Polarimetric multiple scattering LiDAR model based on Poisson distribution.

Multiple scattering is always present in LiDAR measurements. It is one of the major causes of LiDAR signal depolarization when detecting backscattering from water clouds. For a given probing wavelength, the LiDAR signal is a function of the aerosol size distribution, cloud range, and optical depth, and of the LiDAR field of view (FoV). We present a relatively simple polarimetric multiple scattering model. It uses Poisson statistics to determine the photons' scattering order distribution at a given optical depth and takes into account the aerosol's properties as well as the characteristics of the LiDAR. The results are compared with Monte Carlo simulations performed on two types of cumulus clouds and on a moderate water fog. Good agreement is demonstrated for the total LiDAR signal and the depolarization parameter for a FoV of 1 mrad and a large FoV of 12 mrad.

Polarimetric LiDAR backscattering contrast of linearly and circularly polarized pulses for ideal depolarizing targets in generic water fogs.

In this paper, we investigate the backscattering depolarization of linearly and circularly polarized laser sources propagating in dense water fogs. We limit our investigation to a simple case where an active LiDAR system is pointed toward a white depolarizing Lambertian solid target. The receiver captures the reflected signal in the orthogonal channel so as to remove most of the backscattering from the water fog. It is shown that in the studied cases, a circularly polarized signal is depolarized faster than a linearly polarized signal and thus produces less contrast. We show that in the cases that can be described by the small angle approximation, the Rubenson degree of polarization (DoP) of a circularly polarized beam can be predicted by the DoP of a linearly polarized beam as DoPcir=2DoPlin-1, even for low-order multiple scattering events. In these conditions, since the linear DoP is always stronger, the contrast is expected to be better in linear polarization for ideal depolarizing targets.

Physical model of snow precipitation interaction with a 3D lidar scanner.

Snow precipitation interaction with a generic 3D lidar is modeled. The randomness and the intensity of the signal as a function of the visibility and snowflake size and density distribution are reproduced. To do so, a representative snow density distribution is modeled as a function of visibility. Taking into account the laser beam and pulse characteristics, the probability to have one or many snowflakes of a given size in the lidar sampling cell is calculated. Knowing the number and the size of the snowflakes, the magnitude of the lidar signal is calculated. Finally, a filtering algorithm based on the relative intensity of the snowflakes is discussed.

Study of polarization memory's impact on detection range in natural water fogs.

The influence of the initial polarization state of a source on the detection range of a system probing through natural dense water fog is analyzed. Information about the source is conveyed by ballistic, snake, and highly scattered photons. During propagation, the polarization state of ballistic and snake photons is not altered. It is shown that though circular polarization is not altered by simple direction changes during scattering, and has thus a tendency to be preserved longer in the highly scattered photons, it does not necessarily convey more useful information about the source than linear polarization or even an unpolarized beam. It is also shown that in any forward propagating system that can be described by the small-angle approximation the impact of polarization memory can be neglected.

Experimental validation of D parameter model for droplet sizing using off-axis lidar measurements.

Information about the size distribution of liquid droplets in a fog can be retrieved by measuring the backscattering lidar depolarization parameter D in circular polarization. Using a polarimetric off-axis lidar, measurements at different backscattering angles are performed on fogs made of water droplets and of mineral oil. Estimation of the effective droplet size is obtained using constrained linear inversion. Mie theory is used to calculate the variation in depolarization parameters for different effective droplet sizes. The calculation is performed for various scattering angles. These calculations provide a kernel for the constrained linear inversion scheme. It is shown that the refractive index has an effect on the retrieved droplet sizes as well as the choice of scattering angles. These measurements confirm that the circular depolarization parameter measured near the backscattering angle can be modeled as a function of the forward-scattering diffraction peak. The results of the constrained linear inversion of measurements are consistent with in situ measurement of the droplet size distribution.

Scattering phase function depolarization parameter model and its application to water droplets sizing using off-axis lidar measurements at multiple angles.

The backscattering lidar depolarization parameter D of water droplets contains information on their size that can be directly modeled as a function of the forward-scattering diffraction peak. Using a polarimetric Monte Carlo simulator, water clouds having different extinctions and droplet size distributions are analyzed to estimate their depolarization parameter at various backscattering off-axis angles. It is shown that the depolarization parameter of the polarimetric phase function can be found using off-axis lidar measurements at multiple angles, and that it could be used to estimate the water-cloud droplet size.

Inversion of water cloud lidar returns using the azimuthal dependence of the cross-polarization signal.

