl)2]f2 ^ ^ + 1 9 ^ ® } —2‘R j s i n d c o s 6 ^ t x.-oo-o L J V x g fa d ) itdedn. where Kj and g(%0) are given by (2.25) and (2.26) respectively. (2.25) K' = ^ £rl - ^ .. ,i am . .'b’X.sinO') ( d ^cosd} o s |----------|---j~ , i(4 ;r)sin ----------- ctua -------3( X0) = r J V 2 ) y 2 V b' (^.sin 0 )|tf2 - { d f£.cos0)2] (2.26) where R and 6 are the new variables of integration, and a’ and b ’ are the normalized waveguide dimensions (with respect to the wavelength A.). When dealing with lossless media (2.24) has some singularities. This can be resolved by contour integration around singular points of the integrand located on the real axis and take into account the residue. In application to a composite medium which contains generally lossy layers, which is the case with most materials, the poles of the integrand move off of the real axis and the integrand becomes smooth. This allows quick and efficient numerical integration schemes such as Gauss quadrature method (used here) to be applied. 20 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 11.3 Theoretical Results The complex reflection coefficient at the aperture of the waveguide T is related to the normalized complex admittance, y,, by r = |r y #= - ^ i+y, (2.27) which is a complex quantity whose phase and magnitude can be calculated and measured for comparisons. The theoretical formulation for an open-ended rectangular waveguide radiating into a multi-layer dielectric composite was expanded to include a fifteen-layer composite structure (a thirteen-layer sandwich composite, a standoff distance and a freespace backing) as shown in Figure 2.3. The output of this model is the reflection coefficient properties (magnitude, phase, real part and imaginary part) calculated at the waveguide aperture for a given composite geometry, standoff distance and operating frequency. II.3.1 Sample Description This work was a part o f a funded research in which the sponsor supplied us with a description of the composite structure for the theoretical study. The dimensions and the dielectric properties (£,■) of the constituents o f the sandwich composite are as follows: 21 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Adhesive Foam Core W aiveguidej v e g u id e A ir B a c k in g n / S ta n d o ff D ista n c e S ubstrate, S k in L a m in ate Figure 2.3: Schematic of the sandwich composite [Qad.96]. 1. standoff distance - variable size 2. skin laminate - 2.54 mm, £r = 4.5 - j0.045 3. adhesive (glue line) - 0.28 mm, ^ = 3.1 -jO.Ol 4. outer core - 45 mm, ^ = 1 . 1 - j0.0026 5. adhesive (glue line) - 0.28 mm, = 3.1 - jO.Ol 6. substrate - 0.14 mm, £,. = 4.5 - j0.045 7. adhesive (glue line) - 0.28 mm, £r = 3.1 - jO.Ol 8. inner core - 40.64 mm, £r = 1.1 -j0.0026 9. adhesive (glue line) - 0.28 mm, £r = 3.1 - jO.Ol 10. substrate - 0.14 mm, £,. = 4.5 - j0.045 22 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 11. adhesive (glue line) - 0.28 mm, £,. = 3.1 - jO.01 12. outer core - 45 mm, £,. = 1.1 - j0.0026 13. adhesive (glue line) - 0.28 mm, ^ = 3.1 - jO.Ol 14. skin laminate - 2.54 mm, £,. = 4.5 - j0.045 15. air backing (infinite half-space o f free-space) The constituents used in this composite structure are considered to be in the family of low permittivity and low loss dielectric materials. The dielectric properties (£,.) o f the constituents were provided to us by the sponsor at a frequency of 3 GHz. Since these are low permittivity and low loss dielectric materials their dielectric properties remain fairly constant as a function of frequency. Thus, for all frequencies used in this study the values shown earlier were used. However, the dielectric properties of the foam core were measured, at 8.5, 10 and 12 GHz, to be (£r = 1.085 - j0.002) in average which is very close to the provided values. 11.3.2 S tan doff Distance an d Frequency A nalyses For the schematic of the composite shown in Figure 2.3 there are two parameters which may be used for measurement optimization o f disbond detection and depth determination. These two are the standoff distance and the frequency of operation. For all cases described in this section a disbond is assumed to replace an adhesive layer (0.28 23 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. mm thick). Therefor, there are six possible disbond locations in the sandwich composite shown in Figure 2.3. Furthermore, the spatial extent o f a disbond is assumed to be much larger than the area o f the sensing waveguide aperture (greater than a few centimeters squared). In this section the results of the combined standoff distance and frequency analyses are presented. Unless otherwise specified the standoff distance varies between 0 mm (contact) to 6 mm at one millimeter intervals. The frequency range o f 12-40 GHz (Ku-, K- and Ka-bands) was used for these analyses. The waveguide dimensions for Kuband (12-18 GHz) are 15.8 mm x 7.9 mm, for K-band (18-26.5 GHz) are 10.67 mm x 4.32 mm and for Ka-band (26.5-40 GHz) are 7.11 mm x 3.56 mm. II.3.2.1 Ku-Band (12-18 GHz) Results Figure 2.4 shows the phase of the reflection coefficient as a function o f frequency at all discrete standoff distances for the case of no disbond. Figure 2.5 shows the same results except for when there is a disbond under the skin laminate (1st disbond). For the 1 mm standoff distance case there were some calculation difficulties (division by very small number), and thus those results are not shown. Figure 2.6 shows the phase difference between the no disbond and the disbonded case at 24 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. contact 3 mm 5 mm 2 mm 4 mm 6 mm 200 150 100 50 0 -50 -100 -150 -200 12 13 14 16 15 17 18 F re q u e n c y ( G H z ) Figure 2.4: Phase o f the reflection coefficient as a function of frequency at various standoff distances for the case of no disbond in the composite. contact 3 mm 5 mm 2 mm 4 mm 6 mm 200 150 100 50 0 -50 -100 -150 -200 12 13 14 15 16 17 18 F re q u e n c y ( G H z ) Figure 2.5: Phase o f the reflection coefficient as a function of frequency at various standoff distances for the case of a disbond under the skin laminate (1st disbond). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. contact 3 mm 5 mm 2 mm 4 mm 6 mm o -10 12 13 14 15 16 17 18 F re q u e n c y (G H z ) Figure 2.6: Phase difference between no disbond and the first disbond as a function of frequency at various standoff distances [Qad.96], each standoff distance as a function of frequency. The results show maximum phase change o f =9 degrees at 18 GHz at a standoff distance of 3 mm. For this standoff distance the phase variation is relatively constant as a function of frequency. Relatively constant phase variation is a desirable feature from the practical point o f view since no frequency selectivity is required in such cases. Collectively, the results shown in Figure 2.6 are encouraging since not only there is a great deal of frequency independence but also the level o f the phase change due to the first disbond is adequately large (=10 degrees). Figures 2.7-2.11 show phase difference as function o f frequency for all standoff distances for all cases (when the second, third, forth, fifth and sixth adhesive layer is replaced by a disbond, respectively). The results are not as encouraging as those shown in Figure 2.6. In particular, the level o f phase change for all these cases is very small (less than one 26 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. degree) which may not be adequate for detection. Therefore, one may conclude that this frequency band may not be optimum for detecting disbonds at all possible locations using standoff distances in the 0-6 mm range. contact 1.5 1 • * *• mmm 3 mm 4 mm — — 2 mm - • - • 5 mm — i— |— i— r - i -----1----- 1---- t 6 mm ~ r — 1— - 0.5 - 0 - -0.5 - -e- < 12 13 14 15 16 17 18 F re q u e n c y ( G H z ) Figure 2.7: Phase difference between no disbond and the second disbond as a function of frequency at various standoff distances. contact 1 mm 2 mm 3 mm 4 mm 5 mm 6 mm 2 1 0 1 12 13 14 15 16 17 18 F re q u e n c y ( G H z ) Figure 2.8: Phase difference between no disbond and the third disbond as a function of frequency at various standoff distances. 27 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. contact 1 mm 4 mm 5 mm 2 nun 3 mm 1 0 -0.5 1 12 13 14 15 16 17 18 F re q u en c y (G H z ) Figure 2.9: Phase difference between no disbond and the forth disbond as a function of frequency at various standoff distances. 1 1 mm 3 mm 5 mm 2 mm 4 mm 6 mm 0 \ . 1 12 13 14 15 16 17 18 F re q u e n c y (G H z ) Figure 2.10: Phase difference between no disbond and the fifth disbond as a function of frequency at various standoff distances. 28 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. contact 1 mm 2 mm - 3 mm ’■ 4 mm * 5 mm 0.15 0.1 0.05 o -e - < -0.05 - 0.1 -0.15 - 0.2 12 13 14 15 16 17 18 F r e q u e n c y (G H z) Figure 2.11: Phase difference between no disbond and the sixth disbond as a function of frequency at various standoff distances. 11.3.2.2 K -B and (18-26.5 GHz) R esults Figure 2.12 shows the phase o f the reflection coefficient as a function of frequency at all standoff distances for the case of no disbond. Figure 2.13 shows the same results except for when there is a disbond under the skin laminate (1st disbond). The frequency range shown here is 18-24 GHz. We had some calculation difficulties for the 24-26.5 GHz frequency range. However in a couple o f subsequent figures sample results in this frequency range will be shown as later. The calculation difficulty arises from the fact that there are singularities in some of the integral operations which cause this problem. Figure 2.14 shows the phase difference between the no disbond and the 29 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. first disbond at each standoff distance as a function o f frequency. The results show maximum phase change o f =22 degrees at 24 GHz and at a standoff distance of 1 mm. As in the previous frequency band, the phase variation is relatively constant for all standoff distances in the 18-23 GHz frequency range. The results shown in Figure 2.14 are even more encouraging than those for the previous frequency band since the phase change due to the first disbond is in excess of 20 degrees. Figures 2.15-2.18 show the phase difference as function o f frequency for all standoff distances for when the second, third, forth and fifth adhesive layer is replaced by a disbond, respectively. For the sixth disbond the program did not work correctly, however similar results as those of the fifth disbond would have been produced. These results are not as nice as those shown in Figure 2.14. In particular, the level of phase change for all these cases is relatively small (with the exception of a few instances where the phase difference is as high as 5 degrees). Therefore, one may conclude that this frequency band may offer enhanced disbond detection possibilities. However, beyond the first disbond the overall phase differences may still be considered small. 30 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. contact 1 mm 2 mm 6 mm 3 mm 4 mm 5 mm 200 150 100 50 0 -50 -100 -150 18 19 20 21 22 F re q u e n c y (G H z) 24 23 Figure 2.12: Phase of the reflection coefficient as a function o f frequency at various standoff distances for the case of no disbond in the composite. contact 1 mm 2 mm 3 mm 4 mm 5 mm 6 mm 200 150 100 50 0 -50 -100 -150 -200 18 19 20 21 22 23 24 F re q u e n c y (G H z) Figure 2.13: Phase of the reflection coefficient as a function o f frequency at various standoff distances for the case of a disbond under the skin laminate (1st disbond). 31 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 mm 3 mm 4 mm 5 mm contact 1 mm 2 mm o -10 18 19 20 22 21 24 23 F re q u e n c y (G H z ) Figure 2.14: Phase difference between no disbond and the first disbond as a function of frequency at various standoff distances. contact 1 mm 2 mm 3 mm 4 mm 5 mm 6 mm 5 4 3 2 0 1 ■2 ■3 18 19 21 22 F re q u e n c y (G H z ) 20 23 24 Figure 2.15: Phase difference between no disbond and the second disbond as a function of frequency at various standoff distances. 32 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3 mm 4 mm 5 mm contact 1 mm 2 mm 6 mm 6 4 2 0 2 A 18 19 20 21 23 22 24 F re q u e n c y (G H z ) Figure 2.16: Phase difference between no disbond and the third disbond as a function of frequency at various standoff distances. — — -------- 3 mm • 4 mm —• — 5 mm contact 1 mm 2 mm — § mm -e- < 18 19 20 21 22 23 24 F re q u e n c y (G H z ) Figure 2.17: Phase difference between no disbond and the forth disbond as a function of frequency at various standoff distances. 33 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3 mm 4 mm 5 mm contact 1 mm 2 mm “ ■ 6 mm 15 05 a < 18 19 21 20 22 23 24 F re q u e n c y (G H z ) Figure 2.18: Phase difference between no disbond and the fifth disbond as a function of frequency at various standoff distances. To investigate the phase difference characteristics in the frequency band of 2426.5 GHz the following was performed. Since the standoff distance of 1 mm seemed to have been the most sensitive standoff distance in the K-band frequency range, the phase difference between no disbond and all disbonded cases at 1 mm standoff distance was calculated in the 23-26.5 GHz frequency range. Figure 2.19 shows the results of these calculations for the first disbond, while Figure 2.20 shows the results for all other disbonds, respectively. For the first disbond there is a large phase difference which is more than sufficient for its detection. For the other disbonds and at around 25.5 GHz the phase difference is more than those shown in the 18-24 GHz region. Furthermore, the sign of the phase difference may be used as an indicator of the location o f disbond. For example at 25.5 GHz, if a phase difference of 5 degrees is measured and if its sign is 34 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. negative then it is due the fifth disbond, whereas if its sign is positive then it is due to the second disbond. This issue will be discussed further in the subsequent sections. 140 120 100 80 60 40 20 0 23 23.5 24 24.5 25 25.526 26.5 27 F re q u e n c y (G H z ) Figure 2.19: Phase difference as a function of frequency at a standoff distance of 1 mm due to the first disbond [Qad.96]. 2nd 4th 3rd 5th 6th 8 6 4 2 0 •2 ■4 6 23 23.5 24 24.5 25 25.5 26 26.5 27 F re q u e n c y (G H z ) Figure 2.20: Phase difference as a function of frequency at a standoff distance of 1 mm due to all other disbonds [Qad.96]. 35 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. II.3.2.3 Ka-Band (26.5-40 GHz) Results Figure 2.21 shows the phase variation as a function o f frequency and standoff distance for the sandwich composite with no disbond. Figure 2.22 shows the same results except for when the first disbond exists. Figure 2.23 shows the phase difference between these two cases. From the results shown in this figure it is clear that the phase difference necessary for detecting the first disbond is sufficiendy large in this frequency band. For example a phase difference of =50 degrees is measured at a standoff distance of 2 mm and at a frequency of 33 GHz. Furthermore, there are several regions in which the phase difference is not only large but fairly constant (1 mm standoff distance between 34 and 40 GHz and also 2 mm standoff distance between 31.8 to 33.5 GHz). These results are by far more encouraging than those reported earlier. Since this band seems to render better overall detection results we decided to look into the variation of the magnitude o f the reflection coefficient as well. This information may be used in tandem with phase difference information for not only enhanced detection but also possibly for disbond depth discrimination. Figure 2.24 shows the percent magnitude change as a function o f frequency and at different standoff distances for the first disbond. The results show that there is a substantial percentage change in the magnitude o f the reflection coefficient for the contact case and at a frequency range of 3238 GHz. Results of several standoff distances also show =10% change for a wide range 36 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. o f frequencies. It must be noted that the magnitude of the reflection coefficient is relatively easy to measure. Therefore, these results are very important from a practical point of view. Figures 2.25-2.34 show similar results to Figures 2.23 and 2.24 except for second through sixth disbonds, respectively. “ ™ “ contact ■ — — I mm — — 2 mm 6 mm 3 nun 4 mm 200 150 100 O -50 -100 -150 -200 26 28 30 32 34 36 38 40 F re q u e n c y (G H z ) Figure 2.21: Phase of the reflection coefficient as a function of frequency at various standoff distances for the case of no disbond in the composite. 37 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. contact 1 mm 2 mm 3 mm 4 mm 5 mm 6 mm 200 150 100 0 -e-50 -100 -150 -200 26 28 30 32 34 36 38 40 F re q u e n c y (G H z ) Figure 2.22: Phase o f the reflection coefficient as a function of frequency at various standoff distances for the case of a disbond under the skin laminate (1st disbond). contact 1 mm 2 mm 6 mm 3 mm 4 mm 5 mm o ■e<3 r— -20 -40 26 28 30 32 34 36 38 40 F re q u e n c y (G H z ) Figure 2.23: Phase difference as a function of frequency at various standoff distances for the case of a disbond under the skin laminate (1st disbond) [Qad.96]. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. contact 1 mm 2 mm 3 mm 4 mm 5 mm ■ 6 mm < 10 -20 26 30 28 32 34 36 40 38 F re q u e n c y (G H z) Figure 2.24: Percent magnitude change as a function of frequency at various standoff distances for the case of a disbond under the skin laminate (1st disbond). contact 1 nun 2 mm — — ' -6 L 26 . I 28 -------- 3 mm ■ ™ - 4 mm — — 5 mm i ■ i -t— |---- 1—_ ■ 6 mm r_ r - -i— T . — \ . I 30 . I 32 . i . 34 i 36 . I 38 . 40 F re q u e n c y (G H z ) Figure 2.25: Phase difference as a function of frequency at various standoff distances for the second disbond [Qad.96], 39 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. contact 2 mm 4 mm 1 mm 3 mm 3 mm 5 4 3 _ 2 L_ < 1 0 -1 -2 -3 26 28 30 32 34 36 38 40 F re q u e n c y (G H z ) Figure 2.26: Percent magnitude change as a function of frequency at various standoff distances for the second disbond. contact 1 mm 2 mm 3 mm 4 mm * — - 5 mm 6 mm -© - < 26 28 30 32 34 36 38 40 F r e q u e n c y (G H z ) Figure 2.27: Phase difference as a function o f frequency at various standoff distances for the third disbond. 40 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 mm 4 3 2 L 1 < e£ 0 -1 -2 -3 26 28 30 32 34 36 38 40 F re q u e n c y (G H z ) Figure 2.28: Percent magnitude change as a function of frequency at various standoff distances for the third disbond. — — 5 ■ 1 contact 1 mm 2 mm 1/ 1 --------3 mm 4 mm —• —* 5 mm ■ 1 i 1 i 6 mm 1 ' 1 ' i . i . M / \ I I 4 3 2 o ■e- i < 1 0 -1 -2 ■ * * * ■ * • -3 26 28 30 32 i . 34 36 38 40 F re q u e n c y (G H z ) Figure 2.29: Phase difference as a function of frequency at various standoff distances for the forth disbond. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3 ---------3 mm “ “ “ ■ 6 mm **“ “ ■ 4 mm -------- 2 mm —■— 5 mm — '---- 1-----1— 1— r - -T- - i — |---- 1- - I -----1— | - - T - 2 < - contact _ 1 u < * 0 -1 1 * * ■ 1 • 1 • -2 26 28 30 32 34 1 i 36 38 40 F re q u e n c y (G H z ) Figure 2.30: Percent magnitude change as a function of frequency at various standoff distances for the forth disbond. “ “ “ ““ “ contact ----------1 mm --------- 2 mm -------- 3 mm 4 mm —' — 5 mm — 6 mm 6 4 o 2 < 0 -2 * ■ * ■ 1 ■ 1 • -4 26 28 30 32 34 * ■ 1 36 38 40 F re q u e n c y (G H z ) Figure 2.31: Phase difference as a function of frequency at various standoff distances for the fifth disbond. 42 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 mm -------- 3 mm ■■■ 4 mm — — 2 mm — — 5 mm — '---- 1-----'---- 1” - i ---- 1---- 1— |---- 1—n — i— i— 1— contact 26 28 30 32 34 36 38 40 F re q u e n c y (G H z) Figure 2.32: Percent magnitude change as a function of frequency at various standoff distances for the fifth disbond. contact 1 mm 2 mm 6 mm 3 mm 4 mm 5 mm 6 5 4 3 2 1 0 •2 26 28 30 32 34 36 38 40 F re q u e n c y (G H z) Figure 2.33: Phase difference as a function of frequency at various standoff distances for the sixth disbond. