Integral representation of the field of the wave propagating in a medium with large-scale irregularities
TL;DR: In this paper, an integral representation in the form of a single-time weighted Fourier transform (the so-called Fresnel transform) is developed from the obtained integral representation.
Abstract: We consider propagation of waves in a medium with irregularities located at relatively long distances from the source and the observer within the paraxial approximation. The asymptotic approximation, which was obtained earlier by using a double weighted Fourier transform, is reduced to form that is convenient for application under these conditions. By using the stationary-phase method, an integral representation in the form of a single-time weighted Fourier transform (the so-called Fresnel transform) is developed from the obtained integral representation. The conditions of the transition of this representation to the phase-screen method determine the conditions of the applicability of the latter and the criteria for selection of the screen location during higherresolution diagnostics of a non-uniform medium. The results of numerical spatial processing of the signal, which improves the resolution of diagnostics of non-uniform media, are presented.
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TL;DR: In this paper, the authors have shown that when using the spatial processing in the form of Fresnel inversion, the transition from dual-frequency to triple-frequency measurements reduces the average error of measurement.
Abstract: In the geometrical optics approximation, the ionospheric part of error in measuring phase and code delays of the satellite signal may be represented as a rapidly decreasing series in inverse power of frequency. Such a simple frequency dependence allows us to use multi-frequency measurements for eliminating the error in such multi-frequency Global Navigation Satellite Systems as GPS, GLONASS, BeiDou, and Galileo. However, the elimination of errors is handicapped by diffraction effects during signal propagation through turbulent ionospheric plasma. The numerical simulation has shown that when using the spatial processing in the form of Fresnel inversion the transition from dual-frequency to triple-frequency measurements reduces the average error of measurement. Yet fluctuations of the error diminish only if the inner scale exceeds the Fresnel radius. In the opposite case of excess of the Fresnel radius over the inner scale, the random component of the residual error is growing during the transition to triple-frequency measurements. The numerical simulation results also suggest that the Fresnel spatial processing in dual-frequency measurements at the optimal distance to the virtual screen can reduce the average error from centimeter to submillimeter level, which renders the transition to triple-frequency measurements unnecessary. The study of the residual error dependence on the distance from the virtual screen to the observer has revealed that the optimum value of this distance may be found from the minimum condition of amplitude scintillation index of the processed signal. The signal thus processed may be utilized both in geodetic precise measurements and in diagnostics of the lower atmosphere.
14 citations
TL;DR: In this article, the authors used numerical simulation to study the effects of ionospheric irregularities on accuracy of global navigation satellite system (GNSS) measurements, using ionosphere-free (in atmospheric research) and geometry-free dual-frequency phase combinations.
Abstract: We have used numerical simulation to study the effects of ionospheric irregularities on accuracy of global navigation satellite system (GNSS) measurements, using ionosphere-free (in atmospheric research) and geometry-free (in ionospheric research) dual-frequency phase combinations. It is known that elimination of these effects from multifrequency GNSS measurements is handi-capped by diffraction effects during signal propagation through turbulent ionospheric plasma with the inner scale being smaller than the Fresnel radius. We demonstrated the possibility of reducing the residual ionospheric error in dual-frequency GNSS remote sensing in ionosphere-free combination by Fresnel inversion. The inversion parameter, the distance to the virtual screen, may be selected from the minimum of amplitude fluctuations. This suggests the possibility of improving the accuracy of GNSS remote sensing in meteorology. In the study of ionospheric disturbances with the aid of geometry-free combination, the Fresnel inversion eliminates only the third-order error. To eliminate the random TEC component which, like the measured average TEC, is the first-order correction, we should use temporal filtering (averaging).
10 citations
TL;DR: In this paper, the authors explore the capabilities of the spatial signal processing to eliminate the effects of multipath signal propagation in a smoothly inhomogeneous medium and show that the multipathing effects disappear after the spatial processing based on double weighted Fourier transform in a medium with irregularity scales both more and less than the Fresnel radius.
Abstract: One of the important problems of communication, navigation, and diagnostics of inhomogeneous media is multipathing, in which the signal propagates on different paths between the points of emission and reception. In this paper, using a numerical simulation we explore the capabilities of the spatial signal processing to eliminate the effects of multipath signal propagation in a smoothly inhomogeneous medium. It is shown that the multipathing effects disappear after the spatial processing based on double weighted Fourier transform in the presence of multipath propagation in a medium with irregularity scales both more and less than the Fresnel radius.
9 citations
TL;DR: In this article, a wave equation is preliminary reduced using the Fock proper-time method to a parabolic equation that then is solved by the DWFT method for the case of wave reflection and scattering by a layer with random irregularities and linear profile of average permittivity.
