Thin polycrystalline metallic-film conductivity under the assumption of isotropic grain-boundary scattering

The polycrystalline thin-film resistivity and its temperature coefficient of resistivity are calculated from the assumption of isotropic grain-boundary scattering. The proposed simple analytical equations allow separate determination of the transmission coefficient of the grain boundary and the specular reflection coefficient at external surfaces. Good agreement with experiment is found.     

Specular and diffuse scattering of quasiparticles by a macroscopic object moving through superfluid3He-B

When a wire resonator is moving in superfluid³He-B at low temperature, there is a drag force due to scattering of thermally excited quasiparticles. The form of the graph of the drag force against the wire velocity depends strongly on the type of scattering at the wire surface. The force always rises linearly at zero velocity, and it tends to a limiting value at high wire velocity. However the graph is much more sharply curved if the scattering is diffuse than if it is specular. Here we present an analytic study of the form of the graph, by making estimates of the effect of Andreev reflection of scattered quasiparticles in the superflow round the wire. We show that the differences between diffuse and specular scattering can be understood intuitively, by considering the geometrical restrictions imposed by Andreev reflection on the scattering at the wire surface.     

Determination of refractive indices of opaque rough surfaces

The refractive indices of optical materials are usually determined from spectrophotometric and ellipsometric measurements of specular beams. When the roughness of the interfaces increases, the energy in the specularly reflected and transmitted beams decreases and scattering becomes predominant. For strong roughness (compared to the incident wavelength) a surface does not exhibit specular reflection or transmission, making difficult the determination of the refractive index. We describe two techniques, based on scattering measurements, that one can use to determine the refractive indices of opaque inhomogeneous media.     

Analysis of specular resonance in dielectric bispheres using rigorous and geometrical-optics theories

We have recently identified the resonant scattering from dielectric bispheres in the specular direction, which has long been known as the specular resonance, to be a type of rainbow (a caustic) and a general phenomenon for bispheres. We discuss the details of the specular resonance on the basis of systematic calculations. In addition to the rigorous theory, which precisely describes the scattering even in the resonance regime, the ray-tracing method, which gives the scattering in the geometrical-optics limit, is used. Specular resonance is explicitly defined as strong scattering in the direction of the specular reflection from the symmetrical axis of the bisphere whose intensity exceeds that of the scattering from noninteracting bispheres. Then the range of parameters for computing a particular specular resonance is specified. This resonance becomes prominent in a wide range of refractive indices (from 1.2 to 2.2) in a wide range of size parameters (from five to infinity) and for an arbitrarily polarized light incident within an angle of 40 degrees to the symmetrical axis. This particular scattering can stay evident even when the spheres are not in contact or the sizes of the spheres are different. Thus specular resonance is a common and robust phenomenon in dielectric bispheres. Furthermore, we demonstrate that various characteristic features in the scattering from bispheres can be explained successfully by using intuitive and simple representations. Most of the significant scatterings other than the specular resonance are also understandable as caustics in geometrical-optics theory. The specular resonance becomes striking at the smallest size parameter among these caustics because its optical trajectory is composed of only the refractions at the surfaces and has an exceptionally large intensity. However, some characteristics are not accounted for by geometrical optics. In particular, the oscillatory behaviors of their scattering intensity are well described by simple two-wave interference models.     

Markov models of specular and diffuse scattering in restoration ofmedical ultrasound images

Observed medical ultrasound images are degraded representations of the true tissue reflectance. The specular reflections at boundaries between regions of different tissue types are blurred, and the diffuse scattering within such regions also contains speckle. This reduces the diagnostic value of such images. In order to remove both blur and speckle, the authors develop a maximum a posteriori deconvolution algorithm for two-dimensional (2-D) ultrasound radio frequency (RF) images based on a new Markov random field image model incorporating spatial smoothness constraints and physical models for specular reflections and diffuse scattering. During stochastic relaxation, the algorithm alternates steps of restoration and segmentation, and includes estimation of reflectance parameters. The smoothness constraints regularize the overall procedure, and the algorithm uses the specular reflection model to locate region boundaries. The resulting restorations of some simulated and real RF images are significantly better than those produced by Wiener filtering     

