复介电常数的测量和成像中的逆问题研究
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摘要
复介电常数的测量和成像技术在基础科学研究和工业生产中有着重要应用,它们在数学上都属于逆问题。本文主要研究射频／微波频段的复介电常数测量与成像方法。
首先,本文研究了电磁波逆散射成像问题。高介电常数散射体成像是该领域的一个难题。本文基于子空间理论的优化算法(SOM:Subspace based Optimization Method),进一步利用子空间理论,把散射体图像分解成信号子空间部分和噪声子空间部分,解释了SOM算法反演高介电常数散射体困难的原因。此外本文还在SOM算法中引入了适用于反演块状物体的全变分正则化,能够使图像的物体边缘更加清晰,提高了成像质量。
其次,本文研究了一种基于模式匹配方法的宽频带复介电常数的测量方法。通过在数学模型中考虑高次模式的影响,我们可以采用同轴线的突变结构进行复介电常数的测量。与传统的短路同轴线法相比,本文方法可使用更大尺寸的样品容器、并具有更为简洁的结构和和更加简单的校准过程。
最后,通过借鉴“中距”无线能量传输的原理,提出了一种基于耦合谐振线圈的复介电常数非接触式测量方法。该方法使用高Q谐振线圈作为探头,通过谐振线圈的耦合实现了与标准50欧仪表的阻抗匹配。与传统的磁感应法相比,测量灵敏度得到大幅度提高,并可用于测量小尺寸、低电导率的固体和液体材料。利用瑞利近似,理论上得到了测量阻抗与被测复介电常数之间简洁的数学关系,从而只需测量一个电参数已知的材料即可校准测量装置,进而精确反演其它被测材料的复介电常数。
The measurement and imaging of complex permittivity have enormous applications both in scientific research and industrial engineering. Mathematically, they are both inverse problems. In this dissertation, we focus on the measurement and imaging methods at RF and microwave frequency.
First we discussed about the electromagnetic wave inverse scattering imaging. High contrast scatterer imaging is a difficult problem in this area. In this dissertation, based on the subspace based optimization method (SOM), we further decompose the scatterer image into signal subspace part and noise subspace part, and found the reason of difficulty when applying SOM into high contrast scatterer problem. Moreover, we improved the imaging quality by adding total variation regularization to SOM, which is able to sharpen the edges of image, suitable for blocky scatterer.
Then a broadband complex permittivity measurement method is studied, namely the short circuit coaxial line method. By considering the influence of higher order modes using mode matching method, we adopt coaxial discontinuity structure to measure complex permittivity. Compared to the traditional short circuit coaxial line method, the proposed method enables larger sample holder and the fabrication and calibration process is quite easy.
At last, based on the concept of coupled magnetic resonance used in mid-range wireless power transfer, we propose a non-contact complex permittivity measurement method. In this method, high-Q resonant coils are used as sensors, through the coupling of resonant coils, impedance matching is achieved. Compared to traditional magnetic induction method, the proposed method has much higher sensitivity and is suitable for measuring small sized and low conductivity samples. By using Rayleigh approximation, a concise relation between the measured impedance and sample's complex permittivity can be derived. Thus accurate complex permittivity can be retrieved after calibration by measuring one known material.
首先,本文研究了电磁波逆散射成像问题。高介电常数散射体成像是该领域的一个难题。本文基于子空间理论的优化算法(SOM:Subspace based Optimization Method),进一步利用子空间理论,把散射体图像分解成信号子空间部分和噪声子空间部分,解释了SOM算法反演高介电常数散射体困难的原因。此外本文还在SOM算法中引入了适用于反演块状物体的全变分正则化,能够使图像的物体边缘更加清晰,提高了成像质量。
其次,本文研究了一种基于模式匹配方法的宽频带复介电常数的测量方法。通过在数学模型中考虑高次模式的影响,我们可以采用同轴线的突变结构进行复介电常数的测量。与传统的短路同轴线法相比,本文方法可使用更大尺寸的样品容器、并具有更为简洁的结构和和更加简单的校准过程。
最后,通过借鉴“中距”无线能量传输的原理,提出了一种基于耦合谐振线圈的复介电常数非接触式测量方法。该方法使用高Q谐振线圈作为探头,通过谐振线圈的耦合实现了与标准50欧仪表的阻抗匹配。与传统的磁感应法相比,测量灵敏度得到大幅度提高,并可用于测量小尺寸、低电导率的固体和液体材料。利用瑞利近似,理论上得到了测量阻抗与被测复介电常数之间简洁的数学关系,从而只需测量一个电参数已知的材料即可校准测量装置,进而精确反演其它被测材料的复介电常数。
The measurement and imaging of complex permittivity have enormous applications both in scientific research and industrial engineering. Mathematically, they are both inverse problems. In this dissertation, we focus on the measurement and imaging methods at RF and microwave frequency.