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -------- 3 mm “ “ “ * 6 mm ■■ " 4 mm — — 5 mm — — 2 mm ----1-----1-----r - T " -i---- 1---- 1---- 1---- 1-“ 1— i— T —' ■ contact .1 I__ I__ ___I__ I__I__ .__ I__ • I . 26 28 30 32 34 36 I 38 .__ 40 F re q u e n c y (G H z ) Figure 2.34: Percent magnitude change as a function of frequency at various standoff distances for the sixth disbond. The phase difference results indicate that at a standoff distance o f 2 mm and an operating frequency of =29 GHz (and to a lesser extent at =30.5 GHz) the second through the sixth disbond may be consistently detected. Thus, for the sole purpose of detection it is clear that this frequency band in general and =29 GHz in particular is the optimum operating frequency. The percent magnitude changes for these disbonds are not as high as those for the first disbond and may not be considered always useful (although in some cases changes of up to 5% are detected). 44 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. II.3 .3 P o ten tia l o f D isbond D epth D eterm ination Another goal of this research project was to investigate the potential of this particular microwave nondestructive testing technique to determine the depth of a disbond in a sandwich composite as well. There are two parameters that may be used for this purpose, namely the standoff distance and the operating frequency. Thus far we have established that disbonds replacing all adhesive layers may be detected at certain standoff distances and operating frequencies. The depth determination could be performed by using several frequencies at a given standoff distance, several standoff distances at a given frequency or a combination of these. In a sandwich composite of the type addressed here there are six discrete depths at which a disbond could be present. The results o f the potential of this microwave method for disbond depth determination are shown next. I I.3.3.1 K a-band Figure 35 shows the phase of the reflection coefficient, in contact (0 standoff distance), as a function of frequency for the six different disbond locations/depths. The frequency at which the phase transition occurs may be used for disbond depth determination. The first disbond is unambiguously located in the range of =28-32.5 GHz. 45 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The second and third disbond (not uniquely) can be detected at 28.4 GHz since at this frequency there is a phase reversal between the 1 no disbond 1st 2nd 3rd 4th 5th 6th 200 150 100 50 V 0 -50 -100 -150 -200 26 28 30 32 34 36 38 40 F re q u e n c y ( G H z ) Figure 2.35: Phase of the reflection coefficient as a function of frequency for all disbonds, in contact. phase of these two disbonds and that of the no disbond case. However, beyond this information not much more can be said about this case. Figure 36 shows the same results except at a standoff distance of 2 mm. Once again, the first disbond is unambiguously located almost at all frequencies. Not considering the first disbond, Figure 37 shows the phase difference between no disbond and all other disbonds. Operating at =28.9-29.5 GHz the second and the third disbond cluster together while the forth, fifth and the sixth disbonds cluster together. The phase difference between the two clusters is =2 degrees which theoretically should be enough for unambiguous detection. However, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. once again in this case the distinction between the second and the third or the forth, fifth and the sixth disbond is not uniquely possible. 3rd 4th 5th no-disbond 1st 2nd 6th -20 -60 -80 -100 26 28 30 32 34 36 38 40 F r e q u e n c y (G H z ) Figure 2.36: Phase o f the reflection coefficient as a function of frequency for all disbonds at 2 mm standoff distance. 2nd 3rd 4th 5th " 6th 6 4 2 o < 0 2 -4 6 8 26 28 30 32 34 36 38 40 F r e q u e n c y (G H z ) Figure 2.37: Phase difference as a function o f frequency for the second, third, forth, fifth and sixth disbond at 2 mm standoff distance [Qad.96], 47 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 11.3.3.2 K-band The overall results so far indicate that the first disbond is the easiest to detect and locate. Furthermore, the phase change due to the first disbond is much more than all other. This is due to the fact that at this depth (under the skin laminate) the disbond’s influence is more than at other depths since at these depths the disbond is closer to the foam core (or under it) and hence its influence is reduced. Since a standoff distance o f 1 mm was shown to be the most sensitive standoff distance in K-band, the phase difference between no disbond and all disbonded cases, at I mm standoff distance was calculated in the 23-26.5 GHz frequency. Figure 38 (same as Figure 19) shows the results o f these calculations for the first disbond, while Figure 39 (same as Figure 20) shows the results for all other disbonds, respectively. For the first disbond there is a great deal o f phase difference (as large as 130 degrees) which is more than sufficient for its detection. For the other disbonds and at =25.5 GHz the phase difference is more than those shown in the 18-24 GHz frequency range. Furthermore, the sign of the phase difference may be used as an indicator of the location of disbond. For example at 25.3 GHz the following phase differences are calculated and shown in Table 1. 48 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 2.1: Phase differences at 25.3 GHz and at 1 mm standoff distance for all disbonds. 1st 2nd 3rd 4th 5th 6th 115.8° 3.6° 6.3° 0.9° -2.6° -0.5° It is clear that the first disbond causes significantly more phase difference than the rest, thus its depth is unambiguously determined. If the phase difference has a positive sign then it is due to either the second, the third or the forth disbond. If the sign of the phase difference is negative then it is due to the fifth or the sixth disbond. Since a commercial network analyzer is capable of measuring phase within =0.5 degrees and a custom designed phase detector is capable of measuring phase within =1 degree, then the magnitude of the phase difference may be used to distinguish among the second, third, forth or fifth and sixth disbond. The ramification of this result is quite significant since via operating at a single frequency and at 1 mm standoff distance the depth of the disbonds may be unambiguously determined. 49 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 140 120 100 60 23 23.5 24 24.5 25 25.5 26 26.5 27 F re q u e n c y (G H z ) Figure 2.38: Phase difference as a function of frequency at a standoff distance of 1 mm due to the first disbond [Qad.96]. 8 2nd 4th 3rd 5th 6th 6 4 2 0 2 ■A ■6 23 23.5 24 24.5 25 755 26 26.5 27 F re q u e n c y (G H z ) Figure 2.39: Phase difference as a function of frequency at a standoff distance of 1 mm due to all other disbonds [Qad.96]. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. It must also be mentioned that, for example, the forth disbond becomes the third disbond from the opposite side of the composite. Thus, such information may also be utilized to unambiguously determine the depth of a disbond. A combination of the results at Ka-band and at K-band, as described in the last two sections may also be used to unambiguously determine the depth of the forth disbond. Other such combinations may also be possible. However, this would require operating at two different frequencies and as many standoff distances compared to the results shown in Table 1. 11.3.4 R eal P art o f the Reflection C oefficient Since the magnitude and the phase of the reflection coefficient are calculated we may use this information to obtain the real and/or the imaginary part o f the reflection coefficient as well. To illustrate this point Figure 40 shows the percentage change in the real part of the reflection coefficient for the second, third, forth, fifth and the sixth disbond (compared to the no disbond case) at a standoff distance o f 2 mm in the 27-31 GHz frequency range. The results indicate that at a frequency of 30.3 GHz it is not only possible to detect all disbonds, but it is also possible to determine their depths unambiguously. Table 2 shows the percentage changes at this frequency. This approach seems very successful for disbond depth determination for this case. 51 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 2.2: Phase differences at 30.3 GHz and at 1 mm standoff distance for all disbonds. disbond 2nd 3rd 4th 5th 6th % Areal part 44.7 51.5 19.7 25.1 0.1 2nd 3rd 4th 5th /■—V L. o03 06 < -20 -40 27 27.5 28 285 29 29_5 30 30.5 31 F re q u e n c y (G H z) Figure 2.40: Percentage change in the real part of the reflection coefficient as a function of frequency for the second through the sixth disbond [Qad.96]. II.3 .5 K a-Band, / mm T h ick Disbond To illustrate the effect o f disbond thickness, Figure 41 shows the phase difference as a function of frequency for all standoff distances calculated for the second disbond (similar to the results of Figure 25). For this case, and at a wide range of frequencies, 52 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. phase difference levels in excess of 30 degrees were calculated at 1 mm standoff distance. For other standoff distances the phase difference was also relatively large. In contrast, in Figure 25 (0.28 mm thick disbond) at 2 mm standoff distance the maximum phase difference was calculated to be only =8 degrees. contact 50 40 30 o -©< 20 10 0 -10 -20 -30 26 28 30 32 34 36 Frequency (G H z) 38 40 Figure 2.41: Phase difference as a function of frequency at various standoff distances for the second disbond with a thickness of 1 mm [Qad.96], 11.4 Summary and Remarks Theoretical analysis of radiation from a rectangular waveguide into layered dielectric composite media was presented in this chapter. Initially, variational formulation was evoked to come up with a stationary expression for the terminating aperture admittance of general cylindrical waveguides with arbitrary cross section. The formulation was then 53 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. expanded to take into account general N-layer media terminated into an infinite half-space or a perfectly conducting sheet. The results o f a theoretical study, using an open-ended rectangular waveguide radiating into a multi-layered structure, for detecting disbonds in thick sandwich composite structures and determining their depths unambiguously were presented in this chapter. The results indicated that disbond detection at depths is possible at a number of frequencies and standoff distances. Ka-band was shown to be the most optimum frequency band to operate in. K-band also showed promise for not only disbond detection but also for depth determination. It was shown that several frequencies and/or standoff distances may be used for unambiguous depth determination. All of these results involved the calculation of the phase o f the reflection coefficient at the waveguide aperture. It turns out that other related parameters such as the magnitude and/or the real part o f the reflection coefficient may also be used in conjunction (or individually) with other parameters to determine disbond depth unambiguously. In practice, when using a network analyzer or a custom designed phase detector, the microwave characteristics (scattering parameters) of the microwave hardware must be measured and taken into account. It has been shown that the scattering parameters of a microwave system may be used as an optimization tool in certain applications. Such an optimization may also be applied to the calculated results presented here for enhanced detection and depth determination. 54 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The disbond thickness used in this study was assumed to be equal to the thickness o f the adhesive layer (0.28 mm). In practice however, disbond thickness may be in excess o f 0.5 mm to a few millimeters. In such cases the phase difference values that were used for detection will increase, rendering the disbond much easier to detect. Additionally, disbond depth determination in such cases will be easier as well. Since disbond thickness influences the phase o f the reflection coefficient, it is very likely to not only be able to determine its depth but also its thickness (within a given range) as well. Multiple disbonds may exist in a sandwich composite as well. This microwave nondestructive testing method is (should be) capable of detecting multiple disbonds as well (as part o f a future investigation). The formulation used in this general theoretical model is quite complicated. However, in the future, it may be worth looking into the possibility of developing an analytical inverse model to determine disbond properties such as existence, depth and thickness. Furthermore, in the study conducted here the effect of dielectric property variations in each layer of the composite was not investigated. In a future study the influence o f such variations (including layer thickness variations) should also be taken into account as well. 55 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER III N ear-F ield Rectangular W aveguide Probes Used f o r Im aging The increased use of light weight, durable and strong dielectric composites for both industrial and military applications presents quite a challenge to the field of nondestructive testing and evaluation (NDT&E). Due to the inherent anisotropy and physical property inhomogeneities o f these materials, many techniques have been shown to be ineffective when inspecting these materials. Other techniques that can still be used for inspecting these materials have the limitation that they can not be employed in an on-line fashion in addition to the high cost associated with using some o f them (x-ray, proton, etc.). The ability of microwaves to penetrate deeply inside dielectric materials and composites makes microwave NDT techniques very attractive for interrogating such materials [Lav.671 [Bah.82] [Zou.94] [Qad.94], Additionally, the sensitivity of microwaves to the presence of dissimilar layers in these materials allows for accurate thickness variation measurement in the range of a few micrometers at frequencies as low as 10 GHz [Zou.90] [Zou.94] [Bak.94] [Bak.93] [Edw.93]. Microwave NDT hardware systems may be inexpensive, simple in design, hand held, battery operated, operator friendly and easily incorporated into on-line inspection systems. In Chapter 2 a theoretical study was conducted to expand on and demonstrate the ability of utilizing an open-ended rectangular waveguide probe to monitor the existence and to determine the position of a disbond in a layered composite structure. The analyses and procedures applied in detecting and locating air layers (disbonds) can be applied to detect any defective dielectric layer. The transverse to the direction of propagation extent of the 56 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. disbond was assumed to be large enough to consider the disbond a layer. In practice, the extent of a defect is not always larger than the aperture size in addition to the fact that large defects have edges which may significantly contribute to the scattering and diffraction from these defects. In this chapter, near-field microwave imaging of dielectric composite structures using open-ended rectangular waveguides is studied experimentally. In the next section experimental setups are presented and their operations are discussed. The utility of applying near-field microwave techniques to inspect a wide variety of composite structures with different types of defects is demonstrated, and several experimental results will be presented in this chapter. The experimentally obtained raw images provide a great deal of detailed information about the structure under inspection [Qad.95]. To interpret the information contained in such images, it is important to understand the mechanism by which an image is formed. A near-field microwave image is the result of several factors such as the probe type (for example a rectangular waveguide, a circular waveguide, a coaxial line, etc.), field properties (i.e. main lobe, sidelobes, and half-power beamwidth, etc.), geometrical and physical properties of both the defect and the material under inspection. That is why it is important to develop theoretical models that explain the behavior of microwave energy inside the structure under inspection. Chapter 4 will be devoted to study the field properties in the near-field region of an open-ended rectangular waveguide and its interaction with a dielectric material. This study will include investigating the influences of frequency and dielectric properties on the radiation pattern. In chapter 5 a study of the mechanism by which the fields interact with an inclusion will be presented. An effective dielectric constant formula will be used to model the reflection properties of dielectric structures. The influence of the non-uniformity associated with the electric field distribution at the aperture of the waveguide will be investigated and incorporated in calculating the effective dielectric constant 57 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The application o f microwave and millimeter-wave NDT to the inspection of dielectric composites will be discussed in this chapter. Structures with various defects and inhomogenities such as metallic inclusions, corrosion under paint, porosity, resin binder volume content variation and binder cure state, impact damage and voids are experimentally inspected to evaluate the utility of this microwave technique for experimental defect detection. / / / . / Imaging S etu ps an d Techniques A microwave image is obtained by arranging detected microwave signals/data, gathered by performing a raster scan over a structure, to produce a visual impression of the presence of defects or the structural geometry. The microwave data may include information such as the phase and/or the magnitude of either the reflection coefficient or the transmission coefficient. Also, attenuation information can be used to produce a microwave image of a structure as well as any combination of all of the above. The general geometry of a composite panel with an embedded defect is shown in Figures 3.1a and 3.1b. The waveguide operates at a certain frequency and at a certain standoff distance. The side view of the geometry is shown in Figure 3.1a, while Figure 3.1b shows the plan view of the geometry and the scan directions. Microwave imaging is based on transmitting a wave into a dielectric specimen and using the magnitude and/or phase information of the transmitted and/or the reflected waves to create a two or three dimensional image of the specimen [d'Amb.93] [Bol.90] [Gop.94]. 