Showing papers on "Scattering published in 1981"
TL;DR: In this article, an approximate analytic solution for the radiative transfer equation describing particulate surface light scattering, taking into account multiple scattering and mutual shadowing, was derived for the interpretation of reflectance spectroscopy of laboratory surfaces and the photometry of solar system objects.
Abstract: An approximate analytic solution is derived for the radiative transfer equation describing particulate surface light scattering, taking into account multiple scattering and mutual shadowing. Analytical expressions for the following quantities are found: bidirectional reflectance, radiance coefficient and factor, the normal, Bond, hemispherical, and physical albedos, integral phase function and phase integral, and limb-darkening profile. Scattering functions for mixtures can be calculated, as well as corrections for comparisons of experimental transmission or reflection spectra with observational planetary spectra. The theory should be useful for the interpretation of reflectance spectroscopy of laboratory surfaces and the photometry of solar system objects.
1,816 citations
TL;DR: In this paper, the basic principles of radiative transfer in the Earth's atmosphere are discussed, including thermal infrared radiation transfer and light scattering by atmospheric particulates, and the application of radiative transfer principles to remote sensing.
Abstract: Fundamentals of Radiation for Atmospheric Applications. Solar Radiation at the Top of the Atmosphere. Absorption and Scattering of Solar Radiation in the Atmosphere. Thermal Infrared Radiation Transfer in the Atmosphere. Light Scattering by Atmospheric Particulates. Principles of Radiative Transfer in Planetary Atmospheres. Application of Radiative Transfer Principles to Remote Sensing. Radiation and Climate.
1,531 citations
TL;DR: In this article, it was shown that definitions of such quantities as effective atomic number cannot be justified from fundamental theory and the consequences of this result are explored in relation to various experimental conditions and the physical parameters of a complex medium which can be determined by X-ray transmission measurements.
542 citations
TL;DR: In this article, the authors used Raman scattering and x-ray diffraction measurements to correlate finite-size effects on the Raman spectra of nonpolar vibrational modes in BN.
Abstract: Raman scattering and x-ray diffraction measurements are used to correlate finite-size effects on the Raman spectra of nonpolar vibrational modes in BN. The BN microcrystalline samples used exhibited domain sizes varying from 4.4 to 78.5 nm in the plane and 1.5 and 47.5 nm perpendicular to the planes. The Raman measurements indicated that the high-frequency ${E}_{2g}$ mode shifted to higher frequency and broadened as the crystallite size decreased. A formulation of the Raman cross section for scattering from nonpolar microcrystals is presented. The development includes evaluation of the susceptibility correlation function over a limited spatial extent. The results indicate that spectral changes are related to the phonon dispersion, and the wave-vector uncertainty is accounted for. The formulation is applied to describe the BN light scattering results, and good agreement was obtained to describe the observed shift in frequency.
520 citations
IBM1
TL;DR: In this article, the basic theory of lattice scattering for electrons in a semiconductor heterolayer, and resulting transport properties in two dimensions parallel to the layer plane, are investigated, specifically for polar semiconductors such as gallium arsenide.
500 citations
TL;DR: Efficient, numerically stable, methods for the calculation of light-scattering intensity functions for concentrically coated spheres are discussed and are accurate for all refractive indices, for large and small particles, and for cores with any relative size.
Abstract: Efficient, numerically stable, methods for the calculation of light-scattering intensity functions for concentrically coated spheres are discussed. Earlier forms of these equations are subject to various numerical difficulties which give rise to significant errors, especially for thin absorbing shells. The present equations are accurate for all refractive indices, for large and small particles, and for cores with any relative size.
491 citations
378 citations
TL;DR: Under most practical conditions, the process of back projection and coherent summation over spherical surfaces in image space, without prior filtering, is shown to provide a close approximation to the exact inversion procedure.
