Phase Fluctuations of Radio Waves in the Saturated-Scintillation Regime

We consider the problem of phase fluctuations of radio waves behind a strong phase screen and in an optically thick layer. It is shown that the phase-fluctuation distribution of the received radiation at an observation point located in the saturated-scintillation area behind a turbulent phase screen is almost identical to the normal distribution of phase fluctuations of the wave on the screen. Amplitude and phase fluctuations of the received radiation are uncorrelated both for single-point and space-diversity reception if, in the latter case, the distance between the observation points exceeds the spatial scale of the diffraction component of the complex field of the received signal. Expressions for the mean square and the structural function of phase fluctuations of radio waves behind a turbulent phase screen in the saturated-scintillation regime are obtained. It is shown that the structural function of phase fluctuations in the diffraction component of the scattered field, which is exactly the function that forms saturated scintillations of the received radiation, almost coincides with the structural function of phase fluctuations on the screen. It is also shown that the diffraction effects can be neglected and the geometric-optical approximation should be used when calculating statistical characteristics of phase fluctuations of a plane wave in the saturated-scintillation area in an optically thick layer with large-scale refractive-index irregularities. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 4, pp. 275–282, April 2005     

Experimental measurements of non-Gaussian scattering by a fractal diffuser

We report measurements of the statistics of intensity scintillations of 10.6 μm CO₂ radiation scattered by a two-dimensional fractal phase screen. The surface profile of the phase screen is measured and shown to have a Hausdorff-Besicovitch dimension of approximately 1.4. Measurements of the on-axis intensity fluctuations as a function of illuminated spot size in both the Fresnel and Fraunhofer region are presented. This fractal scatterer does not produce the high contrast values found in speckle patterns of smoothlyvarying surfaces. Both direct and heterodyne detection results are reported. Measurements of the average intensity as a function of angle are also presented, and illustrate the failure of theoretical models which assume a Gaussian phase autocorrelation function.     

On a Modification of the Scintillation Method

We solve the problem of diffraction of fluctuating radiation by an optically thin irregular layer (phase screen) with developed turbulent structure. It is shown that in the case of diffraction of radiation with saturated fluctuations and a narrow-band frequency spectrum by a weakly turbulent moving phase screen, the measured frequency spectrum of intensity fluctuations in the observation plane allows one to obtain information on the form of the spectrum of irregularities of an optically thin irregular layer in a wide size range significantly exceeding the size of the first Fresnel zone. Similarly to the well-known phase method of diagnostics of randomly irregular media, the conventional scintillation method modified in such a way yields undistorted information on the form of the irregularity spectrum. However, in contrast to the phase method, it also allows one to obtain data on the drift velocity of irregularities in the studied irregular layer.     

Non-Gaussian Phase Screen Based on log-Poisson Distribution and Effect on Imaging

Gaussian models without intermittency are extensively used in estimating the effect of turbulence, but it also brings some puzzles, for example the observed pulse shape that disagrees with the result of the standard theory of interstellar scintillations. Indeed the property of intermittency is inherent in turbulence, i.e., all the quantities that characterize it suffer from strong fluctuations. So it is necessary to consider turbulent intermittency in manyapplications. In this paper we propose a non-Gaussian phase screen, which obeys log-Poisson statistics, and also offers the corresponding point spread function (PSF). These results describe that intermittency leads to the more extent and different directional distribution of PSF. Theoretical analysis is made under the hypothesis of the phase difference satisfying log-Poissonstatistics, and the average point spread function, which accord qualitatively with the result of the above generated phase screen, is derived.     

Asymptotic analysis of finite-beam scintillations in a turbulent medium

Asymptotic analysis of on-axis intensity fluctuation variance of a finite-sized light beam is performed starting from the functional integral representation for the field in a random medium. Collimated, diverging and converging beams with different diffraction properties are considered. A complete set of asymptotes is obtained using the main and additional coherence channels approach to the fourth moment of field analyses. We study the conditions of weak and strong fluctuation regimes for all these types of beams and obtain relatively simple formulae for on-axis intensity variance, which are valid for the case of stratified turbulence. It is shown that scintillations in the vicinity of the beam focus are governed by double-scattering processes for weak scintillations and double scattering from coherence channels for strong fluctuations.     

