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Showing papers on "Reflection (physics) published in 1988"


Journal ArticleDOI
TL;DR: Experimental results generally verify the theoretical predictions of FKLS, but do find one significant difference between experiment and theory — namely, that the exponential decay of C(x) is observed to set in almost immediately with nonzero x, while the theory predicts that its onset should be decelerated.
Abstract: We verify experimentally for optical waves the striking memory effect predicted very recently by Feng, Kane, Lee, and Stone. We present data for both transmission and reflection, and find general agreement with the theoretical predictions for the linear scale dependence and asymptotic exponential falloff of the memory effect. The theoretical and experimental results suggest that significant information about the spatial variation of the incident waveform is preserved during passage through a highly disordered, strongly multiply scattering medium.

668 citations


Journal ArticleDOI
TL;DR: In this paper, the reflection properties of multiple electric/magnetic Salisbury screens have been studied and it is shown that relatively large reductions in specular reflection are possible over sizeable bandwidths using relatively few Salisbury screen screens.
Abstract: The reflection properties of multiple electric/magnetic Salisbury screens have been studied. Analytical formulae are developed for the maximally flat design of two- and three-screen planar stackups that have taken into account appropriate values for the spacer materials used to separate the screens. The effect of curvature has also been assessed. It is shown that relatively large reductions in specular reflection are possible over sizeable bandwidths using relatively few Salisbury screens. Furthermore, these reductions are not completely destroyed if the incident wave is not normal to the surface, if the surface is curved or if there are errors in fabrication of the screen. >

662 citations


Journal ArticleDOI
TL;DR: In this paper, the reflection from and transmission through a semi-infinite chiral medium is analyzed by obtaining the Fresnel equations in terms of parallel-and perpendicular-polarized modes, and a comparison is made with results reported previously.
Abstract: The reflection from and transmission through a semi-infinite chiral medium are analyzed by obtaining the Fresnel equations in terms of parallel- and perpendicular-polarized modes, and a comparison is made with results reported previously. The chiral medium is described electromagnetically by the constitutive relations D = ∊E + iγB and H = iγE + (1/μ)B. The constants ∊, μ, and γ are real and have values that are fixed by the size, the shape, and the spatial distribution of the elements that collectively compose the medium. The conditions are obtained for the total internal reflection of the incident wave from the interface and for the existence of the Brewster angle. The effects of the chirality on the polarization and the intensity of the reflected wave from the chiral half-space are discussed and illustrated by using the Stokes parameters. The propagation of electromagnetic waves through an infinite slab of chiral medium is formulated for oblique incidence and solved analytically for the case of normal incidence.

368 citations


Patent
26 Sep 1988
TL;DR: In this article, a transparent-type hologram consisting of a transparent hologram-forming layer and a holographic effect-enhancing layer comprising a thin transparent film was presented, with the effect enhancing layer being laminated on the hologram forming portion of the transparent holograms.
Abstract: A transparent-type hologram comprising a transparent hologram-forming layer and a holographic effect-enhancing layer comprising a thin transparent film, the holographic effect-enhancing layer being laminated on the hologram-forming portion of the transparent hologram-forming layer. The holographic effect-enhancing layer has a refractive index different from that of the transparent hologram-forming layer.

332 citations


Journal ArticleDOI
01 Feb 1988-Nature
TL;DR: In this paper, the authors report results from a nearly continuous, 255 km-long reflection seismic survey across the Pyrenean chain, which can help to constrain possible models for the structure and formation of the mountain chain.
Abstract: The Pyrenees are an Alpine-age mountain belt located on the boundary between the Iberian and European plates. Using the same geological and geophysical data, Earth scientists studying the structure of the Pyrenees during the past ten years have not reached a consensus. Here we report the first results from a nearly continuous, 255-km-long reflection seismic survey across the Pyrenean chain. This first deep reflection profile of an entire erogenic belt will help to constrain possible models for the structure and formation of the Pyrenean chain.

233 citations


Book
01 Jan 1988
TL;DR: Bouguer and Bouguer as discussed by the authors described the search for the origin of magnetic anomalies and their geologic sources, and surveyed the Anomalous Magnetic Field (MAGF).
Abstract: The Search. Seismic Waves. Refracted Seismic Waves and Earth Structure. Reflected Seismic Waves and Earth Structure. Seismic Surveying. Seismic Reflection Data Processing and Interpretation. Gravity on the Earth. Gravity Surveying. Bouguer Gravity and Geology. Earth Magnetism. Surveying the Anomalous Magnetic Field. Magnetic Anomalies and Their Geologic Sources. Geoelectrical Surveying. Geophysical Well Logging.

