Feasibility study for the simulation of beam propagation: consideration of coherent lidar performance

To analyze the effects of atmospheric refractive turbulence on coherent lidar performance in a realistic way it is necessary to consider the use of simulations of beam propagation in three-dimensional random media. The capability of the split-step solution to simulate the propagation phenomena is shown, and the limitations and numerical requirements for a simulation of given accuracy are established. Several analytical theories that describe laser beam spreading, beam wander, coherence diameters, and variance and autocorrelation of the beam intensity are compared with results from simulations. Although the analysis stems from a study of coherent lidar performance, the conclusions of the method are applicable to other areas related to beam propagation in the atmosphere.     

Heterodyne lidar returns in the turbulent atmosphere: performance evaluation of simulated systems

Simulations of beam propagation in three-dimensional random media were used to study the effects of atmospheric refractive turbulence on coherent lidar performance. By use of the two-beam model, the lidar return is expressed in terms of the overlap integral of the transmitter and the virtual (backpropagated) local oscillator beams at the target, reducing the problem to one of computing irradiance along the two propagation paths. This approach provides the tools for analyzing laser radar with general refractive turbulence conditions, beam truncation at the antenna aperture, beam-angle misalignment, and arbitrary transmitter and receiver configurations. Simplifying assumptions used in analytical studies, were tested and treated as benchmarks for determining the accuracy of the simulations. The simulation permitted characterization of the effect on lidar performance of the analytically intractable return variance that results from turbulent fluctuations as well as of the heterodyne optical power and system-antenna efficiency.     

Statistical model for fading return signals in coherent lidars

A statistical model for the return signal in a coherent lidar is derived from the fundamental principles of atmospheric scattering and turbulent propagation. The model results in a three-parameter probability distribution for the coherent signal-to-noise ratio in the presence of atmospheric turbulence and affected by target speckle. We consider the effects of amplitude and phase fluctuations, in addition to local oscillator shot noise, for both passive receivers and those employing active modal compensation of wavefront phase distortion. We obtain exact expressions for statistical moments for lidar fading and evaluate the impact of various parameters, including the ratio of receiver aperture diameter to the wavefront coherence diameter, the speckle effective area, and the number of modes compensated.     

Speckle-field propagation in 'frozen' turbulence: brightness function approach

Speckle-field long- and short-exposure spatial correlation characteristics for target-in-the-loop (TIL) laser beam propagation and scattering in atmospheric turbulence are analyzed through the use of two different approaches: the conventional Monte Carlo (MC) technique and the recently developed brightness function (BF) method. Both the MC and the BF methods are applied to analysis of speckle-field characteristics averaged over target surface roughness realizations under conditions of 'frozen' turbulence. This corresponds to TIL applications where speckle-field fluctuations associated with target surface roughness realization updates occur within a time scale that can be significantly shorter than the characteristic atmospheric turbulence time. Computational efficiency and accuracy of both methods are compared on the basis of a known analytical solution for the long-exposure mutual correlation function. It is shown that in the TIL propagation scenarios considered the BF method provides improved accuracy and requires significantly less computational time than the conventional MC technique. For TIL geometry with a Gaussian outgoing beam and Lambertian target surface, both analytical and numerical estimations for the speckle-field long-exposure correlation length are obtained. Short-exposure speckle-field correlation characteristics corresponding to propagation in 'frozen' turbulence are estimated using the BF method. It is shown that atmospheric turbulence-induced static refractive index inhomogeneities do not significantly affect the characteristic correlation length of the speckle field, whereas long-exposure spatial correlation characteristics are strongly dependent on turbulence strength.     

Average speckle size as a function of intensity threshold level: comparisonof experimental measurements with theory

Speckle phenomena result whenever spatially coherent radiation is reflected from a rough surface or propagated through a random medium such as atmospheric turbulence. Speckle characteristics are therefore a major concern in many laser-imaging or wave-propagation applications. We present the results of experimental measurements of target-induced speckle patterns produced in the laboratory from a variety of targets and illumination conditions. We then compare these experimental measurements with a theoretical model for the average speckle size as a function of intensity threshold level. Excellent agreement is obtained for intensity threshold levels greater than approximately twice the mean intensity level.     