基于随机数据元扩张的大气湍流相位屏数值模拟

准确模拟大气湍流相位屏是建立大气湍流数值模型的核心问题。从大气湍流的统计学特性入手,利用大气湍流波前相位结构函数建立了一种新的大气湍流相位屏数值模拟方法,通过随机数据元扩张对大气湍流波前畸变相位分布的尺度随机性和高频分量随机性进行了模拟,并以此为基础通过相位屏近似构建了满足Kolmogorov统计规律的大气湍流数值模型。计算结果表明,随机数据元扩张法生成的相位屏在统计特性上与理论值基本吻合,在低频部分相对于功率谱反演法有明显的提升。同时,随着相位屏网格数的增加,计算结果的高频特性逐渐呈现并逼近理论值。对于由相位屏构建的大气湍流数值模型,在此通过光强闪烁率作为判据进行了验证,结果表明对于弱湍流和中等强度的湍流,模拟结果与理论计算基本相同;对于强湍流则误差较为明显,相对误差最大可达40%。     

Aperture-averaging effects for weak to strong scintillations in turbulent atmosphere

Under the approximations of (1) the received irradiance fluctuations of an optical wave caused by small scale turbulent eddies are multiplicatively modulated by the fluctuations caused by large scale turbulent eddies;(2) the scintillations caused by small- and large-scale eddies, respectively, are statistically independent; (3)the Rytov method for optical scintillation collected by the finite-diameter receiving aperture is valid for light wave propagation under weak to saturation fluctuation regime, we develop the applicable apertureaveraging analytic formulas in the week-to-strong-fluctuation for the scintillations of plane and spherical waves, which include the outer- and inner-scale rules of turbulence.     

On the scintillations of radiation from an extended source in a randomly inhomogeneous medium

Using the method of refractive scattering of radio waves (RSRW), we solve the problem of space correlation of scintillations of radiation from an extended source in a randomly inhomogeneous medium. General expressions are obtained for the index and radius of the space correlation of fluctuations of intensity of radiation from a source with finite angular dimensions as it propagates though a multilayered medium with refractive index fluctuations. The RSRW method is similar to the diffraction calculation of space correlation of scintillations of an extended source in a thick layer with inhomogeneities. We note that under certain conditions an increase in the number of inhomogeneous layers on the radio wave propagation path leads to a pronounced decrease in the scintillation index and an increase in the space correlation of fluctuations of intensity of received radiation from an extended source. The results obtained have a simple geometric-optical interpretation. We indicate a specific feature in determining the angular dimensions of extended radio sources using the known method of scintillations. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 5, pp. 586–593, May, 1997.     

Mimic Simulations of Radio-Wave Propagation in a Randomly Irregular Ionosphere

We present the technique and results of mimic simulations of radio-wave propagation in a randomly irregular ionosphere with allowance for the Earth's sphericity and the background ionosphere. Based on consideration of the probability distributions of the angle of reception and of the corresponding amplitude, eikonal, and angle of radiation, obtained by the mimic modeling, we conclude that the most probable ray path is symmetric with respect to the region of its reflection from the ionosphere and that the mean reception angle and the corresponding mean radiation angle are equal. The simulations yield the statistical characteristics of a wave, such as the variances of the reception angle and the eikonal, as well as the correlation functions of the eikonal and the field. The simulation results concerning the variances of reception angles and eikonal are compared with the results of the first approximation of the perturbation theory. It is shown that the eikonal fluctuations in the irregularity-free space, caused by fluctuations of angles of the lower rays escaping from an ionospheric layer with random irregularities, should be taken into account.     

