Interference in light scattering from slightly rough dielectric layers

The scattering of light from a slightly rough surface overlying a reflecting surface is investigated. It is shown that the long-scale component of the roughness spectrum plays a critical role in the scattering patterns obtained. The scattered interference patterns are critically dependent on small variation of the rms height of the long-scale component of the roughness. Conventional perturbation theory is found to be invalid in cases in which interference phenomena in the scattering are of importance. A model is proposed that quantitatively describes the measured angular intensity distributions.     

An interferometric linear in-plane position transducer

When mutally coherent light beams overlap on an optically rough surface, the scattered light fields or speckle patterns interfere. The intensity at any point depends on the phase difference between the light fields. By matching the sensitive area of a photodetector to speckle size, an electronic signal is obtained which can be used to monitor in-plane rigid body translations of the surface with interferometric precision. Two reliable methods of obtaining directional sensitivity based on polarization properties are described and it is shown that depolarization effects due to rough surfaces, do not cause any difficulty. Intensitivity to motion orthogonal to the plane of the apparatus is demonstrated.     

Determination of the autocorrelation function of height on a rough surface from coherent light scattering

Under the assumption of a Gaussian first order probability density function of height the autocorrelation function of height on a rough surface is obtained from the Fourier transform of the ensemble average far-field scattered light intensity. The theory of the method and some initial results are presented.     

Multiple scattering of plasmons at rough surfaces

We investigated the polarization and angle dependence of the scattered light intensity of surface plasma oscillations (SPO) propagating along rough silver surfaces. The rough silver films were prepared using the methods of pre-evaporating CaF₂ and silver on heated substrates. The scattered light intensity of both systems is explained by surface scattering effects. Differences of the light intensities between the rough silver films prepared by the two methods mainly were observed in “restlight intensities”, which cannot be described by first-order scattering theories. We explain these differences by higher order scattering effects.     

Apparent and real roughness

Some works have studied the light scattering from a rough surface immersed in a liquid, where the light scattered from the immersed rough surface was assumed to be equivalent to that scattered from a fictitious rough surface with a different texture. This work deals with this kind of problems analyzing the light scattered by a reflecting strong scatterer and the light scattered by a rough surface immersed in a transparent liquid. The general Kirchhoff solution for scattering from a rough surface has been used.It is shown that under certain conditions, the mean scattered intensity (MSI) from a surface immersed in a liquid can be quasi-indistinguishable from that scattered from a non-immersed surface with an “equivalent texture”. An expression relating the equivalent texture and the immersed surface texture was obtained.The results of this work allow to evaluate the characteristics of any surface immersed in a liquid with a known refractive index.     

Arbitrary laser beam propagation in free space

The propagation of arbitrary laser beams in free space is examined. For this purpose, starting with an incident field of arbitrary field distribution, the intensity at the receiver plane is formulated via Huygens Fresnel diffraction integral. Arbitrary source field profile is produced by decomposing the source into incremental areas (pixels). The received field through the propagation in free space is found by superposing the contributions from all source incremental areas. The proposed method enables us to evaluate the received intensity originating from any type of source field. Using the arbitrary beam excitation, intensity of various laser beams such as cos-Gaussian, cosh-Gaussian, general type beams are checked to be consistent with the already existing results in literature, and the received intensity distributions are obtained for some original arbitrary beam field profiles. Our received intensity formulation for the arbitrary source field profiles presented in this paper can find application in optics communication links, reflection from rough surfaces, optical cryptography and optical imaging systems.     

3D surface topography from the specular lobe of scattered light

Scattered light from a surface contains a huge amount of information including surface slope, roughness, pattern, texture, etc. In this paper, the relationship between the intensity distribution of scattered light from a surface and the 3D surface topography will be investigated. From the geometrical point of view the intensity distribution of scattered light from a surface may be modelled with three components, the specular spike, specular lobe and diffuse lobe. In the situation when light is scattered from a relatively smooth surface whose roughness is much larger than the wavelength of the incident light, the scattered light intensity distribution will consist of only a diffuse lobe and a specular lobe, which are well described by a combination of the Lambertian and Torrance–Sparrow geometrical models. Based on the light scattering phenomenon, in this paper a scanning method capable of measuring the 3D surface topography with 500 mm scanning width, high scanning speed, and micron resolution is presented. The 3D topography measurement is implemented by using a linear photodiode array to measure scattered light intensity distribution at different angles against the surface normal. Then the specular lobe of the scattered light will be extracted at each scanning point to calculate the surface normal distribution. Sequentially, the 3D surface topography is obtained by using gradient integration techniques.     

Exact multiple scattering of waves from random rough surfaces

The exact multiple scattering theory of waves scattered from a random rough surface is presented. We give an iterative series for the mean scattered intensity (I (Q)) for all order in the statistics. We show that the coherent intensity for large correlation distances approaches the value obtained in the Kirchhoff approximation by Beckmann. Also we prove that a “white noise” surface reflects specularly the whole incident intensity.     