58 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. W a v e g u id e A p ew" ~ T h ic k C o m p o s ite Panel F lan g e Scan D ire c tio n s O p e n -E n d e d W a v e g u id e I Defect S ta n d o ff D ista n c e (Side View) (Plan View) (a) (b) Figure 3.1: Relative Geometry of an open-ended rectangular waveguide sensor and a thick composite panel with a defect: (a) side view, (b) plan view [Qad.94]. Transmission type microwave approaches require access to both sides of the sample [Bol.90]. To achieve fine spatial resolution (detection of small defects) high frequency transmission techniques have been used [Gop.94], A general near-field microwave NDT measurement setup is shown in Figure 3.2. A single frequency transmitter (sweep oscillator or a Gunn-diode) generates a microwave signal that is transmitted through an open-ended rectangular waveguide probe which is terminated into a large metallic flange. As a standard practice, a square flange with sides grater than A.0 is used to terminate the aperture of the waveguide to approximate an infinite ground plane [Cro.67]. As the signal reaches the aperture, part of it gets reflected back into the waveguide depending on the effective dielectric properties of the medium in front of the aperture. A receiver (a detector diode or a mixer) is used to measure a voltage that is related to the properties of the reflected signal. As the scan progresses the measured voltage values are recorded in a matrix form. Assuming that the scan starts at a spot devoid of any 59 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. defect, the detector measures a certain, almost constant, voltage. When a defect is “seen” (i.e. within the sensing range o f the probe) by the aperture, the effective dielectric properties of the structure in front of the aperture varies. This results in a change in the reflected signal, and consequently the measured voltage. Images produced in this fashion are referred to as contrast images (i.e. the presence of an inhomogenity is indicated by a different color, or intensity level, on the image). In this work reflection type measurements are employed. Microwave probes operating at a certain frequency and standoff distance are employed to obtain microwave images o f defective samples. The microwave probes were mounted on a computer controlled 2-D scanning table to scan over dielectric composite samples with embedded defects. As mentioned earlier, a voltage that is related to either the phase of the reflection Probe ' O p e n -E n d e d R e c ta n g u la r W a v e g u id e , C ir c u la r W a v e g u id e o r C o a x ia l L in e Transmitter S w e e p O s c illa to r o r a G u n n Diode, Receiver D io d e D etec to r o r a M ix e r Display Figure 3.2: A general near-field microwave imaging experimental setup. 60 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. coefficient or the magnitude of the reflection coefficient or a combination of both can be used to create microwave images. To show how either one or both can be used, three microwave systems were built. The first system considers both properties (phase and magnitude) o f the reflection coefficient and is similar to the setup shown in Figure 3.3. As a signal is generated, by a Gunn diode or a sweep oscillator, it travels through the waveguide towards the medium in front o f i t Depending on the effective properties of that medium, a certain part of the signal is reflected back into the waveguide. This reflected signal forms a standing wave pattern with the transmitted signal inside the waveguide. The properties o f the standing wave pattern depend on the phase (which determines the positions of maxima and minima) and the magnitude (which determines the ratios of maximum voltage to minimum voltage, i.e. the standing wave ratio) of the effective reflection coefficient at the aperture of the waveguide. A detector diode is used to monitor the properties of the standing wave pattern inside the waveguide. The voltage of the detector diode is related to both the magnitude and the phase of the reflection coefficient. When a defect is present, the effective dielectric properties of the medium, in front of the aperture, changes and so does the properties of the reflected wave. This changes the standing wave pattern in the waveguide and consequently the diode will read a different value. By recording these values (the output of the diode), as a function of scan position in a matrix form, and plotting them a contrast image of the sample is created. Images produced with this setup depend on the phase and magnitude of the reflection coefficient. The second microwave system employs a reflectometer unit operating at a certain frequency band to scan over composite structures, as shown in Figure 3.4. This unit uses a digital sweep oscillator or a Gunn diode to generate the microwave signal. The power level and frequency may be adjusted by the oscillator. A circulator is used to separate the transmitted and reflected signals. A diode detector monitors the reflected signal and records 61 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Digital Voltmeter A d ju sta b le D io d e M o u n t T o S w e e p O s c illa to r A perture Figure 3.3: A single reflectometer module used to produce magnitude and phase images. a voltage that is related to the magnitude of the reflection coefficient. Images created using similar setups will be referred to as magnitude images. The third microwave system employs a similar method, a reflectometert unit that operates at a certain frequency band can also be used to scan over composite structures as shown in Figure 3.5. A directional coupler is used to split the signal into two portions. The first portion is used as a reference signal and is fed to a mixer. The second portion is fed through a circulator and then transmitted through the waveguide aperture to the media in front. The circulator is used to separate the transmitted and reflected signals. The reflected signal is then mixed with the reference signal and a voltage that is related to the phase of the reflection coefficient is measured and recorded. Images created using similar setups will be referred to as phase images. 62 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. D ig ita l V o ltm e te r D e tec to r D io d e ... Ill 1 * D ig ita l S w e e p O sc illa to r C irc u la to r W a v e g u id e A p e rtu re Figure 3.4: A single reflectometer module used to produce magnitude images. DOD D ig ita l V o ltm e ter L O -P o rt R F -P o rt © ■■■ ■ o ■■■ sss i D ig ita l S w e e p O s c illa to r M atch ed D irectio n al C o u p le r C irc u la to r W a v e g u id e A p e rtu r e Figure 3.5: A single reflectometer module used to produce phase images. 63 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. III.2 Optimizing Scan Parameters Optimization of the measurement parameters enhances defect detection sensitivity and increases the dynamic range of contrast due to the presence of a defect As was mentioned earlier a contrast image can be obtained by monitoring a certain location on the standing wave pattern. Figure 3.6 shows the standing wave pattern in a setup without and with a defect. To improve the contrast and to obtain a relatively large dynamic range, the diode detector must be positioned such that maximum difference on the standing wave pattern is measured as shown in Figure 3.6. If the diode is set at position (a), maximum sensitivity is achieved, meanwhile if the diode is set at position (b) no detection is achieved. In many cases the position of the detector is fixed. To improve the detection o f defects (e.g. image quality), the two parameters that can be used to enhance the sensitivity are the standoff distance and the frequency of operation. The reflection coefficient depends on the effective impedance of the medium seen by the aperture [Chapter 2], as the standoff distance (or frequency of operation) changes, the effective impedance seen by the aperture of the waveguide changes. This changes the reflection coefficient at the aperture, and consequently the standing wave pattern. So, by comparing the voltage at several standoff distances (frequency is fixed) when there is no defect and when a defect is present, maximum contrast can be achieved. The frequency can be used in a similar fashion by comparing the voltages measured while sweeping the frequency at a certain standoff when there is no defect and when a defect is present. By repeating this process several times optimal measurement parameters can be obtained. Another influential measurement parameter is the sensitivity of the diode detector. Sensitivity is high if as the input to the diode changes slightly the output of the diode changes drastically. To demonstrate this different diodes were independently connected to 64 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Without Defect M a x im u m D iffe re n c e (a) L oad End Source End W ith D e fe c t M in im u m D iff e re n c e (b ) Figure 3.6: Standing wave patterns in a waveguide produced with and without a defect a sweep oscillator and the diode output voltage was recorded as the power on the oscillator was increased in 0.5 dBm steps at a constant frequency of 10.0 GHz. Figure 3.7 shows the output produced by each diode as the input signal increases. The curve that corresponds to diode 2 has a higher slope than the other two indicating it is the most sensitive to small changes in input signal power (in this range of input signal power). A sensitive diode is much more likely to detect slight changes in the effective dielectric properties o f a medium which is essential for defect detection. In all of the imaging results shown in this work, the measured voltage for each image is normalized with respect to its maximum value and then different colors ate assigned to different normalized voltages (maximum is red and minimum is lavender) to produce an image. Consequently, these images must be viewed from a qualitative point of view since only detection of defects is the goal of these images, although a very good impression o f the size of a defect can be obtained as well. 65 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12 diode 1 • diode 2 1.65 diode 3 ,= k . ■5 •3 1 3 1 5 7 9 11 I n p u t S ig n a l P o w e r (d B m ) Figure 3.7: Change in voltage across three separate diode detectors at 10 GHz with respect to input power to the diode. III.3 Applications and Experim ental Results Experimental results obtained using the near-field microwave imaging setups presented in the previous section to inspect a variety of dielectric composite structures with different types of defects are presented in the following sections. III.3.1 Near-Field Imaging o f Thick Composites With M etallic Defects The results of an experimental study investigating the use of microwaves to inspect the presence o f metallic inclusions in thick composite structures are presented in this section. Specially fabricated thick glass reinforced polymer composite panel with embedded metallic inclusion is inspected using an open-ended rectangular waveguide 66 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. sensor. Phase images of the sample under inspection are created. For optimal detection, the influence of standoff distance between the sensor and the panel is also studied. As will be shown later, results indicate that the proper choice of standoff distance may significandy enhance defect detection capability [Qad.94]. The sample material used in this study was fabricated from S-2 glass reinforced polyester composite. This sample (among others) was developed by the Army Research Laboratory for a series of NDT tests; it was not specifically intended for microwave measurements. However, it does contain intentionally introduced defect and it has been tested and characterized using a variety of NDE techniques [Car.94]. A metallic inclusion was embedded in the sample during hand lay-up prior to cure. The nominal size of the panel is 190 mm x 190 mm x 25 mm. The density of the panel is 1.7 g/cnA III.3.1.1 M easurement Results a n d Discussion The panel, shown in Figure 3.8, has an aluminum inclusion of 6.35 mm by 6.35 mm by 0.8 mm located at a distance of 12.7 mm from the surface of the sample. A phase scan was performed at a frequency of 10.5 GHz (using a setup similar to that shown in Figure 3.5) in a contact fashion. The scan covered an area of 85 mm by 98 mm. Figures 3.9a and 3.9b show the signal intensity and the plan view of this scan, respectively. The contrast is very high, and the defect is clearly visible. Both figures show a very good indication of the fiber bundle pattern associated with the opposite side of the sample. Also, the size of the defect on the image corresponds well with the physical size of the defect. This indicates the high spatial resolution that may be achieved with microwave near-field imaging. Another important observation on the image is the presence of two features along the sides of the defect parallel to the broad dimension of the waveguide. These features are 67 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. due to the sidelobes of the radiator and the edge effects of the defect. These features will be analyzed further in chapter 4. As was mentioned earlier, the measurement parameters (frequency o f operation and standoff distance) may be varied to optimize for a given measurement. To demonstrate this, two measurements were performed in which the standoff distance between the sensor and the surface of the sample was changed. In the first measurement the sensor was pointing directly at the defect (maximum signal), and in the second one it was pointing at a non-defect area (background or minimum signal). Subsequently, the standoff distance was changed, and the voltage proportional to the phase of the effective reflection coefficient at the aperture of the waveguide was recorded as shown in Figure 3.10. 203 mm 6.35 mm Figure 3.8: Descriptive geometry of a thick composite panel with an aluminum inclusion embedded at the center of the panel [Qad.94]. 68 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The results show that operating at a standoff distance of 0 mm (i.e. in contact) and at this frequency (10.5 GHz) the difference between the signals due to defective and non defective areas is maximum. On the other hand, if a standoff distance of around 5 mm or 13 mm is used, there will be no distinction between these two areas of the panel. Another observation is that, operating at a standoff distance of between 5 mm to 13 mm the contrast in the image is reversed. Also, operating in the range where the phase variation as a function of the standoff distance is almost constant (7-10 mm) is important from a practical point of view since slight changes in the standoff distance do not influence the outcome significantly. To illustrate these observations, a phase scan of this sample at a standoff distance of 9 mm was produced. Figure 3.11 shows that the contrast is reduced (i.e. the dynamic range is less) and reversed (compared to the results of Figure 3.9). However, at this standoff distance, the fiber 0 20 40 60 80 Figure 3.9: An in contact phase scan of the composite shown in Figure 3.8 at a frequency of 10.5 GHz [Qad.94]. 69 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.2 0.15 With Defect 0.1 > Without Defect 0.05 oso a o > 0.05 - 0.1 0.15 0 5 10 15 20 S ta n d o f f D ista n c e (m m ) Figure 3.10: The voltage (related to the phase) with and without a defect as a function of the standoff distance [Qad.94]. bundle orientation seems to be more visible than that of Figure 3.9. This is another indication of the sensitivity of the standoff distance to different sample characteristics (e.g. small thickness variation), mm 0 20 40 60 80 Figure 3.11: A phase scan of the composite shown in Figure 3.8 at a standoff distance of 9 mm and a frequency of 10.5 GHz [Qad.94]. 70 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. III.3.2 N ear-F ield Imaging of Rust Under Paint and D ie le c tr ic L a m in a te s In many applications the detection of rust or corrosion under paint and composite laminate coatings is an important practical issue [Bab.95] [Fun.81] [Col.93]. When the detection of rust is conducted accurately and in its early stages, it results in the savings of million of dollars in maintenance costs, damage minimization and reduction in repaint cycles in various industrial and military environments. Microwave NDT techniques posses the ability of detecting minute thickness variations in dielectric coatings as well as slight dielectric property variations in stratified dielectric composites [Bak.94a] [Bak.94b] [Bak.93] [Gan.95] [Chapter 2]. The presence of rust or corrosion may be considered as an additional new thin layer under a coating or a composite laminate. Microwave nondestructive methods are very well suited for inspecting this type of layered materials [Qad.97]. In this section the utility of using open-ended rectangular waveguide sensors for detecting rust under paint and dielectric laminate coating is presented. Several experiments are conducted at two different frequencies on steel specimens with areas of rust in them. III.3.2.I M easurement Results and Discussion A steel specimen with a 40 mm by 40 mm area of rust is shown in Figure 3.12. This specimen was produced by acquiring a relatively flat piece of steel on which a thin layer of rust had already been produced (naturally). A 40 mm by 40 mm area (at the center) was then masked out by a piece of tape and the remaining surface was sand blasted. The 71 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. average thickness of the rust layer was measured (using a micrometer) to be approximately 0.08 mm. Subsequently, this specimen was painted with up to 0.60 mm of common spray paint, as uniformly as possible. 0.60 mm represents ten painting cycles. After applying various layers of paint microwave images of the rust specimen were produced using raster scans (every 2 mm by 2 mm) o f the specimen at 24 GHz. Measurement systems (similar to Figures 3.3 and 3.4) were used to create contrast images of the rust area on the samples. Figures 3.13 and 3.14 show the scans of this specimen at a standoff distance o f 4 mm and at 24 GHz when covered with a paint thickness of 0.145 mm and 0.60 mm, respectively. The rusted/corroded area is clearly visible in the center of all of these images corresponding to the rust region shown in Figure 3.12. There is an elongated region in the upper right hand comer of these images which shows up as a region (e.g. color) inbetween paint and rust. The steel specimen had a very subtle indentation in this region. Consequently, one can consider that this region has a slightly thicker paint layer than the rest o f the painted areas. Therefore, these images not only show the clear possibility of detecting a thin layer of rust under paint, they also illustrate the fact that paint thickness variation can be distinguished from the presence of rust. Figure 3.12: A 40 mm by 40 mm area of rust on a steel plate [Qad.97]. 72 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. f t Figure 3.13: Image of rust under 0.145 mm paint at 24 GHz and a standoff distance of 4 mm [Qad.97], Figure 3.14: Image of rust under 0.60 mm paint at 24 GHz and a standoff distance of 4 mm [Qad.97]. 