Anisotropic Structure of Small-Scale Ionospheric Turbulence

We consider various theoretical models for the spectrum of small-scale ionospheric turbulence. The particular role of the generalized model of the ionospheric-turbulence spectrum, which takes into account that the anisotropy (extension) of small-scale irregularities of the upper ionosphere along the Earth's magnetic field direction depends on the transverse scale of those irregularities, is emphasized. The results of the. rst target experiments on radio sensing of the midlatitude ionosphere by signals from on-orbit satellites at frequencies 150 and 400 MHz under conditions of increased solar activity are presented. The experiments were performed at the radiophysical facility in the Nizhny Novgorod region in 2003. We studied statistical characteristics of the amplitude fluctuations of the received signals for different angles ϑ between the line of sight from a satellite to a ground-based reception point and the Earth's magnetic field direction. It was found in the course of the experiments that the spectrum slope of amplitude fluctuations of the received radiation is a function of the angle ϑ. The obtained result agrees with the generalized model of the ionospheric-turbulence spectrum and can be an argument in favor of the pronounced anisotropic structure of small-scale electron-density irregularities of the midlatitude ionosphere under disturbed geophysical conditions. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 5, pp. 382–387, May 2005.     

Sura-wind radar: Studies of nonlinear effects using VHF-wave occultion of the ionosphere

We present experimental results on reception of VHF signals of the transmitting facility “Sura” of the Radiophysical Research Institute by the NASA spacecraft WIND. The experiments were performed during daytime during the summer seasons 1997–1998. The dependence of power and spectral characteristics of the VHF radio waves on the power of the sounding radiation is analyzed. We find that, in a wide range of effective powers of the VHF radiation from about 40 kW to 160 MW, the phenomena observed in the radiation received onboard WIND (such as focusing, scintillations, or frequency deviations of signals) does not usually depend on the operation mode of the “Sura” facility. At the same time, broadening of the radiation pattern of the facility and decrease of the mean level of the received signal by about 6 dB toward the direction of maximum of the radiation pattern were observed at the peak radiation power of the facility. The experimental results are compared to present concepts on effects of self-focusing instability and nonlinear defocusing of VHF radio waves in the ionospheric plasma. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 8, pp. 799–809, August 1999.     

Saturation of laser irradiance fluctuations beyond a turbulent layer

An asymptotic theory of saturated fluctuations of laser irradiance diffracted by a thin layer of turbulent medium is built. The treatment is carried out in the phase screen approximation for the case of a power law spectrum of inhomogeneities in the layer. Asymptotic forms of the covariance of irradiance fluctuations are obtained and the character of the scintillation index approach to the asymptotic value is investigated. Calculations are made for collimated and focused laser beams.     

Polarization fluctuations in the radiation from cosmic sources due to scattering in a random inhomogeneous magnetoactive plasma

We use Feynman integrals along the trajectories to obtain expressions for the fourth-order statistical moments of polarized radiation propagating through a random inhomogeneous plasma. We write down the correlation functions and dispersion of the fluctuations in the Stokes parameters for the case of small fluctuations in the wave filed. We analyze the correlation functions of the Stokes parameters as a function of the polarization of the radiation from the source and the characteristics of the inhomogeneous plasma. We show that for each of the normal waves, the amplitudes and the phases experience different amounts of decorrelation in a random inhomogeneous magnetoactive plasma. As a result, fluctuations occur in the circular polarization.Radio Astronomical Institute, Academy of Sciences of the Ukrainian SSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 7, pp. 738–747, July, 1991     

Estimation of the power scintillation probability density function in free-space optical links by use of multicanonical Monte Carlo sampling

Free-space optics (FSO) can provide cost-effective, high-bandwidth, wireless connections. However, atmospheric turbulence may degrade the performance of FSO links by causing intensity and power scintillations at the receiver. Multicanonical Monte Carlo sampling is used in conjunction with the phase screen method to calculate the statistics, and particularly the probability density function (PDF), of the power fluctuations at an FSO receiver. This allows the efficient calculation of the PDF even for very small values with a limited number of iterations. The obtained PDF can be used to characterize the performance of the system in terms of the error probability.     

