Validity of rough surface backscattering models

Abstract

A study of the regions of validity for rough surface scattering models is conducted for surfaces with Gaussian and power law power spectra. Models included in the study are physical optics (PO), geometrical optics, small perturbation method and small slope approximation. The range of validity of the PO model is commonly described by a bound on the radius curvature of the surface relative to the electromagnetic wavelength. We show empirically that for backscattering the region of accuracy is more accurately described by a bound on surface slope. For surfaces with a Gaussian power spectrum, the PO model is accurate to within 2 dB for RMS surface slope values less than 0.59 cos³θ. For surfaces with a power law power spectral density, the PO model is accurate for significant slope values (RMS surface height/wavelength of the dominant spectral peak) less than 0.037 cos³θ. These conditions are valid up to approximately 30°. The regions of validity of other models in the study are also shown to be well approximated by bounds on surface slope.     

High-frequency diffraction corrections to backscattering cross sections from a rough three-dimensional surface

Diffraction corrections to scalar wave fields at perfectly free and rigid rough surfaces were derived by two iterations of the corresponding integral equations. These diffraction corrections to the pressure or normal velocity (which, in the geometrical optics limit, are doubled at perfectly rigid and free surfaces, respectively) were obtained with an accuracy of approximately 1k(2), where k is the wave number of incidence radiation. Based on these corrections to the surface fields, the backscattering cross sections at normal incidence from the statistically rough Gaussian surfaces were derived. It was found that for the gentle roughness, diffraction results in effective "smoothing" of roughness for rigid and free surfaces and increasing of the backscattering cross sections, but for a rigid surface with steep roughness, the "fictitious" surface can be more rough than the real one, and the diffraction corrections become negative.     

Amplification of enhanced backscattering from a dye-doped polymer bounded by a rough surface

We report the experimental study of the enhanced backscattering from a random rough surface through a laser dye-doped polymer. The sample is a slice of pyrromethene-doped polymer coupled with a two-dimensional rough gold layer with a large slope. When the sample is illuminated with an s-polarized He-Ne laser and pumped by a cw argon-ion laser, amplified backscattering is observed. The enhanced backscattering peak increases sharply and its width narrows for a sample with low dielectric constant |?(2)|.     

Poly-Gaussian models of a non-Gaussian randomly rough surface

Poly-Gaussian models are developed for non-Gaussian random processes, which make it possible to describe and imitate rough surfaces with various densities of roughness height distribution and correlation properties; the algorithms for numerical and analytical calculations of statistical characteristics of non-Gaussian reliefs are also worked out. Examples are given for the application of the integral poly-Gaussian model.     

Wave scattering from a random rough surface: reciprocal theorem and backscattering enhancement

The present paper gives a more complete treatment of the scattering from a two-dimensional random surface than previous works. Reciprocal theorems for the stochastic wave field and the incoherent scattering distribution (bistatic cross section) are derived and the presence of backscattering enhancement in the case of a slightly random Neumann surface is demonstrated. A physical interpretation of the backscattering enhancement associated with the presence of anomalous scattering on a slightly random Neumann surface is given. Some numerical calculations are performed to show the incoherent scattering distribution and the backscattering enhancement.     

Pulse broadening of enhanced backscattering from rough surfaces

Abstract

Recently, we presented a study of pulse scattering by rough surfaces based on the first-order Kirchhoff approximation which is applicable to rough surfaces with RMS slope less than 0.5 and correlation distance l?λ. However, there has been an increased interest in enhanced backscattering from rough surfaces, study of which requires inclusion of the second-order Kirchhoff approximation with shadowing corrections. This paper presents a theory for the two-frequency mutual coherence function in this region and shows that the multiple scattering on the surface gives rise to an additional pulse tail in the direction of enhanced backscattering. The theory predicts pulse broadening approximately 20% greater than that caused by single scattering alone for a delta-function incident pulse and typical surface parameters. Analytical results are compared with Monte Carlo simulations and millimetre-wave experiments for the one-dimensional rough surface with RMS height 1λ and correlation distance 1λ, showing good agreement.     

Pulse broadening of enhanced backscattering from rough surfaces

Recently, we presented a study of pulse scattering by rough surfaces based on the first-order Kirchhoff approximation which is applicable to rough surfaces with RMS slope less than 0.5 and correlation distance l≳λ. However, there has been an increased interest in enhanced backscattering from rough surfaces, study of which requires inclusion of the second-order Kirchhoff approximation with shadowing corrections. This paper presents a theory for the two-frequency mutual coherence function in this region and shows that the multiple scattering on the surface gives rise to an additional pulse tail in the direction of enhanced backscattering. The theory predicts pulse broadening approximately 20% greater than that caused by single scattering alone for a delta-function incident pulse and typical surface parameters. Analytical results are compared with Monte Carlo simulations and millimetre-wave experiments for the one-dimensional rough surface with RMS height 1λ and correlation distance 1λ, showing good agreement.     