Abstract: It has been previously proposed to describe wave propagation in inhomogeneous media in a small-angle approximation with the aid of a double weighted Fourier transform (DWFT) method. This method agrees with the methods of geometrical optics, smooth perturbations, and phase screen in domains of their applicability; therefore it can be employed to solve direct and inverse problems of radio wave propagation in multi-scale inhomogeneous ionospheric plasma. In this paper, for the DWFT wide-angle generalization a wave equation is preliminary reduced using the Fock proper-time method to a parabolic equation that then is solved by the DWFT method. The resulting solution is analyzed for the case of wave reflection and scattering by a layer with random irregularities and linear profile of average permittivity. We show the transformation of this solution into strict results in the absence of irregularities and in the single-scatter approximation, including backscattering, during weak phase fluctuations. Under certain conditions, the solution takes the form of the small-angle DWFT with respect to refraction in the layer and backscatter effects. Spatial processing in source and observer coordinates brings a beam of received waves into one wave without amplitude fluctuations, which allows an increase in resolution of vertical ionospheric sounding systems.
6 citations
TL;DR: In this paper, the authors studied the possibilities of integral representation for the two-frequency mutual coherence function of the wave field in a randomly inhomogeneous ionosphere and obtained the integral representation using the Double Weighted Fourier Transform (DWFT) method.
Abstract: We study the possibilities of integral representation for the two-frequency mutual coherence function of the wave field in a randomly inhomogeneous ionosphere. The integral representation was obtained using the Double Weighted Fourier Transform (DWFT) method. We point out that the conditions of validity of the geometrical-optics approximation for frequency coherence are weaker than the same condition for individual samples. Examples of calculation of the frequency coherence functions for waves in the ionospheric plasma with the irregularities described by the Gaussian spectrum and Shkarofsky’s model are given. Simulation results show that diffraction effects reduce the width of the frequency coherence function. The capabilities of the methods for spatial processing of the wave field and its two-frequency mutual coherence function, which eliminate these effects through the Fresnel and DWFT inversions, are examined.
5 citations
References
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Book•
01 Jan 1978
TL;DR: This IEEE Classic Reissue presents a unified introduction to the fundamental theories and applications of wave propagation and scattering in random media and is expressly designed for engineers and scientists who have an interest in optical, microwave, or acoustic wave propagate and scattering.
Abstract: A volume in the IEEE/OUP Series on Electromagnetic Wave Theory Donald G. Dudley, Series Editor This IEEE Classic Reissue presents a unified introduction to the fundamental theories and applications of wave propagation and scattering in random media. Now for the first time, the two volumes of Wave Propagation and Scattering in Random Media previously published by Academic Press in 1978 are combined into one comprehensive volume. This book presents a clear picture of how waves interact with the atmosphere, terrain, ocean, turbulence, aerosols, rain, snow, biological tissues, composite material, and other media. The theories presented will enable you to solve a variety of problems relating to clutter, interference, imaging, object detection, and communication theory for various media. This book is expressly designed for engineers and scientists who have an interest in optical, microwave, or acoustic wave propagation and scattering. Topics covered include:
5,877 citations
Book•
01 Jan 1987TL;DR: Properties of Computerized Tomographic Imaging provides a tutorial overview of topics in tomographic imaging covering mathematical principles and theory and how to apply the theory to problems in medical imaging and other fields.
Abstract: Tomography refers to the cross-sectional imaging of an object from either transmission or reflection data collected by illuminating the object from many different directions. The impact of tomography in diagnostic medicine has been revolutionary, since it has enabled doctors to view internal organs with unprecedented precision and safety to the patient. There are also numerous nonmedical imaging applications which lend themselves to methods of computerized tomography, such as mapping of underground resources...cross-sectional imaging of for nondestructive testing...the determination of the brightness distribution over a celestial sphere...three-dimensional imaging with electron microscopy. Principles of Computerized Tomographic Imaging provides a tutorial overview of topics in tomographic imaging covering mathematical principles and theory...how to apply the theory to problems in medical imaging and other fields...several variations of tomography that are currently being researched.
5,620 citations
TL;DR: In this article, the authors propose a method of small and large scale perturbation by large-scale inhomogeneities, based on the distribution laws of the fluctuations in the scattered field.
Abstract: 1. Introduction 3 2. Method of Small Perturbations. First Approximation 6 3. Scattering by Large-scale Inhomogeneities 8 a. Method of Smooth Perturbations 10 b . Parabolic-equation Method 14 c . Markov Approximation 16 d. Distribution Laws of the Fluctuations in the Scattered field 22 4. Theory of Multiple Scattering 23 Bibliography 32
142 citations
TL;DR: In this paper, the results obtained using the Fresnel inversion method were compared to results obtained with the traditional geometrical optics inversion approach and to numerical weather prediction data.
Abstract: Occultation data from the GPS/MET experiment are inverted to temperature profiles of the neutral atmosphere of the Earth using the Fresnel inversion technique. The technique is not limited in resolution by diffraction effects thus a good vertical resolution is achieved. In the derivation a thin screen approximation is used. The influence of this approximation on the results is discussed. The results obtained using the Fresnel inversion is compared to results obtained using the traditional geometrical optics inversion approach and to numerical weather prediction data.
56 citations