Abstract: The problem of reconstructing the reflectivity of a three-dimensional medium with density and compressibility variations is examined. For the special case of continuous-wave (CW) insonification, exact inversion formulas have recently been reported for recovering an unknown scattering parameter from scattering measurements. In this work, exact solutions, or inversion formulas, are obtained for the general case of arbitrary broad-band insonification where the incident wave is assumed to be a spherically diverging broad-bandwidth pulse of arbitrary shape. Solutions are derived under the assumption that the scattering is sufficiently weak for the Born approximation to hold. Exact inversion formulas are obtained for three aperture geometries: a plane, cylindrical, or spherical recording surface enclosing the scattering region. Under most practical conditions, the process of back projection and coherent summation over spherical surfaces in image space, without prior filtering, is shown to provide a close approximation to the exact inversion procedure. Finally, in the case of the spherical geometry, the mathematical equivalence between the three-dimensional inverse Radon transform and the far-field approximation to the exact solution is demonstrated.
349 citations
TL;DR: In this paper, point measurements of particle size, chemical nature, scattering and absorption extinction coefficients have been used to describe the optical or visual effects of trace materials in urban or rural air.
313 citations
TL;DR: In this article, a folded-Yukawa single-particle potential was used to calculate the ground-state masses of 28 nuclei ranging from 109 Cd to 252 Cf.
TL;DR: A method for determining the internal structure of a localized scattering potential from field measurements performed outside the scattering volume is developed by using the Rytov approximation.
Abstract: A method for determining the internal structure of a localized scattering potential from field measurements performed outside the scattering volume is developed by using the Rytov approximation. The theory is compared with the inverse-scattering method within the Born and eikonal approximations and found to reduce to these methods in the weak-scattering (Born) and very-short-wavelength (eikonal) limits.
TL;DR: In this paper, the ionic fraction in the reflected beam when an atom or ion is scattered from a metal surface at finite temperature is considered, and three regimes are distinguished: low temperature, high temperature and low temperature.
TL;DR: Strong evidence supporting the van de Hulst dielectric surface-wave model for these resonances is presented and use of resonances for high precision measurement of sphere size and sphere distortion, index of refraction, temperature, and vapor pressure is discussed.
Abstract: Use of the wavelength and size dependence of light scattering from optically levitated liquid drops is demonstrated as a sensitive means of detecting optical resonances of dielectric spheres. High resolution spectra are presented of the radiation pressure, far- and near-field backscatter, and 90 degrees scatter. Excellent agreement is found between experimental spectra and high resolution Mie calculations of Chylek et al. Strong evidence supporting the van de Hulst dielectric surface-wave model for these resonances is presented. Use of resonances for high precision measurement of sphere size and sphere distortion, index of refraction, temperature, and vapor pressure is discussed.
TL;DR: In this paper, a generalized theory of radiative transfer is presented which includes single and multiple scattering of light in particulate surfaces, and is applicable to both the surfaces of atmosphereless bodies and to laboratory samples.
Abstract: A generalized theory of radiative transfer is presented which includes single and multiple scattering of light in particulate surfaces, and is applicable to both the surfaces of atmosphereless bodies and to laboratory samples. Single scattering is described in terms of the effects of porosity and roughness, and is formulated by means of a probabilistic method. It is shown that, for low-albedo surfaces, the effects of porosity and roughness are separable, the opposition effect is caused by the former, and the slope of the linear part of the phase curve is mainly controlled by the latter. The theory, which is applicable to all albedos and phase angles, may be used in both surface brightness and integrated brightness studies. The limiting case of roughness and volume density tending to zero yields the results of classical radiative transfer theory.
TL;DR: In this paper, a multichannel analysis of low-energy KN data is presented, which simultaneously is required to satisfy dispersion relation constraints coming partly from the measured real parts of the forward K±N amplitudes and partly from forward K−p → K0n and KS0p → KS 0p data.
IBM1
TL;DR: In this paper, the rotational state distributions for NO scattered from Ag(111) have been measured over the incident kinetic energy range of 0.1 to 1.7 eV with use of rotationally cold molecular beam and laser-induced-fluorescence detection.