Enhanced backscattering of waves reflected from a very rough surface formed by a system of open flat waveguides

A plane wave reflection from a statistically rough surface, which consists of a system of open flat waveguides, is considered in the physical optics approximation. It is shown that for sufficiently deep waveguides the backscattered field is comparable to the specularly reflected field.     

Enhanced backscattering of waves reflected from a very rough surface formed by a system of open flat waveguides

Abstract

A plane wave reflection from a statistically rough surface, which consists of a system of open flat waveguides, is considered in the physical optics approximation. It is shown that for sufficiently deep waveguides the backscattered field is comparable to the specularly reflected field.     

Measuring the characteristics of backscattering of sound on a rough surface in the near-field zone of a phased array

The paper presents the results of an experiment on measuring the characteristics of backscattering of sound waves by a rough surface. Measurements were conducted in the near zone of a vertical array, which made it possible with a high degree of accuracy to control the propagation conditions and the angles of incidence of an acoustic wave onto the surface. Tonal signals were emitted in a constant mode at frequencies of 0.5–3.5 kHz. The Doppler spectrum of the scattered signal was analyzed in detail, the spectral component corresponding to Bragg scattering was isolated, and the width of this component was determined. The possibilities of calculating the scattered field using two forms of the sea state spectrum are studied and compared: the two-dimensional spatiotemporal sea state spectrum, which was measured optically, and the conventional one-dimensional time spectrum, measured with a single surveying mark.     

Theoretical study of the Kirchhoff integral from a two-dimensional randomly rough surface with shadowing effect: application to the backscattering coefficient for a perfectly-conducting surface

Abstract

In this paper, the backscattering coefficient of a two-dimensional randomly rough perfectly-conducting surface is investigated using the Kirchhoff approach with a shadowing function. The rough surface height/slope correlations assumed to be Gaussian are accounted for in this analysis. The scattering coefficient is then formulated in terms of a characteristic function for the integrations over the surface heights, in terms of expected values for the integrations over the surface slopes. Numerical comparisons of Kirchhoff's approach (KA) with the stationary-phase (SP) approximation are made with respect to the choice of the one-dimensional surface height autocorrelation function and the shadowing effect. For an isotropic surface the results show that SP underestimated the incoherent backscattering coefficient compared with KA. Moreover, when the correlation between the slopes and the heights is neglected, the shadowing effect may be ignored.     

A time domain rough surface scattering model based on wedge diffraction: application to low-frequency backscattering from two-dimensional sea surfaces

A time domain method for calculating the acoustic impulse response of impenetrable, rough, two-dimensional (2D) surfaces is presented. The method is based on an extension of the wedge assemblage (WA) method to 2D surfaces and objects. Like the WA method for one-dimensional (1D) surfaces, the approach for 2D surfaces uses Biot's and Tolstoy's exact solution for the impulse response of an infinite impenetrable wedge [J. Acoust. Soc. Am. 29, 381-391 (1957)] as its fundamental building block. The validity of the WA method for backscattering from 2D sea surfaces is assessed through comparisons with calculations based on Milder's operator expansion (OE) method [J. Acoust. Soc. Am. 89, 529-541 (1991)]. Average intensities for backscattering from 2D fully developed seas (20 m/s wind speed) were computed by the WA and OE methods using 50 surface realizations and compared at 11 frequencies between 100 and 200 Hz. A single, moderately low grazing angle of incidence (20 degrees) and several scattered grazing angles (90 degrees, 45 degrees, 20 degrees , and 10 ) were considered. Excellent overall agreement between the two models was obtained. The utility of the WA method as a tool to describe the physics of the scattering process is also discussed.     

Theoretical study of the Kirchhoff integral from a two-dimensional randomly rough surface with shadowing effect: application to the backscattering coefficient for a perfectly-conducting surface

In this paper, the backscattering coefficient of a two-dimensional randomly rough perfectly-conducting surface is investigated using the Kirchhoff approach with a shadowing function. The rough surface height/slope correlations assumed to be Gaussian are accounted for in this analysis. The scattering coefficient is then formulated in terms of a characteristic function for the integrations over the surface heights, in terms of expected values for the integrations over the surface slopes. Numerical comparisons of Kirchhoff's approach (KA) with the stationary-phase (SP) approximation are made with respect to the choice of the one-dimensional surface height autocorrelation function and the shadowing effect. For an isotropic surface the results show that SP underestimated the incoherent backscattering coefficient compared with KA. Moreover, when the correlation between the slopes and the heights is neglected, the shadowing effect may be ignored.     