Average scattered field from a random PEC cylinder buried below a slightly rough surface

Scattering from a perfect electric conducting cylinder with random radius buried below a half space dielectric homogenous interface is studied. The cylindrical wave scattered by cylinder is expanded in terms of plane wave spectrum. Small perturbation method is used to study the interaction of each plane wave with the interface. The zeroth order term yields solution for a flat interface, whereas scattering from a rough surface is given by first-order term. Results are obtained for both TM and TE polarizations. Analytical expressions of the average scattered field are obtained and verified using numerical evaluation. Different scattering scenarios are simulated by varying the distribution of the radius. It is observed that average scattering cross section of an ensemble with normal/uniform distribution is almost equal to that of a cylinder with mean radius.     

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

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.     

Double-exposed Gabor holograms: a new approach to storage of information

The interface patterns obtained using doubly-exposed Gabor holograms of rough objects undergoing small axial displacement are investigated by treating the resulting speckle patterns as a system such as an array of slits. The reconstructed images, which are related to each other as separate identical diffusers that are correlated, give rise to an interference phenomenon in their Fourier plane. The resultant intensity is modulated by a ring system, the geometrical characteristics of which are dependent on the geometry of the arrangement. New formulae are obtained and their validity is substantiated by experiments.     

In-situ investigation of the structure of electrolitically deposited cobalt-phosporous alloy upon heating

The effects of heating on the structure of deposited CoP alloy is investigated by means of transmission electron microscopy and electron diffraction. A series of electron diffraction patterns of the in situ annealing process are obtained. Methods for analyzing diffraction patterns and intensity profiles are examined. Custom software is developed to automate the analysis of electron diffraction patterns and the detection of peaks in intensity profiles, along with their parameterization.     

Fractal structure of digital speckle patterns produced by rough surfaces

We report on the fractal analysis of digital speckle patterns experimentally generated using an optical setup to record the light scattered from metallic rough surfaces in the normal direction. Using the differential box counting technique, we have calculated the fractal dimension of digital speckle patterns for six samples with different roughness. Our results show a quadratic dependence between the surface roughness and the fractal dimension of the corresponding digital speckle pattern. As an application a method to determine the surface roughness of metallic surfaces is proposed.     

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.     

Fourth moments of acoustic waves forward scattered by a rough ocean surface

Three types of statistical fourth moments of acoustic waves forward scattered by a randomly rough ocean surface are derived and numerically evaluated. The first one is related to the scintillation index which characterizes intensity fluctuations. The second one is the two-position intensity correlation function which describes the spatial correlation of wave intensity. The third is the fourth-moment two-position coherence function which carries information on the phase fluctuations of the scattered wave. In the range of weak scattering, the ratio of the absolute value of the fourth-moment two-position coherence function over the two-position intensity correlation exactly describes the mean-square fluctuation of the relative phase between the two positions. The acoustic frequency is high so that the Kirchhoff approximation can be used. Two types of spectral functions for surface-height fluctuations are considered: a Gaussian spectrum and the Donelan-Pierson spectrum. The latter is obtained from a model for the fluctuations of the ocean surface height which are controlled by the wind speed at the ocean surface.     

Acoustic scattering by a three-dimensional elastic object near a rough surface

The ensemble-averaged field scattered by a smooth, bounded, elastic object near a penetrable surface with small-scale random roughness is formulated. The formulation consists of combining a perturbative solution for modeling propagation through the rough surface with a transition (T-) matrix solution for scattering by the object near a planar surface. All media bounding the rough surface are assumed to be fluids. By applying the results to a spherical steel shell buried within a rough sediment bottom, it is demonstrated that the ensemble-averaged "incoherent" intensity backscattered by buried objects illuminated with shallow-grazing-angle acoustic sources can be well enhanced at high frequencies over field predictions based on scattering models where all environmental surfaces are planar. However, this intensity must compete with the incoherent intensity scattered back from the interface itself, which can defeat detection attempts. The averaged "coherent" component of the field maintains the strong evanescent spectral decay exhibited by flat interface predictions of shallow-angle measurements but with small deviations. Nevertheless, bistatic calculations of the coherent field suggest useful strategies for improving long-range detection and identification of buried objects.     

随机粗糙表面上相关点的散射

随机粗糙面上邻近两点的高度与坡度是相关的.由这种相关性对散射的贡献是明显的.在计算粗糙表面散射强度时,应包括这一相关性引起的贡献.本文提供了一种解法和修正后的一维散射强度的解析公式,以及数值计算的实例.     

Fourth moments of acoustic waves forward scattered by a rough ocean surface

Abstract

Three types of statistical fourth moments of acoustic waves forward scattered by a randomly rough ocean surface are derived and numerically evaluated. The first one is related to the scintillation index which characterizes intensity fluctuations. The second one is the two-position intensity correlation function which describes the spatial correlation of wave intensity. The third is the fourth-moment two-position coherence function which carries information on the phase fluctuations of the scattered wave. In the range of weak scattering, the ratio of the absolute value of the fourth-moment two-position coherence function over the two-position intensity correlation exactly describes the mean-square fluctuation of the relative phase between the two positions. The acoustic frequency is high so that the Kirchhoff approximation can be used. Two types of spectral functions for surface-height fluctuations are considered: a Gaussian spectrum and the Donelan-Pierson spectrum. The latter is obtained from a model for the fluctuations of the ocean surface height which are controlled by the wind speed at the ocean surface.