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Fractal Characteristics Investigation on Light Scattering from Two Dimensional Rough Surface
Abstract
A normalized two dimensional band-limited Weierstrass fractal function is used for modeling the rough surface. Based on Kirchhoff theory, an analytic solution of the average scattering field and the variance of scattering intensity are derived with emphasis on examining the relation of fractal dimension with the scattering pattern. The important conclusion is obtained that the diffracted envelope slopes of scattering pattern can be approximated to a slope of linear equation.
In this paper, based on the fundamental formulae of the first-order and second-order Kirchhoff approximation and with consideration of the shadowing effect, the backscattering enhancement of the one-dimensional very rough fractal sea surface with Pierson-Moskowitz spectrum is studied under the second-order Kirchhoff approximation at microwave frequency. The numerical results are compared with those of the first-order Kirchhoff approximation and integral equation method. The dependencies of the bistatic scattering cross section and the backscattering enhancement on the incident angle, fractal dimension, and windspeed over the sea surface are analyzed in detail.
Based on the scatteringfrom the rough conductingfractal surface with use of the extended boundary condition method (EBCM), this method is extended to the case of electromagnetic scattering from the rough dielectric fractal sea surface. The numerical result with microwave incidence by EBCM show good agreement with that obtained by the Kirchhoff approximation for the case of the fractal surface with small rms slope. The characteristic of the bistatic angular distribution of the scatteringamplitude is analyzed for different incident angle, different fractal dimension and different spatial wave numbers, the dependence of the backscatteringamplitude on the incidence angle and fractal dimension is also discussed in detail.
A normalized two-dimensional band-limited Weierstrass fractal function is used for modeling the dielectric rough surface. An analytic solution of the scattered field is derived based on Kirchhoff approximation. The variance of scattering intensity is presented to study the fractal characteristics by theoretical analysis and numerical calculations. The important conclusion is obtained that the diffracted envelope slopes of scattering pattern can be approximated to a slope of linear equation. This conclusion will be applicable for solving the inverse problem of reconstructing rough surface and remote sensing.
The EM scattering characteristics of rough surface about mine tunnel wall are connected with field distribution of electromagnetic wave closely. In this paper, electromagnetic scattering from rough surface based on Kirchhoff method was analyzed, and the EM scattering characteristics of horizontal polarization waves and vertical polarization waves were researched too, the calculation formulas of scattering coefficient were presented, the scattering field of rough surface in tunnel was simulated. The results show that the non-correlative scattering intensity would increase with increasing of roughness, and the great influence on electromagnetic waves propagation factors would be brought.
The problem of light scattering from a one-dimensional dielectric fractal rough surface is investigated using Fourier transform within the limitation of the Kirchhoff approximation. A numerical formula for the scattering coefficient is obtained by theoretical derivation. The scattering coefficient is calculated and compared to both the FFT method and the classical Kirchhoff approximation integral solution. This FFT method solves the problem of edge effect that is neglected in the numerical study by the conventional Kirchhoff approximation. The dependence of the distribution of the scattering coefficient on the patch size, the fundamental spatial wave number, and the fractal dimension of the surface are discussed in detail. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 35: 317–322, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10595
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.
This paper reviews the recent progress in surface measurement methods using active vision and light-scattering techniques. The active vision methods with different structured light patterns and the corresponding techniques are summarized. The surface roughness and defects inspection with light-scattering are discussed. After the review, an integrative method to measure surface waviness and form, roughness is proposed.
In this paper, the surfaces are modeled by multiscaled band-limited continuous fractal function and fractional Brownian motion function. The relationship between the scattering behavior and geometrical characteristics of the fractal surface is analysed in detail based on the perturbation solution and Kirchhoff approximation. Finally, some discussions are given about scattering from fractal surface.
One use of radar altimeters is to measure surface wind speeds through their effect on the roughness of the sea surface. The specular point reflection model is only appropriate for surfaces with roughness on scales which are large in relation to the radar wavelengths. This may not be the case for ocean surfaces. Here we model the sea surface as a fractal on the relevant scales. This is based on Hasselmann's model for nonlinear wave action transfer. The radar cross section for nadir backscatter is derived and its dependence on the radar frequency is determined. The results are compared with the cross section obtained by the specular point model for a smoothed surface, yielding the appropriate cutoff wavenumber. Some existing measurements of the sea surface by altimeter and stereophotogrammetry are discussed, suggesting a smaller fractal dimension for short gravity waves. Dual-frequency altimeters may help determine the synoptic spectral shape.
We consider the problem of scattering of optical or electromagnetic waves from a family of irregular rough surfaces characterized by band-limited fractal functions. This method provides a unified and realistic method for examining rough surfaces without the use of random or periodic functions. We relate the angular distribution and the amount of energy in the specularly scattered field to the fractal characteristics of the surfaces by finding their analytical expressions under the Kirchhoff limit and calculating the scattering patterns.
In this paper, a normalized band-limited Weierstrass function is presented for modelling 2D fractal rough surfaces. Some conventional statistical parameters, namely the root mean square and the correlation length of rough surfaces, are used to assess between fractal parameters and the roughness of surfaces. An analytic solution of the scattered light field from these fractal surfaces is derived based on Kirchhoff theory. Three statistical parameters, namely the average scattering coefficient, the average intensity of scattered field, and the root mean square of scattered field, are introduced to study the influence of various fractal parameters on the scattered field by theoretical analysis and numerical calculations.
The theory and applications of scattering of electromagnetic waves from
rough surfaces are addressed. The topics considered include: the general
Kirchoff solution for scattering from rough surfaces; periodically rough
surfaces; random rough surfaces: surfaces generated by random processes
and other models; the statistical distribution of the scattered field;
depolarization of electromagnetic waves scattered from a rough surface;
reflection of electromagnetic waves by a perfectly smooth earth; the
reflection of waves from irregular ground; methods of measurement of the
reflection coefficients of the earth; experimental investigation of the
specular reflection coefficient of the earth; experimental investigation
of diffuse scattering from the earth's surface; practical applications
of specular reflection and of diffuse scattering; scattering by
atmospheric sheets; reflection of radio waves by the moon and the
planets.
We study the light scattering from a one-dimensional rough surface characterized by a self-affine fractal structure. The rigorous Green theorem, integral equations formulation is employed to calculate the scattered electromagnetic field. An increase in the roughness-induced excitation of p-polarized surface plasmon polaritons is found with increasing fractal dimension, leading to very large surface field enhancements.