First we discussed about the electromagnetic wave inverse scattering imaging. High contrast scatterer imaging is a difficult problem in this area. In this dissertation, based on the subspace based optimization method (SOM), we further decompose the scatterer image into signal subspace part and noise subspace part, and found the reason of difficulty when applying SOM into high contrast scatterer problem. Moreover, we improved the imaging quality by adding total variation regularization to SOM, which is able to sharpen the edges of image, suitable for blocky scatterer.
Then a broadband complex permittivity measurement method is studied, namely the short circuit coaxial line method. By considering the influence of higher order modes using mode matching method, we adopt coaxial discontinuity structure to measure complex permittivity. Compared to the traditional short circuit coaxial line method, the proposed method enables larger sample holder and the fabrication and calibration process is quite easy.
At last, based on the concept of coupled magnetic resonance used in mid-range wireless power transfer, we propose a non-contact complex permittivity measurement method. In this method, high-Q resonant coils are used as sensors, through the coupling of resonant coils, impedance matching is achieved. Compared to traditional magnetic induction method, the proposed method has much higher sensitivity and is suitable for measuring small sized and low conductivity samples. By using Rayleigh approximation, a concise relation between the measured impedance and sample's complex permittivity can be derived. Thus accurate complex permittivity can be retrieved after calibration by measuring one known material.
引文
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[41]Courtney C C, Motil W. One-port time-domain measurement of the approximate permittivity and permeability of materials[J]. Microwave Theory and Techniques, IEEE Transactions on, 1999,47(5):551-555.
[42]Huang Y. Design, calibration and data interpretation for a one-port large coaxial dielectric measurement cell[J]. Measurement Science and Technology,2001,12(1):1 11.
[43]Caijun Z, Quanxing J, Shenhui J. Calibration-independent and position-insensitive transmission/reflection method for permittivity measurement with one sample in coaxial line[J]. Electromagnetic Compatibility, IEEE Transactions on,2011,53(3):684-689.
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[46]Santos E J, Silva L B, Varzea R. Methodology for Calculation of Scattering Parameters in a Transmission-Line Transducer[J].
[47]Adous M, Qudffelec P, Laguerre L. Coaxial/cylindrical transition line for broadband permittivity measurement of civil engineering materials[J]. Measurement Science and Technology, 2006,17(8):2241.
[48]Belhadj-Tahar N, Fourrier-Lamer A. Broad-band analysis of a coaxial discontinuity used for dielectric measurements [J]. Microwave Theory and Techniques, IEEE Transactions on, 1986,34(3):346-350.
[49]Huang R, Zhang D. Application of mode matching method to analysis of axisymmetric coaxial discontinuity structures used in permeability and/or permittivity measurement[J]. Progress In Electromagnetics Research,2007,67:205-230.
[50]张善杰.工程电磁理论[M].科学出版社,2009.
[51]Blackham D V, Pollard R D. An improved technique for permittivity measurements using a coaxial probe[J]. Instrumentation and Measurement, IEEE Transactions on, 1997,46(5):1093-1099.
[52]Komarov V, Wang S, Tang J. Permittivity and measurements[J]. Encyclopedia of RF and Microwave Engineering,2005.
[53]Orlob C, Reinecke T, Denicke E, et al. Compact Unfocused Antenna Setup for X-Band Free-Space Dielectric Measurements based on Line-Network-Network Calibration Method[J]. 2013.
[54]Ghodgaonkar D K, Varadan V V, Varadan V K. Free-space measurement of complex permittivity and complex permeability of magnetic materials at microwave frequencies[J]. Instrumentation and Measurement, IEEE Transactions on,1990,39(2):387-394.
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[2]陈抗生.电磁场与电磁波[M].高等教育出版社,2007.
[3]王志宇.具有强非线性和旋电效应的有源微波媒质研究[D].浙江大学,2013.
