Contours of the constant third Brewster angle in the complex plane of a dielectric constant

Three special angles associated with the external reflection of light at the surface of an absorbing medium are well known: the principal angle, the pseudo-Brewster angle, and the second Brewster angle. Another significant angle has been identified recently by Azzam and El-Saba [Appl. Opt. 28, 1365 (1989)]. At this angle, the slope of the differential reflection phase shift with respect to the angle of incidence is maximum negative. For convenience it is called the third Brewster angle. The nature of the contours of the constant third Brewster angle in a complex dielectric constant plane is considered both analytically and graphically in comparison with the other constant special-angle contours.     

What shadows reveal about object structure

In a scene observed from a fixed viewpoint, the set of shadow boundaries in an image changes as a point light source (nearby or at infinity) assumes different locations. We show that for any finite set of point light sources illuminating an object viewed under either orthographic or perspective projection, there is an equivalence class of object shapes having the same set of shadows. Members of this equivalence class differ by a four-parameter family of projective transformations, and the shadows of a transformed object are identical when the same transformation is applied to the light source locations. Under orthographic projection, this family is the generalized bas-relief (GBR) transformation, and we show that the GBR transformation is the only family of transformations of an object's shape for which the complete set of imaged shadows is identical. Finally, we show that given multiple images under differing and unknown light source directions, it is possible to reconstruct both an object's surface and the light source locations up to this family of transformations from the shadows alone.     

SIMBAD: a field radiometer for satellite ocean-color validation

A hand-held radiometer, called SIMBAD, has been designed and built specifically for evaluating satellite-derived ocean color. It provides information on the basic ocean-color variables, namely aerosol optical thickness and marine reflectance, in five spectral bands centered at 443, 490, 560, 670, and 870 nm. Aerosol optical thickness is obtained by viewing the Sun disk and measuring the direct atmospheric transmittance. Marine reflectance is obtained by viewing the ocean surface and measuring the upwelling radiance through a vertical polarizer in a geometry that minimizes glitter and reflected sky radiation, i.e., at 45 degrees from nadir (near the Brewster angle) and at 135 degrees in azimuth from the Sun's principal plane. Relative inaccuracy on marine reflectance, established theoretically, is approximately 6% at 443 and 490 nm, 8% at 560 nm, and 23% at 670 nm for case 1 waters containing 0.1 mg m(-3) of chlorophyll a. Measurements by SIMBAD and other instruments during the Second Aerosol Characterization Experiment, the Aerosols-99 Experiment, and the California Cooperative Oceanic Fisheries Investigations cruises agree within uncertainties. The radiometer is compact, light, and easy to operate at sea. The measurement protocol is simple, allowing en route measurements from ships of opportunity (research vessels and merchant ships) traveling the world's oceans.     

Reduction of skylight reflection effects in the above-water measurement of diffuse marine reflectance: comment

Use of a vertical polarizer has been suggested to reduce the effects of surface reflection in the above-water measurements of marine reflectance. We suggest using a similar technique for airborne or spaceborne sensors when atmospheric scattering adds its own polarization signature to the upwelling radiance. Our own theoretical sensitivity study supports the recommendation of Fougnie et al. [Appl. Opt. 38, 3844 (1999)] (40-50 degrees vertical angle and azimuth angle near 135 degrees , polarizer parallel to the viewing plane) for above-water measurements. However, the optimal viewing directions (and the optimal orientation of the polarizer) change with altitude above the sea surface, solar angle, and atmospheric vertical optical structure. A polarization efficiency function is introduced, which shows the maximal possible polarization discrimination of the background radiation for an arbitrary altitude above the sea surface, viewing direction, and solar angle. Our comment is meant to encourage broader application of airborne and spaceborne polarization sensors in remote sensing of water and sea surface properties.     