73 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In many applications metals could be covered by other laminates than paint. A rusted metallic plate (similar to the one used earlier) was prepared in a similar way, and was covered with layers of laminate material (synthetic rubber) of thicknesses up to 25.5 mm (1”). The sample was again scanned using the same setups used on the other sample. Figure 3.15 shows the image obtained at a frequency of 24 GHz and a standoff distance of 4 mm. Figure 3.16 shows the image obtained at a frequency of 10 GHz and standoff distance of 4 mm. Again the rusted area is detected even under 25 mm thick synthetic rubber laminate. It should be noted that at a frequency of 10 GHz (waveguide dimensions 22.86 mm x 10.16 mm) the rusted area looks smaller than it does at 24 GHz (waveguide dimensions 10.86 mm x 4.32 mm). This is as a direct result of the ratio of the dimensions of the rusted area to those of the waveguide aperture. This also indicates that the spatial resolution is related to the waveguide dimensions. nun Figure 3.15: Image of rust under 25.4 mm laminate at 24 GHz and a standoff distance of 4 mm. 74 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. mm 0 20 40 60 Figure 3.16: Image of rust under 25.4 mm laminate at 10 GHz and a standoff distance of 4 mm. III.3.3 N ear-Field Imaging o f Com posites With Porosity Defects In many composites (e.g. polymers), the presence of porosity causes lowered mechanical performance due to stress concentrations. Localized porosity can be particularly damaging to the joint strength of adhesively bonded components [Gra.95]. In ceramics, the relative density is an important processing parameter, and again the ceramic is extremely sensitive to stress concentration (lowered density). ceramic is weak and has low stiffness. If not fully densified, a In composites, the porosity can be within the matrix material which will affect the performance in a similar fashion to those in bulk materials. However, porosity often concentrates at specific locations in composite materials (either between plies or at the fiber/matrix interface), and can dramatically lower 75 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the flexural and shear performance [Gra.95]. Increases in porosity during operation (material under loading) may precede macroscopic damage and possibly indicate the presence of delamination. In most practical cases porosity in a structure is clustered (local). The results of a study on the detection of local porosity in composites using microwave near-field imaging techniques are presented next. III.3.3.1 M easurem ent Results an d Discussion An epoxy resin disk with a diameter o f 76.5 mm and a thickness of 8.2 mm was produced with three porous inclusions embedded in it. The inclusions were in the shape of a pill with a diameter o f 6.35 mm and thickness of 4.45 mm. These inclusions were made of air-filled microballoons providing three clustered porosity levels of 44%, 49% and 56% as shown in Figure 3.17. The distance between the centers of each two inclusions was 19 mm, and in the thickness direction they were all located in the middle of the disk. An area of 56 mm by 18 mm (as shown in Figure 3.17) was scanned in contact at 34.8 GHz using an open-ended rectangular waveguide sensor. This frequency, in the 26.5-40 GHz range, was chosen since for this range the waveguide aperture is 7.1 mm by 3.5 mm and provides for a higher spatial resolution compared with those at lower frequencies. A magnitude scan was performed to produce an image of the defective disk as shown in Figure 3.18. three inclusions are clearly seen as red spots. The The color intensity (of the red color) associated with each inclusion gives a qualitative measure of the difference in the porosity levels among the three inclusions. The distance between the centers of each two inclusions matches very well the distance in the sample (19 mm). This indicates the high spatial resolution associated with these measurements. The image effectively shows the utility of using microwave nondestructive techniques not only for detecting local porosity, but also for quantitative estimate of the air content associated with it. Such an image, once 76 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. calibrated may indicate absolute porosity level, and the size of the porous inclusion. The quality of the image as it pertains to porosity level determination may be enhanced, for a given composite, by changing parameters such as frequency and standoff distance. Figure 3.18 shows that there are additional ring shaped dark blue areas around the inclusions. These features are due to the side lobes along the broad dimension of the waveguide in addition to the edge effects associated with the inclusions (similar to the features on Figure 3.9). Epoxy Resin Scan Area 44% 49% 56% Air-Filled Microballoons Figure 3.17: The schematic of an epoxy resin sample with three different levels of local porosity [Gra.95]. 77 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3.18: Image of the sample shown in Figure 3.17 at a frequency of 34.8 GHz: (a) plan view, (b) signal intensity [Gra.95]. 7/ 7.3 .4 N ear-F ield Imaging o f Fiberglass Composites With V ariable Binder Percentage and Cure State Low density fiberglass composites are used in many environments for insulation purposes. Nondestructive inspection of thick, low density, low permittivity and low loss dielectric composites poses many challenging problems for most (NDT) techniques. Microwave NDT methods, however, are very well suited for inspecting this type of composite materials [Zou.94] [Qad.95] [Gra.95]. This is particularly true when accurate thickness, thickness variation, material composition uniformity, cure state and density 78 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. variation determination are of interest. Microwave methods have been used to characterize material properties o f several composite mixtures in which curing takes place (a chemical mixing process) [Liv.93] [Jow.87] [Gan.94]. There are several important issues associated with the production of fiberglass products, namely, the uniformity by which the resin binder is applied, resin binder cure state, and variations in the glass fiber density. The utility of applying microwave NDT methods to distinguish among fiberglass samples with different resin binder levels, in a non-contact fashion, using an open-ended rectangular waveguide sensor, is presented next. III.3.4.1 M easurem ent Results a n d Discussion To conduct this experimental study, a 25.4 mm (1”) thick conductor backed real life fiberglass sample with 18.6% resin binder (i.e. base material) was used. Four regions of this sample were first removed and then embedded with fiberglass with resin binder levels (by weight) o f 0%, 9.4 %, 13.4 % and with uncured resin binder, as shown in Figure 3.19. These inclusions had square shapes with sides of approximately 25.4 mm (1”) and the distance between them was 50.8 mm (2”). The influence of the standoff distance was experimentally investigated by placing the microwave sensor in front of the sample (for all five regions) while the standoff distance was varied from 0 to 10 mm. For each standoff distance a dc voltage related to the effective reflection coefficient at the waveguide aperture was recorded. To be able to detect the presence of these local inclusions and distinguish them from one another, a difference between the voltages when the waveguide is over the inclusions and the base material must exist. These differences, can be maximized by choosing the correct standoff distance. 79 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3.19: Schematic of the multibinder fiberglass sample [Qad.96]. Consequently, the voltage difference between the base material and all other local inclusions, as a function of standoff distance was obtained at 24 GHz, as shown in Figure 3.20. From this figure it may be deduced that for some standoff distances it is difficult to distinguish among the different local inclusions (1-3 mm), while for others (4-5 mm) there is a considerable voltage difference between the base signal and the signal from the inclusion regions. Subsequently, a microwave image of this sample was made at a standoff distance of approximately 4 mm, as shown in Figure 3.21. The different intensity levels in the image are proportional to the dielectric properties of each region, and hence related to the difference in their respective resin binder levels. This simple image illustrates the potential of using such a nondestructive and non-contact testing method for distinguishing among different resin binder contents in a 25.4 mm-thick low density conductor backed fiberglass sheet. The voltage readings that produced these images may be calibrated to obtain an estimate of the resin binder level associated with each inclusion regions. 80 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ---------- No Binder — — - Uncured Binder 9.4% . . . . . 13.8% 4 2 0 •2 -4 6 •8 0 2 6 4 S ta n d o ff D is ta n c e (m m ) 8 10 Figure 3.20: Voltage difference as a function o f the standoff distance for all defects at 24 GHz [Qad.96]. Figure 3.21: Image of the sample shown in Figure 3.19 at a frequency of 24 GHz and a standoff distance of 4 mm [Qad.96]. 81 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. II1.3.5 Near-Field Im aging o f Composites With Impact Damage Defects In the design of glass fiber/epoxy composites, the useful life of a composite as it is subjected to impact fatigue loading is a very important issue. Due to the difficulties encountered in monitoring damage accumulation in composites, lifetime predictions of these composites have been a problem since they are being used in a variety of applications. A build up of micro damage, such as matrix micro-cracks and micro-delaminations, is hypothesized to occur even though there is no apparent change in material compliance. A critical level is finally reached at which time the properties of the composite begin to fall and compliance change is evident [Rad.94], The utility of applying microwave NDT methods to detect the initiation and propagation of impact damage, using an open-ended rectangular waveguide sensor, is presented next. III.3.5.1 Measurement Results and Discussion To study the effect o f cyclical impact on composite materials, specific polymer reinforced epoxy samples were subjected to cyclical impact fatigue [Rad.94]. The general experimental approach applied to this set of composite specimens was to introduce cumulative damage by repetitive impact [Rad.94], Out-of-plane impact fatigue test specimens were modeled in a disk geometry of 63.5 mm diameter and 2.5 mm thickness (after polishing). These composite specimens were made up of either 4 or 8 layers of 10 oz stain weave fiberglass fabric in an Epon 813 epoxy resin matrix. The plies were stacked in a mid-plane symmetric, quasi-isotropic fashion with a fiber volume fraction of approximately 20% for the 4 ply and 40% for the 8 ply specimens [Rad.94]. A setup similar to that shown in Figure 3.4 was used to create magnitude images of these samples at a frequency of 34.8 GHz. At the beginning a 4 ply disk was impacted at a load of 0.53 82 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. KN. for 500 cycles. No visible damage was observed on the disk. However, as a scan was performed the presence of damage at the warp/weave crossovers was seen (Figure 3.22). The same setup was used to scan an 8 ply disk after 3000 impact cycles at a load of 0.70 KN. The primary damage region is observed near the center of the image, shown in Figure 3.23. The image shows that the region o f damage is not circular as one would expect, but actually shows accelerated damage propagation along the fiber bundles. The same 8 ply disk was imaged after 4000 impact cycles. Figure 3.24 shows that the central damage zone has grown noticeably and increased damage is apparent across the image. Visual inspection of the specimen showed significant damage growth between 3000 and 4000 cycles. 0 13 30 30 Figure 3.22: Image of the 4 ply disk at a frequency of 34.8 GHz after 500 impact cycles [Rad.94]. Figure 3.23: Image of the 8 ply disk at a frequency of 34.8 GHz after 3000 impact cycles [Rad.94]. 83 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3.24: Image o f the 8 ply disk at a frequency of 34.8 GHz after 4000 impact cycles [Rad.94], III.4 Summary and Remarks The inspection of thick layered composite materials is essential in ensuring structural integrity before and during use. Many types of defects, that cannot be visually detected, can occur in production and in use situations weakening the structural integrity of the composite and endangering structures employing such materials. Early detection of defects is necessary to mitigate damage propagation. The ability of microwaves to penetrate inside dielectric materials makes microwave NDT techniques very suitable for interrogating structures made of thick dielectric composites. Three experimental setups were presented for three different types of near-field microwave imaging. The effects of frequency of operation and the standoff distance as measurement optimization parameters to enhance the sensitivity to a defect were studied and presented. Experimental results obtained from scanning a variety of composite samples with different types of embedded defects were presented. Images of these defective samples were created using a measured voltage that is related to the phase and/or magnitude of the effective reflection coefficient at 84 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the aperture of the rectangular waveguide sensor. These images presented detailed information about the structure and integrity of the inspected samples. On all of these images the size of a defect matches closely its physical size, indicating the high resolution associated with this technique. The resolution is related to the dimensions of the waveguide (i.e. the frequency band). To interpret the information contained in such images, it is important to understand the mechanism by which an image is formed. A nearfield microwave image is the result of several factors such as the probe type (example rectangular waveguide, circular waveguide or coaxial line), field properties (i.e. main lobe, sidelobes, and half power beam width, etc.), geometrical and physical properties of both the defect and the material under inspection. That is why it is important to develop theoretical models that explain the behavior of microwave energy inside the structure under inspection. A study o f the field properties in the near-field region of an open ended rectangular waveguide and the fields interaction with a dielectric material will be presented in Chapter 4. In Chapter 5 a study of the mechanism by which the fields interact with an inclusion will be presented. An effective dielectric constant formula will be used to model the reflection properties of dielectric structures. The influence of the non-uniformity associated with the electric field distribution at the aperture of the waveguide will be investigated and incorporated in calculating the effective dielectric constant. 85 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER IV Analysis o f the Field Properties in the Near-Field o f Rectangular Waveguide Probes Used fo r Imaging The experimentally obtained data using waveguide probes, in Chapter 3, showed that a great deal o f detailed information can be obtained from these near-field microwave images. The spatial resolution associated with these images is high, and it seems to be dependent on the dimensions of the waveguide probe not on the frequency of operation (e.g. wavelength), as in far field imaging. Some features of these images were interpreted to be a result of the presence of sidelobes along the broad dimension of the probing waveguide. In order to understand the information contained in a near-field microwave image and the image formation mechanism it is essential to formulate the properties of the fields in the near-field of an open-ended rectangular waveguide probe. This will help in building an intuitive understanding of the behavior of the fields inside dielectric materials while in the near-field of a probing waveguide. It will also aid in solving the forward problem of imaging defective structures which can be used in solving the inverse problem to obtain defect properties. IV.1 Radiation Pattern Theoretical Modeling The radiation from flange-mounted open-ended rectangular waveguides looking into free space has been considered by several investigators in the past [Com.64], [Lew.51]. The case of radiating apertures into a stratified medium has also been considered by many investigators [Bak.92], [Nik.89], [Teo.85]. In this part of the work, 86 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. theoretical formulation o f the fields radiating out of a waveguide probe into an infinite halfspace of material is presented. The formulation is general and can account for the dominant mode as well as higher-order modes. The analysis assumes that the waveguide aperture is mounted on an infinite conducting flange. In the dielectric medium Fourier integrals are used to express the solution of the wave equation, namely V 2E(x,y,z) + K 2E(x, y,z) = 0 (4.1) where, K 2 = K 02£fi, £ and jl are the permitivity and the permeability of the medium, respectively. The electric field can be written using the Fourier integrals in the xy-plane as (4.2) By substituting Equation 4.2 into Equation 4.1, the following equation is obtained (4.3) which can be written as (4.4) where, y = ^jk2 + k 2 - K 2 87 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Equation (4.4) has a solution of the form E(kx,ky,z) = A e 7t + B e 7z (4.5) where, A = xAz + yAy + zAz and B = xBz + yBy + zBz are unknown vector coefficients to be determined. Using these unknown vector coefficients the electric field can be written as E(x,y,z) = + Bzer‘) + y (Aye~r‘ + Byeri) + z(A2e~rz + Bzer‘)leJ(l-x+t’y)dkxdky (4.6) A dielectric medium is a source-free region (V • E(x,y,z) = 0), using this property with Equation (4.6) yields jkz(Aze-ri + Bze rz) + jky (Aye yz + B/ 1) - y( V ri ~ ^ e 71) = 0 (4.7) Equation 4.7 is now used to obtain the following system of equations (V'M* + jky A, - yA t )e~7z = 0 (4.8a) {jkzBz + jk yBy + y B z)e7z = 0 (4.8b) from which the values of the z-components can be expressed in terms of the x- and ycomponents as 88 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. jk ^ + jk A (49a) r B = J k*B* + j k yBy (4.9b) Now by substituting Equations (4.9a and 4.9b) in Equation (4.6) the electric field can be written as E{x,y,z) = \ ~ _ \ l f { k x,lcr z)eJ{l' " k’y)dkxdky (4.10) where, F(k ,ky, z) = [ A z (x + z i ^y - ) + A ( y + z ^y) ] e ~ r' + [Bx(x - z &y ) + B (y - z ^ y) ] e 7z (4.11) To obtain the magnetic field at any point, Maxwell’s equations can be used V x E(x,y,z) = —jcofi H(x,y,z) (4.12) using Equation (4.10) the magnetic field can be expressed as H(x,y,z) = f V x F(k ,k ,z)eJ(k,x+i’y)dk dk (O f! * (4.13) y To calculate the magnetic field, the coefficients for each of the unknowns A z, B x, Ay, and 89 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. By must be calculated first. To find the coefficients of the unknowns Equations (4.10, 4.11 and 4.13) are used, after simplification, the magnetic field can be expressed as H(x,y,z) = -j— f f [(c,Ax + c2A )e 71 + (c3Bz + c4B )en } ( O f J . 