Local spectral analysis of short-pulse excited scattering from weakly inhomogeneous media-part I: Forward scattering

In this two-part sequence, we extend a previously formulated pulsed plane wave (PPW)-based time-domain (TD) diffraction tomography [1] for forward and inverse scattering from weakly inhomogeneous lossless nondispersive media to a more highly localized pulsed beam (PB) wavepacket-based diffraction tomography. In the PPW version, the incident and scattered fields have been parameterized in the space-time wavenumber domain in terms of slant-stacked TD plane waves whose wavefronts move through the scattering medium at the ambient propagation speed, thereby accumulating information along time-resolved laterally extended planar cuts. The PB parameterized localization confines the laterally sampled regions to the spatial domains of influence transverse to the relevant beam axes. These localizations are performed in two stages. The present paper implements the PB parameterization by PB post processing of the forward scattered fields excited by an incident PPW; the companion paper [2] deals with the inverse problem by back propagation of the PB parameterized data. An "ultimate" localization of a space-time resolved scattering cell, achieved via scattered and incident PB's (PB post and preprocessing) will be addressed elsewhere, but is briefly summarized in [2].