Strong scintillation spectra behind a phase screen containing large-scale anisotropic irregularities

Using the approximation of an anisotropic statistically-homogeneous phase screen, we consider spectra of strong scintillations. Numerical calculations are made for the model of large-scale anisotropic inhomogeneities typical of the Earth’s stratosphere. The spectrum transformation is studied for the transition from weak scintillations to the asymptotic regime of strong scintillations. We show that with increasing level of the scintillations, their spectra rapidly broaden to the region of large wave numbers which exceed both the inverse internal scale of the irregularities and the inverse radius of the Fresnel zone by orders of magnitude. Notable deviations of the two-dimensional spectra from the predictions based on perturbation theory are shown to occur for scintillation variance exceeding 0.1. The obtained two-dimensional spectra of scintillations give a complete picture of the behavior of one-dimensional spectra which can be retrieved from satellite observations made for different angles between the orbit plane and the direction to the source. Vertical and horizontal one-dimensional spectra are studied in detail. Approximate algebraic formulas are derived and their validity is proved by applying them to the calculation of spectra of strong scintillations for a wide (several decades) range of the wave number values. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 9, pp. 747–765, September 2007.     

Reconstruction of the wind velocity profile from the intensity fluctuations of a reflected spherical wave in the turbulent atmosphere

The problem of reconstructing the wind velocity profile from the spatiotemporal statistics of turbulent reflected optical radiation intensity fluctuations is considered in the article. Expressions for the spatiotemporal correlation function and the spectrum of weak intensity fluctuations of the wave scattered on a diffusive screen are derived. An algorithm for reconstructing the wind velocity profile from the spatiotemporal spectra of the intensity of a reflected spherical wave in the turbulent atmosphere is suggested. The results of closed numerical experiments are presented that confirm the efficiency of the suggested algorithm.     

Suppressing amplitude fluctuations of the wave propagating in a randomly inhomogeneous medium

We suggest using spatial processing of the wave field with the aid of the double (in source and observer coordinates) weighted Fourier transform (DWFT) to suppress amplitude fluctuations (amplitude scintillations) during wave propagation in a randomly inhomogeneous medium. We examine the influence of sizes of receiving and transmitting antenna systems on the efficiency of the spatial processing in suppressing scintillations for both weak and strong intensity fluctuations. We demonstrate that the efficiency of the suppression of amplitude fluctuations by the inverse DWFT depends on the excess of sizes of fan beam projections of receiving and transmitting antenna systems over the Fresnel radius in a region with irregularities.     

Amplitude fluctuations in the theory of radio-wave refraction scattering

We consider some aspects of the theory of radio-wave scattering with respect to studies of radiation intensity fluctuations behind a random phase screen. The expressions for a piecewise approximation of the function of distribution of intensity fluctuations in the near zone and in the region of random focusing behind the screen are found. The expressions obtained are used to calculate the radio-wave scintillation index in these regions. The corresponding calculations are performed with allowance for the finite dimensions of external and internal scales of turbulent inhomogeneities of the phase screen. It is shown that the radio-wave refraction scattering, as a rule, is characterized by a pronounced random focusing of the radiation intensity behind the phase screen. However, under strongly developed turbulence of the radio-wave propagation medium (phase screen) the above phenomenon may be absent.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 9, pp. 1114–1124, September, 1996.This paper was supported by the Russian Foundation for Fundamental Research under project 95-02-03716.     

Propagation of a Gaussian-beam wave through a random phase screen

Tractable analytic expressions are developed for a variety of basic statistical quantities involving a Gaussian-beam wave propagating through a random medium confined to a portion of the propagation path between input and output planes, the limiting case of which defines a thin random phase screen. For a plane wave incident on a phase screen located midway between input and output planes, it is well known that the statistics in the receiver plane are in close agreement with those associated with a plane wave propagating through an extended random medium between input and output planes. For a similar comparison between a phase screen and extended turbulence in the case of a Gaussian-beam wave at the input plane, the present analysis reveals that the phase screen must be positioned between input and output planes differently from the plane-wave case, the position being dependent upon the Fresnel ratio of the Gaussian beam. The analytic results developed in this paper for the thin phase screen model are based on the Kolmogorov power-law spectrum for refractive-index fluctuations and the Rytov approximation. Extension of these results to multiple phase screens is also discussed.