Order Small Slope Approximation Research Articles

Efficient Numerical Full-Polarized Facet-Based Model for EM Scattering from Rough Sea Surface within a Wide Frequency Range

A full-polarized facet based scattering model (FPFSM) for investigating the electromagnetic (EM) scattering by two-dimensional electrically large sea surfaces with high efficiency at high microwave bands is proposed. For this method, the scattering field over a large sea facet in a diffuse scattering region is numerically deduced according to the Bragg scattering mechanism. In regard to near specular directions, a novel approach is proposed to calculate the scattered field from a sea surface based on the second order small slope approximation (SSA-II), which saves computer memory considerably and is able to analyze the EM scattering by electrically large sea surfaces. The feasibility of this method in evaluating the radar returns from the sea surface is proved by comparing the normalized radar cross sections (NRCS) and the Doppler spectrum with the SSA-II. Then NRCS results in monostatic and bistatic configurations under different polarization states, scattering angles and wind speeds are analyzed as well as the Doppler spectrum at Ka-band. Numerical results show that the FPFSM is a reliable and efficient method to analyze the full-polarized scattering characteristics from electrically large sea surface within a wide frequency range.

An analytical model of double scattering for SAR imaging of urban structures

An analytical solution of double scattering for urban structures is proposed. This model is based on geometrical optics (GO) and first order small slope approximation (SSA1), thus has a wider scope of application than classical analytical models. In our model, the surface of building is assumed to be smooth and the ground is regarded as Gauss rough surface, then a closed form can be obtained. The radar cross section (RCS) and SAR images of double scattering for buildings surrounded by grass are simulated respectively. By comparing the real and simulated images, it shows that this model can accurately exhibit the effects of aspect angle on the double scattering feature in SAR image. This model is believed to possess great value in SAR image simulation and feature extraction of urban scene for its easy implementation and clear physical interpretation.

A Systematic Study of the Lowest Order Small Slope Approximation for a Pierson–Moskowitz Spectrum

In an earlier work, a model for calculating scattering from rough surfaces at very low grazing angles was presented. The utility of this model depends on the lowest order small slope approximation (SSA1). In order to ascertain when this new model, called the SSA+, is applicable, we present a systematic study of the accuracy of the SSA1 bistatic scattering cross section for 1-D surfaces for a Pierson-Moskowitz roughness spectrum and the Dirichlet boundary condition. Different frequencies, angles of incidence, and wind speeds are combined to examine 112 different cases. The ranges of scattering angles for which the SSA1 is accurate are given, and an analysis of when the SSA+ can be used is presented. All data and plots are available online.

Doppler Shifts of Backscattering Fields from One Dimensional Linear and Nonlinear Oceanic Surface by SSA-II

Based on the general framework of the second order small slope approximation (SSA-II), Doppler shifts of backscattered fields from linear and nonlinear hydrodynamic sea surfaces are predicted. Comparisons are performed at incidence angles varying from near-nadir to moderate-grazing for different radar frequencies. The predicted Doppler shifts for nonlinear hydrodynamic model are somewhat larger than the results corresponding to linear surface. Meanwhile, the dependences of the Doppler shifts on the wind speed and radar polarizations are also analyzed, and the comparisons are shown to confirm the sensitivities to the polarization and wind speed. At the same time, the results of the small perturbation method (SPM) and geometrical optics approximation (GO) are also presented for comparisons.

Investigation on the Doppler shifts induced by 1-D ocean surface wave displacements by the first order small slope approximation theory: comparison of hydrodynamic models

Based on the first order small slope approximation theory (SSA-I) for oceanic surface electromagnetic scattering, this paper predicts the Doppler shifts induced by wave displacements. Theoretical results from three distinct hydrodynamic models are compared: a linear model, the nonlinear Barrick model, and the nonlinear Creamer model. Meanwhile, the predicted Doppler shifts are also compared with the results associated to the resonant Bragg waves and the so-called long waves in the framework of the two-scale model. The dependences of the predicted Doppler shifts on the incident angle, the radar frequency, and the wind speed are discussed. At large incident angles, the predicted Doppler shifts for the linear and nonlinear Barrick models are found to be insensitive to the wind speed and this phenomenon is not coincident with the experimental data. The conclusions obtained in this paper are promising for better understanding the properties of time dependent radar echoes from oceanic surfaces.

Examination of loss mechanisms for a rough bottom Pekeris waveguide using a two‐way coupled mode model.