207 citations


Journal ArticleDOI
TL;DR: In this article, a new scattering matrix formalism for the modeling of electromagnetic wave propagation in stratified media is presented, which is computationally efficient and stable and is well suited to the layer geometry that is characteristic of stratified materials.
Abstract: We present a new scattering matrix formalism for the modeling of electromagnetic wave propagation in stratified media. It is computationally efficient and stable and is well suited to the layer geometry that is characteristic of stratified materials. It is applied successfully to the modeling of total attenuated reflection in nematic liquid crystals with beyond-critical-angle incidence when the conventional transfer matrix methods normally fail.

207 citations


Journal ArticleDOI
TL;DR: In highly scattering media, light energy fluence rate distributions can be described by diffusion theory and the diffusion equation together with its boundary conditions is solved using the finite element method.
Abstract: In highly scattering media, light energy fluence rate distributions can be described by diffusion theory. Boundary conditions, appropriate to the diffusion approximation, are derived for surfaces where reflection of diffuse light occurs. Both outer surfaces and interfaces separating media with different indices of refraction can be treated. The diffusion equation together with its boundary conditions is solved using the finite element method. This numerical method allows much freedom of geometry.

195 citations


Journal ArticleDOI
TL;DR: In this article, the authors derived the expressions needed for predicting multiple reflections that are generated by the water bottom in marine seismic data, in a form that can be used to estimate the reflectivity of a water bottom that has a complex shape and has a reflectivity that varies with lateral position, frequency and reflection angle.
Abstract: Multiple reflections that are generated by the water bottom in marine seismic data can be predicted by a combination of numerical wave extrapolation through the water layer and estimation of the water-bottom reflectivity. Attenuation of the multiples occurs when the predicted wave field is subtracted from the original record. I derive the expressions needed for prediction of the multiples, following the ideas of Morley, in a form that can be used to estimate the reflectivity of a water bottom that has a complex shape and has a reflectivity that varies with lateral position, frequency, and reflection angle. The specific form of the operations needed for prediction is implemented without assumptions about the simplicity or flatness of the water bottom. The derivation implies that the recorded wave field may be interpreted as both an upgoing and a downgoing wave. This interpretation is correct except for a simple surface ghost present in both interpretations.Application of the predictive method to data collected over a hard, complex water bottom demonstrates that it effectively attenuates water-bottom and peg-leg multiples even when the water bottom is complex and changes in character within the span of a shot gather. The same data were processed with various combinations of predictive attenuation, prestack automatic gain control, prestack moveout discrimination, and stacking. The multiple attenuation achieved with the predictive method alone was greater than that achieved by moveout discrimination alone; the net attenuation achieved by sequential application of all the methods was approximately additive.

149 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated the mode coupling and examined the parameter dependence of the damping rate of the global mode in the box model and derived the complex frequencies of the compressional wave by finding the singularities of the associated Green's function.
Abstract: In the terrestrial magnetosphere, the inhomogeneous magnetic field and plasma density give rise to a continuous spectrum of field line resonant frequencies. Compressional disturbances with characteristic frequencies lying within the range of the spectrum may couple to transverse oscillations of resonant field lines. The coupling is of particular interest for global compressional modes trapped in the magnetic cavity. These modes decay in time through the coupling, even in the absence of dissipation. The importance of the process is that, through the damping of the global modes, large-scale motion can drive localized field line resonances. In this study, we investigate the mode coupling and examine the parameter dependence of the damping rate of the global mode. The problem is discussed as an initial value problem in the box model which retains most of the significant physics yet remains mathematically tractable. To treat the coupling, we use the analogy of Landau damping in a homogeneous plasma. From the Laplace transform approach, we obtain the complex frequencies of the compressional wave by finding the singularities of the associated Green's function. Once the complex frequency has been found numerically, we obtain the corresponding waveforms in the box. Many observed wave properties can then be obtained. The calculations agree well with other simulation work and correspond to results obtained for the reflection of radio waves from the ionosphere and for plasma heating by absorption of radiation.