The contrast in the azimuthal pattern of cross-polarized lidar data is used directly to retrieve the extinction coefficient profile of water droplet clouds. Using a Monte Carlo simulation, we demonstrate that there is a simple mathematical relationship between the optical depth and the contrast of the cross-polarization azimuthal pattern. This relationship is independent of the water cloud droplet size, cloud position, and extinction profile. The derivation of the extinction profile of a water droplet cloud is obtained directly using the simple mathematical relationship without performing lidar equation inversion. The technique is limited to spherical particles.

Scanning Lidar Measurements of the Full-Scale RDD Field Trial Puff Plumes.

A vertically scanning lidar (light/radar) was used to measure the time evolution of clouds generated by a small explosive device. Vertical sweeps were performed at a downwind distance of 105 m from the detonation. The measured quantity obtained from the lidar was the light extinction coefficient. This quantity is directly proportional to the aerosol concentration. The background aerosol value was set to 0.0001 m (-1) (assuming a visibility of 40 km), and assuming the scattering properties of the explosively generated cloud is the same as the background aerosol, the authors found that the instantaneous maximal local concentration of aerosol in the cloud did not exceed 500 times the background aerosol value, and the instantaneous concentration was typically less than five times the background aerosol value. In the two trials that were done, the volumes of the clouds were reasonably close at 2,700 m(3) and 4,000 m(3), respectively.

Enhanced scanning agility using a double pair of Risley prisms.

Scanners with one pair of Risley prisms are robust and precise and they can be operated continuously. In this paper, we present a new scanner based on the use of two pairs of Risley prisms. The concept was driven by the need to add flexibility to Risley prism scanners used for lidar 3D mapping applications, while maintaining compactness and robustness. The first pair covers a FOV narrower than the second pair. The second pair is used to position the first Risley pair scan pattern anywhere within its own, larger, FOV. Doing so, it becomes possible, without additional scanner components, to increase the sampling point density at a specific location, to increase the sampling uniformity of the scanned area, and, while in motion, to maintain the sampling of a specific area of interest.

Dynamic behavior of postfilamentation Raman pulses.

We report on the postfilamentation behavior of a Stokes pulse created from intense and collimated ultrashort pulses propagating in air. A systematic analysis of the pulse propagation revealed that the redshifted Raman pulse produced during filamentation had a larger divergence than the postfilamentation intense pump pulse. Also, the analysis of the far-field Stokes transverse ring revealed that the intensity in this ionization-free light channel is still sufficiently high to induce stimulated Raman scattering after ionization had ended. This behavior further extends the potential of filamentation to remotely induce third-order nonlinearities.

Aerosol lenses propagation model.

We propose a model based on the properties of cascading lenses modulation transfer function (MTF) to reproduce the irradiance of a screen illuminated through a dense aerosol cloud. In this model, the aerosol cloud is broken into multiple thin layers considered as individual lenses. The screen irradiance generated by these individual layers is equivalent to the point-spread function (PSF) of each aerosol lens. Taking the Fourier transform of the PSF as a MTF, we cascade the lenses MTF to find the cloud MTF. The screen irradiance is found with the Fourier transform of this MTF. We show the derivation of the model and we compare the results with the Undique Monte Carlo simulator for four aerosols at three optical depths. The model is in agreement with the Monte Carlo for all the cases tested.

Arrest of self-focusing collapse in femtosecond air filaments: higher order Kerr or plasma defocusing?

Experimentally measured conical emission rings on the blue side of the filament supercontinuum of a 800 nm 50 fs pulse in air are reproduced in simulations with plasma and the third-order Kerr as the nonlinear terms. This agreement indicates plasma as the dominant mechanism arresting the self-focusing collapse. The higher order Kerr terms with the recently measured coefficients stop the collapse at a lower intensity than the plasma does and lead to the spherical angle-wavelength spectrum without blueshifted rings.

Effect of growth media and washing on the spectral signatures of aerosolized biological simulants.

We have evaluated the influence of growth media and washing on the laser-induced fluorescence spectra of bacteria. Three different bacterial simulants were cultured in three types of growth media. Three kinds of samples were generated from each culture: the culture itself, the growth medium alone, and a triple-washed sample. The materials were injected as aerosols in a lab-sized lidar aerosol chamber to obtain their spectra. Using two different analysis approaches, signature variations were observed between the three kinds of samples for most combinations of growth media/bacteria. This study concludes that the culture media used influences the spectral signatures.

Inversion of water cloud lidar signals based on accumulated depolarization ratio.

The relation between the accumulated single scattering factor and the layer accumulated depolarization ratio appears to be independent of the geometry of the measurements and contains information on the optical depth and thus on the extinction coefficient. A simple equation is developed to retrieve the extinction coefficient from the total integrated signal and the integrated depolarization ratio measurements. The results compare well with Klett and Weinman lidar inversion techniques. The results from the measurements of the integrated depolarization ratio can be used to set the far end initial extinction coefficient value required for Klett and Weinman lidar inversion or can be used directly.

