References & Further Reading

References

1. W. C. Chew, Waves and Fields in Inhomogeneous Media, IEEE Press, 1995

   The definitive reference on electromagnetic scattering in inhomogeneous media. Covers Green's functions, volume and surface integral equations, the Born and Rytov approximations, and fast algorithms. Sections 5.1--5.6 follow Chew's framework.

2. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Springer, 3rd edition ed., 2013

   The mathematical standard for scattering theory and inverse problems. Provides rigorous existence, uniqueness, and regularity results for the Helmholtz and Maxwell equations.

3. M. Born and E. Wolf, Principles of Optics, Cambridge University Press, 7th edition ed., 1999

   The classic optics text covering diffraction theory, the Born approximation, and the optical theorem.

4. J. D. Jackson, Classical Electrodynamics, Wiley, 3rd edition ed., 1999

   Graduate-level treatment of Maxwell's equations, Green's functions, and radiation theory.

5. A. Ishimaru, Wave Propagation and Scattering in Random Media, Academic Press, 1978

   Covers both the Born and Rytov approximations with emphasis on propagation through random media. Section 5.5 on the Rytov approximation follows Ishimaru's treatment.

6. C. A. Balanis, Advanced Engineering Electromagnetics, Wiley, 2nd edition ed., 2012

   Comprehensive treatment of electromagnetic scattering, RCS, and antenna theory. Sections 5.7 draws on Balanis for canonical RCS formulas.

7. P. M. van den Berg and R. E. Kleinman, A Contrast Source Inversion Method, 1997

   Introduces the contrast source inversion (CSI) method that avoids forward solves in iterative inverse scattering.

8. A. J. Devaney, Mathematical Foundations of Imaging, Tomography and Wavefield Inversion, Cambridge University Press, 2012

   Unified mathematical treatment of diffraction tomography, the Fourier diffraction theorem, and Born/Rytov approximations.

9. G. Caire, A. Rezaei, and W. Jiang, On the Illumination and Sensing Model for RF Imaging, 2023

   Derives the unified Born forward model for RF imaging with OFDM-MIMO signaling, showing the equivalence of the diffraction-tomography and radar views.

10. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging, SIAM, 2001

    Covers both X-ray and diffraction tomography, providing the Fourier-slice and Fourier-diffraction theorems.

11. M. Pastorino, Microwave Imaging, Wiley, 2010

    Comprehensive treatment of microwave imaging for biomedical and nondestructive testing applications.

Further Reading

• Fast multipole methods for scattering

  W. C. Chew, J.-M. Jin, E. Michielssen, and J. Song, *Fast and Efficient Algorithms in Computational Electromagnetics*, Artech House, 2001

  Presents the FMM and related algorithms that reduce MoM forward solves from $O(N^2)$ to $O(N\log N)$, enabling large-scale DBIM inversions.

• Nonlinear inverse scattering methods

  T. M. Habashy, R. W. Groom, and B. R. Spies, *Beyond the Born and Rytov approximations*, J. Geophys. Res., 1993

  Develops extended Born and localized nonlinear approximations that bridge first-order linearizations and full nonlinear inversion.

• Diffraction tomography

  A. C. Kak and M. Slaney, *Principles of Computerized Tomographic Imaging*, SIAM, 2001

  Covers the Fourier-slice and Fourier-diffraction theorems that connect scattering measurements to Fourier-space coverage.

• Electromagnetic scattering computation

  A. F. Peterson, S. L. Ray, and R. Mittra, *Computational Methods for Electromagnetics*, IEEE Press, 1998

  Detailed treatment of MoM, FDTD, and FEM for solving forward scattering problems — the computational engines behind DBIM.