References & Further Reading

References

1. G. Caire, On the Illumination and Sensing Model for RF Imaging, 2026

   The foundational document for this chapter. Develops the unified framework showing that diffraction tomography and radar/wireless matched filtering are two views of the same Born-approximation forward model. Also derives the sensing matrix structure, link budget, and resolution analysis.

2. L. Manzoni, V. Neri, and G. Caire, Wavefield Networked Sensing: Wavenumber-Domain Analysis and Design, 2025

   Systematic analysis of k-space tessellation for networked sensing systems. Develops coverage metrics and optimal sensor placement algorithms. The wavenumber-domain tessellation analysis in Section 6.5 follows this work.

3. M. Cheney and B. Borden, Fundamentals of Radar Imaging, SIAM, 2009

   Comprehensive treatment of radar imaging from the mathematical perspective. Covers the scattering integral, ambiguity functions, resolution theory, and reconstruction algorithms. Our View B (radar/wireless) follows this framework.

4. A. J. Devaney, A Filtered Backpropagation Algorithm for Diffraction Tomography, 1982

   The paper that established the Fourier Diffraction Theorem for coherent scattering, connecting diffraction tomography to Fourier analysis. View A of the unified framework originates from this work.

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

   The authoritative textbook on diffraction tomography and wavefield inversion. Provides rigorous derivations of the Fourier Diffraction Theorem and its extensions to non-Born regimes.

6. E. Wolf, Three-Dimensional Structure Determination of Semi-Transparent Objects from Holographic Data, 1969

   The original paper showing that coherent scattering data samples the spatial Fourier transform of the scattering potential along arcs on the Ewald sphere. This foundational insight underlies all of diffraction tomography.

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

   The standard reference for tomographic imaging, covering the Fourier Slice Theorem, filtered backprojection, and diffraction tomography. Our comparison of X-ray CT and RF diffraction tomography (Section 6.4) draws on this text.

8. M. A. Richards, J. A. Scheer, and W. A. Holm, Principles of Modern Radar: Basic Principles, SciTech Publishing, 2014

   Comprehensive radar engineering reference. The range resolution formula and matched-filter concepts in View B connect to the radar signal processing foundations in this text.

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

   The classic optics reference. Chapter 13 covers diffraction theory and the Ewald sphere construction for X-ray diffraction.

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

    Comprehensive treatment of wave scattering, including the Born and Rytov approximations in the context of propagation through random media.

11. S. Mandelli and L. Henninger, Angular Sampling Theorems for Imaging Arrays, 2024

    Develops the angular sampling theorem for imaging with finite arrays, providing bounds on the number of directions needed to avoid grating lobes.

Further Reading

• Mathematical foundations of diffraction tomography

  Devaney, *Mathematical Foundations of Imaging, Tomography and Wavefield Inversion*, Chs. 8-10

  Provides rigorous proofs of the Fourier Diffraction Theorem beyond the Born approximation, including Rytov and full nonlinear cases.

• SAR imaging as a special case of the unified model

  Cheney & Borden, *Fundamentals of Radar Imaging*, Chs. 6-8

  Shows how synthetic aperture radar fits within the same k-space framework, with the SAR motion providing angular diversity.

• Non-uniform FFT algorithms for image reconstruction

  Barnett et al., "A parallel non-uniform fast Fourier transform library," SIAM J. Sci. Comput., 2019

  The computational tool needed to efficiently reconstruct images from irregularly sampled k-space data (View A).

• Compressed sensing for super-resolution imaging

  Candès & Fernandez-Granda, "Towards a Mathematical Theory of Super-Resolution," CPAM, 2014

  The theoretical foundation for beating the diffraction limit when the scene is sparse — previewed in Section 6.6 and developed in Ch 14.

• ISAC system design

  Liu et al., "Integrated Sensing and Communications: Towards Dual-Functional Wireless Networks," IEEE JSAC, 2022

  Surveys the emerging field where the same waveform and hardware serve both communication and sensing/imaging — the context for Caire's unified model.