Chapter 6: Caire's Unified Forward Model

Learning Objectives

• Understand that diffraction tomography and radar/wireless matched filtering are two views of the same Born-approximation forward model
• Derive the discrete sensing matrix from the Born integral, identifying each entry as a Green's function times an incident field times a voxel volume
• Visualize the Ewald sphere construction and understand how each measurement (Tx, Rx, frequency) maps to a point in wavenumber space
• State and prove the Fourier Diffraction Theorem as the RF analogue of the Fourier Slice Theorem in CT
• Analyze wavenumber-domain tessellation and its dependence on array geometry, bandwidth, and carrier frequency (Manzoni et al.)
• Derive range resolution, cross-range resolution, and the diffraction limit from k-space coverage arguments
• Apply spatial sampling theorems to determine grid spacing and angular sampling requirements for imaging