[4]Kaatze U. Measuring the dielectric properties of materials. Ninety-year development from low-frequency techniques to broadband spectroscopy and high-frequency imaging[J]. Measurement Science and Technology,2013,24(1):12005.
[5]倪尔瑚.材料科学中的介电谱技术[M].科学出版社,1999.
[6]Tan E L, Ng W N, Shao R, et al. A wireless, passive sensor for quantifying packaged food quality[J]. Sensors,2007,7(9):1747-1756.
[7]Chew W C, Gianzero S C. Theoretical investigation of the electromagnetic wave propagation tool[J]. Geoscience and Remote Sensing, IEEE Transactions on,1981(1):1-7.
[8]罗海军.磁感应成像用于颅内监护关键技术基础研究[D].重庆大学,2012.
[9]黄卡玛,赵翔.电磁场中的逆问题及应用[M].科学出版社,2005.
[10]Griffiths H, Stewart W R, Gough W. Magnetic induction tomography:a measuring system for biological tissues[J]. Annals Of The New York Academy Of Sciences,1999,873(1):335-345.
[11]Zakaria Z, Rahim R A, Mansor M S B, et al. Advancements in transmitters and sensors for biological tissue imaging in Magnetic Induction Tomography [J]. Sensors,2012,12(6):7126-7156.
[12]Vauhkonen M, Hamsch M, Igney C H. A measurement system and image reconstruction in magnetic induction tomography [J]. Physiological Measurement,2008,29(6):S445.
[13]Van Den Berg P M, Kleinman R E. A contrast source inversion method[J]. Inverse problems, 1997,13(6):1607.
[14]Devaney A J, Oristaglio M L. Inversion procedure for inverse scattering within the distorted-wave Bom approximation[J]. Physical Review Letters,1983,51(4):237.
[15]Donelli M, Massa A. Computational approach based on a particle swarm optimizer for microwave imaging of two-dimensional dielectric scatterers[J]. Microwave Theory and Techniques, IEEE Transactions on,2005,53(5):1761-1776.
[16]Meng Z Q, Takenaka T, Tanaka T. Image reconstruction of two-dimensional impenetrable objects using genetic algorithm[J]. Journal of electromagnetic waves and applications, 1999,13(1):95-118.
[17]Kaatze U. Techniques for measuring the microwave dielectric properties of materials[J]. Metrologia,2010,47(2):S91.
[18]Gregory A P, Clarke R N. A review of RF and microwave techniques for dielectric measurements on polar liquids[J]. Dielectrics and Electrical Insulation, IEEE Transactions on, 2006,13(4):727-743.
[19]Kaatze U, Feldman Y. Broadband dielectric spectrometry of liquids and biosystems[J]. Measurement Science and Technology,2006,17(2):R17.
[20]Nelson S O. Dielectric properties measurement techniques and applications[J]. Transactions of the ASAE-American Society of Agricultural Engineers,1999,42(2):523-530.
[21]Raymond W J K, Chakrabarty C K, Hock G C, et al. Complex permittivity measurement using capacitance method from 300kHz to 50MHz[J]. Measurement,2013,46(10):3796-3801.
[22]Yu K B, Ogourtsov S G, Belenky V G, et al. Accurate microwave resonant method for complex permittivity measurements of liquids [biological][J]. Microwave Theory and Techniques, IEEE Transactions on,2000,48(11):2159-2164.
[23]Baker-Jarvis J, Janezic M D, Grosvenor Jr J H, et al. Transmission/reflection and short-circuit line methods for measuring permittivity and permeability[J]. NASA STI/Recon Technical Report N, 1992,93:12084.
[24]Nicolson A M, Ross G F. Measurement of the intrinsic properties of materials by time-domain techniques[J]. Instrumentation and Measurement, IEEE Transactions on,1970,19(4):377-382.
[25]Gregory A P, Clarke R N. Dielectric metrology with coaxial sensors[J]. Measurement Science and Technology,2007,18(5):1372.
[26]陈春平.开口同轴探头同时测量复电磁参数技术理论研究与实践[D].上海大学,2004.
[27]Wu M, Yao X, Zhang L. An improved coaxial probe technique for measuring microwave permittivity of thin dielectric materials[J]. Measurement Science and Technology, 2000,11(11):1617.
[28]Kraftmakher Y. Eddy currents:Contactless measurement of electrical resistiviry[J]. American Journal of Physics,2000,68:375.
