Pulse broadening and two-frequency mutual coherence function of the scattered wave from rough surfaces

Abstract

Analytical expressions for the two-frequency mutual coherence function and angular correlation function of the scattered wave from rough surfaces based on the Kirchhoff approximation are presented. The coherence bandwidth depends on the illumination area as well as on the incident and scattered angles and the surface characteristics. Scattered pulse shapes are calculated as the Fourier transform of the two-frequency mutual coherence function. Calculations based on analytical solutions are compared with millimetre wave experimental data and Monte Carlo simulations showing good agreement.     

Pulse broadening and two-frequency mutual coherence function of the scattered wave from rough surfaces

Analytical expressions for the two-frequency mutual coherence function and angular correlation function of the scattered wave from rough surfaces based on the Kirchhoff approximation are presented. The coherence bandwidth depends on the illumination area as well as on the incident and scattered angles and the surface characteristics. Scattered pulse shapes are calculated as the Fourier transform of the two-frequency mutual coherence function. Calculations based on analytical solutions are compared with millimetre wave experimental data and Monte Carlo simulations showing good agreement.     

Pulse broadening of enhanced backscattering from rough surfaces

Abstract

Recently, we presented a study of pulse scattering by rough surfaces based on the first-order Kirchhoff approximation which is applicable to rough surfaces with RMS slope less than 0.5 and correlation distance l?λ. However, there has been an increased interest in enhanced backscattering from rough surfaces, study of which requires inclusion of the second-order Kirchhoff approximation with shadowing corrections. This paper presents a theory for the two-frequency mutual coherence function in this region and shows that the multiple scattering on the surface gives rise to an additional pulse tail in the direction of enhanced backscattering. The theory predicts pulse broadening approximately 20% greater than that caused by single scattering alone for a delta-function incident pulse and typical surface parameters. Analytical results are compared with Monte Carlo simulations and millimetre-wave experiments for the one-dimensional rough surface with RMS height 1λ and correlation distance 1λ, showing good agreement.     

Pulse broadening of enhanced backscattering from rough surfaces

Recently, we presented a study of pulse scattering by rough surfaces based on the first-order Kirchhoff approximation which is applicable to rough surfaces with RMS slope less than 0.5 and correlation distance l≳λ. However, there has been an increased interest in enhanced backscattering from rough surfaces, study of which requires inclusion of the second-order Kirchhoff approximation with shadowing corrections. This paper presents a theory for the two-frequency mutual coherence function in this region and shows that the multiple scattering on the surface gives rise to an additional pulse tail in the direction of enhanced backscattering. The theory predicts pulse broadening approximately 20% greater than that caused by single scattering alone for a delta-function incident pulse and typical surface parameters. Analytical results are compared with Monte Carlo simulations and millimetre-wave experiments for the one-dimensional rough surface with RMS height 1λ and correlation distance 1λ, showing good agreement.     

Two-frequency mutual coherence function and its applications to pulse scattering by random rough surface

An analytic expression of the two-frequency mutual coherence function (MCF) was derived for a two-dimensional random rough surface. The scattered field was calculated by the Kirchhoff approximation, which is valid in the case that the radius of curvature of the surface is much larger than the incident wave length. The scattering problem of narrowband pulse was investigated to simplify the analytic expression of the two-frequency MCF. Numerical simulations show that the two-frequency MCF is greatly dependent on the root-mean-square (RMS) height, while less dependent on the correlation length. The analytic solutions were compared with the results of Monte Carlo simulation to assess the accuracy and computational efficiency. Supported by the National Natural Science Foundation of China (Grant No. 60571058) and the National Defense Foundation of China (Grant No. 51403020505DZ0111)     

Two-frequency mutual coherence function for electromagnetic pulse propagation over rough surfaces

The propagation of a transient electromagnetic pulse over irregular terrain is considered. We model the wave propagation using the parabolic wave equation, which is valid for near-horizontal propagation. We model the effect of scattering from the rough terrain by introducing a surface-flattening coordinate transform. This coordinate transform simplifies the boundary condition of our problem, and introduces an effective refractive index into our wave equation. As a result, the problem of propagation over an irregular surface becomes equivalent to the problem of propagation through random media. The parabolic equation is solved analytically using the path integral method. Both vertically polarized and horizontally polarized signals are treated. Cumulant expansion is introduced to obtain an approximate expression for the two-frequency mutual coherence function. From the mutual coherence function, spatial and temporal dependence of the propagating signal can be determined. It can be shown that scattering from the irregular surface can cause broadening of the transient signal. This can have a significant impact on the performance of radio communication systems.     

