In this work we study theoretically the scattering of p-polarized light of frequency (omega) from a system consisting of a dielectric medium (prism) characterized by a dielectric constant (epsilon) ₀ in the region x₃ $GTR D; a metal film characterized by a complex, frequency-dependent dielectric function(epsilon) ₁((omega) ) in the region 0 < x₃ < D; a dielectric film characterized by a dielectric constant (epsilon) ₂ in the region (zetz) (x₁) < x- 3) < 0; and vacuum ((epsilon) ₃ equals 1) in the region x₃ < (zetz) (x₁). The light whose plane of incidence is the x₁x₃- plane, in incident through the prism. For the surface profile function (zetz) (x₁) we take the form (zetz) (x₁) equals -d(theta) (x₁)(theta) (L-x(₁), where (theta) (x₁) is the Heaviside unit step function. Thus we have a dielectric film thickness d and dielectric constant (epsilon) ₂ covering the half of the lower surface (x₃ equals 0) of the metal film defined by x₁$GTR0, or a dielectric film of thickness d and dielectric constant (epsilon) ₂ covering the part of the lower surface (x₃ equals 0) of the metal film defined by 0 < x₁ < L. The reduced Rayleigh equation for the amplitude of the light scattered back into the prism, R(qk), is obtained, and solved by the Wiener-Hopf method, and the result is used to calculate the intensity of the scattered field in the far field region as a function of x₁ for a fixed value of x₃ for several values of the wavelength of the incident light. The results provide information about the scattering of the surface plasmon polariton at the metal-vacuum interface, excited by the incident light, by an index step on that interface. A brief discussion of the transmission of light through this system is also given.

The elastic scattering of electromagnetic waves from a rough surface containing resonant structures is studied as a function of the frequency of the incident light. A diagrammatic perturbation theory treatment is used. The surface consists of a planar vacuum-metal or vacuum-dielectric interface upon which an array of identical cylindrical dielectric ridges are randomly placed. The axes of the ridges are parallel to one another so that the translational symmetry of the surface is maintained along one axis in the surface, and the scattering of p-polarized radiation within a scattering plane perpendicular to the axes of the ridges is treated. The ridges are composed of a medium which undergoes a dielectric resonance as a function of frequency. The frequencies of the surface shape resonance modes bound to the dielectric ridges are computed for a surface supporting a single dielectric ridge. For the surface supporting a random array of dielectric ridges the specular scattering and diffuse scattering are computed for frequencies in the neighborhood of the dielectric resonance of the dielectric material forming the Gaussian ridges.

The analysis presented in this paper focuses on the calculation of the scattering cross-section of polarized electromagnetic plane waves from 2-D dielectric surfaces with non-Gaussian statistics. The second order small slope approximation is used to evaluate the scattered field from the 2-D rough surface. The gap between the small perturbation method and Kirchhoff's approximation is bridged using the small slope approximation. This method is applicable to surfaces of arbitrary roughness possessing small slopes. The incident and scattered wave vectors are in arbitrary directions. The coherent and incoherent components of the electromagnetic field are calculated for the bistatic case. In this paper we consider dielectric materials. The permittivity of the dielectric field can be complex. A finite conductor in this paper surfaces with Gaussian and non-Gaussian statistics, i.e., a Guassian probability density function is assumed for the random rough surface heights and the correlation function is assumed to be non-Gaussian. Non- isotropic grooves on the dielectric surfaces are modeled by non-Gaussian correlation functions. Numerical simulations are carried out with the second order SSA method and we compare these results with the Kirchhoff's approximation, the small perturbation approximation, and the full-wave method.