1 1 el{k'x+t’y)dkxdky (4.14) where, c, = + y —---- — - z(jky) (4- 15a) tc2 —lr2 k k c2 = - x - -----^ + y - ^ - + z(jk ) 7 7 (4.15b) kk K 2 —k2 c3 = x y^ - y ---------7 - z(jk ) y (4.15c) „ K 2 —k 2 . k k . C4 = x -’ y - ^ + zUk') (4.15d) The derivations outlined above are applicable to structures made of several layers of material and terminated either by an infinite half-space of a material or by a conducting layer. The electric and magnetic fields at any point in space are expressed using the unknowns A z, B z, A y, and B y. These unknowns are obtained by applying the boundary conditions corresponding to a given configuration. In solving for the unknowns, the starting point is the last layer of the structure. This helps in reducing the number of the unknowns in that layer. The unknowns in the layer before the last are then expressed in 90 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. terms o f the unknowns of the last layer. By back propagating the unknowns of the last layer to express the unknowns in each layer in terms of them, the number of unknowns in the structure is minimized. To solve for the unknowns, the boundary conditions at the aperture of the waveguide are applied. Once the unknowns of the last layer are calculated the fields everywhere are determined, and consequently field intensity and power density patterns can be obtained. To understand the properties of the fields in the near-field region of an open-ended rectangular waveguide and the influences of the waveguide dimensions, frequency of operation and the dielectric properties of the medium on an image, the fields in an infinite half-space of a dielectric material will be formulated and their properties will be studied extensively. IV.2 Fields in an Infinite Half-Space o f a Dielectric M aterial The geometry of an open-ended rectangular waveguide radiating into an infinite half-space o f dielectric material with respect to the coordinate system is shown in Figure 4.1. In an infinite half-space of a dielectric material the electric field components should vanish as the distance z increases (z —>°°). From Equations 4.10 and 4.11, the x- component of the electric field can be written as (4.16) 91 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. a b w a v e g u id e Infinite Half-Space z=0 Figure 4.1: An open-ended rectangular waveguide aperture radiating into an infinite half space. To satisfy the boundary condition, Ez = 0, the following equation is obtained (4.17) (Aze~r t +Bzerz)t^ = 0 which indicates that B. =0 (4.18) The y-component of the field can be expressed as Ey = j ^ j y A y e - ri + Byert)ejik-x+k^dkxdky (4.19) To satisfy the boundary condition, Ey = 0, the following equation is obtained 92 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (Aye~r' + B yeri)l^ = 0 (4.20) which indicates that (4.21) By = 0 So, Equation (4.11) reduces to F(kI ,k ,z) = [Ax(x + z ^ - ) + A ( y + z ^ L)]e rz r r (4.22) Now there are only two coefficients to be calculated, namely, Ax and Ay. At the aperture of the waveguide the tangential components of the electric field inside and outside the waveguide must be continuous. Thus, at z = 0 the tangential electric field reduces to =E E (4.23) A where, /a \ (4.24) / = xAx + yA = By applying Fourier transform to Equation (4.23) and equating it to the transform of the aperture fields, the following is obtained 93 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. /=ft]= j j E a r i x ^ e - ’^ ^ d \ *J k ' d (4.25) k , aperture where Ev (x,y) is the field at the aperture o f the waveguide. Therefore, the unknown A x and Ay coefficients can be calculated using the aperture fields. At the aperture of the waveguide the tangential components of the magnetic field inside and outside the waveguide must be continuous. Thus, at z = 0 the tangential magnetic field is given by (4.26) Y Again, once the unknown coefficients A x and A y are expressed in terms of the aperture fields, the magnetic field can be calculated. At this point, the unknowns needed to calculate the field at any point in space are given in terms o f the aperture fields. Now, one may either use the dominant mode to describe the incident and reflected fields at the aperture, or also include higher-order modes. In this work the dominant mode TE10 is considered. To include higher-order modes the aperture fields must be expanded in terms of the dominant and higher-order modes. The aperture field Ev due to the dominant mode and higher-order modes is given by 94 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where, kCi is the cutoff wavenumber of the dominant mode and T is the reflection coefficient at the aperture of the waveguide. The first term in Equation (4.27) is due to the incident and reflected dominant mode components, while the second term is due the reflected higher-order modes for both the TE and the TM waves. In this work only the dominant mode is considered, higher-order modes can be added at this point without changing the derivations. In Equation (4.27) e™ is given by a (4.28) a where a is the broad dimension of the waveguide aperture. The aperture electric field can be written as (4.29) Hence, the unknown coefficients Ax and Ay can now be calculated from the aperture fields. First, for simplicity the aperture field expression is rewritten as Eap= y S s i n ( - x ) a (4.30) where, 95 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. s = m ± L i± £ < (4.31) a To calculate the unknown coefficients, Equation (4.25) is used along with Equations (4.30 and 4.31) (A. 7 = a \ = Q{ y [ \ asin— e-jk'xdkx ]e~jk’ydky lA J where, Q = \ Ay) { Jo (4.32) a S_ -2 , by performing the integration over the apenure (2 n Y n_ a =Qy [e~jk‘a + 7] e jk'b - l (4.33) -jk, from Equation (4.33) it is evident that there is no x-component, thus, A=0 (4.34a) K_ a Ay = N = Q { - ) 2 - k 2x [e~jk-a + 71 £f; V - 7 (4.34b) -jky a Now substituting the expression for the unknown coefficients in Equation 4.22 yields 96 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. F(kx,kx,z) = [N(y + z ^ - ) ) e ~ rx (4.35) and consequently, the electric field (Equation 4.10) can be written as E(x,y,z) = L L ^ C y + z — = L)}e rte Y (4.36) Equation (4.36) indicates that the electric field has two components namely, E y and E t. These two components are (4.37) (4.38) The electric field component in the x-direction ( Ez) does not exist because only the dominant mode was used in the derivations. Thus far, the electric field components can be calculated from the last two integrals. The magnetic field components can now be calculated using Maxwell’s equations (Equation 4.12) which yields the following x cofi dy (4.39) dz 97 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. .= U L (Ofj. dx (4.40) / dE H = - i ----(Ofl dx (4.41) h, In order to calculate the two infinite integrals associated with each field component, a polar coordinate transform of the following form is applied kx = ficosa, k = /Jsin a (4.42) having a Jacobian of the form J = dkt dp dkz da cos a —J3 sin a dky dky sin a (3 cos a d/3 da = f3 [cos2a + sin2 a} = (3 (4.43) The only unknown that is left is the reflection coefficient. The reflection coefficient can be calculated using the derivations outlined in chapter 2, or it can be calculated from the current derivations in the following fashion. The tangential magnetic field in the waveguide at the aperture is given by (4.44) Ke, i= l which when using the dominant mode only reduces to 98 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (4.45) where, h f = [x—(sin—*)] for the dominant mode and a a Y . = ^ - = ^ - 1 ------------------------------------------------------------------------------(4.46) *e. con The magnetic field outside the waveguide is given by Equation 4.13 where, F(kz,ky,z) is as given by Equation 4.35. At the aperture Equations (4.13 and 4.45) should be equal. By multiplying (i.e. dot product) both sides by hJE and integrating over the aperture, the following expression of f is obtained V= (4.47) L +G where, and G= f f 2 F(P, a ) d a dfi (4.49) (0fj.on Jo Jo 99 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. in which, F(fi,cc) = K0[er - p 2 cos2« ] ( -*— ).2 V(P,a}U(P,a) aK0 (4.50) where, it ~aK„ V(P ,a ) = 2 (4.51) [ 1 + cos(aK0P cos a)] - (p cosa)2 + ( - ^ - ) 2 aK„ and U ( p ,a ) = (P since)' ,P sina*0 •[/-cos(6AT0)3sina)] (4.52) b2K2 ,Ps ina = 0 Computer codes for calculating T and all the components of the electric and magnetic fields were developed. The function F(P,a) (Equation 4.50) has a discontinuity at P = ■Je~ which has a much higher effect when the dielectric constant is low. This is primarily due to the fact that the function is of a damping nature, so as the dielectric constant increases, the discontinuity becomes less significant. The final value of p (i.e. the value at which F(P ,a ) —»0) can be determined prior to calculating the fields by plotting the function F ( p , a ) . The final value of p is dependent on the frequency of operation and the dielectric properties of the medium. The function F(P,a) must be integrated to obtain the fields components everywhere. To avoid the discontinuity, the 100 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. integration is carried from 0 to the final value of (3 excluding a very small interval around the discontinuity. Once the electric and magnetic field components are calculated, normalized field intensity and power density patterns can be obtained to study the radiation properties of an open-ended rectangular waveguide. For the power density calculations, the time average Poynting vector P is given by P = t [ E xH'] (4.53) where, * denotes the complex conjugate and E = xE z + yE y +zE2 (4.54) 77 = xHz + yHy + zHt (4.55) In the derivations outlined above the x-component of the electric field was found to be zero, so the poynting vector is expressed as P =L{x{EyH\ - £ , / / ; ) + y (£ ,//; ) + £ ( - £ / / ; ) ] (4.56) The real part of P represents the radiated power density and the imaginary part represents the reactive (stored) power density. 101 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IV.3 Normalized Power Patterns in Different Planes The derivations oudined above were used to calculate the fields radiating out o f an open-ended rectangular waveguide at any point in space. The electric and magnetic fields can now be calculated as a function o f location, frequency of operation and dielectric properties of an infinite half-space o f a dielectric material. To help understanding the near-field properties of an open-ended rectangular waveguide probe, power density patterns in the three planes (xz-, yz-, and xy-planes) are presented next. The power patterns for an infinite half-space of dielectric material with dielectric constant of ( er = 2.5 - j0.5) at a frequency of 24 GHz were calculated as a function of location inside the material. Figure 4.2 shows the normalized power pattern in the xzplane ( y = — plane). Each color level on the figure represents a 3-dB difference. The pattern indicates that the fields remain confined within the aperture’s a-dimension for a long distance inside the material (around 15 mm), and they only broaden after that. No indication of the presence of sidelobes is observed on the pattern in this plane. Figure 4.3 shows the normalized power pattern for the same parameters in the yz-plane ( x = ^ plane). Again, the fields are confined within the aperture’s b dimension up to a long distance inside the material (around 15 mm) and they only broaden after that. Figure 4.3 also indicates the presence of sidelobes along the broad dimension, a, o f the waveguide. To obtain a better vision of the sidelobes, the power pattern in the xy-plane (at z = 1 102 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. mm) is calculated for the same parameters, as shown in Figure 4.4. Again, from the pattern it is clear that the fields are confined within the aperture of the waveguide. Two sidelobes forming along the broad sides o f the waveguide are observed on the pattern. The fact that the fields in the material remain confined within the aperture dimensions of the waveguide explains the high resolution associated with the near-field microwave images obtained in Chapter 3. It also indicates that the spatial resolution is primarily influenced by the waveguide dimensions. The presence of sidelobes along the broad dimension o f the waveguide partially explains the presence of some features on near-field microwave images (e.g. the dark blue features observed on the image shown in Figure 3.9). To confirm that the sidelobes form along one dimension, the following experiment was conducted. Figures 4.5a and 4.5b show two images of an 80 mm x 80 mm area on a glass reinforced plastic composite with a 0.8 mm thick square (6.35 mm x 6.35 mm) aluminum inclusion (the one described in Figure 3.8) [Qad.95]. These two images were obtained using the same probe at a frequency o f 9.2 GFlz and a standoff distance of 3.8 mm. The difference between the two images shown is the orientation of the scanning probe (i.e. polarization o f the electric field). In the first image the electric field was parallel to the vertical axis (i.e. the narrow dimension of the waveguide is parallel to the vertical axis). The second image was obtained with the electric field parallel to the horizontal axis (i.e. the narrow dimension of the waveguide is parallel to the horizontal axis). As expected, with both alignments the aluminum defect was easily detected. In both images the presence of these features was observed along the broad dimension of the waveguide. This indicates that sidelobes are only present along the broad dimension of the waveguide. 103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I 1 10 20 I 30 Figure 4.2: The normalized power pattern in the xz-plane (y = — plane) at 24 GHz inside a material with er = 2.5 —j0.5. mm Figure 4.3: The normalized power pattern in the yz-plane (x plane) at 24 GHz inside a material with er = 2 .5 - j0.5. 104 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -3 0 5 Figure 4.4: The normalized power pattern in the xy-plane (z=l mm plane) at 24 GHz inside a material with er = 2 .5 - j0.5. Figure 4.5: Plan view image o f a phase scan at a standoff distance of 3.8 mm at 9.2 GHz, a) E-field is parallel to vertical axis, b) E-field is parallel to the horizontal axis. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IV.3.1 Influence o f Frequency on the Radiation Pattern In Chapters 2 and 3 the significance of choosing the proper frequency of operation on the outcome of a measurement was mentioned several times. In this section the influence o f the frequency on the radiation pattern is studied and discussed. Two parameters in the x- and z-directions will be used to study the factors that influence the radiation patterns. The half-power beamwidth is a property associated with antenna radiation patterns in their far-fields. In this study, when comparing radiation patterns, a parameter called the half-power width (similar to the half-power beamwidth) will be used. The half-power width is the length in the x-direction (for constant y and z) at which the power reduces to half o f its maximum value. The other parameter which is used for comparison is the distance in the z-direction at which the power density reduces to 32.8% of is maximum value. IV .3 .1 .1 Influence o f the Waveguide D im ensions To study the influences of waveguide dimensions and the frequency of operation on the radiation pattern of an open-ended rectangular waveguide, power patterns (single line or one dimensional patterns from now on) were calculated at different frequencies and in different frequency bands (i.e. different waveguide dimensions) inside an infinite half space of a material. For this case a dielectric material with dielectric constant of ( er = 5 —jO. 1) representing the infinite half-space was used. Figure 4.6 shows three normalized (each with respect to its maximum value) power patterns. These patterns are in 106 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the x-direction (at y = — and z = 3 mm, all x-direction patterns will be calculated at the same values for y and z) and they start at the middle of the aperture of each waveguide and extend to outside the a dimension of the waveguide (i.e. only half of the pattern is shown). The patterns were calculated at three different frequencies in three different frequency bands. These frequencies are 10 GHz (X-band, waveguide dimensions of a=22.86 mm and b=10.16 mm), 14 GHz (Ku-band, waveguide dimensions of a= l5.8 mm and b=7.9 mm) and 22 GHz (K-band, waveguide dimensions o f a=10.67 mm and b=4.32 mm). The half-power widths (in mm) for these three patterns are 10.8 mm at 10 GHz, 7.4 mm at 14 GHz and 4.9 mm at 22 GHz. This indicates that the higher the frequency band (i.e. the smaller the waveguide dimensions) the narrower the half-power width gets (i.e. the higher the spatial resolution). It was observed that the spatial resolution in the experimental images depends on the dimensions of the waveguide [Chapter 3]. To investigate this, the ratios of the broad dimensions of the waveguides, a, were calculated and compared to the ratios of the half-power widths for the different frequencies in different bands as shown in Table 4.1. As the table indicates the ratios of the broad dimensions of the waveguides for the different bands match closely the ratios of the half-power widths at these frequencies. The slight differences are mainly due to the influence of different frequencies as will be shown later. Two other calculations were performed to study the influence o f the waveguide dimensions even further. The power patterns in the x-direction were calculated at frequencies corresponding to the upper end frequency in a band and the lower end frequency of the next band (e.g. X-band 8.2 GHz-12.4 GHz and Ku-band 12.4 GHz-18 GHz). Again the dielectric constant of the infinite half-space layer is (er = 5 - j0 .1 ) . Figure 4.7 shows the patterns obtained at a frequency of 12.4 GHz in the X- and Kubands. The half-power widths for these patterns are 10.7 mm for X-band and 7.4 mm for Ku-band. Figure 4.8 shows the patterns calculated at a frequency of 18 GHz in the Kuand K-bands. The half-power widths for these patterns are 7.55 mm for Ku-band and 5.1 107 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. mm for K-band. In both Figures the half-power width gets narrower as the dimensions of the waveguide get smaller (i.e. higher frequency band). The ratios of the a-dimensions of the bands and the ratios of the half-power widths are illustrated in Table 4.2. The ratios of the half-power widths match very closely the ratios of the a-dimensions of the waveguides in these bands. 1 10 GHz — - 14 GHz - - - 22 GHz 0.8 0.6 0 0 2 4 6 x (m m ) 8 10 12 Figure 4.6: The normalized power patterns in the x-direction at 10, 14 and 22 GHz inside a material with £r = 5 - jO. 1. Table 4.1: The ratios of the a-dimensions of X, Ku- and K-bands and the half-power ___________ widths associated with different frequencies in these bands.___________ frequency and band a dimension ratios half-power width ratios 10 GHz X-band 14 GHz Ku-band 1.447 1.46 2.142 2.204 1.481 1.51 10 GHz X-band 22 GHz K-band 14 GHz Ku-band 22 GHz K-band Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. — 12.4 GHz x-band — - 12.4 GHz ku-band >* *35 c a o * £ ■S .a ■a 0.6 0.4 o Z 0 0 2 4 6 x (m m ) 8 10 12 Figure 4.7: The normalized power patterns in the x-direction at 12.4 GHz in the X- and Ku-bands inside a material with er = 5 —jO. 1. ■ 18 GHz ku-band — - 18 GHz k-band 0.8 C aha <D s S. ■oo N 0.4 o 0.2 z 0.6 0 0 2 4 6 8 10 12 x (m m ) Figure 4.8: The normalized power patterns in the x-direction at 18 GHz in the Ku- and Kbands inside a material with er = 5 —jO. 1. 109 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 4.2: The ratios of the a-dimensions of the X, Ku- and K-bands and the half-power ____________ widths associated with the same frequencies in these bands.____________ half-power width ratios bands a-dimension ratios frequency 12.4 GHz X- and Ku-bands 1.447 1.446 lSGHz Ku- and K-bands 1.4$ 1 1.48 The power density patterns in the z-direction (all z-direction patterns were calculated at x = y mm and y = -j mm) were also calculated at the same frequencies for the same dielectric material. The distance at which the power density reduces to 32.8% of its maximum value was calculated for the cases mentioned above. Figure 4.9 shows the patterns calculated at three different frequencies in three different frequency bands. These frequencies are 10 GHz, 14 GHz and 22 GHz. The distances (in mm) at which the power density drops to 32.8% of its original value, from these three patterns, are calculated to be 13.7 mm at 10 GHz, 10.8 mm at 14 GHz and 6 mm at 22 GHz. This indicates that the lower the frequency band the higher the distances. To assure that this distance depends on the frequency band as well as the frequency of operation, the patterns at frequencies corresponding to the end of a frequency band and the beginning of the next frequency band were calculated. Again the dielectric constant of the infinite half-space layer is (e r = 5 - jO. 1). Figure 4.10 shows the patterns obtained at a frequency of 12.4 GHz in the X- and Ku-bands. The distances at which the power density drops to 32.8% of its original value for these patterns are 15.7 mm for X-band and 9.6 mm for Ku-band. Figure 4.11 shows the patterns calculated at a frequency of 18 GHz in the Ku- and the K-bands. The distances at which the power density drops to 32.8% of its original value for these patterns are 12.5 mm for Ku-band and 5.3 mm for K-band. In both Figures (4.10 and 4.11) this distance increases as the dimensions of the waveguide get larger. Intuitively, this behavior should be explained by attempting to isolate the components of equation 4.36 that varies with z. This dependence can only be observed in the exponential term involving z. Clearly, this expression is not dependent on the waveguide dimensions, however, the denominator of Equation 4.34b includes a singularity which involves the broad dimension 110 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. of the waveguide. Although a clear correlation between the presence of the singularity and the results obtained can not be shown due to the complexity o f the integral, it is clear that for a constant frequency and a constant permittivity of the infinite half-space the only varying components are the waveguide dimensions. 