Comparison of the relationships between lidar integrated backscattered light and accumulated depolarization ratios for linear and circular polarization for water droplets, fog oil, and dust.

Recently, an empirical relationship between the layer integrated backscattered light and the layer accumulated depolarization ratio has been established for linear polarization for the case of water droplet clouds. This is a powerful relation, allowing calibration of space lidar and correction of the lidar signal for multiple scattering effects. The relationship is strongly based on Monte Carlo simulations with some experimental evidence. We support the empirical relationship with strong experimental data and then show experimentally and via second order scattering theoretical calculations that a modified relationship can be obtained for circular polarization. Also, we demonstrate that other empirical relationships exist between the layer accumulated linear and circular depolarization ratios and the layer integrated backscattered light for submicrometer particles and nonspherical particles.

Relation between circular and linear depolarization ratios under multiple-scattering conditions.

A simple relationship is established between the linear and the circular depolarization ratios averaged over the azimuth angle of clouds made of spherical particles. The relationship is validated theoretically using double-scattering calculations; in the framework, the measurements are performed with a multiple-field-of-view lidar (MFOV) lidar. The relationship is also validated using data obtained with MFOV lidar equipped with linear and circular polarization measurement capabilities. The experimental data support theoretical results for small optical depths. At higher optical depths and large fields of view, the contribution of multiple scatterings is important; experimental data suggest that the relationship established between the linear and circular depolarization stays valid as long as the main depolarization mechanism comes from one scattering (most likely a backscattering a few degrees away from 180 degrees ).

Standoff determination of the particle size and concentration of small optical depth clouds based on double scattering measurements: concept and experimental validation with bioaerosols.

A multiple-field-of-view (MFOV) lidar is used to characterize size and optical depth of low concentration of bioaerosol clouds. The concept relies on the measurement of the forward scattered light by using the background aerosols at various distances at the back of a subvisible cloud. It also relies on the subtraction of the background aerosol forward scattering contribution and on the partial attenuation of the first-order backscattering. The validity of the concept developed to retrieve the effective diameter and the optical depth of low concentration bioaerosol clouds with good precision is demonstrated using simulation results and experimental MFOV lidar measurements. Calculations are also done to show that the method presented can be extended to small optical depth cloud retrieval.

Standoff determination of the particle size and concentration of small optical depth clouds based on double-scattering measurements: validation with calibrated target plates and limitations for daytime and nighttime measurements.

Diffractive target plates are used to emulate aerosols of known size and concentration. These target plates are used to validate and determine the sensitivity of a multiple-field-of-view lidar signal inversion technique based on double-scattering measurement to retrieve the particle size and the concentration of small optical depth clouds. We estimate that nighttime and daytime quantification (size and concentration) is possible for optical depths as low as 0.005 and 0.016, respectively. The recovery technique limiting factors are the shot noise, the laser features, the optical lens quality, the background illumination level, the background aerosol fluctuations, and the noise introduced by the lidar detector, a gated intensified camera (camera G-ICCD).

Information content of data measured with a multiple-field-of-view lidar.

Lidars with multiple fields of view (MFOVs) are promising tools for gaining information on cloud particle size. We perform a study of the information content of MFOV lidar data with the use of eigenvalue analysis. The approach we have developed permits an understanding of the main features of MFOV lidars and provides a way to relate the accuracy of particle size estimation with the measurement uncertainty and the scattering geometry such as the cloud-base height and the lidar sounding depth. Second-order scattering computations are performed for an extended range of particle sizes and for a wide range of lidar fields of view (FOVs). The results obtained allow us to specify the areas of possible applications of these lidars in cloud studies. Comparison of results obtained with polarized and cross-polarized scattered components demonstrate that the cross-polarized signal should provide a more stable retrieval and is preferable when double scattering is highly dominant. Our analysis allows for the estimation of the optimal number of FOVs in the system and their angular distribution, so this work can be a useful tool for practical MFOV lidar design.

Simple relation between lidar multiple scattering and depolarization for water clouds.

An empirical relationship is derived between the multiple-scattering fraction and the linear depolarization ratio by using Monte Carlo simulations of water clouds measured by backscatter lidar. This relationship is shown to hold for clouds having a wide range of extinction coefficients, mean droplet sizes, and droplet size distribution widths. The relationship is also shown to persist for various instrument fields of view and for measurements made within broken cloud fields. The results obtained from the Monte Carlo simulations are verified by using multiple-field-of-view lidar measurements. For space-based lidars equipped to measure linear depolarization ratios, this new relationship can be used to accurately assess signal perturbations due to multiple scattering within nonprecipitating water clouds.