Abstract: Rotational state distributions for NO scattered from Ag(111) have been measured over the incident kinetic energy range of 0.1 to 1.7 eV with use of rotationally cold molecular beam and laser-induced-fluorescence detection. The measured distributions divide into two parts: a low rotational state portion ($J\ensuremath{\lesssim}20.5$) which is described by a Boltzmann distribution and a high-$J$ portion which shows a broad structure tentatively interpreted as resulting from a rotational rainbow.
TL;DR: In this paper, a differential anomalous x-ray scattering technique has been developed for structural studies of disordered and amorphous systems, which is consistent with threefold coordinated models of the structure but not with the fourfold-twofold models.
Abstract: A differential anomalous x-ray scattering technique has been developed for structural studies of disordered and amorphous systems. The results on amorphous GeSe/sub 2/ are consistent with the twofold coordination of Se and the fourfold coordination of Ge. The results on amorphous GeSe are consistent with threefold coordinated models of the structure but not with the fourfold-twofold models.
TL;DR: In this article, the effects of Zeeman splitting and spin-orbit scattering on the resistance in two-dimensional disordered systems are theoretically studied. And the field dependence of the magnetoresistance is shown to have the characteristic anisotropy.
Abstract: Effects of Zeeman splitting and spin-orbit scattering on the resistance in two-dimensional disordered systems are theoretically studied. The field dependence of the magnetoresistance is shown to have the characteristic anisotropy. The present theory explains the qualitative features of the experimental observations by Komori et al. in Cu granular films.
TL;DR: In this paper, the authors used a scattering model consisting of randomly distributed spheres to examine observations of shear waves in the range 1-30 Hz reported in the literature and found that geometrical scattering dominates.
Abstract: Observations of lithospheric Q for shear waves in the range 1--30 Hz reported in the literature are examined using a scattering model consisting of randomly distributed spheres. For the single scattering approximation I have assumed 1/Q = 1/Q/sub i/+gv/..omega.., where Q/sub i/ is the intrinsic Q due to anelasticity, v is the velocity of shear waves, ..omega.. is angular frequency and g is the turbidity. g is taken as a constant in this paper, since g = ..integral.. n(a)sigmada, where n(a)da is the number of scattering spheres of radius a/unit volume and sigma is the scattering cross-section for a sphere, this suggests that geometrical scattering dominates. This will be true for ka>1, where k is wavenumber. Based on this criterion and the observation that Q is large (i.e. g small) at a frequency of 0.05 Hz, a is of the order of magnitude 1--10 km. Fits of observations of shear wave Q from Japan and Central Asia indicate that Q/sub i/ = 2000 +- 500 for the lithosphere of both regions; g = 0.01 km for the Japan observations and g = 0.005 km/sup -1/ for Central Asia.
TL;DR: In this paper, the extinction coefficient due to particle absorption and particle scattering were measured with integrating nephelometers operating at both ambient conditions and in a heated mode during 41 consecutive days during November and December, 1978 in Denver, Colorado.
TL;DR: In this article, the deconvolution of the convolution square of a symmetrical function with a limited range of definition is presented. And the influence of imperfect realization of the symmetry conditions is discussed.
Abstract: A method for the deconvolution of the convolution square of a symmetrical function with a limited range of definition is presented. The solution function is approximated by a number of equidistant step functions. This allows the analytical computation of the integrals of overlap in one-dimensional (lamellar) symmetry, in two-dimensional (cylindrical) symmetry and in three-dimensional (spherical) symmetry. A special iterative linearized weighted-least-squares technique solves the non-linear convolution square-root problem without any a priori information on the solution. As an application, the electron or scattering length density ρ(r) from the distance distribution function p(r) of small-angle scattering is computed as well as the propagation of the statistical error from the input. The influence of imperfect realization of the symmetry conditions is discussed. Numerical instabilities that appear under certain conditions can easily be removed by a stabilization procedure.