Simulation of error in optical radar range measurements

We describe a computer simulation of atmospheric and target effects on the accuracy of range measurements using pulsed laser radars with p-i-n or avalanche photodiodes for direct detection. The computer simulation produces simulated images as a function of a wide variety of atmospheric, target, and sensor parameters for laser radars with range accuracies smaller than the pulse width. The simulation allows arbitrary target geometries and simulates speckle, turbulence, and near-field and far-field effects. We compare simulation results with actual range error data collected in field tests.     

Edge technique Doppler lidar wind measurements with high vertical resolution

We have developed a Doppler lidar system using the edge technique and have made atmospheric lidar wind measurements. Line-of-sight wind profiles with a vertical resolution of 22 m have a standard deviation of 0.40 m /s for a ten-shot average. Day and night lidar measurements of the vector wind have been made for altitudes from 200 to 2000 m. We validated the lidar measurements by comparing them with independent rawinsonde and pilot balloon measurements of wind speed and direction. Good agreement was obtained. The instrumental noise for these data is 0.11 m /s for a 500-shot average, which is in good agreement with the observed minimum value of the standard deviation for the atmospheric measurements. The average standard deviation over 30 mins varied from 1.16 to 0.25 m /s for day and night, respectively. High spatial and temporal resolution lidar profiles of line-of-sight winds clearly show wind shear and turbulent features at the 1 -2-m /s level with a high signal-to-noise ratio and demonstrate the potential of the edge-technique lidar for studying turbulent processes and atmospheric dynamics.     

Characterizing output beams for lasers that use high-magnification unstable resonators.

Laser beams generated from high-magnification on-axis unstable resonators by use of hard-edged optics typically have a doughnut-shaped distribution in the near field (i.e., a flat-top profile with a hole in the middle for an axially coupled beam). We derive analytical expressions describing this distribution by using the flattened Gaussian beams concept. The superposition of two flattened Gaussian beams whose flatness and steepness of edges are controlled by defined parameters (i.e., the beam width and the order) is used to analyze the output beam intensity along the propagation axis. Finally, experimental measurements of beam propagation from a copper-vapor laser fitted with a high-magnification unstable resonator show excellent agreement with theoretical predictions.     

Analytical empirical expressions of the transverse coherence properties for monostatic and bistatic lidars in the presence of moderate atmospheric refractive-index turbulence

There have been many analyses of the reduction of lidar system efficiency in bistatic geometry caused by beam spreading and by fluctuations along the two paths generated by refractive-index turbulence. Although these studies have led to simple, approximate results that provide a reliable basis for preliminary assessment of lidar performance, they do not apply to monostatic lidars. For such systems, calculations and numerical simulations predict an enhanced coherence for the backscattered field. However, to the authors' knowledge, a simple analytical mathematical framework for diagnosing the effects of refractive-index turbulence on the performance of both bistatic and monostatic coherent lidars does not exist. Here analytical empirical expressions for the transverse coherence variables and the heterodyne intensity are derived for bistatic and monostatic lidars as a function of moderate atmospheric refractive-index turbulence within the framework of the Gaussian-beam approximation.     

Turbulence-induced measurement errors in coherent differential absorption lidar ground systems

The presence of atmospheric refractive turbulence makes it necessary to use simulations of beam propagation to examine the uncertainty added to the differential absorption lidar (DIAL) measurement process of a practical heterodyne lidar. The inherent statistic uncertainty of coherent return fluctuations in ground lidar systems profiling the atmosphere along slant paths with large elevation angles translates into a lessening of accuracy and sensitivity of any practical DIAL measurement. This technique opens the door to consider realistic, nonuniform atmospheric conditions for any DIAL instrument configuration.     