10 GHz — - 14 GHz - - - 22 GHz 0.8 2 & U 0.6 S, ■8 "5 0.4 o 0.2 Z 0 0 10 20 z (m m ) 30 40 50 Figure 4.9: The normalized power patterns in the z-direction at 10, 14 and 22 GHz inside a material with er = 5 - jO. 1. —- 12.4 GHz x-band — - 12.4 GHz ku-band 0.8 C o * o 0.6 CL ■s3 '■a o Z 0.2 **" I 0 0 10 20 z (m m ) 30 T — t— 40 50 Figure 4.10: The normalized power patterns in the z-direction at 12.4 GHz in the X- and Ku-bands inside a material with er =5 —jO. 1. Ill Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 18 GHz ku-band — * 18 GHz k-band 0.8 c a 0w 1 a. ■8 .a •a o 0.6 0.4 Z 0 10 20 , , 30 z (mm) 40 50 Figure 4.11: The normalized power patterns in the z-direction at 18 GHz in the Ku- and Kbands inside a material with er = 5 —jO. 1. IV.3.1.2 I n fl u e n c e o f The Frequency Within The S a m e B a n d In this section the influence of the frequency in the same band (i.e. the waveguide dimensions are constant) is investigated. The power density patterns in an infinite half space of material with similar properties to that used in the last section ( er - 5 - jO. 1) were calculated. Figure 4.12 shows power patterns in the x-direction (at y = — and z = 3 mm), calculated at frequencies of 18 GHz, 22 GHz, and 26 GHz in the k-band. The half-power widths associated with these frequencies are 5.1 mm at 18 GHz, 4.9 mm at 22 GHz and 4.8 mm at 26 GHz. It is clear that as the frequency increases the half-power width decreases slightly. The influence of the frequency on the half-power width is minimal when compared to that of the waveguide dimensions. 112 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The power density patterns in the z-direction were also calculated at the same frequencies for the same dielectric material. Figure 4.13 shows the patterns corresponding to different frequencies. The figure shows that within the same frequency band the higher the frequency the larger the distances at which the power density drops to 32.8% of its original value. The distances calculated for these patterns are 5.3 mm at 18 GHz, 6 mm at 22 GHz and 7.25 mm at 26 GHz. So, given a frequency band, higher frequencies in the band have a slightly higher distances and higher resolution. i 18 GHz 0.8 22 GHz 26 GHz 0.6 0.4 0.2 0 0 2 3 x (m m ) 4 5 6 Figure 4.12: The normalized power patterns in the x-direction at 18, 22 and 26 GHz inside a material with er = 5 —jO. 1. 113 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ------------18 GHz k-band -2 2 GHz ............... 26 GHz 0.8 0.6 0.4 0.2 0 10 20 z (m m ) 30 40 50 Figure 4.13: The normalized power patterns in the z-direction 18, 22 and 26 GHz inside a material with £r = 5 - jO. 1. IV.3.2 In flu en c e o f the Dielectric Properties on the R a diation Pattern In this section the influence of the dielectric properties on the radiation pattern is investigated. In the next sub-sections, the influence of the real part (permittivity) of the dielectric constant is studied first, then the influence of the imaginary part (loss factor) is investigated. Finally, both portions of the dielectric constant will be varied while maintaining a constant loss tangent (i.e. the ratio of the loss factor to the permittivity). IV .3 .2 .1 Influence o f Perm itivitty The real part of a relative dielectric constant is known as the relative permittivity and it describes the ability o f the material to store microwave energy. All calculations in this 114 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. section were performed at a frequency of 24 GHz in the K-band. Figure 4.14 shows the power patterns in the x-direction calculated for materials with dielectric constants of (3jO.l, 5-jO.l, 7-jO.l and 9-jO.l). The figure indicates that as the permittivity increases, the half-power width varies minimally. Table 4.3 shows the half-power widths obtained for each dielectric material. The patterns in the z-direction were also calculated at the same frequency for the same dielectric materials. Figure 4.15 shows the patterns corresponding to the different dielectric materials. The figure indicates that as the permittivity increases, the distance at which the power density drops to 32.8% of its original value increases as well. Table 4.4 shows the distance obtained for each dielectric material. 3-jO.l 5-jO.l 7-jO.I 9-jO.l 0.8 oc Q u. O £ £ ■S3J '■a 0.6 0.4 0.2 0 2 3 x (m m ) 4 5 6 Figure 4.14: The normalized power patterns in the x-direction at 24 GHz inside dielectric materials with constant loss factor. Table 4.3: The half-power widths for materials with dif 'erent permittivities at 24 GHz. dielectric constant 3-jO.l 5-jO.l 7-jO.l 9-jO.l half-power width (mm) 5.16 4.81 4.8 4.81 115 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3-jO.l — - 5-jO.l - - - 7-jO.l 9-jO.l S ' 0.8 *55 c & S 0.6 £ 1 0.4 0 10 20 z (m m ) 30 40 50 Figure 4.15: The normalized power patterns in the z-direction at 24 GHz in side dielectric materials with constant loss factor. Table 4.4: The distances at which the power density drops to 32.8% of its original value _______________ for materials with different permittivities at 24 GHz._______________ dielectric constant 3-j0.1 5-j0.1 9-jO.l 7-j0.1 distances (mm) 5.2 6.6 8.1 9.1 IV .3 .2 .2 Influence o f Loss Factor The imaginary part of a dielectric material is called the loss factor and it describes the ability of the material to absorb microwave energy. All the calculations in this section were performed at a frequency of 24 GHz in the K-band. Figure 4.16 shows the power patterns in the x-direction calculated for materials with dielectric constants of (5-j0.1, 5j0.5, 5-jl and 5-j2). The figure indicates that as the loss factor increases, the half-power width increases slightly. Table 4.5 shows the half-power widths obtained for each dielectric. 116 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The patterns in the z-direction were also calculated at the same frequency for the same dielectric materials. Figure 4.17 shows the patterns corresponding to the different calculations. The figure indicates that as the loss factor increases, the distances at which the power density drops to 32.8% of its original value decreases. Table 4.6 shows the distances obtained for each dielectric material. 5-jO.l — - S-j0.5 - - - 5-jl S-J2 0 2 3 x (m m ) 4 5 6 Figure 4.16: The normalized power patterns in the x-direction at 24 GHz inside dielectric materials with constant permittivity. Table 4.5: The half-power widths for materials with different loss factors at 24 GHz. dielectric constant 5-jO.l 5-j2 5-j0.5 5-jl half-power width (mm) 4.81 4.88 4.96 5.04 Table 4.6: The distances at which the power density drops to 32.8% of its original value for materials with different loss factors at 24 GHz. dielectric constant 5-jO.l 5-j0.5 5-jl 5-j2 distances (mm) 6.6 5.1 3.85 2.6 117 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5-jO.l — - S-j0.5 —- - 5-jl — S-j2 0.8 0 .6 -I* a. 0.4 0 10 20 z (m m ) 30 40 50 Figure 4.17: The normalized power patterns in the z-direction at 24 GHz inside dielectric materials with constant permittivity. Finally, for a changing permittivity and loss factor, while maintaining a constant loss tangent, the patterns are calculated. Figure 4.18 shows the power patterns in the xdirection calculated for materials with dielectric constants of (5-j0.1, 10-j0.2 and 15-jO.3). The figure indicates that the half-power width increases as the values of both the permittivity and the loss factor increase which means that the influence of the imaginary part dominates at this point in the x-direction. The patterns in the z-direction were also calculated at the same frequency for the same dielectric materials. Figure 4.19 shows the panems corresponding to the different calculations. The figure indicates that the distances at which the power density drops to 32.8% of its original value increases at the beginning (i.e. for 10-j0.2) and then it begins to decrease (for 15-j0.3) which means that the permittivity dominates at the beginning and after the loss factor exceeds a certain value it takes over the properties of the material. 118 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. >. e & 0 5-jO.l 10-J02 0.8 - - - 15-jOJ 0.6 £ 1 0.4 T3 § 2 0.2 0 2 4 3 5 6 x (m m ) Figure 4.18: The normalized power patterns in the x-direction at 24 GHz inside dielectric materials with constant loss tangent. 5-jO.I — - 10-j0.2 C/J a - - - 15-j0.3 a u O * £ •o os a O 0.2 0 10 20 z (m m ) 30 40 50 Figure 4.19: The normalized power patterns in the z-direction at 24 GHz inside dielectric materials with constant loss tangent. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IV.4 Summary and Remarks Near-field microwave imaging is a very powerful NDT tool for inspecting the integrity of dielectric composite materials. Experimental and theoretical results have shown that very high resolutions are obtainable in all directions. To interpret the information in a near-field microwave image, the effect of all the factors influencing the formation of an image must be understood. One of the prime factors influencing an image is the near-field properties of the radiator (i.e. the interaction of the fields with the material). The fields in the near-field region of the radiator were formulated and used to understand the properties of the open-ended rectangular waveguide probe. The effects and locations of sidelobes are now understood and can be used to obtain information about the shape and orientation of a defect. The formulations are general and can be used in obtaining the fields in a multi layered structures backed by either an infinite half-space of material or by a conducting sheet. The properties of the fields in the near-field region were investigated as a function of the frequency of operation, waveguide dimensions and dielectric properties of the material under inspection. The waveguide dimensions influence the spatial resolution drastically, as the frequency band increases (i.e. the waveguide dimensions decrease) the spatial resolution increases as well. On the other hand, lower frequency bands showed that higher distances at which the power density drops to 32.8% of its original value are obtained (i.e. larger waveguide dimensions). So, depending on the application the frequency of operation and the frequency band (waveguide dimensions) can be determined. So, given a certain frequency, if the goal is to have maximum penetration in to material, the lowest frequency band that contains the frequency is the best band to operate within. On the other hand, if the goal is to obtain maximum resolution, the highest frequency band that contains the frequency is the best to operate within. Results indicated that within the same 120 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. frequency band, operating at higher frequencies improves the spatial resolution and the distances at which the power density drops to 32.8% of its original value slightly. As the permittivity increases, the spatial resolution changes minimally and the distances at which the power density drops to 32.8% of its original value improves slightly. As the loss factor increases, the spatial resolution decreases slightly while the distances at which the power density drops to 32.8% of its original value decreases significantly. These results have a very important practical ramifications. For instance in a hose structure, the testing goal is to inspect the wall of the hose independent of the material that is filling the hose (water, oil, gas, etc.). For that the distances at which the power density drops to 32.8% of its original value must be limited to close to the inner side of the wall. To remedy this problem a dielectric slab can be placed in front of the waveguide to obtain the required distance. Up to this point the field properties in the near-field region of an open ended rectangular waveguide and their interaction with a dielectric material have been investigated. In chapter 5 a study of the mechanism by which the fields interact with an inclusion will be presented. An effective dielectric constant formula will be used to model the reflection properties o f dielectric structures. The influence of the non-uniformity associated with the electric field distribution at the aperture of the waveguide will be investigated and incorporated in calculating the effective dielectric constant. 121 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER V Influences o f The E ffective D ielectric Constant a n d N on-L inear Probe A perture F ield D istribution on N ear-F ield M icrow ave Im ages In this part of the investigation, the interaction of the fields, radiating from an openended rectangular waveguide, with a defect is investigated to further understand the mechanism of near-field microwave image formation. An effective dielectric constant formula is used to model the effect of two and three dielectric half-spaces situated side-byside, covered and not covered by layers of dielectric materials, when scanned by an openended rectangular waveguide probe. The influence of the non-uniformity associated with the electric field distribution at the waveguide aperture is investigated as well. A linear and a non-linear volume fraction calculation methods are incorporated to calculate the effective dielectric constant of a specimen made of two or three dielectric half-spaces. Subsequently, the phase and magnitude of the reflection coefficient at the waveguide aperture arc calculated. Theoretical and experimental results are presented and compared. As mentioned earlier, a near-field microwave image is the result of several factors such as the probe type (e.g. open-ended rectangular and circular waveguides, coaxial lines, etc.), antenna pattern (i.e. main lobe, sidelobes and half-power beamwidth), and geometrical and physical properties (e.g. dielectric constant) of both the inclusion (defect) and the host (background) dielectric material under inspection [Qad.95]. The field properties of an open-ended rectangular waveguide radiator and their interaction with several background materials were discussed in Chapter 4. The field/defect interaction will be investigated in this chapter. 122 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V .l The Effective Dielectric Constant o f A Medium To understand the information conveyed by a microwave image, the basics of wave/inclusion interactions must be understood. Dielectric materials are characterized by their relative (to free-space) complex dielectric constant, er = e ’r - j£”r. The reflection coefficient measured at the waveguide aperture is a function of the effective dielectric constant of the specimen under inspection. Thus, while the sensor scans over a dielectric specimen, as long as the effective dielectric constant of the specimen in front of the waveguide sensor does not change (i.e. absence of an inclusion), the effective reflection coefficient remains unchanged, and consequently a constant signal (voltage) is recorded. However, once the effective dielectric constant of the specimen changes (i.e. presence of an inclusion or scanning over one dielectric while moving into another), the effective reflection coefficient changes, and consequently the recorded signal changes indicating the presence of the inclusion. The properties of this recorded signal then provide information about the type and geometry o f the inclusion [Chapter 3]. The production o f near-field microwave images can be described by noting that the waveguide aperture, as it scans a medium with an inclusion, continually “sees” an effective dielectric material whose dielectric properties are a combination of the host and the inclusion. The effective dielectric constant of a material is defined as the ratio between the average electric flux displacement D and the average electric field E D = e tffE where, (5.1) is the effective dielectric constant of the medium. This equation applies to isotropic media (most dielectrics are isotropic). The effective dielectric constant must 123 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. satisfy the relation el < 6 ^ < eu, where, £, is the lower dielectric constant (of either the host or the inclusion) in the mixture and eu is the higher dielectric constant in the mixture. The displacement is given by D = e E +P (5.2) where, £ is the dielectric constant of the material and P is the polarization in the material. The poloraization depends on the polarizability o f the material. V.2 E ffective D ielectric Constant F orm ulae To model the effective dielectric constant of a specimen with an inclusion some type o f an effective dielectric constant model or formula may be used as long as it reflects the nature of the overall dielectric properties of the medium. V.2.1 Far- F ie ld vs. Near-Field In the far-field region the effective dielectric constant of a medium is influenced by the physical and geometrical properties of both the host and the inclusion materials. In the far-field the incident plane wave uniformly irradiates an object. The factor that influences the effective dielectric constant the most is the volume fraction of each constituent. On the other hand, in the near-field region one of the dominant factors influencing the effective dielectric constant of a medium is the field distribution of the probing sensor. The volume fraction of each constituent in the medium is therefore influenced (weighted) by the field 124 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. distribution of the probe. Figure 5.1 shows the dominant mode electric field distribution at a waveguide aperture. Figure 5.1a illustrates the fact that the electric field is maximum in the center of the broad dimension of the waveguide and sinusoidally diminishes to zero at the edges. Figure 5.1b shows the uniformity of this electric field distribution for a fixed location on the broad dimension and as a function of different locations on the narrow dimension of the aperture. y b x a (a) y A L .,.1 i > x a (b) Figure 5.1: Dominant mode electric field distribution at a waveguide aperture. 