TL;DR: In this paper, a Monte Carlo calculation procedure has been developed for computer modelling of the penetration of light into turbid, coloured waters of the type commonly found on the Australian continent, and the vertical attenuation coefficient for downward irradiance at the mid-point of the euphotic zone [Kd(za)] has been studied as a function of the absorption (a) and scattering (b) coefficients and, with the particular normalized volume scattering function used in these simulations, it was found to conform closely to the equation Kd(zm) = (a2 + 0.256
Abstract: A Monte Carlo calculation procedure has been developed for computer modelling of the penetration of light into turbid, coloured waters of the type commonly found on the Australian continent. For monochromatic light the structure of the underwater light field is described in terms of the variation of the average cosine (total, downward, upward) and irradiance reflectance, as a function of optical depth at a given ratio of scattering to absorption (bla), and as a function of bia at a given optical depth. The vertical attenuation coefficient for downward irradiance at the mid-point of the euphotic zone [Kd(za)] has been studied as a function of the absorption (a) and scattering (b) coefficients and, with the particular normalized volume scattering function used in these simulations. has been found to conform closely to the equation Kd(zm) = (a2 + 0.256ab)½ The data generated by the model have been used in conjunction with radiative transfer theory to determine the contribution of the different components of the attenuation mechanism to the vertical diminution of irradiance at different ratios of b to a. Simulation of the penetration of photosynthetically available radiation into four water bodies in the southern tablelands of New South Wales has been carried out using measured absorption coefficients and indirectly estimated values for scattering coefficients. The calculated values for vertical attenuation coefficients are in good agreement with those obtained by measurement within the water bodies. The possible use of this modelling procedure as a predictive tool is discussed.
TL;DR: In this article, the incoherent neutron scattering function for unbounded jump diffusion is calculated from random walk theory assuming a gaussian distribution of jump lengths, and the method is then applied to calculate the scattering functions for spatially bounded random jumps in one dimension.
Abstract: The incoherent neutron scattering function for unbounded jump diffusion is calculated from random walk theory assuming a gaussian distribution of jump lengths. The method is then applied to calculate the scattering function for spatially bounded random jumps in one dimension. The dependence on momentum transfer of the quasi-elastic energy broadenings predicted by this model and a previous model for bounded one-dimensional continuous diffusion are calculated and compared with the predictions of models for diffusion in unbounded media. The one-dimensional solutions can readily be generalized to three dimensions to provide a description of quasi-elastic scattering of neutrons by molecules undergoing localized random motions.
TL;DR: The main objective is to study the feasibility of using the geometrical optics expressions as a basis for practical laser water droplet sizing work, and a criterion is established for the range of applicability of the relationship I(theta,R) = K( theta)R(2), which relates the scattering intensity at a particular angle theta to the radius R of the droplet.
Abstract: The geometrical optics approach is used to derive i(1)(theta) = |S(1)(theta)|(2) and i(2)(theta) = |S(2)(theta)|(2), the angular intensity functions for light scattered by a spherical water droplet of a radius comparable with or larger than the wavelength of light. In contrast to previously published results, these functions are obtained in closed form and as functions of the scattering angle theta, which greatly enhance their usefulness in numerical work and in the reduction of large sphere scattering data. The range of validity of these expressions is investigated by graphical comparison of calculated angular intensity patterns with those obtained from rigorous Mie theory. Our main objective is to study the feasibility of using the geometrical optics expressions as a basis for practical laser water droplet sizing work. A criterion is established for the range of applicability of the relationship I(theta,R) = K(theta)R(2), which relates the scattering intensity at a particular angle theta to the radius R of the droplet. Accuracy of the laser water droplet sizing technique is thus quantitatively established.
TL;DR: In this paper, a theoretical method for calculating the angular scattering curve for any given thin-film multilayer in which the various surfaces and interfaces are assumed to be rough is described.
