Sensitivity Analysis for Antenna Near-Field Imaging

Although imaging and inverse scattering problems have been thoroughly studied during the last century, there is only a partial understanding of these complex problems. Most of the efforts have been placed on the development of efficient inversion algorithms and mathematical uniqueness results. In comparison, there are very few results and a limited knowledge about the information content in the inversion data. In this paper, we provide a mathematical framework for sensitivity analysis of antenna near-field imaging problems, based on the multipole expansion of the electromagnetic field and the Fisher information to quantify the quality of data. By exploiting this framework, a fundamental relation for accuracy and resolution is formulated based on the Crameacuter-Rao bound (CRB). The sensitivity analysis is illustrated using a relevant example with cylindrical measurement data

[1]  Arye Nehorai,et al.  Estimating Directions-of-Arrival of Completely and Incompletely Polarized Signals with Electromagnetic Vector Sensors , 1997 .

[2]  S.T. Smith.  Statistical Resolution Limits and the Complexified , 2005 .

[3]  S. T. Smith.  Statistical resolution limits and the complexified Crame/spl acute/r-Rao bound , 2005, IEEE Transactions on Signal Processing.

[4]  L. Marton,et al.  Advances in Electronics and Electron Physics , 1958 .

[5]  K. T. Wong,et al.  Closed-form direction finding and polarization estimation with arbitrarily spaced electromagnetic vector-sensors at unknown locations , 2000 .

[6]  M. Brereton.  Classical Electrodynamics (2nd edn) , 1976 .

[7]  M.,et al.  Subspace Fitting with Diversely Polarized Antenna Arrays , 2009 .

[8]  R.M. Jha,et al.  Tuning of EM performance for streamlined aircraft radomes , 2004, IEEE Antennas and Propagation Society Symposium, 2004..

[9]  M. Bertero.  Linear Inverse and III-Posed Problems , 1989 .

[10]  Mats Gustafsson,et al.  Wave Splitting in Direct and Inverse Scattering Problems , 2000 .

[11]  A. Lee Swindlehurst,et al.  Subspace Fitting with Diversely Polarized Antenna Arrays , 1993 .

[12]  A. Kirsch.  An Introduction to the Mathematical Theory of Inverse Problems , 1996, Applied Mathematical Sciences.

[13]  Björn E. Ottersten,et al.  Maximum likelihood array processing in spatially correlated noise fields using parameterized signals , 1997, IEEE Trans. Signal Process..

[14]  Sven Nordebo,et al.  Microwave modelling and measurements for early detection of spiral grain in wood , 2005 .

[15]  S. Kay.  Fundamentals of statistical signal processing: estimation theory , 1993 .

[16]  Jian Li,et al.  Efficient parameter estimation of partially polarized electromagnetic waves , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[17]  S. B. Childs,et al.  INVERSE PROBLEMS IN PARTIAL DIFFERENTIAL EQUATIONS. , 1968 .

[18]  M. Viberg,et al.  Two decades of array signal processing research: the parametric approach , 1996, IEEE Signal Process. Mag..

[19]  Thomas Lenart,et al.  High resolution digital transmission microscopy : a Fourier holography approach , 2004 .

[20]  Francesco Soldovieri,et al.  On the information content of the radiated fields in the near zone over bounded domains , 1998 .

[21]  Steven Kay,et al.  Fundamentals Of Statistical Signal Processing , 2001 .

[22]  E. Wolf,et al.  Principles of Optics (7th Ed) , 1999 .

[23]  D. A. Dunnett.  Classical Electrodynamics , 2020, Nature.

[24]  G. Arfken,et al.  Mathematical methods for physicists 6th ed. , 1996 .

[25]  Jian Li,et al.  Efficient parameter estimation of partially polarized electromagnetic waves , 1994, IEEE Trans. Signal Process..

[26]  Arye Nehorai,et al.  Estimating directions of arrival of completely and incompletely polarized signals with electromagnetic vector sensors , 1999, IEEE Trans. Signal Process..

[27]  Benjamin Friedlander,et al.  Maximum likelihood signal estimation for polarization sensitive arrays , 1993 .

[28]  Mats Gustafsson,et al.  Statistical signal analysis for the inverse source problem of electromagnetics , 2006, IEEE Transactions on Signal Processing.

[29]  Richard W. Ziolkowski,et al.  Nonradiating and minimum energy sources and their fields: generalized source inversion theory and applications , 2000 .

[30]  Mats Gustafsson,et al.  Multichannel broadband Fano theory for arbitrary lossless antennas with applications in DOA estimation , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[31]  Arthur D. Yaghjw.  An Overview of Near-Field Antenna Measurements , 2009 .

[32]  Vito Pascazio,et al.  Subsurface inverse scattering problems: quantifying, qualifying, and achieving the available information , 2001, IEEE Trans. Geosci. Remote. Sens..

[33]  Michael A. Jensen,et al.  Analysis of electromagnetic field polarizations in multiantenna systems , 2004, IEEE Transactions on Wireless Communications.

[34]  J. Davenport.  Editor , 1960 .

[35]  Mats Gustafsson,et al.  Reconstruction of equivalent currents using a near-field data transformation - with radome applications , 2004 .

[36]  V. Isakov.  Appendix -- Function Spaces , 2017 .

[37]  R. Collin,et al.  Evaluation of antenna Q , 1964 .

[38]  G. Arfken.  Mathematical Methods for Physicists , 1967 .