125 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V.2.2 Volume Fraction Calculation To account for the non-uniformity of the electric field distribution at the waveguide aperture a non-linear volume fraction calculation approach may be incorporated in accordance with the non-linear integrating influence of the aperture field distribution (i.e. modification to volume fraction used in calculating the effective dielectric constant based on this non-linearity). Figure 5.1 indicates that the distribution o f the electric field is not linear along the broad dimension o f the waveguide sensor. Thus, depending on the position of a certain physical volume of a constituent with respect to the aperture field distribution the influence of that constituent in the overall effective dielectric constant varies. So, one must consider the fact that the weighting influence of the electric field distribution at the waveguide aperture must also be taken into account since the contribution of each material in the specimen is effectively integrated over the aperture in a non-linear fashion (i.e. sinusoidally). Therefore, the non-uniformity of the field distribution at the waveguide aperture suggests that a non-linear volume fraction calculation must be used to calculate the volume fraction of each dielectric material as a function of its position with respect to the waveguide aperture. Consequently, Equation 5.3 which provides for a volume fraction weighted by the aperture field distribution is used in conjunction with effective dielectric constant formulae to obtain a more relevant effective dielectric constant values as a function of the scanning distance (i.e. changing volume fractions as the waveguide scans the structure). Hence, (5.3) “ initia l where V could be either V, (volume fraction of material 1, host,)or V2 (volume fraction of 126 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. material 2, inclusion,) (while V, + V2 = 1) and the integration is carried along the broad dimension of the waveguide (i.e. the x-axis). To obtain a volume fraction that can be used in conjunction with the effective dielectric constant equation (0 < V, and V2 < 1) for each dielectric material, the portion of the aperture that is covered by the dielectric is normalized with respect to the broad dimension o f the waveguide aperture, a. The initial and final values in Equation (5.3) correspond to the normalized position of each material. Since the host and the inclusion materials are assumed to be infinite in the z- and y-directions, the normalized volume fraction is a function only of the different locations on the broad dimension of the waveguide (i.e. the x-axis). To illustrate the importance of using Equation 5.3 to calculate the volume fraction of a material in the near-field of an open-ended rectangular waveguide, three slab like inclusions with physical sizes corresponding to 10%, 30% and 50% the area of the aperture are considered next. The volume fraction of the background material corresponding to each of the three slabs was calculated using the linear (the weight of a material is dependent only on the aperture area covered by that material) and the non-linear approaches. Figure 5.2 shows the volume fractions of background material calculated using the both approaches as a slab with a thickness of 10% moves through the aperture. The volume fraction is calculated as the slab moves in 1% steps through the broad dimension of the waveguide. The linear approach values are those physically enclosed by the aperture, while the non linear approach values are weighted by the field distribution according to Equation 5.3. Figures 5.3 and 5.4 show the volume fractions calculated using the linear and nonlinear apoproaches for the 30% and 50% inclusions, respectively. In Figures 5.2-5.4 the linear model shows that the volume fraction changes linearly as the slab enters and leaves the aperture of the waveguide, while the non-linear model shows that due to the field distribution the volume fraction of the background material does not vary as much once the slab is entering or leaving the aperture. This is because the weight o f the material at these 127 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. positions is small since the field at these locations is weak. Once the slab is within the aperture the linear model yields a constant volume fraction, while the non-linear model yields varying values depending on the position within the aperture. At the middle of the aperture, the field is very strong, the linear model does not vary. However, the non-linear model indicates that due to the strength of the field at the middle of the aperture, the influence of the 10% slab, when it is in the middle of the slab, is more than the physical size and is equivalent to a 16% slab in a linear model. Figures 5.3 and 5.4 demonstrate a similar behavior for wider slabs. Figure 5.4 shows that for the 50% slab, the two models intersect when the slab is in front of half the waveguide. i N'on-Linear 0.95 — — - Linear 0.9 0.85 0.8 0 20 40 60 S can P o sitio n 80 100 Figure 5.2: The volume fraction as a function of scan position as a slab of 10 % the area of the aperture is being seen by the aperture. 128 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. — Non-Linear — - Linear 0.9 e o •3 8 & o 0.8 0.7 o > 0.6 0 20 40 100 60 80 S can P o sitio n 120 Figure 5.3: The volume fraction as a function of scan position as a slab of 30 % the area of the aperture is being seen by the aperture. 0.9 -S Non-Linear — * Linear £ o E -o > 0.6 0.5 0.4 0.3 0.2 0 50 100 150 S can P o sitio n Figure 5.4: The volume fraction as a function of scan position as a slab of 50 % the area of the aperture is being seen by the aperture. 129 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V.2.3 Effective D ielecrtic Constant Form ulae The ability of treating a random dielectric medium (a medium with more than one dielectric) with an effective dielectric property that contains the information on how the inhomogenities of the material affect the reflection properties is essential to researchers in many areas such as, microwave industrial and medical applications, remote sensing and material science. The literature is full of different effective dielectric constant formulae developed for many structures o f heterogeneous materials. For this study, three formulae are considered and compared to each other. To simulate the experimentally obtained data analytically, the formula that was based on a more rigorous investigation is used, as discussed later. V.2.3.1 Sim ple A verage E ffective D ielectric C onstant Formula In this case, the calculation of the effective dielectric constant is based on averaging the dielectric constants of each material “seen” by the aperture weighted directly by its volume fraction. The formula is given by = VfrX + V2^2 (5-4) where e r, erl and er2 are the specimen’s effective relative dielectric constant, the relative dielectric constant of material 1 and the relative dielectric constant of material 2, respectively. Likewise, V, and V2 are the volume fractions ( 0 < {V ,, V2} < 1 and V, + V2 = 1) of material 1 and material 2, respectively. 130 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V.2.3.2 Rayleigh Effective Dielectric Constant Formula This effective dielectric constant formula is among the most commonly used. It was originally developed to simulate spherical inclusions, and it is applied to many heterogeneous structures. The formula is given by (5.5) where e r, er, and er2 are the specimen’s effective relative dielectric constant, the relative dielectric constant of material 1 and the relative dielectric constant of material 2, respectively. Likewise, V, and V2 are the volume fractions ( 0 < {V , , V2} < 1 and V, + V2 = 1) of material 1 and material 2, respectively. V.2.3.3 K .W a k in ’s E ffective D ielectric C onstant F orm ula This effective dielectric constant formula was obtained through rigorous and numerous simulations using finite element methods in which the effect of dielectric polarization and the infringing electric K.Wakin distribution at the boundary regions between the host and the inclusion were taken into account [Wak.93]. The formula is given by (5.6) 131 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where £r, Erl and er2 are the specimen’s effective relative dielectric constant, the relative dielectric constant o f cement paste and the relative dielectric constant of, respectively. Likewise, V, and V2 are the volume fractions ( 0 < [V, , V2) < 1 and V, + V2 = 1 ) of material 1 and material 2, respectively [Wak.93]. V.2.3.4 Com parison The three formulae were used to calculate the effective dielectric constant of a mixture composed o f two dielectric materials. The linear and non-linear volume fraction calculation methods were used in conjunction with each formula. A mixture of two infinite half-spaces of materials arranged side-by-side as shown in Figure 5.5, in this particular case, cement paste with water-to-cement (w/c) ratio of 0.55 resulting in a measured er = 4.3 - j0.07 and ethylene propylene diene or EPDM which is the primary constituent of rubber with a measured er = 1.88 - j0.02, was modeled using all three effective dielectric constant formulae. The three formulae were used with both the linear and the non-linear models to calculate the effective dielectric constant of the structure described in Figure 5.5. Figure 5.6 shows the values of the real part of the effective dielectric constant obtained using K.Wakin’s effective dielectric constant formula as a function of location in front of the aperture. The figure indicates that the values obtained using both approaches (linear and non-linear) match at the beginning and at the end (i.e. when one of the two materials is occupying a small area in front of the aperture). The two approaches match as well when 50% of the aperture is covered by each material. The maximum percentage difference in the real part of the dielectric constant is around 12%. Figures 5.7 and 5.8 show the same when using the Rayleigh and the simple average formulae, respectively. 132 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. For these formulae, similar percentage differences between the linear and the non-linear approaches are present. Figures 5.9-5.11 show the results obtained for the imaginary pan of the effective dielectric constant using the three formulae with the linear and the non-linear approaches. A maximum difference of around 16 % is observed in the results obtained using K.Wakin’s formula. Similar differences are observed for the other two formulae. Figure 5.12 shows the real part of the effective dielectric constant obtained using the three formulae with the non-linear approach as a waveguide scans over the structure shown in Figure 5.5. The figure indicates that on both ends of the graph (i.e. when one of the two constituents dominates the region seen by the sensor) the three formulae results match. A maximum difference o f around 14% is obtained between K.Wakin’s and the simple average formulae. Figure 5.13 shows the results obtained for the imaginary part. The results presented above indicate that the effective dielectric constant is influenced by the volume fraction calculation method and the formula used. So, by using the non-linear approach and the proper effective dielectric constant formula is important in obtaining correct effective dielectric constant values. In the next sections the K.Wakin effective dielectric constant formula will be used since it was obtained through rigorous and numerous simulation using finite element methods in which the effect of dielectric polarization and the infringing electric flux distribution at the boundary regions between the host and the inclusion were taken into account. 133 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Waveguide Sensor ------ ^ Scan Direction Cement Paste EPDM e r = 4 .3 -j0 .0 7 £r = 1.88 - j0.02 Figure 5.5: Two infinite half-spaces of cement paste and EPDM arranged side-by-side to model a large defect. — Non-Linear — - Linear - \ 3.5 1.5 0 0.2 0.6 0.4 S ca n P o sitio n 0.8 Figure 5.6: Real part of the effective dielectric constant obtained using the K.Wakin lines formula. 134 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 43 — Non-Linear — * Linear 4 3 2.5 0 0.2 0.4 0.6 S can P o sitio n 0.8 Figure 5.7: Real part of the effective dielectric constant obtained using the Rayleigh formula. Non-Linear — - Average Linear 4 3.5 V 3 \ 2.5 2 1.5 0 0.2 0.4 0.6 S can P o sitio n 0.8 Figure 5.8: Real part of the effective dielectric constant obtained using the average formula. 135 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -0.01 - 0.02 -0.03 -0.04 -0.05 -0.06 - - — Non-Linear — - Linear -0.07 -0.08 0 0.2 0.6 0.4 S can P o s itio n 0.8 1 Figure 5.9: Imaginary part of the effective dielectric constant obtained using the K.Wakin lines formula. -o.oi - 0.02 -0.03 -0.04 u -0.05 -0.06 Non-Linear — - Linear -0.07 -0.08 0 0.2 0.4 0.6 S can P o sitio n 0.8 Figure 5.10: Imaginary part of the effective dielectric constant obtained using the Rayleigh formula. 136 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -0.01 - 0.02 -0.03 -0.04 u -0.05 — -0.06 Non-Linear — - Linear -0.07 -0.08 0 0.2 0.4 0.6 S can P o sitio n 0.8 Figure 5.11: Imaginary part of the effective dielectric constant obtained using the average formula. 4.5 N- . 4 — Flux Line — - Rayleigh • - - Average 3 2.5 1.5 0 0.2 0.4 0.6 S can P o sitio n 0.8 Figure 5.12: Real part of the effective dielectric constant obtained using the three formulae with the non-linear approach. 137 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -0.01 - 0.02 -0.03 -0.04 CJ -0.05 -0.06 — — - Average — — • Flux Line • * • • • Rayleigh -0.07 -0.08 0 0.2 0.4 0.6 S c a n P o sitio n 0.8 1 Figure 5.13: Imaginary part of the effective dielectric constant obtained using the three formulae with the non-linear approach. V.3 Results Thus far, the effective dielectric constant, using three different methods, has been calculated. Consequently, the phase and the magnitude of the reflection coefficient at the waveguide aperture may be analytically calculated, using the electromagnetic code developed for describing the interaction of the fields radiated from an open-ended rectangular waveguide into a multi-layered composite structure [Bak.94], [Chapter 2], and compared with measurements. As a first step towards modeling a finite sized inclusion such as those discussed in Chapter 3, simpler cases are analyzed first and more complicated ones are analyzed later on using the approach outlined above. To illustrate the influence of the field distribution at the waveguide aperture in the effective dielectric constant, several sets of specimens with known properties were 138 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. prepared. In the following sections, descriptions of the specimens and the obtained results are presented. An HP8510 vector network analyzer was used to record the actual phase (<J>°) and magnitude (ID) of the reflection coefficient ( r = Hie1**) at the waveguide aperture as a function of position. V.3.1 Two In fin ite Half-Spaces This specimen was prepared to model a simple transition from one infinite half space to another simulating the presence of a large inclusion (as a first step in the modeling process). The specimen was produced by arranging, side-by-side, a large cube of cement paste with a water to cement (w/c) ratio o f 0.55 resulting in a measured er = 4.3 - j0.07 and ethylene propylene diene or EPDM which is the primary constituent of rubber with a measured e r = 1.88 - j0.02, as shown in Figure 5.5. The dielectric constant values reported in this chapter were all measured at 10 GHz which is the frequency used to conduct this scan (aperture dimensions are a=22.86 mm by 6=10.16 mm). These two materials were used because they are relatively homogeneous, they were available in the laboratory and their dielectric properties had previously been measured for other purposes [Boi.97], [Gan.94]. Each cube of material was about 8” x 8” x 8” (21 cm x 21 cm x 21 cm) to simulate an infinite half-space situation. The specimen was scanned starting with the waveguide totally on the cement paste and ending with it totally on the EPDM, as shown in Figure 5.5. When the interface between these two materials is within the waveguide aperture, each material is partially contributing to the measured reflection coefficient. Therefore, the measured reflection coefficient is due to the effective dielectric constant of these two materials exposed to the 139 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. aperture. To implement the scanning results theoretically, the K.Wakin line effective dielectric constant formula was used to calculate the effective dielectric constant of an effective medium exposed to the waveguide aperture. To validate the experimental results theoretically, at first the effective dielectric constant formula is used with a linear volume fraction calculation method. Figures 5 .14a-b show the measured and calculated phase and magnitude of the reflection coefficient as a function of the scanning distance, respectively. Figure 5.14a shows a maximum phase difference of about 10 degrees between the measured and the calculated results, while Figure 5.14b shows that the magnitudes differ by more than 0.05 (0 < ID <1). The trend of the calculated results do not agree with their measured counterparts very well. Consequently, the linear volume fraction assumption is shown not to be valid. Figures 5.15a-b show the phase and magnitude of the reflection coefficient calculated incorporating the non-linear volume fraction calculation. Clearly, in this case the calculated results agree much better with the measured results when compared to the results of the linear volume fraction calculation shown in Figures 5.14a-b. 140 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -140 Measured Calculated S can n in g D is ta n c e (m m ) 0.5 Measured Calculated 0.45 [_ 0.4 035 0.3 0 9 18 27 S can n in g D is ta n c e (m m ) Figure 5.14: a) The phase and b) magnitude of the reflection coefficient at the aperture of the waveguide using the linear model for the specimen shown in Figure 5.5. 141 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -140 Measured Calculated S c a n n in g D is ta n c e (m m ) 0.5 Measured Calculated 0.45 .4 035 0.3 0 9 18 27 S c a n n in g D is ta n c e (m m ) Figure 5.15: a) The phase and b) magnitude of the reflection coefficient at the aperture of the waveguide using the non-linear model for the specimen shown in Figure 5.5. 142 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V.3.2 Surface Slab in An Infinite Half-Space The second set of specimens was prepared to model an inclusion with a finite dimension as the second step in the modeling process. This set includes two specimens with slightly different properties. The first specimen was produced by placing a slab of Plexiglas with er = 2.56 - j0.02 and a thickness of 4 mm in between two large and identical cement paste blocks with a water to cement (w/c) ratio of 0.45 having a measured er = 5 .8 - j0.2, as shown in Figure 5.16. To illustrate the effect of the width of the inclusion (Plexiglas), a second specimen similar to the one shown in Figure 5.16 was produced with a Plexiglas slab whose thickness is 5.8 mm. The Plexiglas inclusions were large in length and height and are thus assumed infinite in the y- and z- directions and are only finite in the x-direction. As the sensor, operating at 10 GHz, scanned over each specimen, as shown in Figure 5.16, the magnitude of the reflection coefficient ITI was recorded. First the specimen with the 4 mm thick Plexiglas slab was scanned. The scan is 32 mm long and it starts and ends with the aperture approximately 3 mm away from the cement/Plexiglas interface on each side. Figure 5.17 shows the experimental and calculated results obtained using the linear and non-linear volume fraction models. The linear model shows that once the Plexiglas inclusion is within the aperture, the measured ITI remains fairly constant which is in disagreement with the measurements. However, the results o f the non-linear volume fraction model agree well with the measured results. Figure 5.18 shows the measured and calculated in for the 5.8 mm-thick Plexiglas slab. The scan is 36 mm long and it starts and ends with the aperture approximately 3 mm away from the interface on each side. Again, the results of the non-linear volume fraction model agrees well with the measured results. Furthermore, the width associated with Figures 5.17 and 5.18, as a 143 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. function of scanning distance, is larger for Figure 5.18 than for Figure 5.17, as expected. However, these widths do not correspond to the actual thickness of the Plexiglas inclusions used in the experiments. This fact clearly shows the non-linear integrating effect that the waveguide aperture has when used for near-field imaging. An inverse routine may be used to take this non-linear integrating effect out of such measurements and provide for the actual inclusions size. a Waveguide Sensor Scan Direction Cement Paste Cement Paste e f = 5.8 - j0.2 er = 5 .8 - j0.2 Plexiglass £r = 2.56 - j0.02 Figure 5.16: A thin Plexiglas slab inserted in between an infinite half-space of cement paste to model a one dimensional defect. 144 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.6 Measured Linear Non-Linear • •• U 0.5 0.45 0.4 0 5 10 20 15 25 30 35 40 S c a n n in g D ista n c e (m m ) Figure 5.17: The magnitude of the reflection coefficient for 4 mm-thick Plexiglas in an infinite half-space of cement paste. 0.6 Measured Linear Non-Linear ••••••• U 0.5 0.45 0.4 0 5 10 15 20 25 30 35 40 S c a n n in g D ista n c e (m m ) Figure 5.18: The magnitude of the reflection coefficient for 5.8 mm-thick Plexiglas in an infinite half-space of cement paste. 