Diffraction Tomography in Dispersive Backgrounds Tony Devaney Dept. Elec. And Computer Engineering Northeastern University Boston, MA 02115

Slides:



Advertisements
Similar presentations
Z-Plane Analysis DR. Wajiha Shah. Content Introduction z-Transform Zeros and Poles Region of Convergence Important z-Transform Pairs Inverse z-Transform.
Advertisements

Signal Processing in the Discrete Time Domain Microprocessor Applications (MEE4033) Sogang University Department of Mechanical Engineering.
Chapter 1 Electromagnetic Fields
December 04, 2000A.J. Devaney--Mitre presentation1 Detection and Estimation of Buried Objects Using GPR A.J. Devaney Department of Electrical and Computer.
EEE 498/598 Overview of Electrical Engineering
Ray theory and scattering theory Ray concept is simple: energy travels between sources and receivers only along a “pencil-thin” path (perpendicular to.
Vermelding onderdeel organisatie 1 Janne Brok & Paul Urbach CASA day, Tuesday November 13, 2007 An analytic approach to electromagnetic scattering problems.
Evaluation of Definite Integrals Via the Residue Theorem
Propagators and Green’s Functions
Quantum Optics SUPERLUMINALITY: Breaking the Universal Speed Limit 21 April Brian Winey Department of Physics and Astronomy University of Rochester.
Physics 481/581 Physical Optics Instructor: Oksana Ostroverkhova Weniger 413 Class TA: Matt Cibula
Head Waves, Diving Waves and Interface Waves at the Seafloor Ralph Stephen, WHOI ASA Fall Meeting, Minneapolis October 19, 2005 Ralph Stephen, WHOI ASA.
Department of Computer Science
Introduction: Optical Microscopy and Diffraction Limit
University of Utah Advanced Electromagnetics Image Theory Dr. Sai Ananthanarayanan University of Utah Department of Electrical and Computer Engineering.
Nanoparticle Polarizability Determination Using Coherent Confocal Microscopy Brynmor J. Davis and P. Scott Carney University of Illinois at Urbana-Champaign.
RIP Computational Electromagnetics & Computational Bioimaging Qianqian Fang Research In Progress (RIP 2004)
Prof. David R. Jackson ECE Dept. Spring 2014 Notes 6 ECE
Thin films II Kinematic theory - works OK for mosaic crystals & other imperfect matls Doesn't work for many, more complicated films Kinematic theory -
Medical Image Analysis Dr. Mohammad Dawood Department of Computer Science University of Münster Germany.
Medical Imaging Dr. Mohammad Dawood Department of Computer Science University of Münster Germany.
18/14/2015 Three-dimensional Quantitative Ultrasound Imaging A.J. Devaney Department of electrical and computer engineering Northeastern university Boston,
Fast (finite) Fourier Transforms (FFTs) Shirley Moore CPS5401 Fall 2013 svmoore.pbworks.com December 5,
Consider a time dependent electric field E(t) acting on a metal. Take the case when the wavelength of the field is large compared to the electron mean.
August, 1999A.J. Devaney Stanford Lectures-- Lecture I 1 Introduction to Inverse Scattering Theory Anthony J. Devaney Department of Electrical and Computer.
10/17/97Optical Diffraction Tomography1 A.J. Devaney Department of Electrical Engineering Northeastern University Boston, MA USA
1 EEE 498/598 Overview of Electrical Engineering Lecture 11: Electromagnetic Power Flow; Reflection And Transmission Of Normally and Obliquely Incident.
Scattering by particles
1 Chapter 2 Wave motion August 25,27 Harmonic waves 2.1 One-dimensional waves Wave: A disturbance of the medium, which propagates through the space, transporting.
October 21, 2005A.J. Devaney IMA Lecture1 Introduction to Wavefield Imaging and Inverse Scattering Anthony J. Devaney Department of Electrical and Computer.
BMI I FS05 – Class 9 “Ultrasound Imaging” Slide 1 Biomedical Imaging I Class 9 – Ultrasound Imaging Doppler Ultrasonography; Image Reconstruction 11/09/05.
D. R. Wilton ECE Dept. ECE 6382 Functions of a Complex Variable as Mappings 8/24/10.
Lale T. Ergene Fields and Waves Lesson 5.3 PLANE WAVE PROPAGATION Lossy Media.
Linear optical properties of dielectrics
Gratings and the Plane Wave Spectrum
So far, we have considered plane waves in an infinite homogeneous medium. A natural question would arise: what happens if a plane wave hits some object?
Remcom Inc. 315 S. Allen St., Suite 416  State College, PA  USA Tel:  Fax:   ©
Lecture 13  Last Week Summary  Sampled Systems  Image Degradation and The Need To Improve Image Quality  Signal vs. Noise  Image Filters  Image Reconstruction.
Jan 2001AFOSR San Antonio Meeting Inverse Source Problem A.J. Devaney and Mei-Li, “The inverse source problem in non-homogeneous background media”, accepted.
1 Waveguides. Copyright © 2007 Oxford University Press Elements of Electromagnetics Fourth Edition Sadiku2 Figure 12.1 Typical waveguides.
Tatiana Yu. Alekhina and Andrey V. Tyukhtin Physical Faculty of St. Petersburg State University, St. Petersburg, Russia Radiation of a Charge in a Waveguide.
Fourier transform from r to k: Ã(k) =  A(r) e  i k r d 3 r Inverse FT from k to r: A(k) = (2  )  3  Ã(k) e +i k r d 3 k X-rays scatter off the charge.
4.Dirichlet Series Dirichlet series : E.g.,(Riemann) Zeta function.
Wave Physics PHYS 2023 Tim Freegarde. Fourier transforms Uses of Fourier transforms: Reveal which frequencies/wavenumbers are present identification or.
WAVE PACKETS & SUPERPOSITION
Evaluation of Definite Integrals via the Residue Theorem
Fresnel diffraction formulae
Evaluation of Definite Integrals via the Residue Theorem
UPB / ETTI O.DROSU Electrical Engineering 2
Theory of Scattering Lecture 2.
Plasmonic waveguide filters with nanodisk resonators
Notes 17 ECE 6340 Intermediate EM Waves Fall 2016
Introduction to Diffraction Tomography
ECE 6382 Notes 1 Introduction to Complex Variables Fall 2017
Reza Firoozabadi, Eric L. Miller, Carey M. Rappaport and Ann W
Choosing Mesh Spacings and Mesh Dimensions for Wave Optics Simulation
Diffraction T. Ishikawa Part 1 Kinematical Theory 1/11/2019 JASS02.
ECE 6341 Spring 2016 Prof. David R. Jackson ECE Dept. Notes 35.
Scalar theory of diffraction
Scalar theory of diffraction
Scalar theory of diffraction
Interference P47 – Optics: Unit 6.
Scalar theory of diffraction
Scalar theory of diffraction
SPACE TIME Fourier transform in time Fourier transform in space.
Notes 9 Transmission Lines (Frequency Domain)
Electric field amplitude time A Bandwidth limited pulse
Scalar theory of diffraction
Theoretical Background Challenges and Significance
Presentation transcript:

