Experimental determination of the multiple-scattering effect on the lidar-signal polarization characteristics during liquid- and solid-phase precipitation

We present results of experimental investigations of the signal-polarization characteristics in the case of lidar sounding during precipitation. We show and discuss the lidar signals and the depolarization profiles along the sounding path for liquid- and solid-phase precipitation. In the former case we compare the signal characteristics at different degrees of precipitation rate. In the latter situation, we consider snowfall with particle shape close to that of Chebyshev particles. We also follow the lidar-signal changes depending on the field-of-view of the receiving optics. The experimental data are compared with results of theoretical estimates and models concerning the optical and microphysical characteristics of the rain and snow particles. In the case of liquid-phase precipitation – rain – the observed dependence of the lidar’s signal-polarization structure on the precipitation intensity has two aspects: on the one hand, the change of the raindrops’ shape, and, on the other, the multiple-scattering effects. The lidar data demonstrate that the signal depolarization, and, more specifically, its behavior along the sounding path, can be used as a criterion for the presence of multiple scattering. In the case of a snowfall consisting of Chebyshev particles, the simultaneous role is evident of two factors influencing the lidar-signal depolarization, namely, the non-spherical shape of the particles and the multiple-scattering effects. When the scattering takes place off particles with a large size and a shape strongly differing from spherical, we observed the predominant role of the non-sphericity of the scattering centers in the signal depolarization. Received: 6 December 2000 / Revised version: 11 July 2001 / Published online: 19 September 2001     

Dependence of the lidar signal depolarization on the receiver’s field of view in the sounding of fog and clouds

We report an experimental study of the lidar signal depolarization as a function of the relative contribution of the multiple scattering in case of optically dense objects in the atmospheric planetary boundary layer. Results of the observation of fog and stratus clouds are presented, as well as those obtained by sounding of stratocumulus clouds during a snowfall. The lidar data point to a rise of the depolarization coefficient as the influence of the multiple scattering increases in consequence of both viewing angle enlargement and penetration into the object sounded. The variations of the depolarization coefficient are studied as a function of the field of view. In the case of fog, this dependence is approximated by a three-parameter exponential law; it is found that the depolarization increases steeply when the viewing angle is increased from 9 mrad to 12.5 mrad. The relationships between the approximation parameters and the microphysical characteristics of the scattering medium are considered. The experimentally determined size of the area where multiple scattering occurs is in good agreement with that calculated according to the diffusion model. The results obtained on the multiple scattering effect on the depolarization can also be employed in determining the extinction coefficient profiles in optically dense objects, as well as in evaluating the characteristic size of the scattering particles. Received: 6 September 1999 / Revised version: 7 February 2000 / Published online: 6 September 2000     

Scattering by small thin dielectric particles

In the analysis of electromagnetic scattering by distributions of small dielectric particles an approximation to the scattered field can be obtained by representing the electrical interaction of the particles in terms of the dipole moments of the individual particles. The calculation of the moments necessitates the solution of certain static scattering problems, and this becomes numerically difficult when the particles are thin. An integral equation formulation of the static scattering problem specialized to the case of thin planar dielectric plates is presented, along with an efficient numerical routine. Dipole moments are obtained over a range of permittivities for plates with several thicknesses and a variety of cross-sectional shapes, and the shape dependence is discussed.     

Geometrical optical modeling of femtosecond setups having angular dispersion

A reliable and efficient method based on a geometrical optical approach is presented to model the propagation of ultrashort pulses in optical systems. It is shown that the commonly used method to determine the group delay of the spectral components of a pulse from their geometrical optical path lengths is only correct for aberration-free optical systems. In the case of systems with angular dispersion and imaging errors, a correction to the path values obtained from ray-tracing calculations must be applied, since for specific systems neglect of the correction causes significant errors. A technique for performing this correction is presented. Two optical arrangements used for the generation and detection of tunable THz radiation by the femtosecond tilted-pulse-front excitation technique are analyzed to demonstrate the indispensability of the correction. Received: 29 July 2002 / Revised version: 22 October 2002 / Published online: 29 January 2003 RID="*" ID="*"Corresponding author. Fax: +36-72/501-571, E-mail: kozma@fizika.ttk.pte.hu     

A STUDY OF VARIOUS BARRIERS IN ENCLOSED SOUND FIELD BY USING THE COMPUTER PROGRAM—SOFIS

In the study of the behaviors of barriers in an enclosed field, one should take into account such phenomena as sound energy reflection, absorption, scattering and diffraction. Therefore, the study is much more difficult than that in free field. In this paper, sound barriers are classified into four kinds according to their size, number and shape. Each kind of barriers is modelled by a corresponding method based on a computer program—SOFIS. The program combines the ray-tracing technique and statistical method. The impulse response and some acoustical parameters such as sound pressure level at different positions can be calculated by the program, no matter there are a certain kind of barriers in the field or the field is empty. The ray-tracing program and the algorithms for various barriers are validated by the comparison between measurement and prediction of the reverberation room and the anechoic room of the Northwestern Polytechnic University.     

