Diffuse and specular reflectance from rough surfaces

We present a reflection model for isotropic rough surfaces that have both specular and diffuse components. The surface is assumed to have a normal distribution of heights. Parameters of the model are the surface roughness given by the rms slope, the albedo, and the balance between diffuse and specular reflection. The effect of roughness on diffuse reflection is taken into account, instead of our modeling this component as a constant Lambertian term. The model includes geometrical effects such as masking and shadowing. The model is compared with experimental data obtained from goniophotometric measurements on samples of tiles and bricks. The model fits well to samples with very different reflection properties. Measurements of the sample profiles performed with a laser profilometer to determine the rms slope show that the assumed surface model is realistic. The model could therefore be used in machine vision and computer graphics to approximate reflection characteristics of surfaces. It could also be used to predict the texture of surfaces as a function of illumination and viewing angles.     

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.     

Infrared specular reflection spectroscopy of rough metallic substrates

A study of the infrared reflectance of rough metallic surfaces is presented. We show that one reflectance measurement, made in the specular direction under specific conditions, allows the accurate calculation of the shape of the roughness histogram. As a theoretical background, we use modified expressions from Kirchhoff theory for surface scattering. To illustrate our method, we present experimental results obtained with surfaces having a multimode histogram, which means having several different populations with distinct peaks. For these surfaces, we observe oscillations in the regularly decreasing reflectance (with decreasing wavelength) that are created by a partial interference phenomenon between the peaks. To our knowledge, this effect is presented for the first time in the literature. Our study demonstrates that some very useful information can be obtained in the infrared spectrum of metallic substrates, although they do not have any absorption band. We hope that our results help further the understanding of complex spectral data obtained on such scattering substrates covered with organic films.     

Statistics of specular points at a randomly rough surface

Statistical parameters are obtained for an ensemble of specular points at a randomly rough Gaussian statistically isotropic surface at normal incidence. The joint probability density functions (PDFs) of specular point heights and total curvatures are derived separately for maxima, minima, and saddle points. The joint PDFs of brightness and surface elevations of specular points of different types are obtained analytically in an explicit form.     

Reflectometer for measuring the bidirectional reflectance of rough surfaces

A fully automatic, four-axis gonioreflectometer is described. It has an angular accuracy of 0.3 degrees and a range of 90 degrees in both the theta(i) and the theta(r) zenith angles. The gonioreflectometer is simpler than previous designs because of its use of rotating arms rather than moving carriages to mount the optical components. Where possible, commercial components have been used to reduce the cost. A novel off-axis angular encoding scheme is also described.     

The determination of the extensional compliance perpendicular to the plane of sheet for thin polyethylene terephthalate sheets

The extensional compliance normal to the plane of the sheet has been determined for one-way drawn polyethylene terephthalate (PET) sheet. The method was to measure the compressional strain of narrow strips under load in a compressional creep apparatus. It was established that the strips were fully constrained by friction, and a theoretical analysis in support of this is presented. The values for the compliance constant are discussed with regard to the other compliance constants of the PET sheet and are also compared with previous data for PET fibres.     

Rendering of specular surfaces in polygon-based computer-generated holograms

A technique is presented for realistic rendering in polygon-based computer-generated holograms (CGHs). In this technique, the spatial spectrum of the reflected light is modified to imitate specular reflection. The spectral envelopes of the reflected light are fitted to a spectral shape based on the Phong reflection model used in computer graphics. The technique features fast computation of the field of objects, composed of many specular polygons, and is applicable to creating high-definition CGHs with several billions of pixels. An actual high-definition CGH is created using the proposed technique and is demonstrated for verification of the optical reconstruction of specular surfaces.     

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.     

Pressure dependence of the thermal contact resistance for rough surfaces

The contact resistance is expressed analytically as a function of load for elastic and elastoplastic contacts by taking the rough surface as consisting of spherical projections with a normal distribution.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 19, No. 1, pp. 62–67,July, 1970.     