Multiple scattering and shape-related effects are an active and important field of research in the area of diffraction and scattering of electromagnetic waves by rough surfaces. Most of the rigorous numerical techniques for dealing with this problem were limited to the treatment of single-valued surfaces. We have extended the formulation of Mendoza- Suarez and Mendez (1997) for dealing with multi-valued profile functions in order to study the scattering of reentrant surfaces or cavities in both, the near and far-field. We have evaluated the near-field in circular cavities with narrow entrances, as well as in the case of clusters of rods or cylinders. Resonant frequencies are clearly identified for these structures. We have also found that our model could be useful to predict wave-induced oscillations in harbors of arbitrary geometry. This comes form the fact that the mathematical formulation of the problem of light scattering by cavities (in the case of p polarization) is similar to the one employed in the case of harbors of arbitrary shape, when a water wave arrives at its entrance (Hwang and Tuck, 1970; Lee, 1971). The results obtained with our model are in close agreement with previously reported theories and experimental data.

The physical system we consider in this work consists of vacuum in the region x₃ $GTR (zetz) (x₁), and a dielectric medium characterized by a complex dielectric constant (epsilon) in the region x₃ < (zetz) (x₁). The surface profile function (zetz) (x₁) is assumed to be a single-valued function of x₁, that is differentiable as many times as is necessary, and to constitute a zero-mean stationary, Gaussian random process. It has been recently been shown that a local relation can be written between L(x₁(omega) ) equalsV [deltaH₂$GTR(x₁,x₃(omega) )/(delta) x₃]_x3equals0) and H(x₁(omega) ) equalsV [H₂$GTR(x₁,x₃(omega) )]_x3equals0, where H₂$GTR(x₁,x₃(omega) ) is the single nonzero component of the total magnetic field in the vacuum region, in the case of a p-polarized electromagnetic field whose plane of incidents is the x₁x₃-plane. This relation has the form L(x₁(omega) ) equals I(x₁(omega) )H(I(x₁(omega) ), where the surface impedance I(I(x₁(omega) ) depends on the surface profile function (zetz) (x₁) and on the dielectric constant (epsilon) of the dielectric medium. A completely analogous relation exists when L(x₁(omega) ) equalsV [(delta) E₂$GTR(x₁,x₃(omega) )/(delta) x₃]_x3equals0) and H(x₁(omega) ) EQV [E₂(x₁,x₃(omega) )]_x3equals0, where E₂$GTR(x₁,x₃(omega) ) is the single nonzero component of the electric field in the vacuum region, in the case of an s-polarized electromagnetic field whose plane of incidence is the x₁x₃-plane. Our goal in this work is to obtain the relation between the values of L(x₁(omega) ) and H(x₁(omega) ) averaged over the ensemble of realizations of the surface profile function (zetz) (x₁). This we do by the use of projection operators and Green's second integral identity in the plane.

An inversion algorithm for the reconstruction of surface profiles from far-field amplitude scattering data is considered. The algorithm is based on a wavefront matching principle, and is related to interferometric profiling techniques. The performance of the algorithm is studied using rigorous numerical data for the field scattered by one- dimensional surfaces.

We consider a scattering system consisting of a dielectric film deposited on a semi-infinite metal, and focus on the wavelength dependence of the total integrated scattering and angle resolved scattering from such a system. In particular we study theoretically by a large scale rigorous numerical simulation approach the reflectivity, R((lambda) ), as well as the total scattered energy, U((lambda) ), of such systems as functions of the wavelength of the incident light. The scattering system consists of vacuum in the region x₃ $GTR d₁+(zetz) ₁(x₁), a dielectric film in the region, d₂+(zetz) ₁(x₁), and a metal in the region x₃ < d₂ + (zetz) (x₁). This system is illuminated from the vacuum side by p-polarized light whose wavelength is allowed to vary from 0.2micrometers to 1.2micrometers . The film is assumed to have a dielectric function that is insensitive to the wavelength of the incident light. In obtaining the numerical results reported here the metal substrate is taken to be silver. The dielectric function of silver for a given wavelength is obtained by interpolation from experimental values. The surface profile functions,(zetz) _1,2(x₁), are assumed to be either zero or single-valued functions of x₁ that are differentiable as many times as is necessary, and to constitute zero-mean, stationary Gaussian random processes. Their surface height auto-correlation function is characterized by a Gaussian power spectrum. We study and discuss the wavelength dependence of R((lambda) ) and U((lambda) ) for several scattering systems obtained by turning on and off the surface profile functions (zetz) _1,2(x₁) and/or the correlation between these two surface profile functions.