Abstract: A theoretical method is described for calculating the angular scattering curve for any given thin-film multilayer in which the various surfaces and interfaces are assumed to be rough. The energy that is scattered in any particular direction depends on two factors. The first is solely a function of the characteristics of the ideal multilayer and the observation conditions. The second depends on the roughnesses of the various surfaces, that is, on their autocorrelation and cross-correlation functions. The expressions that are obtained are completely general because no restrictive hypothesis has been developed on the relationship that may exist between the roughnesses of the various interfaces. The principal features of the apparatus used for the scattering measurements are briefly described. Next, several results of calculation and measurement are given as illustrations. The measurements show that polished surfaces of high optical quality often show marked anisotropy.
TL;DR: In this paper, a set of polarization transfer experiments are described, including relevant formulas and numerical estimates, which appear to offer a feasible way to separate the deuteron charge and quadrupole form factors and measure the neutron and proton electric form factors.
Abstract: We present a description, including relevant formulas and numerical estimates, of a set of polarization transfer experiments which appear to offer a feasible way to separate the deuteron charge and quadrupole form factors and measure the neutron and proton electric form factors. The experiments require a 2 to 4 GeV high-intensity, high-duty factor, longitudinally polarized electron beam and require that the polarization of the recoiling hadron be measured in a second, analyzing, scattering. The relevant asymmetries are fairly large, and our calculations show that they are sensitive to different models obtained from existing data. Attention is called to the fact that the proposed deuteron measurements will require new 10% measurements of vector and tensor analyzing powers of deuterons with kinetic energy from 150 to 450 MeV.
TL;DR: In this paper, the authors define the region within which the Born approximation may be regarded as reasonably accurate and compare it with the exact solution for scattering by an embedded sphere, showing that the inequalities obtained, governing the ranges of the parameters of the problem, are appropriate.
Abstract: Summary. In view of recent work on seismic scattering by small-scale heterogeneities in the Earth, which has been based on single-scattering perturbation theory (that is, the Born approximation), we attempt to define the region within which this approximation may be regarded as reasonably accurate. Comparison with the exact solution for scattering by an embedded sphere shows that the inequalities obtained, governing the ranges of the parameters of the problem, are appropriate. However, application of these constraints on the parameters imply that, in almost all cases, application of the Born approximation to upper and lower mantle scattering is probably invalid.
TL;DR: In this paper, Monte Carlo calculations of fast secondary electron production have been performed with a hybrid model for the discrete and continuous energy-loss processes, which predicts a larger absorbed energy density than the old model for an isolated line source exposure on a resist film.
Abstract: Monte Carlo calculations of fast secondary electron production have been performed with a hybrid model for the discrete and continuous energy‐loss processes. The Moller theory was adopted for the differential inelastic scattering cross‐section which determines the production rate of fast secondary electrons. The calculations were made for both a bulk polymethyl methacrylate (PMMA) sample and 4000‐A‐thin films of PMMA (with and without a silicon substrate) at 10 and 20 keV. The new model is discussed and comparison made with results obtained from the old model, which is based on the continuous slowing down approximation of Bethe for energy loss and the screened Rutherford equation for elastic angular scattering. The new model predicts a larger absorbed energy density than the old model for an isolated line source exposure on a resist film. The consequences of this fast secondary electron contribution on the ultimate limit in electron lithography is discussed.
TL;DR: In this paper, the authors used the Foldy approximation to find an equation for the mean field and derived an effective permittivity for the scattering medium from this equation, from which the correlation of the scattered field was found by employing the distorted Born approximation, i.e., particles embedded in the effective medium are assumed to be single scatterers.
Abstract: Electromagnetic backscattering from a sparse distribution of lossy dielectric particles having random orientation and position is studied. The paper begins by using the Foldy approximation to find an equation for the mean field. From this equation, an effective permittivity for the scattering medium is obtained. The correlation of the scattered field is found by employing the distorted Born approximation, i.e., particles embedded in the effective medium are assumed to be single scatterers. The above method is then used to find the backscattering coefficients from a leaf canopy. The leaf canopy is modeled by a half space of dielectric discs that are small in comparison to a wavelength. Numerical results show that the depolarized cross section is a sensitive function of leaf inclination angle statistics.