Active lighting applied to three-dimensional reconstruction of specular metallic surfaces by polarization imaging

In the field of industrial vision, the three-dimensional inspection of highly reflective metallic objects is still a delicate task. We deal with a new automated three-dimensional inspection system based on polarization analysis. We first present an extension of the shape-from-polarization method for dielectric surfaces to metallic surfaces. Then, we describe what we believe to be a new way of solving the ambiguity concerning the normal orientation with an active lighting system. Finally, applications to shape-defect detection are discussed, and the efficiency of the system to discriminate defects on specular metallic objects made by stamping and polishing is presented.     

A discrete-scatterer model for ultrasonic images of rough surfaces

Automated analysis of ultrasonic images could be greatly improved with model-based Bayesian methods for image analysis. Such an approach would require an accurate probabilistic image model representing ultrasonic images in terms of the gross shape of underlying anatomical structure. Existing probabilistic models for ultrasonic image data do not adequately incorporate structure shape or system characteristics; thus, a substantially new approach is warranted. Toward that goal, we have developed models for the imaging system and rough surface with the following objectives: (1) accuracy in representation of basic image characteristics such as the texture and intensity, (2) a minimum of computational requirements, and (3) a form that is naturally extendable to an appropriate probabilistic image model. The imaging system was modeled as a linear system with a separable three-dimensional point-spread function with an envelope of Gaussian curves in each dimension. The rough surface was modeled as a collection of discrete scatterers placed on the continuum and parametrized by a surface roughness and scatterer concentration. Models were evaluated by a visual comparison of actual and simulated images of a cadaveric lumbar vertebra. The gross shape of the vertebral surface was estimated from computed tomography images of the vertebra, and simulated images were generated using the models and the gross surface shape. Actual images were registered with the surface and simulated images to within 2 mm. The similarity of the actual and simulated images was quite remarkable considering the simplicity of the models. Differences between the images were less than those between two simulated images separated by 0.4 mm or one-fifth the registration error. Further assessment of the models would require a statistical approach not yet available. The models do, however, provide the basis for the development of a computationally tractable probabilistic image model for image analysis. Such a model will provide the means for a statistical evaluation of the system and surface models.     

Frequency dependence of the specular and diffuse phonon scattering from silicon surfaces

Phonon backscattering experiments with polished silicon surfaces show that there is no Kapitza anomaly at frequencies corresponding to the aluminum junction detector threshold (80 GHz), whereas at higher frequencies the anomalous transmission into liquid helium or solid nitrogen increases (reduced backscattering by the coverage), closely related to the increase of the diffuse scattering at the uncovered surface.     

Second-order perturbation theory for scattering from heterogeneous rough surfaces

We propose a model to calculate scattering from inhomogeneous three-dimensional, rough surfaces on top of a stratified medium. The roughness is made up of an ensemble of deposits with various shapes and permittivities whose heights remain small with respect to the wavelength of the incident light. This geometry is encountered in the remote sensing of soil surfaces, or in optics wherever there are contaminated planar components. Starting from a volume-integral equation involving the Green's tensor of the stratified medium, we derive a height-perturbative expansion up to second-order. Our formulation, which depends explicitly on the profiles of each deposit and on the Fresnel coefficients of the layered substrate, accounts for double-scattering events and permits an evaluation of depolarization in the plane of incidence. Comparisons with rigorous calculations in the simplified case of two-dimensional geometries are presented. It is shown that the second-order scattering term can be much more important for heterogeneous surfaces than for their homogeneous counterparts.     

Bidirectional reflectance distribution function of specular surfaces with hemispherical pits

We derive the bidirectional reflectance distribution function for a class of opaque surfaces that are rough on a macroscale and smooth on a microscale. We model this type of surface as a distribution of spherical mirrors. Since our study concerns geometrical optics, it is only the aperture of the concavities that is relevant, not the dimension. The three-dimensional problem is effectively transformed into a much simpler two-dimensional one involving the possibly infinitely many reflections in a spherical mirror. We find that these types of surface show very strong backscattering when the pits are deep but forward scattering when the pits are shallow. Such surfaces also show spectral effects as a result of multiple reflections and polarization effects that are due to the orientation of the effective surface. Both this model and the locally diffuse thoroughly pitted surface model [Int. J. Comput. Vision 31, 129 (1999)] are superior to other models in that they allow for an exact treatment for physically realizable surface geometries.