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Quantitative characterization of micro-topography a bibliography of industrial surface metrology

Publisher Summary This chapter describes enhanced backscattering in optics. The chapter considers backscatter enhancement in light scattered from a body embedded in a random medium. A similar phenomenon occurs in multiple scattering of light in a randomly inhomogeneous medium where there are no clear-cut scatterers that stand out against a background. The effects of backscatter enhancement and weak localization are phenomena, in which coherent paths of the Watson-Ruffine type are essential. The chapter describes multiple new manifestations of coherent effects in backscattering. These include the effects of long-distance correlations, the partial reversal of the phase front in a random medium, the magic cap effect, antispecular scattering by very rough random surfaces, and backscattering involving surface waves. The chapter also discusses the opposite case of a small number of scatterers, in which summation cannot be replaced with integration.

II Enhanced Backscattering in Optics

A numerical study of 14-GHz backscattering from ocean-like surfaces, described by a Pierson-Moskowitz spectrum, is presented. Surfaces rough in one and two dimensions are investigated, with Monte Carlo simulations performed efficiently through the use of the canonical-grid expansion in an iterative method of moments. Backscattering cross sections are illustrated for perfectly conducting surfaces at angles from 0 to 60/spl deg/ from normal incidence, and the efficiency of the numerical model enables the composite surface theory to be studied in the microwave frequency range for realistic one-dimensional (1D) surface profiles at low wind speeds (3 m/s). Variations with surface spectrum low-frequency cutoff (ranging over spatial lengths from 21.9 to 4.29 cm) are investigated to obtain an assessment of composite surface model accuracy. The 1D surface results show an increase in hh backscatter returns as surface low-frequency content is increased for incidence angles larger than 30/spl deg/, while /spl nu//spl nu/ returns remain relatively constant, all as predicted by the composite surface model. Similar results are obtained for surfaces rough in two dimensions, although the increased computational complexity allows maximum surface sizes of only 1.37 m to be considered. In addition, cross-polarized cross sections are studied in the two-dimensional (2D) surface case and again found to increase as surface low-frequency content is increased. For both 1D and 2D surfaces, backscattering cross sections within 20/spl deg/ of normal incidence are found to be well matched by both Monte Carlo and analytical physical optics (PO) methods for all low-frequency cutoffs considered, and a comparison of analytical PO and geometrical optics (GO) results indicates an appropriate choice of the cutoff wavenumber in the composite surface model to insure an accurate slope variance for use in GO predictions. This choice of cutoff wavenumber is then applied in the composite surface theory for more realistic ocean spectra and compared with available experimental data.

A numerical study of the composite surface model for ocean backscattering

An inversion algorithm, based on the Kirchhoff approximation, for the reconstruction of a rough-surface profile from measurements of the scattered field is described. It is shown that the data can be related to the surface profile through a Fourier-transform relationship by a specific choice of data and so lead to a simple fast-Fourier-transform-based procedure. The algorithm is illustrated through the use of numerical results.

Reconstruction of rough-surface profiles with the Kirchhoff approximation

Numerical simulations, using both exact and approximate methods, are used to study rough surface scattering in both the smd and large roughness regimes. This study is limited lo scattcring lrom rough one-dimensional surfaces that obey the Dirichlet boundary condition and have a Gaussian roughness spectrum. For surfdces with small roughness (kh≪1, where k is the radiation wavenumber and h is the root-mean-square (RMS) Surface height), perturbation theory is known to be valid. However, it is shown numerically that when kh≪1 and kl≳6 (where I is the surface correlation length) the Kirchhoffapprorimation is valid except at low grazing angles, and one must sum the first three orders of perturbation theory obtain the correct result. For kh≪1 and kl≅1, first-order perturbation theory is accurate. In this region, the accuracy of the first two terms of the iterative series solution of the exact integral equation is examined; the first term a1 this series is the Kirchhoff approximation, It is shown numeric...

Studies of scattering theory using numerical methods

In this article, a formulation is given for two‐dimensional scattering of a plane wave incident on an infinitely long surface with a Gaussian distribution of surface height. The surface height may have any physically reasonable correlation function. This method generalizes previous work by the present authors, in which a finite length surface was treated numerically by Fourier methods. For each numerically generated random surface, an integral equation must be solved to find the pressure gradient on the surface. The reflection coefficients, describing the angular distribution of scattered energy, are then formed. It is shown how the various moments of the scattered pressure may be obtained efficiently from averages of these reflection coefficients. Using these techniques, numerical results are presented for the angular distribution of energy for a surface with a Gaussian correlation function of surface height and for a correlation function modeling a more realistic sea surface. Results are presented showing that it is not necessary to taper the incoming wave field in order to obtain accurate answers. For large values of the ratio of the standard deviation of height to the surface correlation length, it is found that the mode of scattering is very different to that found at small surface heights. For some cases, the maximum in the angular distribution is found in the backscatter direction, with the specular peak not at all apparent. It appears that this phenomenon is due to multiple scattering of the acoustic wave at the surface. Finally, it is shown that for the class of problems treated here, the ensemble average intensity is constant at all normal distances from the surface, while the normalized covariance of intensity varies with normal distance from the surface in a way that is, in some limiting cases, very similar to the scattering of a wave passing through a phase modulating screen or an extended random medium.

Numerical evaluation of the statistics of acoustic scattering from a rough surface

A method is described for dealing with acoustic scattering from a time‐independent pressure‐release surface. As in work by previous authors, the problem is formulated as an integral equation on the surface. This formulation takes account of arbitrarily large surface roughness and multiple scattering phenomena at the surface. The problem may be considered naturally in two stages. The first part of the problem is to invert the integral equation to find the pressure gradient on the surface. The eigenfunction expansion method used by Holford [J. Acoust. Soc. Am. 70, 1116–1128 (1981)] for periodic surfaces is extended to deal with more general aperiodic surfaces. It is then shown that this approach is almost exactly equivalent to a direct collocation method. The second part of the problem is to evaluate the scattered pressure away from the surface. The method used here is to calculate the reflection coefficients from the Fourier transform of the pressure gradient on the surface. The reflection coefficients giv...

B. J. Kachoyan

Papers

Numerical evaluation of the statistics of acoustic scattering from a rough surface

Acoustic scattering from an arbitrarily rough surface