Two-frequency mutual coherence function for electromagnetic pulse propagation over rough surfaces

The propagation of a transient electromagnetic pulse over irregular terrain is considered. We model the wave propagation using the parabolic wave equation, which is valid for near-horizontal propagation. We model the effect of scattering from the rough terrain by introducing a surface-flattening coordinate transform. This coordinate transform simplifies the boundary condition of our problem, and introduces an effective refractive index into our wave equation. As a result, the problem of propagation over an irregular surface becomes equivalent to the problem of propagation through random media. The parabolic equation is solved analytically using the path integral method. Both vertically polarized and horizontally polarized signals are treated. Cumulant expansion is introduced to obtain an approximate expression for the two-frequency mutual coherence function. From the mutual coherence function, spatial and temporal dependence of the propagating signal can be determined. It can be shown that scattering from the irregular surface can cause broadening of the transient signal. This can have a significant impact on the performance of radio communication systems.     

Two-Frequency Mutual Coherence Function of Millimeter Wave in Rain

In this paper, the general formulations of two-frequency mutual coherence function, , for a pulse wave propagating in random discrete media are summarized. The relations of the amplitudes and phases of the to _d are given by Ishimaru et al, based on average particle in cloud and rain. In practice, since the particles sizes in random discrete media are in a size distribution spectrum, the ought to be derived from a particles size distribution. Based on an approximately solution, we describe these examples of millimeter waves (94, 220GHz) pulse propagating in rain and show that the 's amplitudes and phases obvious varies as rainfall and frequency. For a kind of rain, considering raindrops size distribution and average raindrop size, respectively, the 's amplitudes and phases are calculated. The numerical results show that the differences between the results calculated by raindrops size spectrum and by average size are remarkable, especially for heavy rainfall. Therefore, It is shown that the calculated by a particles size distribution is more reasonable than by average size. For the numerical analyses, particles size distribution ought to be adopted. This study is important for us to provide adequate bandwidths to achieve high-rate pulse communications and improve MMW radar system performances and atmospheric remote-sensing techniques.     

Scattering and propagation of UV pulses in soot aerosols

Scattering and propagation of a UV pulse in soot aerosols are studied using generalized multi-sphere Mie theory (GMM) and a two-frequency mutual coherence function. Soot aerosols are obtained by the diffusion-limited aggregation (DLA) model. Scattering characteristics of aggregate structures in soot aerosols are analyzed by GMM theory in detail. Scattering intensities versus scattering angles are given and discussed. The effects of different-positions of the aggregate on the scattering intensities, scattering cross section, extinction cross section, absorption cross section and asymmetry factor are computed and compared. The two-frequency mutual coherence functions of UV pulses in soot aerosols are simulated, and the effects of optical distance, frequency difference are analyzed.     

Temporal broadening of pulsed waves propagating through turbulent media

Pulse signals, propagating through a turbulent medium such as the ionosphere, can be distorted by dispersion and scattering from both the background medium and irregularities embedded in. Thus, the mean square pulse width is changed, and temporal broadening is introduced. We carry out a study on the temporal broadening with theoretical analyses and numerical simulations by using an analytical solution of two-frequency mutual coherence function obtained recently by iteration. As a case of study, pulse broadening is investigated in detail in trans-ionospheric propagation. Results show that most contributions are mainly from the dispersion of the background ionosphere and scattering effects of electron density irregularities in most cases.     