Electromagnetic backscattering from one-dimensional drifting fractal sea surface Ⅱ:Electromagnetic backscattering model

Sea surface current has a significant influence on electromagnetic(EM) backscattering signals and may constitute a dominant synthetic aperture radar(SAR) imaging mechanism. An effective EM backscattering model for a one-dimensional drifting fractal sea surface is presented in this paper. This model is used to simulate EM backscattering signals from the drifting sea surface. Numerical results show that ocean currents have a significant influence on EM backscattering signals from the sea surface. The normalized radar cross section(NRCS) discrepancies between the model for a coupled wavecurrent fractal sea surface and the model for an uncoupled fractal sea surface increase with the increase of incidence angle,as well as with increasing ocean currents. Ocean currents that are parallel to the direction of the wave can weaken the EM backscattering signal intensity, while the EM backscattering signal is intensified by ocean currents propagating oppositely to the wave direction. The model presented in this paper can be used to study the SAR imaging mechanism for a drifting sea surface.     

Radar backscattering from Gerstner's sea surface wave

In the framework of a two-scale scattering model, radar backscattering from the rough sea surface was considered. The sea surface was modelled as a superposition of a nonlinear, large-scale Gerstner's wave and small-scale resonant Bragg scattering ripples. The zero-order diffracted field was found by a geometrical optics approach, with shadowing taken into account, and by an 'exact' solution of the diffraction problem obtained numerically. For vertical and horizontal polarizations, the spatial distribution of specific scattering cross sections along the large-scale wave was obtained. The spatially averaged specific backscattering cross sections, as well as the mean Doppler frequency shifts at both polarizations, obtained by the geometrical optics approach are compared with those obtained by using the 'exact' solution of the large-scale diffraction problem. The roles of shadowing and multiple wave scattering processes are discussed, and qualitative explanations of the difference between these two approaches are given.     

Short pulse backscattering by a rough surface: analytical results and computer simulation of travel times and intensities of the earliest arrivals

Statistical properties of travel times and intensities of the first two arrivals of short pulses backscattered by a Gaussian rough surface in two-dimensions are obtained by computer simulation. Two specific cases are investigated: a collimated incident beam that is sufficiently wide with a plane wavefront, and a spherical wavefront generated by a point source located sufficiently far from the surface. The simulated results obtained are in a good agreement with theoretical estimates published recently by Fuks and Godin (see Waves in Random and Complex Media, 2004, 14 (2004) 539–562).     

Short pulse backscattering by a rough surface: analytical results and computer simulation of travel times and intensities of the earliest arrivals

Statistical properties of travel times and intensities of the first two arrivals of short pulses backscattered by a Gaussian rough surface in two-dimensions are obtained by computer simulation. Two specific cases are investigated: a collimated incident beam that is sufficiently wide with a plane wavefront, and a spherical wavefront generated by a point source located sufficiently far from the surface. The simulated results obtained are in a good agreement with theoretical estimates published recently by Fuks and Godin (see Waves in Random and Complex Media, 2004, 14 (2004) 539-562).     

Enhanced backscattering and blazing effect from gratings, quasi-gratings and randomly rough surfaces

The blazing effect is probably the most important property of diffraction gratings used for spectroscopic purposes. On the other hand, the enhanced backscattering phenomenon has been generally studied in the framework of scattering from randomly rough surfaces. Using numerical results from rigorous theories, it will be shown that these phenomena, which have very different origins, should have more precise definitions. In a special case of a randomly rough surface formed by random corners, it will be shown that the effects of these phenomena are sometimes very difficult to distinguish.     

Enhanced backscattering and blazing effect from gratings,quasi-gratings and randomly rough surfaces

Abstract

The blazing effect is probably the most important property of diffraction gratings used for spectroscopic purposes. On the other hand, the enhanced backscattering phenomenon has been generally studied in the framework of scattering from randomly rough surfaces. Using numerical results from rigorous theories, it will be shown that these phenomena, which have very different origins, should have more precise definitions. In a special case of a randomly rough surface formed by random corners, it will be shown that the effects of these phenomena are sometimes very difficult to distinguish.