Double-scattering Approximation Research Articles

Modal evaluation of the anthropogenic night sky brightness at arbitrary distances from a light source

The artificial emissions of light contribute to a high extent to the observed brightness of the night sky in many places of the world. Determining the all-sky radiance of anthropogenic origin requires solving the radiative transfer equation for ground-level light sources, generally resorting to a double-scattering approximation in order to account for the observed radiance patterns with a reasonable degree of accuracy. Since the all-sky radiance distribution produced by an elementary light source depends on the distance to the observer in a way that is not immediately obvious, the contributions of sources located at different distances have to be computed on an individual basis, solving for each one the corresponding scattering integrals. In this paper we show that these calculations may be significantly alleviated by using a modal approach, whereby the hemispheric night-sky radiance is expanded in terms of a convenient basis of two-dimensional (2D) orthogonal functions. Since the modal coefficients of this expansion do vary smoothly with the distance to the observer, the all-sky brightness distributions produced by light sources located at arbitrary intermediate distances can be efficiently estimated by interpolation, provided that the coefficients at a discrete set of distances are accurately determined beforehand.

Double-Scattering Approximation Theory of Enhanced Backscatterings of Light Produced from Aggregated Particles

We theoretically analyze the spatial anisotropy and polarization dependences of enhanced backscattering of light using a double-scattering approximation. The polarization of light is calculated in terms of the Jones vector and the scattering amplitude matrix. We discuss the cases where the individual scattering event is isotropic and governed by Rayleigh scattering for the media in which scatterers are homogeneously dispersed and aggregated. The spatial properties of the far-field intensity distribution can be demonstrated by asymptotic expansions in the region of the large backscattering angle. As a result, we theoretically reveal the polarization anisotropy of the decreasing variation in the far-field intensity distribution dependent on the fractal dimension, the azimuth in the backscattering angle, and the polarization state.

Coherent opposition effects for semi-infinite discrete random medium in the double-scattering approximation

The rigorous equations of the theory of multiple scattering of light by a layer of disordered medium have been used in the double-scattering approximation for semi-infinite medium to determine the influence of the particle properties on the coherent opposition effects. The effects were found to be strongly dependent on the concentration of scatterers in the medium. The polarization opposition effect is more sensitive to the properties of the scatterers than the photometric opposition effect. The interference of waves could result in the negative polarization at the backscattering direction as well as in the positive polarization.

The half-on-shell Coulomb T-matrix in a double-scattering approximation to the ionization of helium by fast protons

We investigate the application of the Faddeev-Watson multiple-scattering series to the ionization of atoms by ion impact. Singularities in the first- and second-order terms are discussed. Different forms of the half-shell Coulomb T-matrix are used in impulse approximations to double-differential cross sections (DDCSs) for proton-impact ionization of helium, and are compared with experiment. By using the regularized half-shell T-matrix we derive a double-scattering approximation which includes the full projectile-residual-ion interaction. While the latter approximation does not improve on the impulse approximations for DDCSs, in contrast to other models, we conjecture that it might adequately describe triple-differential cross sections for large angles of deflection of the projectile.

Verification of a localization criterion for several disordered media

We analytically compute a localization criterion in the double-scattering approximation for a set of dielectric spheres or perfectly conducting discs uniformly distributed in a spatial volume which may be either spherical or layered. For every disordered medium, we numerically investigate a localization criterion and examine the influence of the system parameters on the wavelength localization domains.

Enhanced backscattering of light from a random grating

By the use of Green's second integral theorem we have obtained exact expressions for the scattered electromagnetic field produced by a p- or s-polarized beam of finite width incident from the vacuum side onto a random grating whose grooves are perpendicular to the plane of incidence. The scattered field is expressed in terms of the total magnetic (electric) field in the vacuum and its normal derivative, evaluated on the surface of the grating in the case of p- ( s-) polarization. The coupled pair of inhomogeneous integral equations satisfied by these source functions is solved numerically for each of several thousand realizations of the surface profile, which are generated numerically and possess a Gaussian spectrum. The incoherent component of the differential reflection coefficient averaged over these realizations of the surface profile displays a well-defined peak in the retroreflection direction in the scattering of s-polarized light from a large amplitude random metallic grating but not in the scattering of s-polarized light from a small amplitude random metallic grating. The mean scattering amplitude, regarded as a function of the component of the wave vector of the scattered light parallel to the mean surface at the frequency of the incident light, displays a pole in the nonradiative region in the former case but not in the latter. This suggests that electromagnetic waves of s-polarization are trapped by large amplitude roughness but not by small amplitude roughness. Enhanced backscattering is also observed in the scattering of s-polarized light from a large amplitude random grating on the surface of a nearly transparent dielectric medium. Evidence is presented that the enhanced backscattering observed in the scattering of both p- and s-polarized light from a large amplitude random grating on a perfect conductor is not a single-scattering effect, but is already present in a double-scattering approximation. Finally, it is demonstrated that the enhanced backscattering present in our simulation results is an effect that lies outside the statistical errors caused by our use of a finite number of surface profiles in our calculations.

McRae's multiple-scattering approach extended to electron scattering by molecules

McRae's (1967) approach to multiple scattering by crystals is re-examined in order to adapt it to elastic scattering of electrons by molecules, the ultimate goal being to treat chiral electron scattering which would be difficult by standard electron-molecule theories. His working equation is shown to be exact provided his definition of the effective partial scattering amplitude is amended properly. The Fourier transform of a scattered wave from constituent atoms is then expanded in terms of spherical harmonics, the expansion conforming with his assumption that the scattered wave can be expressed by a superposition of plane waves of a fixed wavenumber. An approximate yet practicable set of coupled linear equations for the expansion coefficients is derived. In the double-scattering approximation the cross section is expressed in terms of the modified scattering amplitudes, falpha ( beta ) for atom alpha which reflects double-scattering effects due to atom beta . A resonance-like behaviour is qualitatively discussed.

Double-scattering approximation of lidar equation for inhomogeneous atmosphere

The lidar equation in a double-scattering approximation, applicable for the case of an inhomogeneous atmosphere, has been derived. It is shown that a doubly scattered flux contains information on the microstructure of the medium investigated. Calculations of the intensity of doubly scattered radiation reflected from clouds are given as an illustrative example. It follows from these calculations that double scattering depends essentially on the distance from the lidar to the cloud sounded.

Use of double scattering in lidar applications

The lidar approximation for a monostatic sounding system is obtained in a double-scattering approximation. The result is an integral Volterra equation of the first kind with a difference kernel. A numerical analysis is made of the limits of validity of the double-scattering approximation. The Monte Carlo method is used in calculations for two types of media. Quantitative estimates of the functional nature of the kernels are obtained for three types of fog and three cloud models.

Multiple Scattering Corrections inπ±Deuteron Scattering

Multiple-scattering corrections to the impulse approximation are calculated for the scattering of ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ mesons by deuterons. These corrections are model-dependent since the scattered wave propagates off the energy shell between the first and last scatterings whereas experimental scattering phase shifts are available only for elastic scattering. Various assumptions are made concerning the off-the-energy-shell behavior of the scattering amplitudes and the double-scattering approximation is analyzed for meson energies of 45 Mev and 169 Mev. The results are tabulated and are found to be sensitive to the different scattering models. The cross sections at 169 Mev were calculated with both the Fermi and Bethe solutions for the meson-nucleon scattering phase shifts and are in close agreement. It thus does not seem to be feasible to use ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$-D scattering as a means of distinguishing between these two solutions.