Influence of ionospheric irregularities on the form of radio signal scattering spectrum in over-the-horizon radar sounding of the rough sea surface

This paper is concerned with the backscattering of HF radio waves from the rough sea surface, which have propagated through the ionosphere with random large-scale irregularities.

For the sake of simplicity, it is assumed in calculations that the rough sea surface is a perfectly conducting surface with the known Philips power spectrum of irregularities. Ionospheric irregularities of a random medium that are isotropic and single-scale ones, with a Gaussian spectrum, are considered within the limits of the hypothesis of frozen-in irregularities.

Within the first approximation of perturbation theory, using, as the incident wave and the Green function, their geometrical-optics approximations, we obtained the expression for the backscattering spectrum of the ionospheric chirp radio signal with a Gaussian envelope. The expression involves the parameters of the receive-transmit antenna, the signal, the propagation medium, and of the scattering surface. Numerical simulation was used to investigate the influence of all the above-mentioned parameters on the backscattering spectrum. It is shown that travel of ionospheric irregularities has the largest influence on the scattering spectrum, the signal parameters mainly determine the size of the scattering area in the range, and the form of the coherent integration window determines the form of the received signal and can distort it.     

Numerical,analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

Abstract

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

Perturbation theory results for the diffuse scattering of light from two-dimensional randomly rough metal surfaces

Abstract

Using the unitarity and reciprocity preserving formulation of Brown et al a perturbation treatment, correct to fourth order in the surface profile function, is given for the scattering of electromagnetic waves from a weakly rough, two-dimensional, random metal surface. In this formulation the boundary conditions on the electromagnetic fields are satisfied using the extinction theorem in conjunction with the Rayleigh hypothesis and the vector equivalent of the Kirchhoff integral. The theory is applied to, and results are presented for, several different types of rough surfaces which are characterized by power spectra that are extensions to two-dimensional random surfaces of the power spectrum of some one-dimensional random surfaces recently fabricated by West and O'Donnell. These surfaces, which can be realized experimentally, favor coherent, interferent, multiple scattering of electromagnetic waves via surface plasmon polaritons in intermediate states, and clearly exhibit enhanced backscattering caused by the surface plasmon polariton mechanism. Theoretical results are presented for silver surfaces at optical wavelengths.     

Multiple scattering effects on the radar cross section (RCS) of objects in a random medium including backscattering enhancement and shower curtain effects

Abstract

This paper presents a theory of the radar cross section (RCS) of objects in multiple scattering random media. The general formulation includes the fourthorder moments including the correlation between the forward and the backward waves. The fourth moments are reduced to the second–order moments by using the circular complex Gaussian assumption. The stochastic Green's functions are expressed in parabolic approximation, and the objects are assumed to be large in terms of wavelength; therefore, Kirchhoff approximations are applicable. This theory includes the backscattering enhancement and the shower curtain effects, which are not normally considered in conventional theory. Numerical examples of a conducting object in a random medium characterized by the Gaussian and Henyey–Greenstein phase functions are shown to highlight the difference between the multiple scattering RCS and the conventional RCS in terms of optical depth, medium location and angular dependence. It shows the enhanced backscattering due to multiple scattering and the increased RCS if a random medium is closer to the transmitter.     

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.     

Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

Bistatic scattering coefficient from one- and two-dimensional random surfaces using the stationary phase and scalar approximation with shadowing effect: comparisons with experiments and application to the sea surface

Abstract

In this paper, the bistatic scattering coefficient from one- and two-dimensional random surfaces using the stationary phase method and scalar approximation with shadowing effect is investigated. Both of these approaches use the Kirchhoff integral. With the stationary phase, the bistatic cross section is formulated in terms of the surface height joint characteristic function where the shadowing effect is investigated. In the case of the scalar approximation, the scattering function is computed from the previous characteristic function and in terms of expected values for the integrations over the slopes, where the shadowing effect is analysed analytically. Both of these formulations are compared with experimental data obtained from a Gaussian one-dimensional randomly rough perfectly-conducting surface. With the stationary-phase method, the results are applied to a two-dimensional sea surface.     

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.     

Polarization characteristics of an electromagnetic wave scattered from a slightly random surface: +45° polarized incidence

Abstract

The present paper deals with the scattering of an obliquely polarized electromagnetic (EM) wave from a slightly rough surface, which is assumed to be a two-dimensional (2D), homogeneous and isotropic Gaussian random field. In contrast to the cases of TE(s) and TM(p) polarized incidence, the scattering profile for an obliquely polarized incidence is not symmetric with respect to the incident plane, despite the fact that the random surface is statistically isotropic.     

The Structure of a Chirp Signal in the Randomly Inhomogeneous Earth-Ionosphere Channel

We analyze theoretically the structure of a chirp-ionosonde signal for the cases of one- and two-hop propagation in the randomly inhomogeneous ionosphere. For the case of two-hop propagation, wave scattering by the rough ground is taken into account. Our numerical simulation showed that random ionospheric irregularities and ground roughnesses play a significant role in the formation of a signal structure. We compare numerical results with experimental data obtained at oblique ionospheric sounding.     

Acoustic scattering from a rough sea surface: the mean field by the integral equation method

Abstract

The scattering of an acoustic signal incident from below at low angles on a rough sea surface is treated by the integral equation method in the parabolic approximation. Equations are obtained allowing the mean scattered field to be calculated even when the surface causes a large phase modulation in the incident wave. Solutions are found using the method of Laplace transforms and some results are presented for a specific type of rough surface.     

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.     