Polarization of specular reflection and near-specular scattering by a rough surface

Polarization of specular reflection and near-specular scattering (NSS) by a randomly rough surface is investigated by the use of a Mueller matrix formulation. The collective effect by a rough surface on the average specular field results in reflectance loss and polarization, which can be explained by an effective medium theory. Effects of random NSS can be represented by a scattering matrix that is partially coherent and polarized. The incoherent and unpolarized part of scattering causes depolarization, and the coherent and polarized parts of scattering change the apparent polarization properties of specular reflection. Results of a simulation and least-squares fit of ellipsometric data to the models including the NSS effect, for a black anodized aluminum sample, are presented. Simultaneous least-squares fits for both ellipsometric data and reflectance data at multiple angles of incidence at three different wavelengths gave approximately the same rms roughness, which agrees with the profilometric values reported previously.     

Split off-specular reflection and surface scattering from woven materials

We measured radiance distributions for black lining cloth and copper gauze using the convenient technique of wrapping the materials around a circular cylinder, irradiating it with a parallel light source and collecting the scattered radiance by a digital camera. One family of parallel threads (weave or weft) was parallel to the cylinder generator. The most salient features for such glossy plane weaves are a splitting up of the reflection peak due to the wavy variations in local slopes of the threads around the cylinders and a surface scattering lobe due to the threads that run along the cylinder. These scattering characteristics are quite different from the (off-)specular peaks and lobes that were found before for random rough specular surfaces. The split off-specular reflection is due to the regular structures in our samples of man-made materials. We derived simple approximations for these reflectance characteristics using geometrical optics.     

小斜率近似方法分析粗糙界面声散射问题

利用小斜率近似方法计算了起伏海面的声散射特性,得到了具有高斯分布粗糙海面的平均反射系数（即镜反射系数）计算公式,并与微扰法和Kirchhoff近似做了比较,结果表明小斜率近似是一种非常有效的分析起伏表面散射特性的近似方法。最后讨论了海面镜反射系数随海面的不平整度（波浪的均方根高度）、声波频率和声波入射方向的变化关系,得出了只有在声波波长和起伏波浪高度可比拟时,才有明显的镜反射的结论。这为分析浅海目标声散射特性时,选择是否需要考虑海面（海底）所引起的多途效应提供了理论依据。     

Optical properties (bidirectional reflection distribution functions) of velvet

A detailed investigation has been made of the unusual characteristics of the angular distribution of surface scattering from velvet in the visual region. We present a novel method in which samples of velvet fabric are wrapped around a right-circular cylinder so that reemitted radiance can be measured by a digital CCD camera. This setup makes it relatively simple to acquire a large set of bidirectional reflection distribution function (BRDF) samples. The study reveals that, apart from the grazing specular lobe and an anisotropic backscattering peak near 50 degrees , the overall BRDF's are rather uniform across the whole angular span of observation. Attempts are made to relate these scattering characteristics to the physical and the geometrical structure of velvet.     

Scattering of a transversely confined Neumann beam by a spherical particle

Various properties of an electromagnetic wave whose spherical multipole expansion contains only Riccati-Neumann functions are examined. In particular, the novel behavior of the beam phase during diffractive spreading is discussed. When a Neumann beam is scattered by a spherical particle, the diffraction and external reflection portions of the scattering amplitude constructively interfere for large partial waves. As a result, a set of rapidly decreasing beam shape coefficients is required to cut off the partial wave sum in the scattering amplitudes. Because of its strong singularity at the origin, a Neumann beam can be produced by a point source of radiation at the center of a spherical cavity in a high conductivity metal, and Neumann beam scattering by a spherical particle can occur for certain partial waves if the sphere is placed at the center of the cavity as well.     