134 citations


Journal ArticleDOI
TL;DR: The resolution of near field optical scanning microscopy (NFOS microscopy) is determined by the dimensions of the microscopic light source rather than the diffraction limit as mentioned in this paper, and the resolution of NFOS in reflection is measured by intensity changes in the (backward) scattering from a 70-100 nm diam hole in a metal film.
Abstract: The resolution of near‐field optical scanning microscopy (NFOS) is determined by the dimensions of the microscopic light source rather than the diffraction limit. To demonstrate NFOS in reflection, intensity changes in the (backward) scattering from a 70–100 nm diam hole in a metal film were recorded while the sample was scanned in close proximity to this aperture. Raster‐scan images of a planar metal test pattern yield a resolution comparable to the size of the aperture.

Journal ArticleDOI
TL;DR: The probability of internal reflection is calculated more accurately, and the effect on absorption of the decrease of the relative refractive index (liquid to material instead of air to material) is estimated, which decreases the albedo of the wetted surface.
Abstract: Angstrom has proposed that rough absorbing materials are darker when wet because their diffuse reflection makes possible total internal reflection in the water film covering them, increasing the likelihood of the absorption of light by the surface His model is extended here in two ways: the probability of internal reflection is calculated more accurately, and the effect on absorption of the decrease of the relative refractive index (liquid to material instead of air to material) is estimated Both extensions decrease the albedo of the wetted surface, bringing the model into good agreement with experiment

01 Sep 1988
TL;DR: In this article, an efficient algorithm has been developed for solving the depth-separated wave equation in general fluid/solid horizontally stratified media, which is applicable to a wide range of problems in many disciplines, from seismology to ultrasonics.
Abstract: : An efficient algorithm has been developed for solving the depth- separated wave equation in general fluid/solid horizontally stratified media. The algorithm has been built into a general-purpose packages of computer codes called SAFARI. The package consists of three modules providing plane wave reflection coefficients, continuous wave transmission losses, and broadband pulse response. This document describes the mathematical model for seismo- acoustic propagation in stratified media. Then the numerical solution technique is outlined followed by a description of the three different SAFARI modules and their implementation. The actual use of the different modules is described, including a detailed discussion on the numerical considerations that are crucial for successful use of this type of numerical model. SAFARI is applicable to a wide range of problems in many disciplines, from seismology to ultrasonics. Here its use is illustrated by a series of examples from underwater acoustics. Keywords: Attenuation; Beam propagation; Fast field program; Green's function; Normal mode propagation; Numerical modelling; Pulse propagation; Reflection coefficient; Seismic interface wave; Seismo-acoustic propagation; Wave equations; Wave propagation; NATO-furnished. edc

Journal ArticleDOI
TL;DR: The effect of the ionosphere on the detectability, polarization, structure and decay of low frequency magnetospheric hydromagnetic waves has been a topic of interest for thirty years as mentioned in this paper.
Abstract: The effect of the ionosphere on the detectability, polarization, structure and decay of low frequency magnetospheric hydromagnetic waves has been a topic of interest for thirty years. There are two classes of signal behavior in the atmosphere and ionosphere, one where the ionosphere has little effect and one where the ionospheric conductivity controls the reflection, the amplitude detected on the ground and rate of signal decay. It has been assumed that the latter type of behavior is pertinent in most practical applications. Recent interest in global modes of the magnetospheric cavity requires a reassessment of the assumption. We investigate one simple case, the hydromagnetic surface wave, and discuss what happens in more complicated modes. We conclude that signals in the vicinity of field line resonance will be strongly coupled to the local ionosphere but far away will not.


Journal ArticleDOI
TL;DR: In this article, a multiple-reflection algorithm is developed which takes account of primary reflection first, then provides for inclusion of higher-order reflections as well, formulated to generate the TDR trace from a sequence of known dielectrics.
Abstract: The application of time domain reflectometry (TDR) to determine soil water content, using only the time axis of a TDR trace, has been widely investigated. Other interpretations from the TDR trace, such as the determination of electrical conductivity, make use of the amplitude or reflection coefficient values. These latter interpretations must take account of multiple reflections in the media. A multiple-reflection algorithm is developed which takes account of primary reflection first, then provides for inclusion of higher-order reflections as well. The algorithm is formulated to generate the TDR trace from a sequence of known dielectrics. The inverse case is analyzed where the dielectric constant of the layered medium is calculated from a measured TDR trace. The model allows for both conductive and nonconductive dielectrics. Experiments showed that the model is a reasonably good qualitative representation of the layered nonconductive media with a wide range of dielectric constants. There is insufficient information in a TDR trace to solve the conductive cases except for a single layer. From KCl solutions at two concentrations the experiments showed that instantaneous reflection and transmission are inadequate assumptions for conductive systems. This indicates the need for caution when applying the model to conductive media such as soils, especially where soil water content is not uniform.

