James C. West

On iterative approaches for electromagnetic rough-surface scattering problems

Iterative techniques developed for solving general systems of linear equations have been applied to systems resulting from electromagnetic rough-surface scattering problems. Previously used iterative procedures that model the multiple scattering of the electromagnetic energy are shown to be mathematically equivalent to the application of stationary iterative procedures to the system of equations resulting from the standard moment method. Convergence difficulties that are sometimes observed with these approaches are due to the inherent limitations of the stationary techniques. The performances of the stationary approaches are compared with that of several conjugate-direction-based nonstationary iterative procedures through the application to a series of scattering surfaces that yield rapidly changing conditioning of the moment method interaction matrix. The stationary algorithms give the quickest convergence when applied to the systems with the best conditioning, but the nonstationary techniques prove much more robust in other more ill-conditioned situations.

Low-grazing scattering from breaking water waves using an impedance boundary MM/GTD approach

The radar backscattering from water waves of various degrees of breaking Is numerically examined. A hybrid moment method geometrical theory of diffraction (MM/GTD) technique previously used for small-grazing scattering from perfectly conducting surfaces is reformulated using impedance boundary conditions, allowing the treatment of large (but finite) conductivity scattering media such as sea water. This hybrid MM/GTD approach avoids the artificial edge effects that limit the standard moment method when applied to rough surfaces, allowing the calculation of the scattering at arbitrarily small grazing angles. Sample surfaces are obtained through the edge-detection of video stills of breaking waves generated in a wave tank. The numerical calculations show that the strength of the backscatter is closely associated with the size of the plume on the breaking wave. Strong interference appears in the both horizontal (HH) and vertical (VV) backscatter when the surfaces are treated as perfectly conducting. The VV interference is dramatically reduced when a sea water surface is used, but the HH interference is unaffected. The interference leads to HH/VV ratios of up to 10 dB. The behavior of the scattering is consistent with the multipath theory of sea-spike scattering.

Low-grazing-angle (LGA) sea-spike backscattering from plunging breaker crests

The low-grazing-angle (LGA) microwave backscattering from a series of wave profiles representing the time evolution of a plunging breaker water wave is numerically calculated and compared with modeled predictions. The crest regions of the waves are isolated to remove large-scale multiple back-reflection paths that give interference. The horizontally polarized backscatter (HH) significantly exceeds that at vertical polarization (VV) during the breaking, despite the lack of multipath. Existing scattering models with some heuristic corrections are applied to the profiles to identify the dominant scattering mechanisms. The large HH-to-VV ratio is predicted from single scattering using an extended geometrical optics (EGO) approach. The initial rise in the backscatter as the wave steepens is predicted as diffraction from inflection points in the surface curvature at the crest using a modification of the geometrical theory of diffraction. The calculations show that the LGA backscattering from breaking wave crests is very complicated even in the absence of multipath and simple optically based models that treat the crest cross sections as equal at the two polarizations will be inaccurate.

Analysis of scattering from rough surfaces at large incidence angles using a periodic-surface moment method

The moment method is used to calculate electromagnetic backscattering from one-dimensionally rough surfaces at near-grazing incidence (angles of incidence up to 89/spl deg/). A periodic representation of the scattering surface is used to prevent edge effects in the calculated scattering without the use of an artificial illumination weighting function. A set of universal series common to all elements of the moment interaction matrix are derived that allow the efficient application of the moment method to the periodic surface. Comparison with other moment method implementations demonstrates the efficiency of this approach. The scattering from surfaces with Gaussian roughness spectra is calculated at both horizontal and vertical polarizations, and the results are compared with the theoretical predictions of the small-perturbation method (SPM) and Kirchhoff approximation (KA). SPM shows the expected loss of accuracy in predicting the vertically polarized backscattering from small-roughness, short-correlation-length surfaces at large incidence angles. SPM accurately predicts the backscattering from the same type of surface at incidence up to 89/spl deg/ at horizontal polarization, KA provides accurate estimates of the scattering from long correlation-length surfaces as long as the incidence angle is small enough that surface self-shadowing does not occur. When shadowing occurs, KA severely underpredicts vertically polarized backscattering and less severely overpredicts backscattering at horizontal polarization. >

