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An exact multiple-scattering series for the scattering of two heavy ions is derived and compared to the Glauber approximation. An optical model potential operator is indicated which is an accurate approximation to the multiple-scattering formalism.
Mathematical model of multiple-scattering of light by clouds as in optical communication
An efficient numerical method of multiple quadratures, the Conroy method, is applied to the problem of computing multiple scattering contributions in the radiative transfer through realistic planetary atmospheres. A brief error analysis of the method is given and comparisons are drawn with the more familiar Monte Carlo method. Both methods are stochastic problem-solving models of a physical or mathematical process and utilize the sampling scheme for points distributed over a definite region. In the Monte Carlo scheme the sample points are distributed randomly over the integration region. In the Conroy method, the sample points are distributed systematically, such that the point distribution forms a unique, closed, symmetrical pattern which effectively fills the region of the multidimensional integration. The methods are illustrated by two simple examples: one, of multidimensional integration involving two independent variables, and the other, of computing the second order scattering contribution to the sky radiance.
In planetary applications it is sometimes important to know the degree to which multiple scattering is influencing the photometric properties of a surface. An investigation is conducted concerning the point at which the single-scattering approximation used in the theory developed by Hapke (1963) and Irvine (1966) breaks down. It is shown that the Hapke-Irvine photometric function provides an adequate representation of the scattering properties of particulate surfaces whose geometric albedos (or normal reflectances) do not exceed 0.3. An experiment is conducted to estimate the normal reflectance below which the Hapke-Irvine equation considered provides an adequate representation of the scattering properties of a particulate surface. The investigation makes use of a set of samples which were prepared by mixing magnesium oxide and charcoal powders. The samples have a range in normal reflectance from 0.04 to 1.04.
Effects of multiple scattering on the reflectivity measurement for millimeter-wavelength weather radars are studied, in which backscattering enhancement may play an important role. In the previous works, the backscattering enhancement has been studied for plane wave injection, the reflection of which is received at the infinite distance. In this paper, a finite beam width of a Gaussian antenna pattern along with spherical wave is taken into account. A time-independent second order theory is derived for a single layer of clouds of a uniform density. The ordinary second-order scattering (ladder term) and the second-order backscattering enhancement (cross term) are derived for both the copolarized and cross-polarized waves.
A new method for the determination of multiple scattering effects is described. A polarization Raman elastic backscatter lidar is used, which allows the measurement of the depolarization of both the elastically backscattered light and the light Raman scattered from nitrogen molecules. With this technique the depolarization effect due to multiple scattering can be separated from single scattering polarization. Presented here are a short discussion of the idea and a measurement example.
The results are presented of investigations on the various aspects of multiple scattering effects on visible and infrared laser beams transversing dense fog oil aerosols contained in a chamber (4' x 4' x 9'). The report briefly describes: (1) the experimental details and measurements; (2) analytical representation of the aerosol size distribution data by two analytical models (the regularized power law distribution and the inverse modified gamma distribution); (3) retrieval of aerosol size distributions from multispectral optical depth measurements by two methods (the two and three parameter fast table search methods and the nonlinear least squares method); (4) modeling of the effects of aerosol microphysical (coagulation and evaporation) and dynamical processes (gravitational settling) on the temporal behavior of aerosol size distribution, and hence on the extinction of four laser beams with wavelengths 0.44, 0.6328, 1.15, and 3.39 micrometers; and (5) the exact and approximate formulations for four methods for computing the effects of multiple scattering on the transmittance of laser beams in dense aerosols, all of which are based on the solution of the radiative transfer equation under the small angle approximation.
The locally self-consistent multiple scattering (LSMS) method can perform efficient first-principles calculations of systems with a large number of atoms. Here, in this paper, we combine the Kubo-Greenwood equation with LSMS, enabling us to calculate the first-principles residual resistivity of large systems. This has been implemented in the open-source code LSMS . We apply this method to selected pure elements and binary random alloys. The results compare well with experiment, and with values obtained from a first-principles effective medium technique (the Korringa-Kohn-Rostoker coherent potential approximation). We discuss future applications of this method to complex systems where other methods are not applicable.
Multiple scattering in Kapitza-Dirac effect describing electron scattering by standing electromagnetic wave, noting transition probability less than unity
Multiple scattering affects propagation of light beams in turbid media. Backscattering or forward scattering based measurements of atmospheric parameters are influenced by this effect. Although largely studied theoretically, the effect needs measurements in control of situations due to the large variety of situations of practical importance. The results of laboratory measurements pertaining to the transmission of a collimated light beam (Helium-Neon souce, 10 mW) through suspensions of latex spheres in water are presented and a comparison was made with the predictions of calculation in a foggy atmosphere will also be presented.