Diffraction of horizontally polarized ultrasonic plane waves on a periodically corrugated solid-liquid interface for normal incidence and Brewster angle incidence

The theory, and the use at normal incidence, of shear-vertically polarized waves (with polarization vector in the plane containing the incident wave vector and the normal on the interface) using the mode conversion method has been tackled by others. Here we develop the theory for shear-horizontally polarized incident waves (with polarization vector perpendicular to both the normal on the interface and the incoming wave vector). We take into account normal incidence as well as oblique incidence. For normal incidence, we discover the generation of Love waves. If oblique incidence is considered, we discover the existence of a Brewster angle of incidence, comparable with the Brewster angle in optics, in which a diffraction grating can be used as a polarization filter.     

Shadow-angle method for anisotropic and weakly absorbing films

A method for determining the optical properties of a film on an isotropic substrate is proposed. The method is based on the existence of two specific incidence angles in the angular interference pattern of the p-polarized light where oscillations of the reflection coefficient cease. The first of these angles, theta(B1), is the well-known Abelès angle, i.e., the ambient-film Brewster angle, and the second angle theta(B2) is the film-substrate Brewster angle. In the conventional planar geometry and in a vacuum ambient there is a rigorous constraint epsilon(1) + epsilon > epsilon(1)epsilon on the film and the substrate dielectric permittivities epsilon(1) and epsilon, respectively, for the existence of the second angle theta(B2.) The limitation may be removed in an experiment by use of a cylindrical lens as an ambient with epsilon(0) > 1, so that both angles become observable. This, contrary to general belief, allows one to adopt the conventional Abelès method not only for films with epsilon(1) close to the substrate's value epsilon but also for any value of epsilon(1). The method, when applied to a wedge-shaped film or to any film of unknown variable thickness, permits one to determine (i) the refractive index of a film on an unknown substrate, (ii) the vertical and the horizontal optical anisotropies of a film on an isotropic substrate, (iii) the weak absorption of a moderately thick film on a transparent or an absorbing isotropic substrate.     

Reflection of light in the vicinity of the Brewster angle from a multilayer system of ultrathin inhomogeneous dielectric films

An analysis of the influence of nanoscopically stratified dielectric overlayer on the reflection parameters of linearly polarized light from transparent substrates is carried out. The second-order formulas for characteristic Brewster angles are derived and their accuracy is estimated by using exact numerical methods for the solution of the inhomogeneous reflection problem. The possibilities are discussed for determining the parameters of nanometre-scale dielectric layers by means of characteristic reflection angles. A novel scanning angle differential reflectance method in the vicinity of the classical Brewster angle, whose sensitivity is in principle the same as that of ellipsometry, is developed.     

Scattering of light from the random interface between two dielectric media with low contrast

We calculate the coherent and incoherent scattering of p- and s-polarized light incident from a dielectric medium characterized by a real, positive, dielectric constant epsilon0 onto its one-dimensional, randomly rough interface with a dielectric medium characterized by a real, positive, dielectric constant epsilon. We use a perturbation theory with a new small parameter, namely, the dielectric contrast eta = epsilon0 - epsilon between the medium of incidence and the scattering medium. The proper self-energy entering the expression for the reflectivity is obtained as an expansion in powers of eta through the second order in eta, and the reducible vertex function in terms of which the scattered intensity is expressed is obtained as an expansion in powers of eta through the fourth. The roughness-induced shifts of the Brewster angle (in p polarization) and of the critical angle for total internal reflection (epsilon0 > epsilon) are obtained. The angular dependence of the intensity of the incoherent component of the scattered light displays an enhanced backscattering peak, which is due to the coherent interference of multiply scattered lateral waves supported by the interface and their reciprocal partners. Analogs of the Yoneda peaks observed in the scattering of x rays from solid surfaces are also present. The results obtained by our small-contrast perturbation theory are in good agreement with those obtained in computer simulation studies.     

Electric polarization and the extinction of the extraordinary reflected ray

Abstract

When light is incident from an isotropic medium on to an interface with a uniaxial crystal, the idea of an effective electric polarization is useful. We show that the same idea may be extended to the reverse situation where the light is incident from the uniaxial crystal. In this case, when the optical axis lies in the plane of incidence, there is a Brewster angle associated with the extinction of the reflected ray, because the waves have a definite polarization. We analyse the relation between the Brewster angle and the effective electric polarization at the interface.     

