Light scattering by a spheroidal bubble with geometrical optics approximation

This paper proposes the spheroidal model for analyzing the light scattering characteristics of an air bubble. The angular distributions of light scattered by a large spheroidal bubble with end-on incidence are calculated using geometrical optics approximation. The divergence factor, diffraction, and phase shift are considered in the computation. The MATLAB code was developed and verified using the Mie result for a spherical bubble, and the scattering patterns of the two methods agreed well. The effects on the scattering properties are analyzed in terms of the size and shape parameter of the bubble and the incident beam width. The relations between the deviation angle and incident angle, emergent light intensity, and scattering angle are analyzed and used to explain the scattering patterns of a spheroidal bubble.     

Geometrical optics approximation for light scattering by absorbing spherical particles

By means of geometrical optics, an approximation method is presented to compute the light scattering intensity of absorbing spherical particles illuminated by a plane wave. For absorbing particles, the effective refractive index and the effective refractive angle are related to the complex refractive index and incident angle. The formulas for calculation of the break of phases of reflection and refraction, which are different from the case of transparent particles, are exactly derived. Verification of the geometrical optics approximation (GOA) was performed by case studies and comparison of the present results with the Mie scattering. It is found that agreement between the GOA and the Mie theory is excellent in forward directions for weakly/moderately absorbing particles. Differently, for strongly absorbing particles, good agreement between the calculation methods is in the forward directions and large scattering angles. The agreement between the GOA and the Mie theory is better for larger particles.     

Light scattering by particles of toroidal shape in the Rayleigh-Gans-Debye approximation

Expressions for the calculation of the amplitude and indicatrix of light scattering by optically soft toroidal and tubular particles are obtained in the Rayleigh-Gans-Debye (RGD) approximation. Light scattering cross sections of toroidal particles in the RGD approximation and cross sections obtained by the method of discrete dipoles are numerically compared.     

Numerical simulation of multiple light scattering in layers consisting of opaque particles with a dull surface (geometrical optics approximation)

A numerical model is presented which allows one, in the geometrical optics approximation, to calculate scattering contributions of specified multiplicity in layers comprised of opaque particles with dull surfaces. For definiteness, the particles are assumed to be spherical with the Lambertian law of light scattering by the particle surface. The greatest scattering multiplicity is restricted, in this model, only by computer capacity. In this paper, the scattering multiplicities up to the sixth order inclusively are studied. Layers of moderate optical thickness, as well as the case of a semi-infinite medium with different particle packing densities, are analyzed for different geometries of illumination and observation. It is shown that for conservative scattering by the particle surface, the contribution of higher-order scattering decreases with increasing order number, which is related to the shadow-hiding effect. The scattering indicatrices of higher orders approach the isotropic case. The even and odd scattering orders show a systematic difference between themselves.     

New regime map of the geometric optics approximation for scattering from random rough surfaces

The electromagnetic wave scattering from random roughness surfaces is a technologically important but challenging problem. There is a significant amount of interest in understanding the radiative properties of the rough surfaces for diverse applications. On one end, the rigorous models require the solutions of complex formulations of the Maxwell's equations or rely on various numerical schemes, which typically are computationally intensive. On the other hand, it has been found that the geometric optics (GO) ray tracing approximation method produces reasonably accurate radiative property predictions in some cases and with little computational effort. However, the latter ignores the wave interference and polarization effects, which are important when the wavelength is on the same order or larger than the geometrical length scale. It is therefore important to quantify the accuracy of the GO approximation. This study reports a new regime map based on the comparisons of the GO and finite-difference time-domain solutions.     

Mathematical modeling of the Magnus effect in the geometrical optics approximation

The Magnus effect in multimode fibers with triangular and parabolic refractive index profiles (RIPs) is simulated in the geometrical optics approximation. The calculations confirm the linear relation between the angle of rotation Δ? and the fiber length z. The results of calculations for a spiral path with constant radius are compared with the analytical solution obtained. For a fiber with a parabolic RIP, the value of Δ? obtained in this work is one-half the result obtained in the wave approach.     

Estimates of the albedo of powderlike surfaces in the geometrical optics approximation

Results of computer simulation of light scattering by powderlike media composed of large semitransparent particles of different shapes are presented. The geometrical optics approach is used. The cases of particles of spherical, cubic, and random shapes are considered. The one-dimensional geometrical optics model of light scattering by powderlike media, which finds application in investigations of planetary surfaces, meteorites, and lunar samples, is briefly described. The numerical simulation allowed us to estimate the error of this model, which turned out to be within the limits of several percent. The albedo calculated by using the one-dimensional model is shown to be closest to the “three-dimensional” reflectance of the surfaces at a phase angle of about 60°. This albedo also approximates fairly well the integrated reflectance, which in laboratory measurements is determined with the help of an integrating sphere.     