The coherence theory predicts that the correlation in the fluctuations of a source distribution can cause frequency shifts in the spectrum of the emitted radiation, even when the source is at rest relative to the observer. Recently, we have measured the Wolf Effect, or frequency shifts from a real image of a point source, and further verified the coherent interference effect of a finite-band source.

We report the experimental study of the amplified enhanced backscattering through dye-doped polymer. The sample is a slice of pyrromethene-doped polymer coupled with a one-dimensional rough gold film with a large slop. When the sample is illuminated with a p- polarized He-Ne laser, and pumped by a cw Argon-ion laser, the amplified scattering is observed. It is found that the enhanced backscattering peak with its associated satellites is sharply increased and their widths narrowed for a pyrromethene-doped polymer with low dielectric constant $epsolin₂.

This paper presents a new analytical BRDF model allowing the simulation of the optical behavior of a kind of multilayers formed of homogeneous and isotropic thin films with identically rough boundaries. The boundaries are supposed to be locally smooth and the roughness is generated by a stationary Gaussian process characterized by two parameters: RMS height (sigma) and the correlation length (tau) . The BRDF is composed of three terms: specular, directional-diffuse and uniform diffuse. The expressions for the coherent (specular) and incoherent (directional diffuse) components of the BRDF are derived in the framework of the Kirchhoff theory of diffraction. By means of the Abeles [1] formalism and using the small-slope assumption, we derive a first order expansion for the amplitude reflection coefficient of the multilayer system. Replacing the reflection coefficient by this approximate formula in the Helmholtz-Kirchhoff integral allows us to evaluate both the coherent and incoherent components of the BRDF. This model was integrated into a spectral ray tracing algorithm to produce pictures of composite multilayer materials which will be displayed and commented hereafter. We also provide a visual evaluation of the model, studying the effect of a variation of the parameters (number of layers, composition of the multilayer, surface parameters.)

Papermaking process consists in a succession of unit operations having for main objective the expression of water out of the wet paper pad. The three main stages are successively, the forming section, the press section and finally the drying section. Furthermore, another operation (calendering) may be used to improve the surface smoothness. Forming, pressing and drying are not on the scope of this paper, but the influence of formation and calendering on surface roughness is analyzed. The main objective is to characterize the materials and specially its superficial structure. The proposed model is described in order to analyze this topographical aspect. Some experimental results are presented in order to illustrate the interest of this method to better understand physical properties. This work is therefore dedicated to the description of the proposed model: the studied surface is measured at a microscopic scale using for example, a classical stylus profilometry method. Then the obtained surface is transformed using a conformal mapping that retains the surface orientations. Due to the anisotropy of the fiber distribution in the plane of the sheet, the resulting surface is often not isotropic. Hence, the micro facets that identify the interfaces between pores and solid (fibers in the studied case) at the micro level are transformed into a macroscopic equivalent structure. Furthermore, an ellipsoid may be fit to the experimental data in order to obtain a simple model. The ellipticities are proved to be linked for paper to both fiber orientation (through other optical methods) and roughness. These parameters (ellipticities) are shown to be very significant for different end-use properties. Indeed, they shown to be correlated to printing or optical properties, such as gloss for example. We present in a first part the method to obtain a macroscopic description from physical microscopic measurements. Then measurements carried on different paper samples, using a classical profilometry methods, illustrate the proposed methodology. Some comparisons with conventional roughness indexes are presented. Finally, some applications, and more precisely end use properties, are shown to underline the interest of the proposed method. These geometrical characteristics may be deduced from experimental results whatever the microscopic size is.

