Spectral analysis of time domain diffraction tomography

This paper is concerned with the spectral content of short‐pulse field scattered from an inhomogeneous medium. Direct diffraction tomography type relations between the time‐dependent data and the medium are determined via two spectral formulations: a time‐dependent plane wave spectrum and a local phase‐space spectrum. The former is formulated in the Radon space, wherein the time‐dependent plane wave spectrum of the data is directly related to the Radon transform of the medium. The latter is formulated as a local Radon transform in the space‐time domain, wherein scattered pulsed beams (space‐time wave packets) are directly related to localized scattering subdomains. This result leads to the formulation of a local inverse scattering scheme, wherein pulsed beams are back propagated and focused to form local images of any desirable region.