Journal ArticleDOI
TL;DR: In this paper, the authors used a total-transmission criterion for leaky plate wave propagation in fiber-reinforced composites and found that the results of the Cremer coincidence condition were not consistent with the experimental data.
Abstract: Guided wave propagation in fluid‐coupled plates of fiber‐reinforced composites has been investigated by studying ultrasonic reflection in these structures. From measurements of ultrasonic reflection on unidirectional graphite‐epoxy plates over a range of incident angles, experimental dispersion curves using a total‐transmission criterion for leaky plate waves have been constructed. Theoretical calculations with no adjustable parameters demonstrate excellent agreement with the experimental data. Unusual behavior observed in the fundamental total‐transmission curve led to a reexamination of the mode identification criteria. Both the total‐transmission curves and the normal modes of the fluid‐coupled plate differ significantly from the result expected on the basis of the widely used Cremer coincidence condition to identify propagating plate waves. It is found that these differences are particularly pronounced in cases where the ratio of fluid to solid densities is high, as for composite materials. The existence of such behavior is also demonstrated numerically in a fluid‐coupled aluminum plate by arbitrarily increasing the density of the fluid.

Journal ArticleDOI
TL;DR: In this paper, the quasi-static distributed spring model is used to derive the ultrasonic reflectivity of an imperfectly-bonded interface as a function of frequency and angle of incidence.
Abstract: The quasi-static distributed spring model is used to derive the ultrasonic reflectivity of an imperfectly-bonded interface as a function of frequency and angle of incidence. The results are then incorporated in a model for the corner reflection from a diffusion-bonded joint between two abutting plates, the corner being defined by the bond plane and the common lower surface plane of the plates. An immersion-inspection geometry is assumed, and seven categories of corner reflections are identified and examined in detail. These fall into two classes: those having parallel incident and exiting rays in water (φ′=φ), and those having nonparallel water rays (φ′ ≠ φ). The φ′ = φ categories are suitable for single probe (pulse-echo) inspections of the joint. Based on the amplitude of the outgoing corner-reflected signal, two φ = φ′ geometries appear promising. These employ, respectively, a corner reflection involving only longitudinal waves with the interface illuminated at near-grazing incidence (LLL), and a corner reflection involving only transverse waves with the interface illuminated at near 45° incidence (TTT). In addition, two practical φ′ ≠ φ geometries are indicated; these both involve mode conversion upon reflection from the interface, with the incident or outgoing longitudinal wave traveling nearly parallel to the interface. Model predictions for LLL and TTT reflections are compared to measurements on diffusion-bonded Inconel specimens, and techniques for applying the model results to more complicated bond geometries are discussed.

Journal ArticleDOI
TL;DR: In this article, the properties of sound waves emitted by uniformly heated spherical droplets are found as a frequency domain solution to a boundary value problem for the acoustic pressure, and the expression for the pressure is Fourier transformed to give the time domain pressure response to a delta function light pulse.
Abstract: In general, the absorption of amplitude‐modulated radiation by a body results in heating and a subsequent thermal expansion that gives rise to the emission of sound waves. Here, the properties of sound waves emitted by uniformly heated spherical droplets are found as a frequency domain solution to a boundary‐value problem for the acoustic pressure. The expression for the pressure is Fourier transformed to give the time domain pressure response to a delta function light pulse. Owing to the different sound speeds and densities in the sphere and its surrounding medium, the effects of reflection, dispersion, and phase cancellation can be seen in the acoustic signal.

Book ChapterDOI
01 Jan 1988
TL;DR: In this article, a spectrometer (VIRAF-spectrometer) was developed to detect absorption, fluorescence and reflection spectra as well as fluorescence induction kinetics with one leaf sample.
Abstract: The reflection signature of vegetation is the basis for the detection of tree damage by remote sensing. Damaged trees are characterized by (a) an increase of the signal betwenn 500 and 680 nm, (b) a decrease of the signal above 750 nm and (c) a “blue shift” of the inflection point of the rise towards 750 nm. The comparison of reflection and fluorescence spectra demonstrates that fluorescence emission might influence the shape of the reflection spectra. Especially in the region of the rise of the reflection signal towards 750 nm (“red edge”) the detection of fluorescence cannot be excluded in reflection measurements. The measurement of fluorescence signatures parallel to reflection signatures is proposed for remote sensing. A spectrometer (VIRAF-spectrometer), which has recently been developed to detect absorption, fluorescence and reflection spectra as well as fluorescence induction kinetics with one leaf sample, is presented as a help for the interpretation of remote sensing signatures more based on physiological data.