On the use of shadows in stance recovery

The image of an object and of the shadow it casts on a planar surface provides important cues for three‐dimensional (3D) stance recovery. We assume that the position of the plane on which the shadow lies with respect to a pinhole camera is known and that the position of the light source is unknown. If the light source is sufficiently far away that parallel projection may be assumed, then knowledge of two point correspondences between images of feature points and images of their shadows is enough to determine the position of the object and the direction of the light source. If the light source is close enough that the shadow points are obtained via perspective projection, then there is a one‐parameter infinite family of solutions for the position of the object and the light source. Determining the stance of an object is highly sensitive to noise, so we provide algorithms for stance recovery that take into account known information about the object. In our experiments, the errors for the location of the 3D feature points obtained by these algorithms are generally less than 0.2% times the error in pixels in the image points and the errors for the 3D directions of the links is roughly 0.04° times the error in pixels, normalized by the distance to the object from the camera and the length of the link. © 2001 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 11, 315–330, 2000     

Mach bands and airplane shadows cast on dry terrain

Luminous rings are often seen surrounding the shadow of a high-flying airplane. Some of these phenomena are due to water droplets (glories, the Heiligenschein), but a different sort of explanation is required when a luminous ring (sometimes simply a bright spot) is seen while the plane is flying over dry terrain. Demonstrations involving distances and shadows manyfold smaller than those of an airliner's shadow show that Mach bands can produce illusory luminance phenomena that greatly resemble those associated with a plane's shadow over dry terrain. Luminance rings have recently also been observed over dry, sparsely vegetated terrain, around the shadow of an adjacent airplane (i.e., far from the observer's antisolar point), thereby excluding all previous alternative interpretations; Mach bands are thus a likely explanation for at least some instances of dry-terrain luminous rings around airplane shadows.     

用特殊辅助面解画法几何交线问题

提出利用特殊位置辅助面截交线投影的特点(45°投影面垂直面、底角45°圆锥面及其它特殊位置垂直面)求解画法几何中的截交线与相贯线(平面立体截交线、圆柱与圆锥的截交线;圆柱与圆柱,圆柱与圆锥的相贯线)以及直线的落影、回转曲面立面阴影的作图方法。     

Robust and accurate estimate of the orientation of partially polarized light from a camera sensor

Polarized light carries valuable information about where the light has been and the various physical parameters that have been acting upon it. Thus there are several methods in computer vision that make it possible to obtain information on the observed object by studying the polarization of light reflected on the object. Most studies using this principle are interested in the determination of the object orientation in three-dimensional space. The basis of these studies rests on the estimate of a parameter that connects the orientation of the observed surface and the polarization of the reflected light wave. This parameter is the angle of polarization phi, also called the orientation of polarization. Generally, one using these methods estimates the phi angle by observing the reflected light wave through a linear polarizing filter and grabbing multiple frames for different angular orientations of the polarizer. So, between each acquisition, the polarizer is rotated of an angle theta relative to a horizontal reference axis. The accuracy of the phi estimate is then directly related to the positioning of the polarizer. But, in practice, it is difficult to guarantee the exact value of the rotation of this polarizer. It is all the more difficult to guarantee the reliability of positioning in time. We thus propose a robust and accurate solution, based on the self-calibration principle, for measuring the orientation of partially polarized light using CCD cameras. In contrast to methods generally discussed in computer vision journals, our estimate of the angle of polarization is independent of the reliability of the polarizer positioning.     

Minimization of the shadow patterns produced by periodic mesh grids in extreme ultraviolet telescopes

Thin metallic films are used as passband filters in space telescopes operating in the extreme ultraviolet (EUV). Because of their thinness, typically 100 to 200 nm, they are very sensitive to static pressure differentials and to mechanic and acoustic vibrations. Therefore, they are difficult to manage in all phases of a space program, from manufacturing to vacuum testing to launch. A common solution to this problem is to reinforce them with fine mesh grids with pitches ranging from a few hundred micrometers to a few millimeters. Depending on their location in the optical path, the main effect of these periodic grids is either to diffract light or to cast penumbral shadows on the focal plane. In this paper, we analyze the formation of the shadow modulation patterns and derive design rules to minimize their amplitude. The minimization principle is illustrated by an application to a solar EUV telescope.     