[29]Delaney J A, Pippard A B. Electrodeless methods for conductivity measurement in metals[J]. Reports on Progress in Physics,1972,35(2):677.
[30]Barai A, Watson S, Griffiths H, et al. Magnetic induction spectroscopy:non-contact measurement of the electrical conductivity spectra of biological samples[J]. Measurement Science and Technology,2012,23(8):85501.
[31]Chen X. Subspace-based optimization method for solving inverse-scattering problems[J]. Geoscience and Remote Sensing, IEEE Transactions on,2010,48(1):42-49.
[32]Chew W C, Wang Y M. Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method[J]. Medical Imaging, IEEE Transactions on,1990,9(2):218-225.
[33]van den Berg P M, Abubakar A, Fokkema J T. Multiplicative regularization for contrast profile inversion[J]. Radio Science,2003,38(2).
[34]van den Berg P M, Van Broekhoven A L, Abubakar A. Extended contrast source inversion[J]. Inverse Problems,1999,15(5):1325.
[35]Chen X. Application of signal-subspace and optimization methods in reconstructing extended scatterers[J]. JOSA A,2009,26(4):1022-1026.
[36]Zhong Y, Chen X. Twofold subspace-based optimization method for solving inverse scattering problems[J]. Inverse Problems,2009,25(8):85003.
[37]Peterson A F, Ray S L, Mittra R. Computational methods for electromagnetics[M]. IEEE press New York,1998.
[38]Agarwal K, Song R, D'Urso M, et al. Improving the Performances of the Contrast Source Extended Bom Inversion Method by Subspace Techniques[J].2013.
[39]Rudin L I, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms [J]. Physica D:Nonlinear Phenomena,1992,60(1):259-268.
[40]Roberts S, Von Hippel A. A new method for measuring dielectric constant and loss in the range of centimeter waves[J]. Journal of Applied Physics,1946,17(7):610-616.
[41]Courtney C C, Motil W. One-port time-domain measurement of the approximate permittivity and permeability of materials[J]. Microwave Theory and Techniques, IEEE Transactions on, 1999,47(5):551-555.
[42]Huang Y. Design, calibration and data interpretation for a one-port large coaxial dielectric measurement cell[J]. Measurement Science and Technology,2001,12(1):1 11.
[43]Caijun Z, Quanxing J, Shenhui J. Calibration-independent and position-insensitive transmission/reflection method for permittivity measurement with one sample in coaxial line[J]. Electromagnetic Compatibility, IEEE Transactions on,2011,53(3):684-689.
[44]Cataldo A, Catarinucci L, Tarricone L, et al. A combined TD-FD method for enhanced reflectometry measurements in liquid quality monitoring[J]. Instrumentation and Measurement, IEEE Transactions on,2009,58(10):3534-3543.
[45]Cataldo A, Piuzzi E, Cannazza G, et al. Dielectric spectroscopy of liquids through a combined approach:evaluation of the metrological performance and feasibility study on vegetable oils[J]. Sensors Journal, IEEE,2009,9(10):1226-1233.
[46]Santos E J, Silva L B, Varzea R. Methodology for Calculation of Scattering Parameters in a Transmission-Line Transducer[J].
[47]Adous M, Qudffelec P, Laguerre L. Coaxial/cylindrical transition line for broadband permittivity measurement of civil engineering materials[J]. Measurement Science and Technology, 2006,17(8):2241.
[48]Belhadj-Tahar N, Fourrier-Lamer A. Broad-band analysis of a coaxial discontinuity used for dielectric measurements [J]. Microwave Theory and Techniques, IEEE Transactions on, 1986,34(3):346-350.
[49]Huang R, Zhang D. Application of mode matching method to analysis of axisymmetric coaxial discontinuity structures used in permeability and/or permittivity measurement[J]. Progress In Electromagnetics Research,2007,67:205-230.
[50]张善杰.工程电磁理论[M].科学出版社,2009.
[51]Blackham D V, Pollard R D. An improved technique for permittivity measurements using a coaxial probe[J]. Instrumentation and Measurement, IEEE Transactions on, 1997,46(5):1093-1099.
[52]Komarov V, Wang S, Tang J. Permittivity and measurements[J]. Encyclopedia of RF and Microwave Engineering,2005.
[53]Orlob C, Reinecke T, Denicke E, et al. Compact Unfocused Antenna Setup for X-Band Free-Space Dielectric Measurements based on Line-Network-Network Calibration Method[J]. 2013.
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