In this work we consider a structure consisting of vacuum in the region x₃$GTR(zetz) (x₁); a dielectric film characterized by a real,positive, dielectric constant (epsilon) in the region -D < x₃ < (zetz) (x₁); and a vacuum in the region x₃<-D. The surface profile function (zetz) (x₁) is assumed to be a single-valued funtion of x₁, that is differentiable, and constitutes a random process. This structure is illuminated from the region x₃ $GTR (zetz) (x₁) by s-polarized light whose plane of incidence is the x₁x₃-plane. By the use of the geometrical optics limit of phase perturbation theory we show how to design the surface profile function (zetz) (x₁) in such a way that the mean differential transmission coefficient has a prescribed form within a specified range of the angle of transmission, and vanishes outside this range. In particular, we consider the case in which the transmitted intensity is constant within a specified range of the angle of transmission, and vanishes outsides it. Rigorous numerical simulation calculations show that the transmitted intensity indeed has this property.

We present numerical calculations for a model illumination mode Scanning Near-field Optical Microscope (SNOM) that provide some guidelines for the determination of the resolution of such instruments. The calculations of the near-field intensity distribution inside the tapered waveguide show that the metal employed in their coating determines the degree of confinement of the radiation and, thus, the size of the effective source at the exit end of the waveguide. It is argued that simple measure of the ultimate resolution of near-field microscopes is provide by the skin depth of the metal employed in the coating of the tapered waveguide. These ideas are supported by the calculated near- field intensity distributions in the neighborhood of the tapered waveguide, and by the simulated images of a two-cylinder object.

Numerical modelling is applied to investigation of scattering of plane linearly polarized monochromatic wave by sine variations of dielectric surface relief. The modelling is based on finite-different time-domain technique. Results of modelling include 1) space distribution of scattered light, 2) dependence of field amplification on ratio of roughness amplitude to laser wavelength, and 3) dependence of field amplification on ratio of roughness period to laser wavelength. Obtained results show that for TE polarization a) transmitted signal is more sensitive to roughness parameters than reflected on, b) there is narrow resonance in dependence of amplitude of scattered field on laser wavelength and roughness period, c) dependence of amplitude of scattered field on roughness amplitude is described by parabolic function for small values of relief amplitude. Depending on relief amplitude and period, scattering by sine roughness can result in formation of inhomogeneous space field distribution consisting of periodic field maxima inside dielectric or formation of homogeneous distribution such that both transmitted and reflected signals are close to plane wave. We consider the following applications of obtained results: 1) possibility to develop a new technique for in-situ surface roughness characterisation, and 2) anti-reflection effect.

This paper deals with applications of angle resolved light scatter (ARS) measurements as well as with the discussion of design and application problems of ARS sensors. The first section gives a description of the experimental sensor setup. In the second section of the paper two applications will be outlined, firstly particle detection on smooth Si surfaces, and secondly defect detection in small Si v-grooves. In the third section of the paper principal drawbacks of the experimental ARS sensor and their elimination will be discussed.

The directional dependence of the intensity and polarization of light scattered by a series of steel surfaces was measured. The samples differ by polishing procedure. Theories for light scattering from microroughness and permittivity variations are reviews and used to interpret the results. It is shown that the experimental data can be fit to a combination of the two scattering mechanisms, whereby the relative amplitude of the two scattering sources and the complex degree of correlation are treated as adjustable parameters. The fits show at low degree of correlation at high spatial frequencies. This correlation has a characteristic phase, common for all of the samples. Comparison at the fitted roughness power spectral density (PSD) functions with those obtained by atomic force microscopy (AFM) showed reasonable but not perfect agreement. This study demonstrates how measurements of the polarization of scattered light can be used to quantify the scatter from two different scattering sources.

It is well known that functional surfaces in microelectronics and optics can be inspected very fast with scatterometers or scatter sensors. However, there is an increasing interest in looking at specific sample areas in more detail, i.e., the micro topography of the surface has to be measured. Since far-field optical profilers are diffraction limited, the means of choice are very often Scanning Probem Microscopes (SPMs), and namely, Atomic Force Microscopes (AFMs). Various methods for processing data obtained by AFMs will be discussed. An AFM measurement should deliver the surface micro topography to enable the determination of characteristic values, in particular rms roughness. Normally, a superposition of the surface characteristics and artifacts due to the AFM is obtained.

