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Computational Electromagnetics & Computational Bioimaging

Computational Electromagnetics & Computational Bioimaging. Qianqian Fang Research In Progress (RIP 2004). Outline. Macroscopic Electromagnetics Computational Electromagnetics (CEM) Inverse Problems Computational Biomedical Imaging (CBI) CBI and CEM. From DC to Light. Circuit Theory.

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Computational Electromagnetics & Computational Bioimaging

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  1. Computational Electromagnetics&Computational Bioimaging Qianqian Fang Research In Progress (RIP 2004)

  2. Outline • Macroscopic Electromagnetics • Computational Electromagnetics (CEM) • Inverse Problems • Computational Biomedical Imaging (CBI) • CBI and CEM

  3. From DC to Light Circuit Theory Matrix Electromagnetics Wave Electromagnetics Quantum Mechanics Optics http://www.lbl.gov/MicroWorlds/ALSTool/EMSpec/EMSpec2.html

  4. Electromagnetism • Macroscopic Electromagnetism • Foundation • Core equations • Core theorems • Wave (amplitudes,phase,wavelength,polarization..) • Radiation • Scattering • Circuit(Network)(impedance,S parameters,power,gain...) • Distributed parameter circuit networks analysis • Filter design • Quantum Electro-Dynamics (QED)

  5. Macroscopic Electromagnetics Core Wave equations Transient EM wave/ Time-Harmonic EM wave/ Time/Frequency domain/ Vector/Scalar Helmholtz equation Vector/Scalar Wave equation Energy Conservation Poynting theorem Maxwell equations Momentum Conservation Constitutive relations Boundary Conditions Auxiliary Functions vector/scalar elec. potential vector/scalar mag. potential vector/scalar Herzian potential Scalar/dyadic Green’s function Material Properties: isotropic/anisotropic/ Bi-anisotropic/uniaxial/ Positive/negative axial/ Dispersive/stationary Lorenz force Mechanics

  6. Electromagnetics: Core Theorems Duality Principal Uniqueness Theorem Green’s Theorem Huygens’ Principal Reciprocity Theorem Equivalence Theorem

  7. Computational Electromagnetics • Definition • Numerical <-> Linearization • High-frequency-> geometric approx • Low-frequency-> difference/variational

  8. Computational Electromagnetics

  9. Forward: Integration • Integration Equation: MoM, BEM, EFIE/MFIE/CFIE http://www.lcp.nrl.navy.mil/cfd-cta/CFD3/img_gallery/f117/

  10. Forward: Differential Finite Element Method (FEM) Finite Difference-Time Domain (FDTD) http://www.remcom.com/xfdtd6/ http://sdcd.gsfc.nasa.gov/ESS/annual.reports/ess98/kma.html

  11. Comparison: IE/DE

  12. response known structure known System Parameter Source source unknown Forward operator Measurement source known structure unknown mine response known Inverse Problems • Inverse Source Problems • Inverse Scattering Problems • Mixed Inverse Problems

  13. Approaches of Solving Inverse Problems • Operator Equation • Root Finding • Optimization Misfit functional Regularization functional

  14. Biomedical Imaging • Principal • Encoding/Decoding of information • Imaging Agent • Functional Imaging and Structural Imaging

  15. CBI and CEM • CT -> Linear attenuation -> Filted Backprojection -> Linear Inverse problem • MRI -> Inverse Fourier Transform • Ultrasound • EIT, MWI, NIR, GPR, …-> Nonlinear propagation -> iterative reconstructions -> Nonlinear inverse problem

  16. Reference • W.C. Chew, “Waves and Fields in Inhomogeneous Media,” Van Nostrand Reinhold, New York, 1990. • J.A. Kong, “Electromagnetic Wave Theory,” Wiley-Interscience, New York, 1990. • Yvon Jarny, “The Inverse Engineering Handbook, Chapter 3”, CRC Press, 2003. • C. Vogel, “Computational methods for inverse problem,” SIAM, Philadelphia, 2002.

  17. Acknowledgement • Prof. Paul M. Meaney • Prof. Keith D. Paulsen • Margaret Fanning • Dun Li • Sarah A. Pendergrass • Colleen J. Fox • Timothy Raynolds Thanks for all my friends at Thayer School.

  18. Questions?

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