Enhanced specular peaks in diffuse light scattering from weakly rough metal surfaces

We employ Monte Carlo techniques based on the reduced Rayleigh equations to study an enhanced specular peak that appears in the light scattered from weakly rough metal surfaces. This peak is not associated with the specular reflection but instead appears, with finite angular width, at the specular angle of the mean diffusely scattered intensity. As is the case with backscattering enhancement, the specular peak arises from the interference of contributions of multiple-scattering processes related to surface plasmon polariton excitation. We demonstrate that the specular peak is seen clearly for surface roughness that has a conventional Gaussian power spectrum. Further, we show that the peak appears more distinctly for roughness whose power spectrum has a new rectangular form, which is proposed here with the intent of better isolation of the scattering processes essential to the specular peak. Finally, for a pair of rough surfaces that have appropriately correlated surface roughness, it is found that the cross correlation of scattered amplitudes presents a well-isolated specular peak, which directly demonstrates the constructive interference that produces the effect.     

Modeling the bidirectional reflectance of emissive displays

The reflection properties of a display device influence the available contrast and affect the perception of subtle detail. The display reflection characteristics of flat-panel displays (FPDs) are appropriately described by a six-dimensional bidirectional reflectance distribution function (BRDF). I describe a Monte Carlo method for modeling the bidirectional reflectance of multilayer emissive structures used in electronic display devices. I estimate the complete BRDF using a one-dimensional angular distribution function of the luminance. I apply the method to model typical high-performance cathode-ray tube and FPD structures. I find that, for the BRDF signatures of cathode-ray tubes characterized by a specular and a quasi-Lambertian components, the estimated values for the specular and diffuse reflection coefficients agree well with low-resolution experimental measurements conducted with a rotation arm and a collimated probe. I show that emissive FPDs with thin-film organic layers on reflective substrates can exhibit a predominant specular peak broadened by short-range light scattering.     

Fourth- and higher-order small-perturbation solution for scattering from dielectric rough surfaces

A recursive solution of the small-perturbation method for rough surface scattering is presented. These results permit fourth- and higher-order corrections to rough surface scattering coefficients to be determined in a form that explicitly separates surface and electromagnetic properties. Sample results are presented for the fourth-order correction to the specular reflection coefficient of a rough surface and the sixth-order correction to incoherent scattering cross sections.     

Analytical expression for the total electrical conductivity of unannealed and annealed metal films

Previous studies have shown that the Cottey function constitutes an alternative formulation for the Fuchs-Sondheimer size-effect function, provided that a new parameter is used. This result is used for calculating the effects of scattering at a grain boundary, and a good agreement with the Mayadas-Shatzkes model is found. When background, grain-boundary and external-surface scattering are simultaneously operative, a simple analytical expression for the electrical conductivity of polycrystalline, monocrystalline and columnar metal films can be obtained in the whole experimental domain and may conveniently replace the sophisticated expression of Mayadas and Shatzkes. This expression is similar to that obtained in the framework of the multidimensional models, previously presented. No limitation exists in the value of the electronic specular reflection coefficient, and the theoretical expression is related both to annealed and unannealed films.     

Resonant scattering of light from a glass/Ag/MgF2/air system with rough interfaces and supporting guided modes in attenuated total reflection

We report experimental results of the resonant scattering of light from a prism-glass/Ag/MgF2/air system with use of the attenuated total reflection technique for p and s polarized light. Two MgF2 film thicknesses were used. The system with the thinner dielectric layer supports two transverse magnetic (TM) and two transverse electric (TE) guided modes at a wavelength of 632.8 nm, and the system with the thicker dielectric layer supports three TM and three TE guided modes. In both cases we found dips in the specular reflection as a function of incident angle that is due to excitation of guided modes in the MgF2 film. The scattered light shows peaks at angles corresponding to the measured excitation of the guided modes. These peaks are due to single-order scattering and occur for any angle of the incident light. All features in the scattering response are enhanced in resonance conditions, and the efficiency of injecting light into the guide is reduced.     