A new device for rapid non-contact characterization of roughness spatial distribution of flat surfaces is developed. Its operational principle is based on the strong dependence on roughness of the intensity of x-rays reflected from a superpolished surface. This effect may be used to obtain a two-dimensional map of the roughness spatial distribution for flat surfaces with a rms, roughness height of the order of one nanometre. The key components of this device are a precision mechanical one-dimensional scanning stage, a parabolic collimator with vacuum beam path, and a temperature stabilized cooled x-ray linear detector array.

The nitration process influences the mechanical and chemical properties of steel and changes the near-surface characteristics. The nitrided surfaces are less sensitive to corrosive fluids and show a better stability against abrasion. Unfortunately, during treatment pores emerge at the surface. In general this is not desired, since the pores reduce the wear stability. The change of the near-surface characteristics also leads to a remodeling of the surface topography. For example, ground, smooth surfaces show an increased but isotropic roughness after nitration. During the recent years, various speckle techniques for an in-process characterization of surface topography have been improved significantly. One of these promising techniques is the method of trichromatic speckle autocorrelation. Its measuring principle is based on trichromatic light scattering and enables to determine an integral parameter of the surface roughness by the evaluation of the speckle elongation. Especially in the case of nitration, where the specimen is located in a stove filled with ammonia at a temperature of 580 degrees Celsius, this technique offers an in-processing monitoring of surface topography changes from outside the stove. In this paper, the in-process characterization of surface topography by speckle autocorrelation will be introduced. In this context an algorithm has been developed, which allows to estimate the position of the optical axis within the speckle pattern and therefore to determine the surface roughness as well as the local inclination of isotropic surfaces. An important goal of the current research is to realize a reliable process control based on the speckle autocorrelation, that is necessary to produce nitrided surfaces without pores in the compound layer and with good abrasive and corrosive resistance.

Scattering of slow neutron or x-rays on roughness in geometry of total reflection is considered. Part of radiation scattered on roughnesses at the front interface of a plane sample penetrates into the sample and outgoes through its back and edge surfaces. Theory for calculation of angular distribution of transmitted radiation after such a scattering is presented. It is shown that there is a range of angles below the critical one, which does not contain transmitted radiation. If, nevertheless, the radiation is present in this range, it gives information about additional scattering of transmitted radiation on the back surface roughnesses.

The method of conformal mapping, through the Schwartz-Christoffel transformation, is applied to solve the scattering of electromagnetic beams from planar surface with a Koch corrugation. We use the integral method with the calculation of admittance of the transformed plane which is the kernel in the equations. The problem is planted for both polarization for the far field.

Many surfaces scatter light in an anisotropic way, that is, for a normally incident beam, the distribution of scattered light varies as a function of the azimuthal angle of the scattered direction. Examples of surfaces with anisotropic scattering characteristics are brushed metal reflectors and certain types of diffusers. A model, based on an anisotropic scatter model proposed by Ward is introduced. The ability to fit this model to various sets of measured BSDF data is investigated. Raytracing simulations are performed using the fitted parameters, and the results are compared with experiments.

Most probably scanning probe microscopy will play a key role in surface characterization while entering the nanotechnology era. Today, however, nearly all SPMs have only scan ranges up to 100 micrometers x 100 micrometers . The production of microsystems with nano-structured elements requires measuring instruments with extremely high resolutions and working areas in millimeter range. Therefore, a Nanometer Coordinate Measuring Machine (NCMM) with a working volume of at least 10 x 10 x 5 mm³ will be developed. We have to make great demands on the positioning system in this case, especially the design of the control algorithms is very critical. An electromechanical model of the xyz-positioning system shall support the optimization of the controllers. This paper describes some problems of the development of a NCMM. First simulation results will be discussed in short. Results of measuring the dynamic behaviour of the xyz-positioning system describe the observed difficulties of positioning in different orders of magnitude (nm - micrometers - mm).