145 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V.3.3 Deep Slab in An Infinite Half-Space This set of specimens (three in all), was prepared to model an inclusion with a finite dimension under a layer of material as a step forward in the modeling process. Figure 5.19 shows a specimen that was produced by inserting a slab of Plexiglas with er = 2.56 - j0.02 and a thickness of 5.8 mm in an infinite half-space of cement paste with a water to cement (w/c) ratio of 0.5 having a measured er = 6.35 - j 1.5. The Plexiglas slab was inserted at a depth of 8 mm from the scan surface, as shown in Figure 5.19. To illustrate the effect of the inclusion (Plexiglas) width and depth two other specimens, similar to the one shown in Figure 5.19, were produced. In the first, a Plexiglas slab whose thickness is 5.8 mm was inserted in a similar cement past infinite half-space at a depth of 4.8 mm. In the second, an 8.8 mm thick Plexiglas slab was inserted in a similar half-space of cement paste at a depth of 4.8 mm. The Plexiglas inclusions were large in length and height and are thus assumed infinite in the y- and z- directions and are only finite in the x-direction. Since the Plexiglas was inserted at different depths in the cement, the field pattern in an infinite half-space of cement paste was calculated to assure that the beam at all depths is still confined to within the waveguide aperture. Figure 5.20 shows the normalized YZplane field pattern at 7 GHz (the frequency at which the measurement and calculation are performed, waveguide dimensions are 34.84 mm by 15.8 mm). The figure indicates that the fields remain confined to within the aperture dimensions up do depths of around 20 mm. The three specimens were scanned at a frequency of 7 GHz and the magnitude of the reflection coefficient ITI was recorded as a function of the scan location. Figures 5.215.23 show the results obtained from scanning the three specimens. The scans are 100 mm 146 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. long with a step size of 1 mm. Good agreement between the measurement results and the theoretical results is obtained. Figures 5.21 and 5.22 show that the width of the detected inclusion (on both figures) is the same in both cases even though the Plexiglas slabs are at different depths. This again indicates that the resolution is similar at both depths. The width associated with Figure 5.23 as a function of the scanning distance is larger than those associated with Figures 5.21 and 5.22. These results indicate that information about the depth and width of a defect can be obtained. a Waveguide Sensor Scan Direction I Cement Paste Ef = 6.35 - j 1.5 Cement Paste ef = 6.35 - j 1.5 Plexiglass er = 2.56-j0.02 Figure 5.19: A thin Plexiglas slab inserted at depth d in an infinite half-space of cement paste to model a one dimensional defect under a layer of material. Figure 5.20: The normalized YZ-plane field pattern at 7 GHz in an infinite half space of cement. 147 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.55 Measurement Theory a 0 x 20 i a 40 60 80 100 S c a n n in g D istan ce (m m ) Figure 5.21: The magnitude of the reflection coefficient for a 5.8 mm-thick Plexiglas slab 8 mm deep in an infinite half-space of cement paste. Measurement Theory u o 20 40 60 80 100 S c a n n in g D istan ce (m m ) Figure 5.22: The magnitude of the reflection coefficient for a 5.8 mm-thick Plexiglas slab 4.8 mm deep in an infinite half-space of cement paste. 148 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.6 Measurement Theory 0.55 X X 0 20 40 60 80 100 S can n in g D is ta n c e (m m ) Figure 5.23: The magnitude of the reflection coefficient for a 8.8 mm-thick Plexiglas slab 4.8 mm deep in an infinite half-space of cement paste. V.3.4 Deep Slab in A M ulti-Layered Structure Finally, to model an inclusions in a multi-layer structure, a 3.17 mm thick layer of synthetic rubber was laid on top of each of the specimens described in the last section as shown in Figure 5.24. The magnitude of the reflection coefficient ITI was recorded and calculated as a function of the scan location. Figures 5.25-5.27 show the results obtained from 100 mm long scans performed at a frequency of 7 GHz. The different depth as well as the different width influences are indicated again. In Figure 5.27 a dip like feature is observed on each side of the defect is observed. The calculation results show this feature as well. This feature is due to the way the fields interact with a dielectric medium to produce a certain reflection coefficient. 149 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Waveguide | Sensor Synthetic Rubber • e r = 4.9 -jO.l Scan Direction 1 Cement Paste ef = 6.35 - jl.5 Cement Paste ef = 6.35- j 1.5 Plexiglass er = 2.56-j0.02 Figure 5.24: A thin Plexiglas slab inserted at depth d in an infinite half-space of cement paste under a 3.17 mm thick layer of synthetic rubber to model a one dimensional defect in a multi-layered structure. 0.5 0.495 u 0.49 Measurement 0.485 Theory 0.48 0 20 40 60 80 100 S c a n n in g D ista n ce (m m ) Figure 5.25: The magnitude of the reflection coefficient for a 5.8 mm-thick Plexiglas slab 8 mm deep in an infinite half-space of cement paste. 150 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.509 Measurement Theory t_ 0 20 40 60 SO 100 S ca n n in g D ista n c e (m m ) Figure 5.26: The magnitude o f the reflection coefficient for a 5.8 mm-thick Plexiglas slab 4.8 mm deep in an infinite half-space of cement paste. Measurement Theory 0 20 40 60 80 100 S c a n n in g D ista n c e (m m ) Figure 5.27: The magnitude o f the reflection coefficient for a 8.8 mm-thick Plexiglas slab 4.8 mm deep in an infinite half-space of cement paste. 151 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V.4 Summary and Remarks Near-field microwave imaging using open-ended rectangular waveguide sensors is an effective nondestructive tool for the inspection of materials particularly when determining the size and shape o f inclusions. The non-uniformity associated with the electric field distribution at the waveguide aperture is an important factor that must be explicitly taken into account when trying to understand and interpret images obtained in the near-field of such sensors. In this chapter, this issue was discussed using four sets of dielectric specimens as steps towards modeling a finite sized inclusion in a host material. A simple formula was used to obtain the effective dielectric constant o f a material made of two or three dielectric half-spaces arranged side-by-side covered or uncovered by layers of dielectric material. The non-uniformity of the field distribution was incorporated in the effective dielectric constant formula by using a non-linear volume fraction calculation consistent with the aperture field distribution of the rectangular waveguide probe. The results were compared to a linear volume fraction formula and it was determined that the linear volume fraction method does not sufficiently predict the properties of the specimen under inspection. The results presented indicate that the effective dielectric constant is influenced by the volume fraction calculation method and the formula used. So, using the non-linear approach and the proper effective dielectric constant formula is important in obtaining correct effective dielectric constant values. The foreword problem of imaging relatively simple structures and the field-defect interaction is now understood. More complicated structures can be analyzed in a similar fashion and the inverse problem of determining defect size and properties can no be solved. The volume fraction calculation outlined in this chapter assumes that the distribution associated with the aperture fields is sinusoidal (i.e. that of the dominant mode only). 152 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. However, for a more detailed analysis, the influence of the higher-order modes on the nonlinearity associated with the aperture field distribution must be considered. The properties of the higher-order modes are influenced by the physical and geometrical properties o f the structure under consideration and the frequency of operation. Another assumption that was made by using the sinusoidal (i.e. dominant mode) distribution is that wave bending doesn’t occur as two dielectric materials with different dielectric properties are partially seen by the aperture. High dielectric materials tend to pull the fields into them. The same phenomena happens at the aperture of the waveguide when two materials are seen by the aperture. The higher dielectric tend to attract more fields into it, thus, changing the sinusoidal distribution of the field at the aperture. The variation of the field distribution (i.e. wave bending) is influenced by the difference in the dielectric properties between the materials and the position of each dielectric material in front of the aperture. The bending is significant if the difference between the dielectric properties is large and both dielectrics occupy relatively large portions of the space in front of (or seen by) the aperture. The influence of wave bending can be mathematically incorporated using higher-order modes. In this study the effect of wave bending would be minimal because the dielectric properties of the materials considered were close to each other. However, for a more detailed study the higher-order modes and the wave bending effects must be considered. 153 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER VI C onclusions The accumulation of flaws or defects (and damage) in a composite structure is closely tied to its loaded physical and mechanical properties such as strength, durability, stiffness, etc. It is imperative to have a good knowledge of the integrity of a composite structure before and during use. In composite media, defects may be divided into two groups (depending on the size with respect to the footprint (sensing area) of the microwave sensor), namely: large and small defects. A large defect, is a defect whose area is several times larger than the footprint (e.g. a disbond or a delamination), and it can be considered as an extra layer in the structure. This layer can be detected and characterized using the measured reflection coefficient. If the defect is small (i.e. its extent is smaller than the footprint) it will have a different interaction with the fields, due to the boundaries and edges, and this interaction will influence the refection coefficient and consequently the signal measured by the microwave sensor. Characterization of defects (determining their sizes, locations and properties), after they are detected, is a very important part o f any nondestructive testing technique. In Chapter 2 a theoretical study was conducted to expand on and demonstrate the ability of utilizing an open-ended rectangular waveguide probe to monitor the existence and to determine the position of a disbond in a layered composite structure. Theoretical analysis of radiation from a rectangular waveguide into layered dielectric composite media was presented in this chapter. Initially, variational formulation was evoked to come up 154 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. with a stationary expression for the terminating aperture admittance of general cylindrical waveguides with arbitrary cross section. The formulation was then expanded to take into account general N-layer media terminated into an infinite half-space or a perfectly conducting sheet. The results of a theoretical study, using an open-ended rectangular waveguide radiating into a multi-layered structure, for detecting disbonds in thick sandwich composite structures and determining their depths unambiguously were presented in Chapter 2. The results indicated that disbond detection at depths is possible at a number of frequencies and standoff distances. Ka-band was shown to be the most optimum frequency band to operate in. K-band also showed promise for not only disbond detection but also for depth determination. It was shown that several frequencies and/or standoff distances may be used for unambiguous depth determination. All of these results involved the calculation of the phase of the reflection coefficient at the waveguide aperture. It turns out that other related parameters such as the magnitude and/or the real pan of the reflection coefficient may also be used in conjunction (or individually) with other parameters to determine disbond depth unambiguously. The disbond thickness used in this study was assumed to be equal to the thickness of the adhesive layer (0.28 mm). In practice however, disbond thickness may be in excess of 0.5 mm to a few millimeters. In such cases the phase difference values that were used for detection will increase, rendering the disbond much easier to detect. Additionally, disbond depth determination in such cases will be easier as well. Since disbond thickness influences the phase of the reflection coefficient, it is very likely to not only be able to determine its depth but also its thickness (within a given range) as well. Multiple disbonds may exist in a sandwich composite as well. This microwave nondestructive testing method is (should be) capable of detecting multiple disbonds as well (as part of a future investigation). 155 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The formulation used in this general theoretical model is quite complicated. However, in the future, it may be worth looking into the possibility of developing an analytical inverse model to determine disbond properties such as existence, depth and thickness. Furthermore, in the study conducted here the effect of dielectric property variations in each layer o f the composite was not investigated. In a future study the influence of such variations (including layer thickness variations) should also be taken into account as well. In Chapter 3, near-field microwave imaging of dielectric composite structures using open-ended rectangular waveguides was studied experimentally. Experimental setups were presented and their operations were discussed. The utility of applying near-field microwave techniques to inspect a wide variety of composite structures with different types of defects was demonstrated, and several experimental results were presented in Chapter 3. The inspection of thick layered composite materials is essential in ensuring structural integrity before and during usage. Many types of defects that cannot be visibly observed can occur in production and in use situations weakening the structural integrity of the composite and endangering structures employing such materials. Early detection of defects is necessary to mitigate damage propagation. The ability of microwaves to penetrate inside dielectric materials makes microwave NDT techniques very suitable for interrogating structures made of thick dielectric composites. Three experimental setups were presented for three different types o f near-field microwave imaging. The effects of frequency of operation and the standoff distance as measurement optimization parameters to enhance the sensitivity to a defect were studied and presented. Experimental results obtained from scanning a variety of composite samples with different types of embedded defects were presented. Images of these defective samples were created using a measured voltage that is related to the phase and/or magnitude of the effective reflection coefficient at the aperture of 156 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the rectangular waveguide sensor. These images presented detailed information about the structure and integrity of the inspected samples. On all of these images the size of a defect matches closely its physical size, indicating the high resolution associated with this technique. Chapter 4 was devoted to study the field properties in the near-field region of an open-ended rectangular waveguide and its interaction with a dielectric material. This study included investigating the influences of frequency and dielectric properties on the radiation pattern. One of the prime factors influencing an image is the near-field properties of the radiator (i.e. the interaction of the fields with the material). The fields in the near-field region of the radiator were formulated and used to understand the properties of the openended rectangular waveguide probe. The effects and locations of sidelobes are now understood and can be used to obtain information about the shape and orientation of a defect. The formulations, outlined in Chapter 4, are general and can be used in obtaining the fields in a multi-layered structures backed by either an infinite half-space of material or by a conducting sheet. The properties of the fields in the near-field region were investigated as a function of the frequency of operation, waveguide dimensions and dielectric properties o f the material under inspection. The waveguide dimensions influence the spatial resolution drastically, as the frequency band increases (i.e. the waveguide dimensions decrease) the spatial resolution increases as well. On the other hand, lower frequency bands showed that higher penetration depths are obtained (i.e. larger waveguide dimensions). So, depending on the application the frequency of operation and the frequency band (waveguide dimensions) can be determined. So, given a certain frequency, if the goal is to have maximum penetration in to material, the lowest frequency band that contains the frequency is the best band to operate within. On the other hand, if the goal is 157 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. to obtain maximum resolution, the highest frequency band that contains the frequency is the best to operate within. Results indicated that within the same frequency band, operating at higher frequencies improves the spatial resolution and the depth of penetration slightly. As the permittivity increases, the spatial resolution changes minimally and the penetration depth improves slightly. As the loss factor increases, the spatial resolution decreases slightly while the penetration depth decreases significantly. In Chapter 5 a study of the mechanism by which the fields interact with an inclusion was presented. An effective dielectric constant formula was used to model the reflection properties o f dielectric structures. The non-uniformity associated with the electric field distribution at the waveguide aperture is an important factor that must be explicitly taken into account when trying to understand and interpret images obtained in the near-field of the sensor. In Chapter 5, this issue was discussed using four sets of dielectric specimens as steps towards modeling a finite sized inclusion in a host material. A simple formula was used to obtain the effective dielectric constant of a material made of two or three dielectric half-spaces arranged side-by-side covered or uncovered by layers of dielectric material. The non-uniformity of the field distribution was incorporated in the effective dielectric constant formula by using a non-linear volume fraction calculation consistent with the aperture field distribution of the rectangular waveguide probe. The results presented indicate that the effective dielectric constant is influenced by the volume fraction calculation method and the formula used. So, using the non-linear approach and the proper effective dielectric constant formula is important in obtaining correct effective dielectric constant values. The volume fraction calculation outlined in Chapter 5 assumed that the distribution associated with the aperture fields is sinusoidal (i.e. that of the dominant mode only). However, for a more detailed analysis, the influence of the higher-order modes on the nonlinearity associated with the aperture field distribution must be considered. Also, the influence of wave bending due to two dielectric materials with different dielectric properties 158 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. being partially seen by the aperture should be considered as a part of a future study. 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