Scattering by gamma-distributed phase screens

The multipoint statistics of a joint gamma process are investigated. Analytical expressions are derived for the generating functions of the fourfold probability densities of the process and results are also obtained for its slope statistics. The results are used to characterize the wavefront distortion introduced into an incident beam of radiation by a phase changing screen and the scintillation index of the scattered intensity in the Fresnel region is calculated for various spectral models. Properties of the ray density functional are also investigated for the sub-fractal case when the wavefront is once differentiable.     

Spacetime correlation functions of dynamic speckles produced by a series of moving phase screens

Spacetime correlation functions of the time-varying speckle intensity have been evaluated for the case where speckle patterns are produced in the Fresnel diffraction region by light propagating through a series of moving random-phase screens. The correlation functions are given by a set of recursion formulae which are useful for numerical computations. Three statistical quantities relating to the motion of speckle patterns are derived to examine the relationship between the velocity distribution of the phase screens and the temporal behaviour of resultant speckle patterns. It is found that the velocity differences between the phase screens have a strong effect on both the decorrelation of speckle patterns and the fluctuating speed of the speckle intensity.     

Spacetime correlation functions of dynamic speckles produced by a series of moving phase screens

Abstract

Spacetime correlation functions of the time-varying speckle intensity have been evaluated for the case where speckle patterns are produced in the Fresnel diffraction region by light propagating through a series of moving random-phase screens. The correlation functions are given by a set of recursion formulae which are useful for numerical computations. Three statistical quantities relating to the motion of speckle patterns are derived to examine the relationship between the velocity distribution of the phase screens and the temporal behaviour of resultant speckle patterns. It is found that the velocity differences between the phase screens have a strong effect on both the decorrelation of speckle patterns and the fluctuating speed of the speckle intensity.     

Scattering phase shift in stochastic fields

A very simple model of a spherically symmetric potential likeμ/r, withμ varying randomly alongr, the distance from the scattering centre is analysed and it is found that ifμ changes its sign in a stochastic fashion, the average potential felt at each pointr consists of a coulomb part as well as a short range Yukawa type component. Using the non linear equations for the phase function for potential scattering of a Schrödinger particle, the average and other moments of the phase shifts can be computed in certain approximations.     

Effects of imaging properties on dynamic speckles produced by a set of moving phase screens

Space-time correlation functions have been derived for the time-varying intensities of speckle patterns in image space produced by a series of moving random-phase screens. The time-correlation length, which measures the changing rate of intensity fluctuations, is evaluated from the correlation functions to examine the effects of the imaging properties on the temporal behaviour of the speckles resulting from the multiple scattering. It is shown that the average velocity and velocity dispersion of the phase screens can be measured from the time-correlation length by using imaging systems which have a small and a large point spread at the front focal plane of the systems, respectively. Theoretical results for the relationship between the focal position of the imaging lens and the time-correlation length are also presented.     

Distribution characteristics of intensity and phase vortices of speckle fields produced by N-pinhole random screens

We analyze the distribution properties of phase and phase vortices in a speckle field generated by N-pinhole random screens, and find that the phase vortex distributions show similarity and clustering in local regions. The phase patterns have a lot of sets composed of two phase vortices with opposite signs or four phase vortices which are positive and negative vortices alternately. Cases are also found where two adjacent phase vortices have the same topological charges. The density of phase vortices becomes larger with the increase of the radius of circumference and the number of pinholes on screen.Then, the relative positions of phase vortices can be adjusted by changing the radius of circumference and the number of pinholes.     

Dynamics of ray propagation beyond a series of space-periodic phase screens

The dynamics of ray propagation through a regularly inhomogeneous medium consisting of a series of identical, deep, sinusoidal phase screens is examined. Discrete mapping is used to analyze the propagation process. A characteristic parameter of the problem is found that determines the transition from regular (nonlinear oscillator and ray capture) to chaotic regimes of ray behavior. Diffuse (stochastic) ray propagation in the given medium is studied—by analogy with a random walk—by a method of fractal analysis based on finding the scaling characteristics of the given process (associated with the fractal dimension).Scientific-Research Radiophysics Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 8, pp. 825–831, August, 1993.     

Absorption and Scattering of Light by Highly Concentrated Two‐phase Flows

The spray cone emerging during an extended metal atomization process (called spray forming) has been investigated in order to quantify the influence of highly concentrated multiphase flows on phase‐Doppler‐anemometry (PDA) measurements. Using this non‐intrusive, optical measurement technique not only the local particle size and velocity distributions of the spray can be obtained but also additional information about the mass flux in the multiphase flow. Since standard phase‐Doppler systems can be easily applied to low concentrated particle systems (spherical particles with smooth surfaces and an optical transparent continuous phase taken for granted) the application of this measurement technique to highly concentrated multiphase flows is more complex. Both the laser light propagating from the PDA device to the probe volume and the scattered one going backward to the PDA receiving system are disturbed by passing the highly concentrated multiphase flow. The resulting significant loss in signal quality especially concerns the measurement of the smaller particles of the spray because of their reduced silhouette (in comparison with the bigger ones). Thus, the detection of the smallest particles becomes partially impossible leading to measurement of a distorted diameter distribution of the entire particle collective. In this study the distortions of the measured distributions dependent on the particle number concentration as well as on the path length of the laser light are discussed.     