Simulation of laser propagation in a turbulent atmosphere

The split-step Fourier-transform algorithm for numerical simulation of wave propagation in a turbulent atmosphere is refined to correctly include the effects of large-scale phase fluctuations that are important for imaging problems and many beam-wave problems such as focused laser beams and beam spreading. The results of the improved algorithm are similar to the results of the traditional algorithm for the performance of coherent Doppler lidar and for plane-wave intensity statistics because the effects of large-scale turbulence are less important. The series solution for coherent Doppler lidar performance converges slowly to the results from simulation.     

大气湍流对贝塞尔高斯光束轴上光强的影响

针对光束在大气中传播时,大气湍流引起的光强起伏等现象.为了探索寻求减弱或者消除湍流的影响的途径,本文采用数值模拟的方法,分析了湍流大气对(零阶)贝塞尔高斯光束轴上光强的影响.分析发现,在湍流环境中,贝塞尔高斯光束的轴上光强都随着传播距离的增加而减小,湍流越强,光束的轴上光强减小越快.贝塞尔高斯光束的径向波矢量越小,轴上光强的稳定性越好.贝塞尔高斯光束轴上光强的稳定性随着传播距离的增加而变坏.贝塞尔高斯光束跟同样束宽的高斯光束相比较,贝塞尔高斯光束的轴上光强受湍流的影响较大.     

涡旋光束轨道角动量在大气湍流传输下的特性分析

从拉盖尔-高斯涡旋光束表达式出发,基于瑞利衍射理论,通过研究涡旋光束在大气湍流中传输时的旋转相干函数的变化规律,总结了涡旋光束在大气湍流中传输时各轨道角动量之间的串扰情况,使用了拓扑荷数探测概率描述串扰规律,并推导了拓扑荷数探测概率的解析表达式。研究了涡旋光束通过湍流后的拓扑荷数的分布情况,并将结果与涡旋光束通过大气随机相位屏的数值仿真结果进行了对比,给出了理论与仿真的拓扑荷数的探测概率随湍流强度以及初始涡旋光束拓扑荷数大小的关系图对比,验证了推导的拓扑荷数探测概率解析表达式的正确性。通过该表达式可进一步研究大气湍流与涡旋光束相互作用从而影响涡旋光束轨道角动量散射的本质,为涡旋光束的空间光通信中选择合适的拓扑荷数间隔,以及在不同湍流强度下选择合适束腰大小以减少串扰带来的误码率提供了理论依据。     

Performance modeling of an airborne Raman water-vapor lidar

We have developed a sophisticated Raman lidar numerical model to simulate the performance of two ground-based Raman water-vapor lidar systems. After verifying the model using these ground-based measurements, we then used the model to simulate the water-vapor measurement capability of an airborne Raman lidar under both daytime and nighttime conditions for a wide range of water-vapor conditions. The results indicate that, under many circumstances, the daytime measurements possess comparable quality to an existing airborne differential absorption water-vapor lidar whereas the nighttime measurements have improved spatial and temporal resolution. In addition, an airborne Raman lidar can offer measurements that are difficult or impossible with the differential absorption lidar technique.     

Numerical simulation of the effect of refractive turbulence on coherent lidar return statistics in the atmosphere

We propose an algorithm and the results of a numerical study of random realizations and statistics of a pulsed coherent lidar return that allow for refractive turbulence. We show that, under conditions of refractive turbulence, the relative variance of the lidar return power can exceed unity by a factor of as much as 1.5. Clear manifestations of the turbulent effect of backscattering amplification have been revealed from simulations of space-based lidar sensing of the atmosphere with coherent lidar. Under conditions of strong optical turbulence in the atmospheric boundary layer, as a result of the backscattering amplification effect, the mean lidar return power can exceed the return power in the absence of turbulence by a factor of 3.     

Investigation of seeing by means of an atmospheric mesoscale numerical simulation

We intend to show the potential of the numerical simulation of atmospheric turbulence to help find optimal sites for astronomical observation. We present results obtained with an atmospheric model, in which a representation of turbulence has been included. The model simulates the atmospheric flow over any given area, including the gross characteristics of the turbulence, from which maps of the astronomical seeing can be retrieved. A validation of the approach is obtained with actual measurements of the seeing, taken during field campaigns on two different sites. We find a good correlation in time between the observed and simulated values of the seeing, and we argue that this result can be extrapolated to space correlations.     