Pair-structure matrix of random collection of particles: Implications for light scattering

Scattering of light fields from random collections of particles of different types is considered. A new matrix called pair-structure matrix characterizing the correlations between particles of the same and of different types is introduced. This matrix reduces to the pair-structure factor of scattering collection [Opt. Lett. 34, 1762 (2009)] in the case when the particles in the collection are all of the same type. For illustration of the importance of the new matrix the formula for the degree of coherence of a polychromatic plane wave scattered from a collection of particles of different types is derived.     

Light scattering by Gaussian random ellipsoid particles: First results with discrete-dipole approximation

We introduce the stochastic geometry of a Gaussian random ellipsoid (GE) and, with the discrete-dipole approximation, carry out preliminary computations for light scattering by wavelength-scale GE particles. In the GE geometry, we describe the base ellipsoid by the three semiaxes a?b?c. The axial ratios b:a and c:a appear as two shape parameters additional to those of the Gaussian random sphere geometry (GS). We compare the scattering characteristics of GE particles to those of ellipsoids. Introducing irregularities on ellipsoids smoothens the angular scattering characteristics, in a way analogous to the smoothening of spherical particle characteristics in the case of GS particles.     

The Coulomb sum for electron scattering in the relativistic random phase approximation

The Coulomb sum value for electron scattering is estimated using the relativistic random phase approximation (RPA) in the field theory for nuclear matter. RPA correlations due to σ-, ω- and ϱ-meson exchanges reduce the sum value of the relativistic Hartree approximation by about 15–20%.     

HMO in geometrical optics

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Imaging of random surfaces and inverse scattering in the Kirchoff approximation

Abstract

Imaging of random surfaces can be modelled by integration over angular spectra of scattered plane waves. This approach suggests the representation of surface scattering in the Kirchhoff approximation using the concept of three-dimensional spatial frequencies. Optical methods of surface profiling can thus be modelled, leading to an insight into reconstruction of surface profiles from scattering data. The methods can also be extended to cover thin-film multilayer structures.     

Ray-wave approximation for the calculation of laser light scattering by transparent dielectric particles,mimicking red blood cells or their aggregates

A theoretical model is presented for the fast calculation of light scattering by transparent dielectric particles with sizes much larger than the wavelength. In this model, the light incident onto the particle and the light propagating inside the particle are represented by sets of rays while the scattered light is represented by a set of spherical waves emitted by different elements of the particle surface (ray-wave approximation, RWA). It is shown that RWA is comparable in precision with the discrete-dipole approximation but significantly exceeds the latter in the calculation rate for the particles with size parameters higher than 50.     

Singular value distribution of the propagation matrix in random scattering media

The distribution of singular values of the propagation operator in a random medium is investigated, in a backscattering configuration. Experiments are carried out with pulsed ultrasonic waves around 3 MHz, using an array of 64 programmable transducers placed in front of a random scattering medium. The impulse responses between each pair of transducers are measured and form the response matrix. The evolution of its singular values with time and frequency is computed by means of a short-time Fourier analysis. The mean distribution of singular values exhibits a very different behaviour in the single and multiple scattering regimes. The results are compared with random matrix theory. Once the experimental matrix coefficients are renormalized, experimental results and theoretical predictions are found to be in a very good agreement. Two kinds of random media have been investigated: a highly scattering medium in which multiple scattering predominates and a weakly scattering medium. In both cases, residual correlations that may exist between matrix elements are shown to be a key parameter. Finally, the possibility of detecting a target embedded in a random scattering medium based on the statistical properties of the strongest singular value is discussed.     

The shape influence on the overall single scattering properties of a sample in random orientation

In order to identify the type of scattering profile that corresponds to some specific shapes, we have performed calculations of some scattering properties for those shapes with a fixed size distribution. Aggregates of different numbers of spheres have been used to fit the laboratory measurements of fly ashes. The results for other shapes, such as rectangular prisms with different axial proportions, particles made of joined cubes, and particles with different fluffiness, are also shown. From all these calculations, it is concluded that the size-averaged scattering matrix elements resembles Rayleigh features, for the size distribution stopping at , when either the number of spheres or cubes of the aggregates is increased, the shape becomes flatter or the particles become fluffier. We also show the effect of the refractive index on the Q_sca vs. X curve in the case of strongly absorbing particles. A tendency to reach the geometric optic regime is observed instead of the Rayleigh regime using the same size distribution.