Journal ArticleDOI
TL;DR: The SAM system has been used to determine inhomogeneities in surface acoustic properties of mineralized tissues and implant materials, in many cases as a complement to using ultrasonic wave propagation techniques to measure the bulk anisotropic properties.

Journal ArticleDOI
TL;DR: In this paper, conservation laws for reflection and transmission of electromagnetic waves on a plane interface of isotropic transparent media are determined using these laws, relations have been established between the transverse shift (TS) of a centre of gravity of reflected and transmitted wavepackets, the change of the normal component of the intrinsic Minkowski angular momentum of the electromagnetic field and the Transverse electromagnetic power flow (TPF) phenomena.
Abstract: The conservation laws for the process of reflection and transmission of electromagnetic waves on a plane interface of isotropic transparent media are determined Using these laws, relations have been established between the transverse shift (TS) of a centre of gravity of reflected and transmitted wavepackets, the change of the normal component of the intrinsic Minkowski angular momentum of the electromagnetic field and the Abraham transverse momentum (or the transverse electromagnetic power flow (TPF)) The previous investigations of the TS and TPF phenomena are discussed from the point of view of conservation laws

Journal ArticleDOI
TL;DR: In this article, a Joseph filter analogous to the one proposed in this paper was constructed for a reflection sequence with a power spectrum proportional to f and a negative autocorrelation at small lags.
Abstract: Common practice in seismic deconvolution is to assume that the reflection sequence is uncorrelated, that is, that the sequence has a white power spectrum and a delta function autocorrelation A white spectrum implies that the acoustic impedance function has a power spectrum proportional to 1/f2, which is characteristic of a nonstationary Brownian process (f is frequency) However, the maximum power spectrum permissible for the acoustic impedance function is 1/f; we call a spectrum of this kind a Joseph spectrum A Joseph spectrum corresponds to a reflection sequence with a power spectrum proportional to f and a negative autocorrelation at small lags Joseph spectrum behavior for reflection sequences has been seen before and we show it again in a well off Newfoundland and in two wells from Quebec If the power spectrum is proportional to f, then the first term of the discretized autocorrelation function is −0405 of the zero‐lag term and higher terms are negligible We construct a Joseph filter analogous t

Journal ArticleDOI
TL;DR: In this article, the authors have studied the characteristics of clear air echoes in the lower stratosphere and troposphere from simultaneous observations of vertical echo power and temperature profiles, from which the mean gradient of generalized potential refractive index, M, was determined.
Abstract: We have studied some characteristics of clear air echoes in the lower stratosphere and troposphere from simultaneous observations of vertical echo power and temperature profiles The vertical echo power has been oversampled every 75 m with a height resolution of 150 m by the middle and upper atmosphere (MU) radar (35°N, 136°E) During the radar observations a radiosonde was launched at the MU radar site in order to measure temperature, humidity, and pressure with a height resolution of a few tens of meters, from which the mean gradient of generalized potential refractive index, M, was determined In the lower troposphere (below 10 km altitude), M is enhanced owing to humidity by about 10–20 dB, and its fine structure is mainly determined by the vertical gradient of humidity The relatively large time-height variation of tropospheric echo power seems to be attributed to rapid changes in the humidity profile On the other hand, in the upper troposphere (above 10 km altitude) and stratosphere the vertical structure of M is mainly determined by the Brunt-Vaisala frequency and air density, where the former determines fine vertical structure of M and the latter the gradual decrease in M with a scale height of about 7 km The measured M2 profile agrees well with the vertical echo power profile down to the radar height resolution of 150 m That is, the vertical structure of the reflection coefficient is mainly determined by M2, and therefore the energy density of 3-m scale fluctuations E(2k) seems to be distributed uniformly with height The vertical spacing of intense reflection layers usually ranges from 500 m to a few kilometers, which corresponds to the dominant vertical scale of fluctuations in the Brunt-Vaisala frequency profile The vertical distribution of intense reflection layers seems to be explained by a predominance of a saturated vertical wave number spectrum of gravity waves with a slope of −3 and a dominant vertical scale of a few kilometers

01 Feb 1988
TL;DR: In this article, the authors used high-resolution P-wave reflection seismology to locate water-filled cavities in a 1-m (3-ft) thick coal seam at depths of 9 m (29 ft) in southeastern Kansas.
Abstract: Surface collapse over abandoned sub-surface coal mines continues to be a problem in many parts of the world. High-resolution P-wave reflection seismology was successfully used to locate water-filled cavities in a 1-m (3-ft) thick coal seam at depths of 9 m (29 ft) in southeastern Kansas. A dominant frequency of 275 Hz was attained enabling us to delineate the top of the coal seam. This study is one of the first to locate water-filled coal mine cavities at depths of less than 30 m (100 ft) using high-resolution P-wave seismic reflection techniques.