Ozone and water-vapor measurements by Raman lidar in the planetary boundary layer: error sources and field measurements

A new lidar instrument has been developed to measure tropospheric ozone and water vapor at low altitude. The lidar uses Raman scattering of an UV beam from atmospheric nitrogen, oxygen, and water vapor to retrieve ozone and water-vapor vertical profiles. By numerical simulation we investigate the sensitivity of the method to both atmospheric and device perturbations. The aerosol optical effect in the planetary boundary layer, ozone interference in water-vapor retrieval, statistical error, optical cross talk between Raman-shifted channels, and optical cross talk between an elastically backscattered signal in Raman-shifted signals and an afterpulse effect are studied in detail. In support of the main conclusions of this model study, time series of ozone and water vapor obtained at the Swiss Federal Institute of Technology in Lausanne and during a field campaign in Crete are presented. They are compared with point monitor and balloon sounding measurements for daytime and nighttime conditions.     

Propagation properties of rectangular Laguerre–Gaussian-correlated Schell-model beams in atmospheric turbulence

Based on the extended Huygens–Fresnel principle and the second-order moments of the Wigner distribution function (WDF), the analytical expressions for the cross-spectral density (CSD) and the propagation factor of a rectangular Laguerre–Gaussian-correlated Schell-model (LGCSM) beam propagating in atmospheric turbulence are derived. The statistical properties, such as the average intensity, the spectral degree of coherence (SDOC) and the propagation factor, of a rectangular LGCSM beam in free space and atmospheric turbulence are comparatively analysed. It is illustrated that a rectangular LGCSM beam exhibits self-splitting and combing properties on propagation in atmospheric turbulence, and the self-splitting properties of such beam are closely related to its beam orders m and n, which is quite different from other self-splitting beams. In addition, the rectangular LGCSM beam has an advantage for reducing the turbulence-induced degradation compared with the conventional partially coherent beams.     

Performance of a laser Earth-to-satellite link over turbulence and beam wander using the modulated gamma-gamma irradiance distribution

We present an analytical framework for the performance evaluation of laser satellite uplinks over the major probabilistic impairments, i.e., atmospheric turbulence and beam wander. Specifically, we consider a ground-station-to-space laser uplink with a Gaussian beam wave model, and we focus on the particular regime assuming untracked beams where beam wandering takes place. In that regime, the modulated gamma-gamma distribution has been proposed as an effective irradiance model to characterize the combined effect of turbulence and beam wander. First we provide a closed-form expression of the probability density function and deduce the fundamental statistics of the new model. Then we evaluate the performance of the laser system assuming coherent detection for several modulation schemes. An appropriate set of numerical results is presented to verify the accuracy of the derived expressions.     

Coherent Doppler lidar signal covariance including wind shear and wind turbulence

The performance of a coherent Doppler lidar is determined by the statistics of the coherent Doppler signal. The derivation and calculation of the covariance of the Doppler lidar signal for random atmospheric wind fields and wind shear are presented. The signal parameters are defined for a general coherent Doppler lidar system in terms of the atmospheric parameters. There are two distinct physical regimes: one in which the transmitted pulse determines the signal statistics and the other in which the wind field and the atmospheric parameters dominate the signal statistics. When the wind fields dominate the signal statistics, Doppler lidar data are nonstationary and the signal correlation time is proportional to the operating wavelength of the lidar. The signal covariance is derived for signal-shot and multiple-shot conditions. For a single shot, the parameters of the signal covariance depend on the random, instantaneous atmospheric parameters. For multiple shots, various levels of ensemble averaging over the t emporal scales of the atmospheric processes are required. The wind turbulence is described by a Kolmogorov spectrum with an outer scale of turbulence. The effects of the wind turbulence are demonstrated with calculations for a horizontal propagation path in the atmospheric surface layer.