Self-referencing measurement of an ultrashort pulse by the standard shear interferometry method

A new method for the self-referencing measurement of the amplitude-phase shape of an ultrashort pulse is proposed. The method uses a two-frequency characteristic of the pulse, which is defined as S(F ₁)S(F ₂), where F is the frequency, S(F) is the complex Fourier spectrum of the pulse, and F ₁ and F ₂ are two independent variables. It is shown that this characteristic can be generated as a two-dimensional polychromatic light wave upon generation of the sum frequency of two crossed spectral decompositions of one and the same pulse, as well as upon space-time Fourier transform of radiation of the noncollinearly generated second harmonic of the pulse. In an orthogonal system of transverse coordinates F ₁ + F ₂ and F ₁ ? F ₂, at any given value of F ₁ + F ₂, the radiation frequency of this wave in the direction of the second coordinate F ₁ ? F ₂ does not change. Therefore, the phase structure of the two-frequency characteristic can be reconstructed by the standard method of lateral shear interferometry in the direction of this coordinate. In the reconstructed two-dimensional phase structure of the two-frequency characteristic, any section by the plane F ₁ = const or F ₂ = const yields the phase structure of the spectrum of the pulse under study. This makes it possible to reconstruct the amplitude-phase shape of the pulse.     

Propagation of the two-frequency coherence function in an inhomogeneous background random medium

The spatial and temporal structures of time-dependent signals can be appreciably affected by random changes of the parameters of the medium characteristic of almost all geophysical environments. The dispersive properties of random media cause distortions in the propagating signal, particularly in pulse broadening and time delay. When there is also spatial variation of the background refractive index, the observer can be accessed by a number of background rays. In order to compute the pulse characteristics along each separate ray, there is a need to know the behaviour of the two-frequency mutual coherence function. In this work, we formulate the equation of the two-frequency mutual coherence function along a curved background ray trajectory. To solve this equation, a recently developed reference-wave method is applied. This method is based on embedding the problem into a higher dimensional space and is accompanied by the introduction of additional coordinates. Choosing a proper transform of the extended coordinate system allows us to emphasize 'fast' and 'slow' varying coordinates which are consequently normalized to the scales specific to a given type of problem. Such scaling usually reveals the important expansion parameters defined as ratios of the characteristic scales and allows us to present the proper ordering of terms in the desired equation. The performance of the main order solution is demonstrated for the homogeneous background case when the transverse structure function of the medium can be approximated by a quadratic term.     

Short pulse detection and imaging of objects behind obscuring random layers

This paper presents a theory of imaging objects behind layers of scattering media. The transmitter is a focused array or an aperture emitting a short pulse. The scattered pulse is received by a focused array or aperture. The received signal consists of two components: the pulse scattered from a random medium and from the target, and these two components can be distinguished by the use of ultra wide band (UWB) pulse. The second moment of the received signal includes the fourth-order moments of stochastic Green's functions, which are reduced to the second moments by the use of the circular complex Gaussian assumption, and of the generalized two-frequency mutual coherence function. This imaging theory is a generalization of optical coherence tomography (OCT), SAR and confocal imaging. It clarifies the relationships among resolution, coherence length, shower curtain effects and backscattering enhancement.     

Mutual effects of temporal and spatial coherence of laser radiation during wind refraction

Conclusions Generalizing our results, one can identify the basic mechanism responsible for the mutual influence of temporal and spatial fluctuations in the amplitude of a light field in a moving medium with thermal nonlinearity.A necessary condition for this type of mutual interaction is a nonlinear incoherent effect connected nonlinearly with the induced fluctuations in the refractive index n_n. The mutual coupling of temporal and spatial variations is detectable only when the fluctuating part of n_n is comparable in magnitude to the normal refractive index, and when the distribution is nonuniform over the beam cross section and unstable during the pulse.The fundamental relationships of mutual interaction are that the slow fluctuations, which peel off the nonlinear medium over time, lead to a degradation of the spatial coherence of the light beam while it is being nonlinearly refracted. In all cases the spatial coherence of the laser radiation is reduced. The reverse effect of spatial fluctuations on the degradation of temporal coherence of a light pulse that is spatially-incoherent at the entrance to the medium is similar in its characteristics. This mutual interaction is substantially reduced when the nonstationary self-interaction regime promotes smoothing of fluctuations in the induced optical channel.Finally, we note that if the noise component of the pulse is a stable, uniform process, the transformations of the temporal and spatial coherence of a light field will occur independently in a nonlinear medium.Moscow State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 7, pp. 816–822, July, 1989.     