Generalized quasi mode theory of macroscopic canonical quantization in cavity quantum electrodynamics and quantum optics. II. Application to reflection and refraction at a dielecric interface

Abstract

The generalization of the quasi mode theory of macroscopic quantization in quantum optics and cavity QED presented in the previous paper, is applied to provide a fully quantum theoretic derivation of the laws of reflection and refraction at a boundary. The quasi mode picture of this process involves the annihilation of a photon travelling in the incident region quasi mode, and the subsequent creation of a photon in either the incident region or transmitted region quasi modes. The derivation of the laws of reflection and refraction is achieved through the dual application of the quasi mode theory and a quantum scattering theory based on the Heisenberg picture. Formal expressions from scattering theory are given for the reflection and transmission coefficients. The behaviour of the intensity for a localized one photon wave packet coming in at time minus infinity from the incident direction is examined and it is shown that at time plus infinity, the light intensity is only significant where the classical laws of reflection and refraction predict. The occurrence of both refraction and reflection is dependent upon the quasi mode theory coupling constants between incident and transmitted region quasi modes being nonzero, and it is seen that the contributions to such coupling constants come from the overlap of the mode functions in the boundary layer region, as might be expected from a microscopic theory.     

Effect of interpolation on specular reflections in texture‐based automatic colonic polyp detection

Reflections of LED light cause unwanted noise effects called specular reflection (SR) on colonoscopic images. The aim of this study was to seek answers to the following two questions. (a) How are the texture features used in automatic detection of polyps affected by the interpolation on specular reflections? (b) If they are affected does it really affect the classification performance? In order to answer these questions, we used 610 colonoscopy images, and divided each image into tiles whose sizes were 32‐by‐32 pixels. From these tiles, we selected the ones without any specular reflection. We added different shape and size specular reflections cropped from real images onto the reflection‐free tiles. We then used the nearest neighbors, bilinear and bicubic interpolation techniques on the tiles on which SRs were added. On these tiles we extracted 116 texture features using 3 second‐order approaches, and 4 first‐order statistics. First, we used paired sample t test. Second, we performed automatic classification of polyps and background using random forest and k nearest neighbors (k‐NN) approaches using the texture features for different combinations of specular reflections added on the tiles from the polyp or background. The results showed that depending on the size of specular reflection, interpolation can cause a significant difference between the texture features that were coming from reflection‐free tiles and the same tiles on which interpolation was performed. In addition, we note that bicubic interpolation may be preferred to eliminate specular reflection when texture features are used for background and polyp discrimination.     

Bidirectional reflectance distribution function of Spectralon white reflectance standard illuminated by incoherent unpolarized and plane-polarized light

A Lambert surface would appear equally bright from all observation directions regardless of the illumination direction. However, the reflection from a randomly scattering object generally has directional variation, which can be described in terms of the bidirectional reflectance distribution function (BRDF). We measured the BRDF of a Spectralon white reflectance standard for incoherent illumination at 405 and 680?nm with unpolarized and plane-polarized light from different directions of incidence. Our measurements show deviations of the BRDF for the Spectralon white reflectance standard from that of a Lambertian reflector that depend both on the angle of incidence and the polarization states of the incident light and detected light. The non-Lambertian reflection characteristics were found to increase more toward the direction of specular reflection as the angle of incidence gets larger.     

Grain-boundary scattering in aluminium films deposited on to calcite substrate

Electrical resistivity and temperature coefficient of resistivity of polycrystalline aluminium films deposited onto calcite substrates have been measured in situ. It was observed that films deposited at 130° C substrate temperature show reversible and reproducible behaviour with thermal cycling. The grain-boundary scattering theory of Mayadas and Shatzkes reproduces the experimental observations quite faithfully with the coefficient of specular reflection p=0 and grain-boundary reflection coefficient R=0.38 indicating that the grain-boundary scattering plays a significant role in electron transport in aluminium film deposited on to calcite substrate.     

金银卡纸的镜面反射对颜色复制的影响

目的针对金银卡纸表面因具有强烈的镜面反射作用且印刷适性较差的缺点,研究金银卡纸镜面反射对印刷品颜色的质量控制。方法试验分析金银卡纸印刷镜面反射作用对印品明度值的影响,用曲线拟合的方法找出包含和不包含镜面反射作用测出的明度值之间的关系。结果经过检验分析,SCE条件下的测量数据相对于SCI明度偏小,这是因为SCE测量模式中,镜面反射光被排除在外面,只测量了漫射光。从青色的线性拟合图来看,所得线性拟合图大致为一条斜率为45°的直线。结论包含和不包含镜面反射明度值这2组数据之间存在数学关系,在实际应用中,可以考虑使用明度差这种线性关系来作为金银卡纸颜色控制和评价的依据。