Diffraction Tomography in Dispersive Backgrounds Tony Devaney Dept. Elec. And Computer Engineering Northeastern University Boston, MA A.J. Devaney, “Linearized inverse scattering in attenuating media,” Inverse Problems 3 (1987) Other approaches discussed in: A. Schatzberg and A.J.D., ``Super-resolution in diffraction tomography, Inverse Problems 8 (1992) K. Ladas and A.J.D., ``Iterative methods in geophysical diffraction tomography, Inverse Problems 8 (1992) R. Deming and A.J.D., ``Diffraction tomography for multi-monostatic gpr, Inverse Problems 13 (1997) 29-45

Experimental Configuration n(  ) s0s0 s O(r,  ) Generalized Projection-Slice Theorem E. Wolf, Principles and development of diffraction tomography, Trends in Optics, Anna Consortini, ed. [Academic Press, San Diego, 1996]

Born Inverse Scattering Ewald Spheres Forward scatter data Back scatter data z Limiting Ewald Sphere Ewald Sphere k 2k k=real valued

Born Inversion for Fixed Frequency Inversion Algorithms: Fourier interpolation (classical X-ray crystallography) Filtered backpropagation (diffraction tomography) Problem: How to generate inversion from Fourier data on spherical surfaces A.J.D. Opts Letts, 7, p.111 (1982) Filtering of data followed by backpropagation: Filtered Backpropagation Algorithm Fourier based methods fail if k is complex: Need new theory

Pulse Propagation in a Dispersive Background n(  ) s0s0 s O(r,  )

Fourier Transformed Scattered Field Choose a complex frequency  0 such that k (  0 ) is real valued There is no reason a priori to dismiss this possibility, but will it work? Close in u.h.p. Roots of dispersion relationship with real k are in l.h.p.

Simple Conducting Medium Real valued Complex in l.h.p. Complex  plane Desired frequency  0 Im  Re  X  <0 Will not be able to close in u.h.p.: can only drop contour to branch points X Branch point

Lorentz Model b 2= 20x10 32  0= 16x10 16  =.28x10 16 Real n Imag n K.E. Oughstun and G.C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics [Springer-Verlag, 1994, New York]

Lorentz Medium X Complex  plane Branch Cuts Im  Re  Desired frequency  0  <0 Roots of dispersion relationship must lie above branch points -- Im  0 >-  x x Poles of n(  ) -- ++

Contour Plot of Re ik(  ) Real k Branch point Re  Im 

Mesh Plot of Re ik(  )

Exciting the Plane Wave s0s0 O(r,  ) n(  ) Non-attenuating mode of medium Close in l.h.p.

The Complete Pulse X X Complex  plane Branch Cuts Precursors Im  Re  Can the non-attenuating plane wave be excited; i.e., is it dominated by the precursors? 00 -0-0

Asymptotic Analysis K.E. Oughstun and G.C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics [Springer-Verlag, 1994, New York] XX Complex  plane Im  Re  00 -0-0 X X X XX Plane wave excited Plane wave not excited Steepest Descent Contour Saddle point

Summary and Questions Have reviewed one possible approach to inversion in dispersive backgrounds Method is based on computing the temporal Fourier transform of pulsed data at complex frequencies for which the wavenumber of the background is real Method will not work for simple conducting media but appears feasible for Lorentz media The idea behind the approach suggests that it may be possible to excite non-decaying, plane wave pulses using complex frequencies Asymptotic analysis is required to determine the feasibility of the theory