Selection of magnetic screens by numerical calculations

To choose the parameters of magnetic screens, a technique for numerically calculating the 3D magnetic field distribution is developed for the case when field sources are locates in open regions. The problem is solved in vector magnetic potential by the finite integration method. A modification of the method of perfectly matched absorbing boundary layers for the case of magnetic field allows calculation of the field in real 3D screens. The numerical solutions are tested using absorbing layers by comparing with the known analytical solutions. The parameters of finite-size screens effectively decreasing the magnetic field intensity are found.     

Scattering properties of aqueous suspensions with absorbing dispersed phase

Scattering matrices of aqueous suspensions of copper oxide and graphite the particles of which are characterized by strong absorption at a wavelength of 0.63 μm have been measured in the scattering angle range of 10°–155°. The results of the measurements are compared with calculation data for axially symmetric scatterers (ellipsoids of revolution and cylinders). It is shown that, if the size parameter equals 4–6, even under conditions of strong radiation absorption by particles of the dispersive medium, deviation of their shape from axial symmetry has an effect on the scattering properties of the medium.     

Scattering phase functions of horizontally oriented hexagonal ice crystals

Finite-difference time domain (FDTD) solutions are first compared with the corresponding T-matrix results for light scattering by circular cylinders with specific orientations. The FDTD method is then utilized to study the scattering properties of horizontally oriented hexagonal ice plates at two wavelengths, 0.55 and 12 μm. The phase functions of horizontally oriented ice plates deviate substantially from their counterparts obtained for randomly oriented particles. Furthermore, we compute the phase functions of horizontally oriented ice crystal columns by using the FDTD method along with two schemes for averaging over the particle orientations. It is shown that the phase functions of hexagonal ice columns with horizontal orientations are not sensitive to the rotation about the principal axes of the particles. Moreover, hexagonal ice crystals and circular cylindrical ice particles have similar optical properties, particularly, at a strongly absorbing wavelength, if the two particle geometries have the same length and aspect ratio defined as the ratio of the radius or semi-width of the cross section of a particle to its length. The phase functions for the two particle geometries are slightly different in the case of weakly absorbing plates with large aspect ratios. However, the solutions for circular cylinders agree well with their counterparts for hexagonal columns.     

Simulation of extended phase screens in problems of optical wave propagation through the atmosphere

Turbulent medium in problems of optical wave propagation through the atmosphere is usually nodeled as a set of statistically independent plane screens with a random two-dimensional field of phase progress. In this paper, we develop methods for the formation of nonperiodic phase screens infinitely extended in a certain direction, which are required in problems of dynamic simulation of wave propagation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 1, pp. 21–34, January 2006.     

Sound diffraction by multiple wedges and thin screens

A theoretical formula that is based on the geometrical theory of diffraction (GTD) is proposed for computing sound diffraction by multiple wedges, barriers, and polygonal-like shapes. The formula can treat both convex and concave edges, where edges may or may not be inter-connected. Comparisons of theoretical predictions with other results done by the BEM or experiments for scaled model confirm the accuracy of the present formula. Numerical examples such as double wedges and doubly inclined barrier show that when there exist several diffraction paths for given source and receiver positions, the insertion loss is dominated by the diffraction associated with the shortest propagation path. It is also found that although the partially inclined barrier increases the shadow zone as compared to the simple screen type of the same total height, it does not necessarily increase the insertion loss at all heights.     

Scattering phase of quantum dots: emergence of universal behavior

We investigate scattering through chaotic ballistic quantum dots in the Coulomb-blockade regime. Focusing on the scattering phase, we show that large universal sequences emerge in the short wavelength limit, where phase lapses of π systematically occur between two consecutive resonances. Our results are corroborated by numerics and are in qualitative agreement with existing experiments.     

Generation of infinitely long phase screens for modeling of optical wave propagation in atmospheric turbulence

Numerical modeling of optical wave propagation in atmospheric turbulence is traditionally performed by using the so-called 'split'-operator method, where the influence of the propagation medium's refractive index inhomogeneities is accounted for only within a set of infinitely narrow phase distorting layers (phase screens). These phase screens are generated on a numerical grid of finite size, which corresponds to a rather narrow slice (spatial area) of atmospheric turbulence. In several important applications including laser target tracking, remote sensing, adaptive optics, and atmospheric imaging, optical system performance depends on atmospheric turbulence within an extended area that significantly exceeds the area associated with the numerical grid.

In this paper we discuss methods that allow the generation of a family of long (including infinitely long) phase screens representing an extended (in one direction) area of atmospheric turbulence-induced phase distortions. This technique also allows the generation of long phase screens with spatially inhomogeneous statistical characteristics.