PART I - FUNDAMENTALS Introduction Background Inverse Scattering Problem Overview Diffraction Tomography Theoretical Issues and Concerns Electromagnetic Waves Maxwell''s Equations Green Functions Plane Waves Evanescent and Propagating Waves Scattering Fundamentals Material Properties and Modeling Weak Scatterers Scattering from Compact Structures Inverse Scattering Fundamentals Categorization of Inverse Scattering Problems Inverse Scattering in Two Dimensions First Born Approximation Rytov Approximation PART II - INVERSION METHODS Data Processing Data Inversion in " k " Space: A Fourier Perspective Target Modeling and Data Generation Target Modeling Environment Imaging Algorithm Implementations: Example Reconstructions Born Approximation Observations Degrees of Freedom Requirements for Degrees of Freedom for Sources Requirement for Degrees of Freedom for Receivers Relationship Between Born Approximation and Mie Q Factor Alternate Inverse Methods Iterative Methods Born Iterative Method Distorted Born Iterative Method Conjugate Gradient Method Prior Discrete Fourier Transform Homomorphic (Cepstral) Filtering Cepstral Filtering Cepstral Filtering with Minimum Phase Generating the Minimum Phase Function Preprocessing Data Two Dimensional Filter Methods Removing the Reference PART III - APPLICATIONS Applications to Real Measured Data Ipswich Data Results Institut Fresnel Data Results Comparison of Reconstruction Methods Final Observations and Summary Advanced Cepstral Filtering Processing Source Data Independently Effects of Modified Filters in Cepstral Domain Effects of Random Under-Sampling Advanced Topics in Inverse Imaging Practical Steps for Imaging Strong Scatterers An Overall Approach to Degrees of Freedom in Imaging Conclusion PART IV - APPENDECIES Appendix A - Fourier Analysis Review Appendix B - The Phase Retrieval Problem Appendix C - Prior Discrete Fourier Transform Appendix D - The Poynting Vector Appendix E - Resolution and Degrees of Freedom Appendix F - MATLAB®Exercises with COMSOL® Data ART II - INVERSION METHODS Data Processing Data Inversion in " k " Space: A Fourier Perspective Target Modeling and Data Generation Target Modeling Environment Imaging Algorithm Implementations: Example Reconstructions Born Approximation Observations Degrees of Freedom Requirements for Degrees of Freedom for Sources Requirement for Degrees of Freedom for Receivers Relationship Between Born Approximation and Mie Q Factor Alternate Inverse Methods Iterative Methods Born Iterative Method Distorted Born Iterative Method Conjugate Gradient Method Prior Discrete Fourier Transform Homomorphic (Cepstral) Filtering Cepstral Filtering Cepstral Filtering with Minimum Phase Generating the Minimum Phase Function Preprocessing Data Two Dimensional Filter Methods Removing the Reference PART III - APPLICATIONS Applications to Real Measured Data Ipswich Data Results Institut Fresnel Data Results Comparison of Reconstruction Methods Final Observations and Summary Advanced Cepstral Filtering Processing Source Data Independently Effects of Modified Filters in Cepstral Domain Effects of Random Under-Sampling Advanced Topics in Inverse Imaging Practical Steps for Imaging Strong Scatterers An Overall Approach to Degrees of Freedom in Imaging Conclusion PART IV - APPENDECIES Appendix A - Fourier Analysis Review Appendix B - The Phase Retrieval Problem Appendix C - Prior Discrete Fourier Transform Appendix D - The Poynting Vector Appendix E - Resolution and Degrees of Freedom Appendix F - MATLAB®Exercises with COMSOL® Data ) Filtering Cepstral Filtering Cepstral Filtering with Minimum Phase Generating the Minimum Phase Function Preprocessing Data Two Dimensional Filter Methods Removing the Reference PART III - APPLICATIONS Applications to Real Measured Data Ipswich Data Results Institut Fresnel Data Results Comparison of Reconstruction Methods Final Observations and Summary Advanced Cepstral Filtering Processing Source Data Independently Effects of Modified Filters in Cepstral Domain Effects of Random Under-Sampling Advanced Topics in Inverse Imaging Practical Steps for Imaging Strong Scatterers An Overall Approach to Degrees of Freedom in Imaging Conclusion PART IV - APPENDECIES Appendix A - Fourier Analysis Review Appendix B - The Phase Retrieval Problem Appendix C - Prior Discrete Fourier Transform Appendix D - The Poynting Vector Appendix E - Resolution and Degrees of Freedom Appendix F - MATLAB®Exercises with COMSOL® Data ;/P> An Overall Approach to Degrees of Freedom in Imaging Conclusion PART IV - APPENDECIES Appendix A - Fourier Analysis Review Appendix B - The Phase Retrieval Problem Appendix C - Prior Discrete Fourier Transform Appendix D - The Poynting Vector Appendix E - Resolution and Degrees of Freedom Appendix F - MATLAB®Exercises with COMSOL® Data.