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.

Computation of a single-scattering matrix for nonspherical particles randomly or horizontally oriented in space.

The computation of the scattering properties of cirrus cloud ice crystals by the ray-tracing approach is described. A light beam is represented by its Stokes quadrivector I, which describes intensity as well as polarization, and the scattering properties of particles (molecules, droplets, or ice crystals) are introduced by means of a 4 x 4 transformation matrix M known as the Mueller matrix, or M matrix. Obtaining such a matrix for each kind of particle gives access to a complete description of the scattering medium. Most computations of the M matrices of cirrus ice crystals have introduced several simplifying hypotheses, by using basic shapes, by assuming a random orientation of the particles, or both. The present study focuses on the calculation of the complete M matrix for a specific shape of particles (i.e., hexagonally based crystals) either with optional oscillation about the horizontal plane or with random orientation. The validity of the computation code is checked against specific well-known cases for randomly oriented particles. For horizontally oscillating particles the computation of this matrix is a new result. Sensitivity of the M matrix to the following variables is studied: refractive index, amplitude of oscillation, particle shape and size, and angle of incidence.

Spectral diversity technique for heterodyne Doppler Lidar that uses hard target returns.

A two-mode CO(2) laser is used as transmitter in a 10-microm heterodyne Doppler lidar (HDL) to take advantage of a spectral diversity technique, i.e., independent realizations obtained with different spectral components. The objective is to improve the properties (i.e., less variance) of power returns from a hard target. The statistical properties are presented first for a broad-spectrum laser transmitter and then for a two-mode laser transmitter. The experimental results for a cooperative diffuse hard target show that the return signals for a frequency separation Deltaf = 15 MHz can be decorrelated, depending on the angle of incidence and the target roughness. The experimental results show that the spectral diversity technique improves the performance of the HDL.

Four-Element Receiver for Pulsed 10-mum Heterodyne Doppler Lidar.

A four-element photomixer receiver has been tested in a 10-mum heterodyne Doppler lidar. It addresses a reduction of the variance of the power scattered off distributed aerosols targets at ranges as long as 8 km. An improvement in performance is expected when the four independent signals recorded on every single shot are combined. Two summation techniques of the four signals have been implemented: a coherent summation of signal amplitude and an incoherent summation of intensities. A phasing technique for the four signals is proposed. It is based on a more suitable correlation time with discernible self-consistent packets (SCP's). The SCP technique has been successfully tested, and the results obtained with a coherent summation of the four signals, i.e., variance reduction, carrier-to-noise ratio improvement, and velocity accuracy improvement, are in agreement with theory.

Urban boundary-layer height determination from lidar measurements over the paris area.

The Paris area is strongly urbanized and is exposed to atmospheric pollution events. To understand the chemical and physical processes that are taking place in this area it is necessary to describe correctly the atmospheric boundary-layer (ABL) dynamics and the ABL height evolution. During the winter of 1994-1995, within the framework of the Etude de la Couche Limite Atmosphérique en Agglomération Parisienne (ECLAP) experiment, the vertical structure of the ABL over Paris and its immediate suburbs was extensively documented by means of lidar measurements. We present methods suited for precise determination of the ABL structure's temporal evolution in a dynamic environment as complex as the Paris area. The purpose is to identify a method that can be used on a large set of lidar data. We compare commonly used methods that permit ABL height retrievals from backscatter lidar signals under different meteorological conditions. Incorrect tracking of the ABL depth's diurnal cycle caused by limitations in the methods is analyzed. The study uses four days of the ECLAP experiment characterized by different meteorological and synoptic conditions.

Refractive-index structure parameter in the planetary boundary layer: comparison of measurements taken with a 10.6-microm coherent lidar, a 0.9-microm scintillometer, and in situ sensors.

An optical technique is described that determines the path-averaged value of a refractive-index structure parameter at 10.6 microm by use of a pulsed coherent CO(2) lidar in direct detection and hard-target returns. The lidar measurements are compared with measurements taken by a 0.9-microm scintillometer and temperature probe (with humidity corrections). The experimental results show good agreement for C(n)(2) >or= (-14) m(-2/3). With respect to practical applications the new technique permits C(n)(2) lidar measurements in a neutral meteorological situation to an unstably stratified convective boundary layer over long ranges (1 km or more).

Lidar effective multiple-scattering coefficients in cirrus clouds.

We delimit a regime, valid for most ground-based lidar probings of cirrus clouds, in which the field-of-view dependence of multiple scattering reaches a plateau. In this regime and assuming the phase function to be constant around pi, we formally demonstrate Platt's modification of the single-scattering lidar equation, with a parameter eta(P) accounting for the reduction of the effective scattering coefficient defined so that (1 - eta(P)) is the amount of energy scattered in the forward peak. Then, to cope with nonconstant backscattering functions, we discuss the introduction of an effective backscattering coefficient that is an average of the scattering probabilities around pi.

Iterative method to determine an averaged backscatter-to-extinction ratio in cirrus clouds.

An iterative method to determine an average backscatter-to-extinction ratio and extinction coefficient simultaneously in cirrus clouds is proposed. The method is based on Klett's inversion, which is constrained by the total optical depth. A signal-to-noise ratio greater than 3 at the cloud top is required for an error in the backscatter-to-extinction ratio lower than 20% to result. The method has been tested with simulated lidar signals. An application to an experimental lidar signal is discussed.

Simulation in the time domain for heterodyne coherent laser radar.

A feuilleté model for assessment of the performance of heterodyne coherent laser radar (HCLR) under nonstationary atmospheric conditions such as wind shear and a fine layering of scattering properties is proposed. The model is an end-to-end signal simulation in the time domain at intermediate frequency from beam propagations to signal processing. The model takes into account the full transversedimension of the problem of laser-atmosphere interaction. The scatterers are grouped into slices, then an integration is performed over the slices that contribute to the HCLR signal. Two applications are presented: wind-shear detection for 10-µm HCLR and wind-vortex detection for 2-µm HCLR.

Characterization of pulsed coherent Doppler LIDAR with the speckle effect.

The relationships among heterodyne efficiency γ, number of speckle cells M, and the ratio of receiver area to coherence area S(R)/S(C) for a pulsed coherent laser radar (CLR) are written through the use of mutual coherence functions. It is shown that numerical values for S(R)/S(C) that follow Goodman's definition [J. W. Goodman, in Laser Speckles and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 9-75] or that are obtained through the use of a transverse-field coherence length agree. In the frame of the Gaussian model proposed by Frehlich and Kavaya [Appl. Opt. 30, 5325 (1991)] a new equation is derived: M = (1 + S(R)/S(C)). This equation agrees with our experimental results. Our theoretical analysis shows that the number of speckle cells for an optimal monostatic CLR system is M ~ 4. An experiment has been conducted with a ground-based pulsed CO(2) LIDAR and remote hard targets to study the probability density function of LIDAR returns as a function of M and to study the dependence of M on S(R)/S(C). An assessment of CLR performance through the use of M or the collecting aperture S(R) is discussed.