Rod Frehlich

Coherent laser radar performance for general atmospheric refractive turbulence

The signal-to-noise ratio (SNR) and heterodyne efficiency are investigated for coherent (heterodyne detection) laser radar under the Fresnel approximation and general conditions. This generality includes spatially random fields, refractive turbulence, monostatic and bistatic configurations, detector geometry, and targets. For the first time to our knowledge, the effects of atmospheric refractive turbulence are included by using the path-integral formulation. For general conditions the SNR can be expressed in terms of the direct detection power and a heterodyne efficiency that can be estimated from the laser radar signal. For weak refractive turbulence (small irradiance fluctuations at the target) and under the Markov approximation, it is shown that the assumption of statistically independent paths is valid, even for the monostatic configuration. In the limit of large path-integrated refractive turbulence the SNR can become twice the statistically independent-path result. The effects of the main components of a coherent laser radar are demonstrated by assuming untruncated Gaussians for the transmitter, receiver, and local oscillator. The physical mechanisms that reduce heterodyne efficiency are identified by performing the calculations in the receiver plane. The physical interpretations of these results are compared with those obtained from calculations performed in the target plane.

Performance of Mean-Frequency Estimators for Doppler Radar and Lidar

Abstract The performance of mean-frequency estimators for Doppler radar and lidar measurements of winds is presented in terms of two basic parameters: Φ, the ratio of the average signal energy per estimate to the spectral noise level; and Ω, which is proportional to the number of independent samples per estimate. For fixed Φ and Ω, the Cramer-Rao bound (CRB) (theoretical best performance) for unbiased estimators of mean frequency (normalized by the spectral width of the signal), signal power, and spectral width are essentially independent of the number of data samples M. For Φ, the estimators of mean frequency are unbiased and the performance is independent of M. The spectral domain estimators and covariance based estimators are bounded by the approximate periodogram CRB. The standard deviation of the maximum-likelihood estimator approaches the exact CRB, which can be more than a factor of 2 better than the performance of the spectral domain estimators or covariance-based estimators for typical Ω. For sma...

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.

Coherent Doppler Lidar Measurements of Wind Field Statistics

Coherent Doppler lidar measurements of wind statistics in the boundary layer are presented. The effects of the spatial averaging by the lidar pulse are removed using theoretical corrections and computer simulations. This permits unbiased estimates of velocity variance, spatial velocity structure functions, energy dissipation rate, and other point statistics of the velocity field.

Effects of Wind Turbulence on Coherent Doppler Lidar Performance

Abstract The effects of wind turbulence on pulsed coherent Doppler lidar performance are investigated theoretically and with computer simulations. The performance of velocity estimators is determined for the case of a single realization of a wind field described by a Kolmogorov spatial spectrum and for an ensemble average over many realizations. The results are compared with previously published data. The important normalized physical parameters are identified to reduce the parameter space. For a given realization of a random wind field, the mean Doppler lidar velocity (an ensemble average over the random aerosol particles) is a function of the lidar parameters and the instantaneous radial velocity over the sensing volume of the lidar pulse. Various approximations for the mean Doppler lidar velocity are compared using computer simulations. The best approximation for the mean Doppler lidar velocity is used to calculate the effects of the spatial averaging of the radial velocity by the lidar pulse on Dopple...

Estimating Spatial Velocity Statistics with Coherent Doppler Lidar

The spatial statistics of a simulated turbulent velocity field are estimated using radial velocity estimates from simulated coherent Doppler lidar data. The structure functions from the radial velocity estimates are processed to estimate the energy dissipation rate e and the integral length scale Li, assuming a theoretical model for isotropic wind fields. The performance of the estimates are described by their bias, standard deviation, and percentiles. The estimates of e 2/3 are generally unbiased and robust. The distribution of the estimates of Li are highly skewed; however, the median of the distribution is generally unbiased. The effects of the spatial averaging by the atmospheric movement transverse to the lidar beam during the dwell time of each radial velocity estimate are determined, as well as the error scaling as a function of the dimensions of the total measurement region. Accurate estimates of Li require very large measurement domains in order to observe a large number of independent samples of the spatial scales that define Li.

Measurements of Boundary Layer Profiles in an Urban Environment

Boundary layer profiles of mean temperature, velocity, and small-scale turbulence from in situ sensors, Doppler lidar, sodar, and rawinsondes are intercompared for an urban environment. A new Doppler lidar algorithm is presented to produce high-resolution profiles of small-scale velocity statistics. The lidar-derived profiles are robust and accurate even for challenging conditions such as stable boundary layers with a low-level jet, low turbulence, and low wind speed. Similar results are expected for other locations and convective conditions.

Probability distribution of irradiance for the onset of strong scintillation

We calculated the probability distribution function (PDF) from simulations for an initially spherical wave propagated through homogeneous atmospheric turbulence. The onset of strong scintillation was calculated. By onset of strong scintillation, we mean conditions of weak scintillation changing to the condition of strong focusing. In addition, one case in the saturation regime was calculated. The simulations’ PDF’s are compared with several heuristic models of the PDF and are seen to progress from close to log normal for the cases of weakest scintillation to close to the log normally modulated exponential PDF (LNME PDF) for the cases of strong scintillation. The simulations’ PDF’s are not in agreement with the K PDF for any of the calculated cases. The best agreement was obtained in comparison with Beckmann’s PDF [P. Beckmann, Probability in Communication Engineering (Harcourt, Brace, & World, 1967)]. Beckmann’s PDF varies from being the log-normal PDF for weak scintillation to being the LNME PDF for strong scintillation and progresses further to the theoretically expected exponential PDF in the limit of saturated scintillation. We recommend that simulation be used to predict the irradiance PDF for plane and diverged waves in homogeneous turbulence in preference to using heuristic models. More complicated propagation cases remain in the domain of heuristic argumentation.

Simulation of wave propagation in three-dimensional random media

Quantitative error analyses for the simulation of wave propagation in three-dimensional random media, when narrow angular scattering is assumed, are presented for plane-wave and spherical-wave geometry. This includes the errors that result from finite grid size, finite simulation dimensions, and the separation of the two-dimensional screens along the propagation direction. Simple error scalings are determined for power-law spectra of the random refractive indices of the media. The effects of a finite inner scale are also considered. The spatial spectra of the intensity errors are calculated and compared with the spatial spectra of intensity. The numerical requirements for a simulation of given accuracy are determined for realizations of the field. The numerical requirements for accurate estimation of higher moments of the field are less stringent.

Laser Scintillation Measurements of the Temperature Spectrum in the Atmospheric Surface Layer

Abstract The locally stationary temperature spectrum in the atmospheric surface layer is estimated using laser scintillation. The fluctuations of the parameters of the turbulence spectrum (the structure constant CT2 and inner scale l0) have a lognormal distribution. The average spectrum is calculated by averaging the locally stationary spectrum over these fluctuations. The average spectrum does not have a universal form. The fluctuations in the turbulence parameters produces a bias in measurements of the Obukhov-Corrsin constant and in estimates of energy dissipation rate ϵ based on average scintillation statistics. The performance of the scintillation technique and the accuracy of scintillation measurements of inner scale and structure constant are estimated using Monte Carlo simulation. One scintillation measurement can provide accurate estimates of the important turbulence parameters and the statistics of the fluctuations of these parameters. The scintillation estimates are true path-averaging estimate...