Detection of small forest fires by lidar

The possibility of detecting small forest fires with the help of a simple and cheap lidar operating at 0.532-μm wavelength up to distances of about 6.5 km is demonstrated. The values of the signal-to-noise ratio (SNR) achieved in the experiments are consistent with theoretical estimations obtained by computational modeling of the lidar detection process, including simulation of the smoke-plume shape and of the laser beam–plume interaction. This model was used to assess the potential of the lidar technique for fire surveillance in large forest areas. In particular, the upper limiting range for effective detection (SNR>5) of small localized fires in dry- and clear-weather conditions is estimated at 7–15 km depending on operation mode, burning rate, and observation geometry. Received: 29 August 2001 / Published online: 29 November 2001     

Multiply scattered component of lidar returns

The results of statistical simulation of the spatiotemporal structure of the multiply scattered component of lidar returns by the Monte Carlo method are discussed for the case of monostatic sensing geometry. The spatial characteristics of the region of the medium where occurs the last scattering of photon before arriving at the reciever. This region of the medium is called the instantaneous brightness body of multiply scattered radiation. It is demonstrated that the instantaneous brightness body of multiply scattered radiation that propagates toward the receiver may occupy a large volume that does not necessarily coincide with the region of formation of the singly scattered component. The main factors influencing the spatial and brightness characteristics of this volume source are established. The effect of scattering order on the spatiotemporal structure of lidar returns is analyzed for the case of sensing of aerosol haze and advective and radiative fogs with optical thickness 2<τ<8. Received: 2 August 2001 / Revised version: 7 January 2002 / Published online: 25 September 2002 RID="*" ID="*"Corresponding author. Fax: +7-38/2225-8026, E-mail: belov@iao.ru     

An algorithm to determine cirrus properties from analysis of multiple-scattering influence on lidar signals

A Monte Carlo-based evaluation of the multiple-scattering influence on ground-based Raman lidar measurements is presented. The lidar returns from cirrus clouds are analyzed in order to evaluate vertical profiles of the extinction and backscattering coefficients. Results show that for the typical cirrus cloud, the presence of the multiple scattering can lead to an underestimation of the extinction coefficient by as large as 200% whereas the backscattering coefficient is almost unaffected for the Raman lidar technique. An algorithm to select one or a set of phase functions which fit to the lidar data is also presented. It is an iterative procedure based on Monte Carlo scattering simulation. By comparison of the experimental value of the lidar ratio, corrected for the multiple scattering influence, and the phase function used in the Monte Carlo simulation, one can determine a suitable phase function. The validity and sensitivity of the algorithm have been demonstrated by applying it to simulated cases. The application to some real cases indicates that our procedure allows for the establishing of a practical scattering model for the cirrus clouds.     

Polarized angular dependence of out-of-plane light-scattering measurements for nanoparticles on wafer

Bidirectional ellipsometry has been developed as a technique for distinguishing among various scattering features near surfaces. The polarized angular dependence of out-of-plane light-scattering by the nanoparticles on wafer is calculated and measured according to Rayleigh limit. These calculations and measurements yield angular dependence of bidirectional ellipsometric parameters for out-of-plane scattering. The experimental data show good agreement with theoretical predictions for different diameter of nanoparticles. The results suggest that improvements for accuracy are possible to perform measurements of scattering features from nanoparticles. The angular dependence and the polarization of light scattered by nanoparticles can be used to determine the size of nanoparticulate contaminants on silicon wafers.     

The DORT solution in acoustic inverse scattering problem of a small elastic scatterer

The DORT (French acronym for Décomposition de l’Opérateur de Retournement Temporel) method is a novel approach for active detection and focusing of acoustic waves on the targets in the scattering medium. This technique involves the determination of the invariant of the time-reversal operator obtained by measurement of the scattering data in a pulse-echo mode. In this paper, a proposed approach based on the DORT method is developed to solve the acoustic inverse scattering problem of a small metallic scatterer. The proposed approach not only estimates the position of the scatterer, but also determines the physical properties of an unknown metallic scatterer such as the shape (cylinder or sphere), the material (density), and the size (radius) in an anisotropic scattering case. Theoretical and numerical simulation results are also studied and investigated to show that the proposed approach can simultaneously characterize all those properties of an unknown metallic scatterer. Moreover, the advantage of the proposed approach is to avoid the complex iterative scheme in solving the direct scattering problem and results in smaller computational load and faster implementation.     