A benchmark scattered‐field solution for a two‐dimensional rough‐bottom Pekeris ocean waveguide has been generated from a two‐way coupled‐mode model with normal modes evaluated in the complex horizontal wave‐number plane. The received level time series coupled‐mode solution for a range monostatic source/receiver geometry with a 250 Hz center frequency, 20 Hz band, Gaussian pulse was shown previously to be consistent with a single scatter Born approximation solution [Stotts et al., J. Acoust. Soc. Am. 122, 3075 (2007)]. A new result for a 1 kHz center frequency, 60 Hz band, pulse deviates significantly from the Born approximation solution. Alternative approaches, obtained with the Born approximation but including the additional propagation loss for Kirchhoff scattering [E. I. Thorsos, J. Acoust. Soc. Am. 83, 78–92 (1988)] with and without second order small slope approximation effects are examined. The solutions at 1 kHz with these alternative methods are compared to the coupled‐mode solution. The forward scattered fields propagated over finite length roughness segments of varying lengths are analyzed to understand the role of mode‐mode interactions in the forward propagation loss mechanisms and for comparison with the Kirchhoff scattering loss description.

A comparison of perturbation theory and the small-slope approximation for acoustic scattering from a rough interface for a Biot medium

In this paper, the lowest order small-slope approximation (SSA) scattering cross section for Biot theory is derived. Numerical results are obtained for both backscattering and bistatic scattering using a modified power law spectrum, and these results are compared with those of lowest order perturbation theory (PT). Frequencies ranging from 100 Hz to 3 kHz are used for surfaces with RMS heights h of 0.1 and 1 m and a correlation length l of 10 m. The angle of incidence for the bistatic results is limited to 45/spl deg/. It is found that for the smaller surface height roughness (h = 0.1 m), the SSA and PT give the same results for frequencies up to almost 1 kHz for both backscattering and bistatic scattering. For h = 1 m, the SSA and PT backscatter results are in good agreement at all frequencies for incident grazing angles up to approximately 45/spl deg/. For the bistatic results, the SSA and PT results agree only at low grazing angles of scatter. In the specular region, the results differ significantly.

Numerical study of the extended Kirchhoff approach and the lowest order small slope approximation for scattering from ocean-like surfaces: Doppler analysis

The validity of the lowest order small slope approximation (SSA(1)) and the extended Kirchhoff approach (EKA) (Elfouhaily et al., 1999) has been studied by comparing the Doppler spectra of the backscattered signals predicted by these models to their counterparts from exact integral equation-based numerical simulations. The study is conducted at L and S bands (electromagnetic wavelengths 23 and 10 cm); the rough ocean-like surfaces correspond to the wind speed of 5 m/s and were generated using both linear and nonlinear (Creamer) models. The incidence angle varies from normal to low grazing. Expressions for the two analytical models possess many similarities but contain different incidence/scattering angle-dependent factors. The analysis of the bistatic scattering cross sections predicted by the two models reveals that SSA(1) follows the exact numerical results more closely than the EKA. Moreover, at horizontal polarization the extended Kirchhoff bistatic cross section displays certain anomalies (unlimited growth at grazing scattering angles) that are indicative of the problems with this model. However, in the backscattering direction, the expressions for the two models are identical. Doppler analysis of the backscattered signals shows that in general, the analytical models provide better agreement with the numerical results for smaller incident angles. In addition, the agreement between the models and the exact numerical simulations is always better in the case of vertical polarization for which the analytical models give a satisfactory prediction of the Doppler spectrum for incident angles as large as 85/spl deg/ from the normal for both linear and nonlinear surfaces. For horizontal polarization, the models give increasingly poor predictions of the shape, magnitude, and location of the Doppler spectrum for incident angles in the range from 60/spl deg/ to low grazing. Doppler analysis proves to be a much more precise and sensitive tool in assessing the scattering model's validity than the usual comparison of cross sections.

Comparison of modeled and measured second azimuthal harmonics of ocean surface brightness temperatures

Second azimuthal harmonics of ocean surface brightness temperatures predicted by the second order small slope approximation (SSA) are compared to an empirical model based on WindRAD experiments performed by the Jet Propulsion Laboratory (JPL), Pasadena, CA. SSA predictions are illustrated for three differing models of the ocean surface directional spectrum, and results as a function of wind speed are shown to be in reasonable agreement with the WindRAD model at 19.35 and 37 GHz and at polar observation angles of 45/spl deg/, 55/spl deg/, and 65/spl deg/. None of the three spectral models, however, completely matches all the trends of the empirical data. A slight modification to one of the spectra is demonstrated to yield an improved agreement.