Spectral estimation techniques for multilook SAR images of ocean waves

When deriving a directional ocean wave spectrum from a synthetic-aperture radar (SAR) image of the ocean surface, spectral analysis of the image data is a key step. In this paper, a quantitative comparison of spectral analysis techniques for analysis of multilook SAR image data of ocean waves is presented. Performance is rated using a spectral SNR, defined as the ratio of the desired spectral signature to the speckle noise as it appears in the SAR image spectrum. Spectral techniques considered cover all of those now in use (including SAR processor focus adjustment) as well as new experimental methods. It is shown that the spectral-phase-shift technique, introduced in this paper, is the best approach: it maximizes the spectral SNR, it allows resolution of the 180 degrees directional ambiguity, and it applies simultaneously to all wave components present in the scene. >

On the control of edge diffraction in numerical rough surface scattering using resistive tapering

The use of resistive loading to remove edge effects in electromagnetic scattering from rough surfaces with finite conductivity has been considered. An electric field integral equation formulation using impedance boundary conditions was implemented to model the conductivity of sea water at X band. The resistive loading was added over surface sections within three wavelengths of the modeled edges. A resistive taper synthesized to control the sidelobe level in scattering from flat, perfectly conducting plates proved better able to reduce edge diffraction than a power-law taper of a type that is often used. The calculated scattering from test profiles that model breaking water waves using the resistive loading show good agreement with those found using a reference scattering approach provided that the local grazing angle on the loaded surface section is greater than 20/spl deg/.

Integral equation formulation for iterative calculation of scattering from lossy rough surfaces

The application of iterative routines to finite conductivity surfaces is considered. In particular, an integral equation formulation that yields rapid convergence for horizontally polarized scattering from one dimensionally rough surfaces without loss of accuracy is examined.

Preconditioned iterative solution of scattering from rough surfaces

Extensions to the functionally identical forward-backward (FB) and method of ordered multiple interactions iterative techniques have been introduced that improve the convergence characteristics with specific scattering geometries. These extensions are shown to be mathematically equivalent to applying preconditioners to the discretized integral equation that is iteratively solved. The same preconditioners can be used with any iterative solution technique. Numerical examples show that the generalized minimal residual (GMRES) and bi-conjugate gradient-stable (BICGSTAB) algorithms give similarly rapid convergence when applied to a preconditioned discretized integral equation.

Ray analysis of low-grazing scattering from a breaking water wave

Low-grazing-angle backscattering from a modeled breaking-wave surface profile has been calculated using a ray-optical approach and compared with reference scattering found using an extended moment method. The calculations show that interference between the direct backscatter from the breaking plume and multipath scattering between the plume and wave face can lead to the HH-to-VV polarization-backscattering ratios of greater than 9 dB that characterize sea-spike events. The multipath effects can be accurately predicted from simple reflection from the front face at the smallest grazing angles. At higher angles, diffraction from rapid changes in the surface curvature must also be considered.

Low-grazing-angle microwave scattering from a three-dimensional spilling breaker crest: a numerical investigation

The microwave backscattering from a three-dimensional (3-D) target approximating the rough crest of a gently spilling water wave at low grazing angle illumination has been numerically examined. The target surfaces were synthesized from the direct two-dimensional (2-D) measurement of the time evolution of the upwave-downwave cross-section of a wave-tank breaker. The reference scattering was found using the multilevel fast multipole algorithm implemented with impedance boundary conditions and resistive surface loading to suppress nonphysical edge diffraction. The scattering was compared with the predictions of the two-scale model and a synthesis of the 3-D backscattering from individual 2-D calculations. Specular reflection from a bulge feature that appeared on the crest prior to breaking dominated the backscattering at both polarizations, overwhelming even the strong vertical polarization Bragg scattering that appeared in the corresponding scattering from the individual 2-D profiles used to synthesize the 3-D target. The scattering from the surface including the bulge could be accurately modeled using a coherent addition of the scattering from the 2-D profiles. The two-scale model performed poorly whenever there are steep sections on the surface that provide significant quasi-specular back-reflection. Accuracy improved when the specular points were eliminated and the dominant scattering roughness was fully illuminated, but was still sensitive to the surface-roughness scale-separation threshold used in its application.