Size and Shape Analysis of Sedimentary Grains by Automated Dynamic Image Analysis

The application of Automated Dynamic Image Analysis (ADIA) for measuring the size and shape of sedimentary grains is presented. This technique determines the size and shape of a large number of particles (typically 5,000 to 50,000 or greater) in the size range between 10 to 1,500 μm. ADIA measurements are carried out using a RapidVue particle analyzer. The size and shape of particles are obtained by analyzing digital images. Each image is composed of shapes representing two‐dimensional projections of particles. The analysis yields the area and perimeter of each particle cross‐section, which are transformed into size‐independent shape values. The analysis of such a large number of particles results in a very small statistical variation of the results, ca. 0.3% for 50,000 particles. Since operator selection of images does not enter the measurement procedure, the risk of bias caused by subjective sample selection is eliminated. The combination of ADIA with a two‐dimensional Kolmogorov‐Smirnov test, allows the identification of similarities and differences between sedimentary grains.     

Study of atmospheric water in gaseous and. liquid state by using combined elastic–Raman. depolarization lidar

A combined elastic–Raman lidar system based on a tripled Nd:YAG laser is used for the separate detection of elastic backscatter and Raman signals from atmospheric nitrogen, water vapor and liquid water and for their depolarization measurement. Vertical profiles of water-vapor and liquid-water content measured under clear-sky conditions behave differently: inside the boundary layer the ratio of liquid-water to water-vapor Raman backscatters rises with altitude. The depolarization measurements bring additional information about atmospheric scattering. The observed depolarization ratio of the water-vapor Raman signal is about 14%, while for liquid water this ratio varies in the 30–75% range, which exceeds the depolarization of bulk water and is attributed to the water-aerosol effects. Raman contours of water vapor and liquid water are partially overlapped, and bleed-through of liquid-water Raman backscatter leads to enhancement of depolarization of the water-vapor Raman signal. This parameter may be used as a convenient indicator of liquid-water interference in water-vapor measurements. Received: 12 December 2000 / Revised version: 27 September 2001 / Published online: 7 November 2001     

Fourier-wavelet regularized deconvolution (ForWaRD) for lidar systems based on TEA-CO2 laser

Lidar is an efficient tool for remotely measuring physical quantities or detecting targets. To improve the range resolution in long pulse lidars, such as lidar systems based on TEA-CO₂ lasers, deconvolution methods were used by previous investigators. Deconvolution is a noise sensitive process. In order to avoid noise amplification during the deconvolution process, the Fourier-wavelet regularized deconvolution method is used to deconvolve and denoise the back-scattered lidar signal simultaneously. This method is applied to lidar systems based on the TEA-CO₂ laser and the results are compared to nitrogen tail clipping method. Numerical simulation shows, in comparison to the clipping nitrogen tail technique, by using the ForWaRD method; the range resolution and working distance of the lidar is improved and the clipping tail apparatus is also eliminated.     

Direct measurement of the Rayleigh scattering cross section in various gases

Using the laser-based technique of cavity ring-down spectroscopy extinction measurements have been performed in various gases straightforwardly resulting in cross sections for Rayleigh scattering. For Ar and N₂ measurements are performed in the range 470-490 nm, while for CO₂ cross sections are determined in the wider range 470-570 nm. In addition to these gases also for N₂O, CH₄, CO, and SF₆ the scattering cross section is determined at 532 nm, a wavelength of importance for lidar applications and combustion laser diagnostics. In O₂ the cross section at 532 nm is found to depend on pressure due to collision-induced light absorption. The obtained cross sections validate the cross sections for Rayleigh scattering as derived from refractive indices and depolarization ratios through Rayleigh's theory at the few %-level, although somewhat larger discrepancies are found for CO, N₂O and CH₄.     

