The phase-space beam summation is a general analytical framework for local analysis and modeling of radiation from extended source distributions. In this formulation the field is expressed as a superposition of beam propagators that emanate from all points in the source domain and in all directions. The theory is presented here for both time-harmonic and time-dependent fields: in the later case, the propagators are pulsed-beams (PB). The phase-space spectrum of beam propagators is matched locally to the source distribution via local spectral transforms: a local Fourier transform for time-harmonic fields and a "local Radon transform" for time-dependent fields. These transforms extract the local radiation properties of the source distributions and thus provide a priori localized field representations. Some of these basic concepts have been introduced previously for twodimensional configurations. The present paper extends the theory to three dimensions, derives the operative expressions for the transforms and discusses additional phenomena due to the three dimensionality. Special emphasis is placed on numerical implementation and on choosing a numerically converging space-time window. It is found that the twice differentiated Gaussian-window is both properly converging and provides a convenient propagator that that can readily be tracked in complicated inhomogeneous medium.

Abstruct-We consider certain characteristics of the radiation from collimated, ultrawideband short-pulse aperture distributions. It is shown that an efficient radiation must account for the multifrequency nature of the field. Two alternative schemes for wideband aperture synthesis of an impulse-like radiation pattern are examined. The first, entitled the "Iso-width aperture," utilizes only temporal shaping of the excitation pulse. In the other, the "Iso-diffracting aperture," we suggest source shaping in spacetime so that all the frequency components in the field have the same collimation distance. The "iso-diffracting" scheme yields higher directivity and more efficient pulsed radiation. Explicit examples for the pulsed source distribution and for the pulsed radiation patterns are presented, parametrized, and contrasted.

No abstract

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].

Time-domain inversion of a three-dimensional inhomogeneous medium is formulated as a time-domain diffraction tomography. The scattered data are expanded into a spectrum of time-dependent plane waves using the slant-stack transform. It is then shown that each time-dependent plane-wave constituent in the data is directly related to the Radon transform of the medium's inhomogeneity along the direction that bisects the angle between the plane wave and the incident wave. This new tomographic relation provides the basis for two inversion approaches: a Radon-space reconstruction and a time-dependent filtered backpropagation. Finally, the reconstruction errors due to the limited spacetime aperture are identified via analysis and a numerical example.