References & Further Reading

References

1. E. Wolf, Three-Dimensional Structure Determination of Semi-Transparent Objects from Holographic Data, vol. 1, no. 4, pp. 153--156, 1969

   The original paper establishing the Fourier diffraction theorem. Section s02 follows Wolf's derivation.

2. A. J. Devaney, A Filtered Backpropagation Algorithm for Diffraction Tomography, vol. 4, no. 4, pp. 336--350, 1982

   Introduces filtered back-propagation for diffraction tomography and the multi-frequency extension. Sections s02--s03 adapt this to RF imaging.

3. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging, Society for Industrial and Applied Mathematics (SIAM), 2001

   The definitive textbook on CT reconstruction. Section s01 follows Kak and Slaney's presentation of the Fourier slice theorem and FBP.

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

   Comprehensive reference for diffraction theory, the Ewald sphere, and the Born and Rytov approximations used in Sections s02 and s04.

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

   Essential reference for Green's functions, scattering theory, and near-field spectral representations used in Section s04.

6. J. G. Pipe and P. Menon, Sampling Density Compensation in MRI with Gridding, vol. 41, no. 1, pp. 179--186, 1999

   The iterative density compensation algorithm adapted for non-uniform Fourier sampling in Section s02.

7. A. Dutt and V. Rokhlin, Fast Fourier Transforms for Nonequispaced Data, vol. 14, no. 6, pp. 1368--1393, 1993

   Foundational paper on the NUFFT used for efficient gridding in Section s02.

8. F. Simonetti, Multiple Scattering: The Key to Unravel the Subwavelength World from the Far-Field Pattern of a Scattered Wave, vol. 73, no. 3, 036619, 2006

   Demonstrates that multiple scattering provides sub-wavelength resolution from far-field data. Referenced in Section s04 super-resolution discussion.

9. P. M. Meaney, M. W. Fanning, D. Li, S. P. Poplack, and K. D. Paulsen, A Clinical Prototype for Active Microwave Imaging of the Breast, vol. 48, no. 11, pp. 1841--1853, 2000

   Pioneering near-field microwave imaging system. Section s04 discusses near-field considerations.

10. K. H. Jin, M. T. McCann, E. Froustey, and M. Unser, Deep Convolutional Neural Network for Inverse Problems in Imaging, vol. 26, no. 9, pp. 4509--4522, 2017

    Introduces FBPConvNet: U-Net post-processing of FBP reconstructions. Section s01 discusses the FBP-to-CNN paradigm.

11. W. C. Chew and Y. M. Wang, Reconstruction of Two-Dimensional Permittivity Distribution Using the Distorted Born Iterative Method, vol. 9, no. 2, pp. 218--225, 1990

    Extends diffraction tomography beyond the Born approximation via iterative linearization.

Further Reading

• Full-waveform inversion

  J. Virieux and S. Operto, *An Overview of Full-Waveform Inversion in Exploration Geophysics*, Geophysics, 2009

  Generalizes diffraction tomography to strongly scattering media by iteratively solving the full wave equation -- the natural extension for objects violating the Born approximation.

• Compressed sensing for DT

  L. Li, W. Zhang, and F. Li, *A Novel Autofocusing Approach for Compressive Sensing Diffraction Tomography*, IEEE Trans. Antennas Propagat., 2014

  Combines the Fourier diffraction framework with sparse recovery algorithms for undersampled diffraction tomography.

• Microwave imaging for NDT

  R. Zoughi, *Microwave Non-Destructive Testing and Evaluation*, Kluwer, 2000

  Comprehensive treatment of practical microwave imaging systems applying many concepts from this chapter.

• Near-field MIMO imaging

  F. Gao, B. Wang, C. Xing, J. An, and G. Y. Li, *Wideband Beamforming for Hybrid Massive MIMO Terahertz Communications*, IEEE JSAC, 2021

  Extends near-field beamfocusing concepts to terahertz frequencies where the near-field region is even more dominant.