A bio-optical model suitable for use in forward and inverse coupled atmosphere-ocean radiative transfer models

A simple, yet complete bio-optical model for the inherent optical properties (IOPs) of oceanic waters is developed. This bio-optical model is specifically designed for use in comprehensive, multiple scattering radiative transfer models for the coupled atmosphere-ocean system. Such models can be used to construct next-generation algorithms for simultaneous retrieval of aerosol and marine parameters. The computed remote sensing reflectance R_rs(λ) is validated against field measurements of R_rs(λ) compiled in the SeaBASS data base together with simultaneous chlorophyll concentrations (C) ranging from 0.03 to . This connection between R_rs and C is used to construct a chlorophyll concentration retrieval algorithm that yields reliable results for a large range of chlorophyll concentrations. The overall performance of a MODIS/VIIRS chlorophyll concentration retrieval algorithm is found to be less satisfactory.     

A four-wavelength depolarization backscattering LIDAR for polar stratospheric cloud monitoring

A four wavelength backscattering depolarization LIDAR designed for polar stratospheric cloud and stratospheric aerosol measurement is described. The system uses the following wavelengths: 355 nm, 532 nm, 750 nm, and 850 nm. These wavelengths, obtained by means of the third- and second-harmonic of a Nd: YAG laser and by means of a tunable Ti: Sapphire laser, are chosen in a way to better characterize the particel size of such stratospheric aerosols. They are not emitted simultaneously as the LIDAR system is designed with only two detection channels permitting to detect, in the analog and in the photon counting mode, both the direct and the depolarized backscattered signal. The system has been operational in northern Finland since the end of November 1991.     

Beam wander characteristics of cos and cosh-Gaussian beams

Within the context of a general beam formulation, beam wander characteristics of cos and cosh-Gaussian beams are derived and numerically evaluated. In our graphs, the fundamental Gaussian beam is used as a benchmark for comparisons. The associated plots reveal that at small source sizes, a cos-Gaussian beam has the lowest beam wander, while this property is enhanced with increasing values of the displacement parameter. At large source sizes however, this advantage is taken over by cosh-Gaussian beam. Joint examination against the changing source sizes and propagation lengths shows that the range of source sizes, where the beam wander of cos-Gaussian beam remains lower, is enlarged as we go toward higher propagation lengths. Asymmetric beams tend to exhibit higher beam wanders both at small and large source sizes, but for the intermediate source size ranges, the beam wanders of asymmetric beams will fall below those of the symmetric beams. Explanations concerning these behaviors are offered. A historical account of beam wander formulation is also included.     

Upward penetration of grains through a granular medium

We study experimentally the creeping penetration of guest (percolating) grains through densely packed granular media in two dimensions. The evolution of the system of the guest grains during the penetration is studied by image analysis. To quantify the changes in the internal structure of the packing, we use Voronoï tessellation and a certain shape factor which is a clear indicator of the presence of different underlying substructures (domains). We first consider the impact of the effective gravitational acceleration on upward penetration of grains. It is found that the higher effective gravity increases the resistance to upward penetration and enhances structural organization in the system of the percolating grains. We also focus our attention on the dependence of the structural rearrangements of percolating grains on some parameters like polydispersity and the initial packing fraction of the host granular system. It is found that the anisotropy of penetration is larger in the monodisperse case than in the bidisperse one, for the same value of the packing fraction of the host medium. Compaction of initial host granular packing also increases anisotropy of penetration of guest grains. When a binary mixture of large and small guest grains is penetrated into the host granular medium, we observe size segregation patterns.     

Visible Infra-red Double Extinction Measurements in Densely Laden Media,New Progress

This paper describes new progress obtained with an optical technique called V.I.D.E. (Visible Infra-red Double Extinction) which simultaneously measures mean particle size in the range of 10–120 μm and mean number density in densely laden media (up to 0.1% volume fraction). The underlying theory, taking account of multiple light scattering, is recalled. Simultaneous size and concentration measurements are obtained by simultaneously recording transmittances of the medium at two well chosen wavelengths. Experimental results for suspensions of glass particles in air, are described and discussed. The size of particles given by the technique agrees with that given by optical microscopy and Malvern diffractometry. The V.I.D.E. technique is shown to be very suitable to investigate dense media whose optical thickness is up to nine and for which other techniques fail.     

Veselago’s lens consisting of left-handed materials with arbitrary index of refraction

We study Veselago’s lens with arbitrary index of refraction and characteristic impedance. Using a full wave optics calculation, we show that this lens can be considered as an imaging system and we derive the appropriate lens formula. The lens with arbitrary index and impedance retains some of the properties of the matched lens, such as the invariance of its optical axis, three-dimensional imaging and easy manufacturing, but it loses the property of sub-wavelength resolution. We also show that identical results can be obtained for the impedance matched lens in the framework of paraxial geometrical optics, from which it can be inferred that optical systems containing such a lens can be studied and designed using traditional ray-tracing tools.