Wave-oriented signal processing of dispersive time-domainscattering data

Phase-space data processing is receiving increased attention because or its potential for furnishing new discriminants relating to classification and identification of targets and other scattering environments. Primary emphasis has been on time-frequency processing because of its impact on transient, especially wideband, short-pulse excitations. Here, we investigate the windowed Fourier transform, the wavelet transform, and model based superresolution algorithms within the context of a fully quantified and calibrated test problem investigated by us previously: two-dimensional (2-D) short-pulse plane wave scattering by a finite periodic array of perfectly conducting coplanar flat strips. Because the forward problem has been fully calibrated and parametrized, some quantitative measures can be assigned with respect to the tradeoffs of these time-frequency algorithms, yielding tentative performance assessments of the tested processing algorithms     

Time-domain radiation from large two-dimensional apertures via narrow-waisted Gaussian beams

This paper deals with the short-pulse radiation of three-dimensional (3-D) vector electromagnetic fields from arbitrarily polarized large two-dimensional (2-D) truncated aperture distributions, which are parameterized in terms of narrow-waisted ray-like pulsed Gaussian basis beams centered on a discretized Gabor lattice in a four-dimensional (4-D) configuration-spectrum phase space. The study extends our previous Gabor-based investigation of time-domain (TD) short-pulse radiation of 2-D fields from 1-D large truncated apertures with nonphased, linearly phased (delayed) and nonlinearly phased focusing aperture field profiles . We begin with, and summarize, a Gabor-based frequency domain (FD) formulation of the 2-D aperture problem which has been presented and tested elsewhere, but we include additional numerical examples for validation and quality assessment. As done by Galdi, Felsen and Castanon (see ibid., vol 49, p. 1322-32, Sept. 2001) we access the time domain by Fourier inversion from the FD, starting from the initial 3-D space-time Kirchhoff formulation (whose numerical integration furnishes reference solutions), and then passing on to Gabor-parameterized field representations in terms of pulsed beam (PB) wavepackets which are launched by linearly and nonlinearly phase-delayed focusing aperture distributions. Example calculations and comparisons with numerically generated reference data serve to calibrate the Gabor-PB algorithms and assess their domains of validity.     

Short-pulse three-dimensional scattering from moderately rough surfaces: a comparison between narrow-waisted Gaussian beam algorithms and FDTD

In this paper, with reference to short-pulse three-dimensional scattering from moderately rough surfaces, we present a comparison between Gabor-based narrow-waisted Gaussian beam (NW-GB) and finite-difference time-domain (FDTD) algorithms. NW-GB algorithms have recently emerged as an attractive alternative to traditional (ray-optical) high-frequency/short-pulse approximate methods, whereas FDTD algorithms are well-established full-wave tools for electromagnetic wave propagation and scattering. After presentation of relevant background material, results are presented and discussed for realistic parameter configurations, involving dispersive soils and moderately rough surface profiles, of interest in pulsed ground penetrating radar applications. Results indicate a generally satisfying agreement between the two methods, which tends to improve for slightly dispersive soils. Computational aspects are also compared.     

Gaussian beam and pulsed-beam dynamics: complex-source and complex-spectrum formulations within and beyond paraxial asymptotics.

Paraxial Gaussian beams (GB's) are collimated wave objects that have found wide application in optical system analysis and design. A GB propagates in physical space according to well-established quasi-geometric-optical rules that can accommodate weakly inhomogeneous media as well as reflection from and transmission through curved interfaces and thin-lens configurations. We examine the GB concept from a broad perspective in the frequency domain (FD) and the short-pulse time domain (TD) and within as well as arbitrarily beyond the paraxial constraint. For the formal analysis, which is followed by physics-matched high-frequency asymptotics, we use a (space-time)-(wavenumber-frequency) phase-space format to discuss the exact complex-source-point method and the associated asymptotic beam tracking by means of complex rays, the TD pulsed-beam (PB) ultrawideband wave-packet counterpart of the FD GB, GB's and PB's as basis functions for representing arbitrary fields, GB and PB diffraction, and FD-TD radiation from extended continuous aperture distributions in which the GB and the PB bases, installed through windowed transforms, yield numerically compact physics-matched a priori localization in the plane-wave-based nonwindowed spectral representations.     

Groundwave propagation modeling: problem-matched analyticalformulations and direct numerical techniques

In this overview of groundwave propagation, we address a particular class of propagation scenarios in the presence of surface terrain and atmospheric refractivity. Beginning with idealized analytically solvable models over a smooth spherical Earth, we trace the progression toward more "reality" through physics-based numerical algorithms, operating in the frequency and short-pulse time domain, which take advantage of computational resources. An extensive sequence of simulations for various terrains and atmospheric refractivities, as well as different source-receiver arrangements and operating frequencies, serves to calibrate these algorithms one against the other, and establishes the range of problem parameters for which each is more effective     

Weakly dispersive spectral theory of transients, part II: Evaluation of the spectral integral

In the spectral theory of transients formulated in Part I of this paper, the transient response for weakly dispersive wave processes has been expressed in terms of canonical integrals in the complex spatial wavenumber domain. The real and complex singularities in the integrands, which dominate the behavior of the spectral integrals, have been categorized and associated with generic physical wave processes. The integrals are now evaluated by Contour deformation around the singularities. This yields general expressions for the transient Green's function that are applicable to a broad class of propagation and diffraction problems. The generic results, which can be grouped into contributions from real or complex singularities; express the transient field in terms of compact (and therefore physically incisive) wave spectra, in contrast to alternative procedures that always constrain the spectra to be real. These aspects, together with simplifying explicit wavefront approximations, are explored in the present paper, with the application to specific problems relegated to Part III.     

Propagating pulsed beam solutions by complex source parameter substitution

The complex source point method is extended to the time domain by considering the field due to an impulsive source point with complex space coordinates and a complex initiation time. The resulting solution, which is a particular analytic continuation of the free space time-dependent Green's function, describes a propagating pulsed beam that has a moving peak along the beam axis. Near the pulse maximum in the paraxial region, this new field type is the Fourier transform into the time domain of the time-harmonic paraxial Gaussian beam field but the method also accommodates, in closed form, observation points far from the beam axis and observation times long before and after the peak has passed. By corresponding analytic continuation of available space-time Green's functions for various propagation and diffraction environments, one may generate directly the response due to the pulsed beam incident on the environment.