Journal ArticleDOI
TL;DR: In this article, the authors investigated wave propagation in a periodic truss-work beam and found that the beam exhibits complicated mechanical filtering properties, which are illuminated by investigation of wave-mode power flow.

Journal ArticleDOI
TL;DR: In this paper, the reflection of a guided mode obliquely incident to a periodic, shallow, surface corrugation, waveguide grating is analyzed using the local normal mode expansion of coupled-mode theory.
Abstract: The reflection of a guided mode obliquely incident to a periodic, shallow, surface corrugation, waveguide grating is analyzed using the local normal mode expansion of coupled-mode theory. The coupling coefficients which give the strength of the TE-TE, TE-TM, TM-TE, and TM-TM mode interactions are evaluated as a function of incidence angle. The results are compared to the coupling coefficients obtained using a number of other analytical techniques. >

Journal ArticleDOI
TL;DR: In this article, a complete ray theory of reflection from the illuminated portion of a smooth object with inflection points must include specularly reflected real as well as complex rays, with the latter originating from the complex extension of the surface contour.
Abstract: Reflection from a smooth target with inflection points, when investigated by the physical optics method, reveals far-zone contributions arising from real and complex stationary points. The former represent conventional specularly reflected real-ray fields whereas the latter, which are nonspecular in real space, can be interpreted as complex-ray fields reflected specularly from the complex extension of the scatterer surface. To explain the nonspecular contributions, the complex stationary point fields are regarded as specular reflections of complex incident rays from the analytic extension of the boundary into a complex coordinate space. It is verified that this construction using complex geometrical optics is in complete agreement with physical optics asymptotics and that the complex reflection points for far-zone fields lie near the concave-to-convex transitions on the physical contour. Numerical results supporting the validity of this assertion are provided. It is concluded, therefore, that a complete ray theory of reflection from the illuminated portion of a smooth object with inflection points must include specularly reflected real as well as complex rays, with the latter originating from the complex extension of the surface contour. >

Journal ArticleDOI
TL;DR: In this article, the absorption properties of the system were quantitatively described by considering the system as a multi-layer dielectric stack, and it was shown that strong absorption is obtained provided that a large optical electrical field perpendicular to the quantum wells is generated.
Abstract: The observation of resonant inter-sub-band absorption in AlxGa1-xAs/GaAs single quantum wells using a total internal reflection geometry is reported. It is shown that strong absorption is obtained provided that a large optical electrical field perpendicular to the quantum wells is generated. Such conditions occur when the well is close to the reflecting boundary and reflection occurs at a semiconductor/metal interface, but not when reflection occurs at a semiconductor/vacuum interface. The optical properties of the whole structure can be quantitatively described by considering the system as a multi-layer dielectric stack.

Proceedings ArticleDOI
12 Mar 1988
TL;DR: In this article, the Torrance-Sparrow model was used to measure the surface orientation of a wide variety of isotropically rough material surfaces, which can be achieved from knowledge of the polarization states of both incident and reflected light radiation upon and from the surface respectively.
Abstract: It is demonstrated that measurement of local surface orientation for a wide variety of isotropically rough material surfaces can be achieved from knowledge of the polarization states of both incident and reflected light radiation upon and from the surface respectively. The reflection model used is the Torrance-Sparrow model assuming combined specular and diffuse reflection. The specular and diffuse reflection components have distinct polarization states which makes it possible to resolve intersecting specular and diffuse equireflection curves in gradient space thereby measuring surface orientation. The light source incident orientation and the viewer orientation are assumed to be known along with the complex index of refraction of the material surface and the root mean square slope of planar microfacets characterizing surface roughness. The theoretical development is very comprehensive with respect to the nature of the incident and reflected light radiation which is assumed to be quasi-monochromatic having arbitrary degree of polarization. Thus determination of surface orientation is feasible using incident incoherent natural sunlight which is completely unpolarized, using incident partially polarized light such as specularly reflected natural sunlight, or using completely polarized incident light such as light which is elliptically polarized including circular and linear polarizations.