Electromagnetic wave scattering from a random medium layer with a random interface

Abstract

The problem of electromagnetic wave scattering from a random medium layer with a random interface is considered. The layer has planar boundaries on average. Assuming that both the random perturbations of the interface and the random fluctuations of permittivity of the medium are small, a first-order perturbation solution to the scattered field is obtained. Using this solution, the bistatic scattering coefficients γ_αβ are calculated and expressed in a compact and meaningful form. The various terms that constitute γ_αβ are identified with distinct scattering processes. Since it is often of particular interest, the special case of backscattering is considered. Finally, the results are compared with those of others.     

Scattering of an electromagnetic wave from a slightly random dielectric surface: Yoneda peak and Brewster angle in incoherent scattering

Abstract

The scattering of an electromagnetic wave from a two-dimensional, slightly rough dielectric surface is studied based on the stochastic functional approach. It is shown that in the case of TM(p)-polarized incidence there exists a zero in the incoherent scattering at the angle we call the ‘Brewster scattering angle’, which depends on the incident angle in contrast to the Brewster angle of coherent reflection which is independent of the incident angle, that a ‘quasi-anomalous scattering’ can generally occur in the optically denser medium at the critical angle of total reflection in both TE(s)- and TM(p)-polarized incidence, regardless of which side of the random surface is illuminated, and that the Yoneda peak in the x-ray scattering can be interpreted as a special case of the quasi-anomalous scattering which becomes sharper when the relative refractive index becomes closer to unity as in the x-ray region. Cross-polarized scattering and enhanced backscattering due to the second-order effect are also calculated.     

A Study of Optical Backscattering Enhancement from One-Dimensional Rough Surface Using Monte Carlo Method

In this paper, according to Kirchhoff approximation, the optical backscattering enhancement of one-dimensional random rough surface, which includes fractal rough surfaces and random rough surfaces with Gaussian and exponential correlation simulated by Monte Carlo method, is obtained. It is shown that backscattering enhancement of random rough surfaces will increase with increasing the rms height of rough surface for a given correlation length. The angle width of backscattering enhancement is directly proportional to incident wavelength and inverse proportional to correlation length of rough surface. Complex phase of scattering field from superposed rough surface is uniformly distributed, none of the directions is of more overweight. The backscattering enhancement is also studied by wavelet analysis. The numerical results show good consistent with that of the relative references.     

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.     

Measurements of light scattering by a characterized random rough surface

Abstract

Measurements are presented of the angular distribution of four wavelengths of light scattered by a one-dimensional random rough surface, whose probability density function is Gaussian with a standard deviation σ=1.22±0.02 μm and whose lateral correlation function is also Gaussian with 1/e width τ=3.17±0.07 μm. The wavelengths used are 0.63, 1.15, 3.39 and 10.6 μm. The surface is used in two forms: coated with gold and as an almost lossless dielectric. The results are compared to those predicted by a double scattering form of the Kirchhoff formulation. Agreement is good at small angles of incidence but less good at larger angles of incidence.     

Angular correlation function of wave scattering by a random rough surface and discrete scatterers and its application in the detection of a buried object

Abstract

The scattering of waves by a buried object is often obscured by the clutter around it. Such clutter can be attributed to the scattering by random rough surfaces and random discrete scatterers. Recent studies show that, because of the memory effect, the angular correlation function can suppress the effects of clutter and make the scattering by the buried object more conspicuous. In this paper, we study the angular correlation function of wave scattering by a buried object underneath a layer of random discrete scatterers and a non-Gaussian random rough surface. Such problems are common when the target is buried below a rough surface that is underneath a layer of vegetation. Numerical results are illustrated for various parameters of rough surfaces and discrete scatterers. The angular correlation function is calculated by frequency and angular averaging. It is shown that the use of the angular correlation function can enhance target detection in the presence of clutter.     

Bistatic scattering and depolarization by randomly rough surfaces: application to the natural rough surfaces in X-band

Abstract

The scattering of waves by random rough surfaces has important applications in the remote sensing of oceans and land. The problem of developing a model for rough surfaces is very difficult since, at best, the scattering coefficient σ⁰ is dependent upon (at least) the radar frequency, geometrical and physical parameters, incident and observation angles, and polarization. The problem of electromagnetic scattering from a randomly rough surface is analysed using the Kirchhoff approximation (stationary phase, scalar approximation), the small-perturbation model and the two-scale models. A first major new consideration in this paper is the polarimetric signature calculations as a function of the transmitter location and receiver location for a bistatic radio-link. We calculate the like- and cross-polarized received power directly using the scattering coefficients, without calculating the Mueller matrix. Next, a study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models (in the bistatic case) is presented. Comparisons between the numerical calculations and the models are made for various surface rms heights and correlation lengths both normalized to the incident wavenumber (denoted by σ and L, respectively). By using these two parameters to form a two-dimensional space, the approximate regions of validity are then established. The second major new consideration is the development of a theoretical two-scale model describing bistatic reflectivity as well as the numerical results computed for the bistatic radar cross section from rough surfaces especially from the sea and snow-covered surfaces. The results are used to show the Brewster angle effect on near-grazing angle scattering.     

高斯分层介质粗糙面光波透射问题的微扰法研究

运用微扰法研究平面波入射分层介质粗糙面的光波透射问题,推出了不同极化状态的透射光波散射系数公式。采用高斯粗糙面来模拟实际的分层介质粗糙面,结合高斯粗糙面的功率谱导出了平面波入射高斯分层介质粗糙面的透射系数计算公式。通过数值计算得到HH极化透射系数随透射光波散射角变化的曲线,讨论底层介质介电常数、中间介质介电常数和厚度、粗糙面参数及入射光波长对透射系数的影响。数值计算结果表明：底层介质介电常数、中间介质介电常数和厚度、粗糙面参数及入射光波长对透射系数的影响是非常复杂的。