Generalized Investigations into the Brewster Angle

The standard elementary theory of the Brewster angle generated by a plane interface separating two homogeneous isotropic media, through which incident and transmitted electromagnetic waves are propagating, is well known. We introduce here a more general inhomogeneous medium for which a Brewster wave and a Brewster angle can be defined. The properties of this wave are investigated, together with a model whose field can be expressed in terms of a special degenerate hypergeometric function. Other angles of incidence also yield zero reflectivity, but these are carefully distinguished from the Brewster angle.     

Polarization properties of thin films of diamond

Thin films transparent to optical radiation offer polarization properties that are enhanced when the thickness of the film is an odd multiple of the quarter-wavelength. The transmission and reflection properties of a 1.16-μm-thick film of diamond realized by plasma-assisted chemical vapor deposition have been studied at 10.6 μm. A compact polarizer built with four films at a Brewster angle revealed an extinction ratio of better than 1:1000 of the S polarization. The interest in optics in which parasitic-reflected or transmitted beams do not exist is pointed out. The high damage threshold of diamonds opens the possibility of controlling the polarization characteristics of high-power lasers used, for example, for soldering and cutting applications.     

Polarization and statistical analysis of scenes containing a semireflector

We present an approach to recover scenes deteriorated by reflections off a semireflecting medium (e.g., a glass window). The method, based on imaging through a polarizer at two or more orientations, separates the reflected and transmitted scenes and determines which is which. We analyze the polarization effects, taking into account internal reflections within the medium. The scene reconstruction requires the estimation of the orientation (inclination and tilt angles) of the transparent (invisible) surface. The inclination angle is estimated by seeking the value that leads to the minimal mutual information of the estimated scenes. The limitations and the consequences of noise and angle error are discussed, including a fundamental ambiguity in the determination of the plane of incidence. Experimental results demonstrate the success of angle estimation and consequent scene separation and labeling.     

Ray theory analysis of the shadow blister effect

When an extended light source such as the Sun illuminates two objects so that their shadows lie close to each other, the shadow of one of the objects occasionally appears to bulge out toward the shadow of the other. This effect is caused by the overlap of the penumbras of the shadows and is analyzed here with ray theory. A laboratory demonstration of this phenomenon is performed and compared with theoretical predictions.     

Expressions for determination of layer absorbances of a weakly absorbing double-layer sample through reflectance at the Brewster angles

A new technique for determining absorbances of interferenceless (incoherent) layers based on measurements of the ratio of the front and the back reflectivities of a double-layer sample at the Brewster angles is proposed. A double-layer stack must have at least one absorbing layer, and the two layers should be interferenceless and should be thicker than the wavelength of the incident light. We found that under these conditions the ratio of the front and the back reflectivities at the Brewster angle of a sample surface is directly related to layer absorbance. For a layer with a known thickness this means finding the extinction coefficient of the layer material. In comparison with the conventional method for measuring transmittance, the advantage of this approach is that it affords an opportunity to get rid of the influence of surface effects on the measuring volume absorption coefficient. For a thick layer with known thickness, it makes possible the determination of a small bulk absorption on a background with even greater surface effects. We trust that this technique will prove to be powerful for measuring the extinction coefficients of weakly absorbing materials.     

Anisotropic protective coating for brewster angle windows

We propose what we believe is a new type of dielectric anisotropic coating of arbitrary thickness that can protect Brewster angle windows without degrading their optical quality. Such a coating may be fabricated as a multilayer two-component structure. The parameters of the structure, i.e., the dielectric permittivities of the components and their concentrations, are calculated. For ZnSe windows two examples of anisotropic coatings are presented. The optical quality of the multilayer films does not depend on their precise thickness, which makes them less sensitive to surface damage.