The depolarization of ruby lidar backscattering caused by multiple scattering in marine stratus clouds was examined systematically from a field site on the southern California coast. Investigated were the effects on the linear depolarization (delta) of lidar receiver field of view (FOV), elevation angle and laser beam pointing errors. An approximately linear increase in maximum delta values was observed with increasing receiver FOV, and the importance of accurate transmitter/receiver beam alignment was demonstrated during experiments in which the laser axis was deliberately misaligned. An elevation angle dependence to the delta values was observed as a consequence of the natural vertical inhomogeneity of water cloud content above the cloud base. Time histories of the depolarization characteristics of dissipating stratus clouds revealed significant spatial and temporal variability in delta values attributed to cloud composition variations. Employing a 1 mrad transmitter FOV, maximum delta values of 0.21 nd 0.33 were observed with 1 and 3 mrad receiver FOVs, respectively, from the low stratus clouds. The fundamental causes and effects on the lidar equation of multiple scattering are also discussed.
It is shown that the Monte Carlo method can provide useful information on the polarization and its direction for homogeneous layers corresponding to the haze C, nimbostratus, and ice crystals models. Results for various optical thicknesses and two solar zenith angles show the variation with these parameters. In most cases the direction of polarization with respect to the meridian plane (which contains the outgoing photon) does not change appreciably with the optical thickness of the scattering layer, so that the conclusion that the direction of polarization is determined mainly by the direction of the incident and scattered photons, obtained for single scattering, should apply approximately when multiple scattering is taken into account.
The Galileo Ultraviolet Spectrometer obtained a Lyman-alpha celestrial sphere map on 13,14 December 1990 near the first Earth encounter, with spacecraft near the interstellar wind downwind axis. The data show solar flux longitudinal and latitudinal asymmetries which are modeled with He 10830 Ssolar images. The difference between the observed brightness and a single scattering model is attributed to multiple scattering effects, which we also calculate. The data constrain the solar wind flux latitude variation at solar maximum. Other 1990-1992 Galileo Lyman-alpha data will be discussed.
The University of Wisconsin High Spectral Resolution Lidar (HSRL) provides unambiguous measurements of backscatter cross section, backscatter phase function, depolarization, and optical depth. This is accomplished by dividing the lidar return into separate particulate and molecular contributions. The molecular return is then used as a calibration target. We have modified the HSRL to use an I2 molecular absorption filter to separate aerosol and molecular signals. This allows measurement in dense clouds. Useful profiles extend above the cloud base until the two way optical depth reaches values between 5 and 6; beyond this, photon counting errors become large. In order to observe multiple scattering, the HSRL includes a channel which records the combined aerosol and molecular lidar return simultaneously with the spectrometer channel measurements of optical properties. This paper describes HSRL multiple scattering measurements from both water and ice clouds. These include signal strengths and depolarizations as a function of receiver field of view. All observations include profiles of extinction and backscatter cross sections. Measurements are also compared to predictions of a multiple scattering model based on small angle approximations.
Warm dense matter plays an important role in astrophysical objects and technological applications, but the rigorous diagnostics of corresponding experiments is notoriously difficult. In this work, we present a model-free analysis of x-ray Thomson scattering (XRTS) measurements on isochorically heated graphite obtained at the Linac Coherent Light Source at multiple scattering angles. We demonstrate that the recent imaginary-time thermometry technique works for scattering data that have been measured in both forward and backward scattering geometry. This opens up the way toward a rigorous quantification of nonequilibrium effects in future experiments, where XRTS measurements are being obtained from multiple scattering angles from the same sample.
A radiative transfer method for treating nongray gaseous absorption and thermal emission in vertically inhomogeneous multiple scattering atmospheres is described. Probability density distributions of absorption coefficient strength are derived from line-by-line calculations to construct line-by-line and band model based k distributions. The monotonic ordering of absorption coefficient strengths in these k distributions implicitly preserves the monochromatic structure of the atmosphere at different pressure levels, thus simulating monochromatic spectral integration at a fraction of the line-by-line computing cost. The k distribution approach also permits accurate modeling of overlapping absorption by different atmospheric gases and accurate treatment of nongray absorption in multiple scattering media. It is shown that the correlated k distribution method is capable of achieving numerical accuracy to within 1 percent of cooling rates obtained with line-by-line calculations throughout the troposphere and most of the stratosphere.
Multiple scattering by large particles in optically thick layers, using scalar transfer equations
Doubling method application to multiple scattering of polarized light, studying Venus visible disk reflection of sunlight