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.

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.

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.

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.

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.

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.

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.