Short pulse detection and imaging of objects behind obscuring random layers

This paper presents a theory of imaging objects behind layers of scattering media. The transmitter is a focused array or an aperture emitting a short pulse. The scattered pulse is received by a focused array or aperture. The received signal consists of two components: the pulse scattered from a random medium and from the target, and these two components can be distinguished by the use of ultra wide band (UWB) pulse. The second moment of the received signal includes the fourth-order moments of stochastic Green's functions, which are reduced to the second moments by the use of the circular complex Gaussian assumption, and of the generalized two-frequency mutual coherence function. This imaging theory is a generalization of optical coherence tomography (OCT), SAR and confocal imaging. It clarifies the relationships among resolution, coherence length, shower curtain effects and backscattering enhancement.     

Two-frequency effects in nuclear quadrupole resonance

A number of new effects which occur in the two-frequency excitation of a multilevel spin-system in nuclear quadrupole resonance are described. Three programs for observing the effect of trapping, used to detect some transitions in a multilevel system in terms of others, for an accurate determination of the asymmetry parameter of the gradient of the electric field, to identify lines of the multiplet spectrum of nuclear quadrupole resonance, and to investigate the phenomenon of cross-relaxation, are proposed. Quantitative estimates are given of the value of the trapping when two neighboring transitions are excited. The phenomenon of slow beats between signals of a two-frequency echo and the frequency of the transition ±3/2±5/2 for = 0 when an external magnetic field is applied is explained. The reason for the short spin-spin relaxation times in the secondary echoes is established. The experimental method and a block diagram of a two-frequency nuclear quadrupole resonance system are described.This paper was presented at an All-Union Symposium on Magnetic Relaxation in June 1971 in Leipzig.Translated from Izvestiya VUZ, Fizika, No. 3, pp. 82–88, March, 1973.In conclusion we wish to thank V. A. Shishkin, M. Z. Yusupov, and A. D. Gordeev, for their help and for useful discussions.     

Scattering and propagation of terahertz pulses in random soot aggregate systems

Scattering and propagation of terahertz pulses in random soot aggregate systems are studied by using the generalized multi-particle Mie-solution(GMM) and the pulse propagation theory. Soot aggregates are obtained by the diffusion-limited aggregation(DLA) model. For a soot aggregate in soot aggregate systems, scattering characteristics are analyzed by using the GMM. Scattering intensities versus scattering angles are given. The effects of different positions of the aggregate on the scattering intensities, scattering cross sections, extinction cross sections, and absorption cross sections are computed and compared. Based on pulse propagation in random media, the transmission of terahertz pulses in random soot aggregate systems is determined by the two-frequency mutual coherence function. Numerical simulations and analysis are given for terahertz pulses(0.7956 THz).     

脉冲波在空间等离子体介质中传播的矩分析及其应用

根据随机介质波传播理论，开展脉冲波在星际空间等离子体介质中的传播特性的分析方法研究.在强起伏条件下，推导双频互相关函数的二阶矩和四阶矩方程，利用不同电子密度模型，计算双频衍射强度相关函数和闪烁指数，并应用到闪烁的动态谱观测和相关分析中，得到自相关图谱、相关带宽和相关时间等闪烁特征参数，为脉冲在等离子体中的传输特性的分析，提供必要的理论基础.     

Reducing pulse distortion in fast-light pulse propagation through an erbium-doped fiber amplifier using a mutually incoherent background field

It was reported earlier that it is possible to obtain large pulse advancement with minimum pulse distortion in fast-light propagation through an erbium-doped fiber amplifier by placing the pulse on top of a mutually coherent constant background field. Here we show that comparable distortion reduction can be obtained through use of a mutually incoherent background field, a procedure that could be much more readily implemented under many circumstances. We also show that further improvement can be obtained by means of adjusting the pulse power, and for a pulse-power of the distortion decreases about 56% from 0.56 with no background while the fractional advancement decreases only about 3% from 0.16.