Probability density functions of Gaussian laser beam irradiance measured after propagation over 7km atmospheric path in comparison with various theoretical models are presented. The initial laser beam diameter at the e-2 intensity level was about 6 mm, the receiving aperture size was 14.4 cm. The experimental observations were performed in a wide range of turbulence strengths. The cases of weak, moderate, and strong intensity fluctuation regimes have been analyzed. Different receiving aperture radiuses were considered. The chi-square metric was used to estimate the agreement between the experimental and different theoretical statistics. The fractional gamma distribution has shown the best results for probability density distributions of apertures with sizes about 1 cm and 4 cm under strong turbulence conditions. The aperture averaging effect results in excluding near-zero irradiance values, which are typically observed on-axis at strong turbulence and high value of scintillation index which qualitatively transforms the observed statistics, so that experimental probability density functions can be well approximated by the fractional gamma distribution. With the increase of the aperture size, a further transformation of the statistics was observed. The statistics of experimental data for moderate and weak fluctuation regimes approached the lognormal and gamma distributions.
Propagation of optical waves in the atmosphere is influenced by refractive index spatial inhomogeneities resulting from complicated dynamics of air masses. Both large-scale deviations of refractive index (refractivity) and small-scale random refractive index inhomogeneities (turbulence) can significantly impact performance of atmospheric remote sensing systems including both imaging and laser-based electro-optics systems. Typically, in analysis of atmospheric sensing systems only turbulence effects are accounted for. This simplification is justified for only operation at relatively short distances and in absence of strong refractivity layers. In this paper we discuss more general propagation scenarios for which atmospheric refraction can play an important role and could significantly alter the major laser beam and image characteristics. Atmospheric refractivity is described by a combination of the standard MUSA76 and inverse temperature layer models, and atmospheric turbulence effects are accounted for using the classical Kolmogorov turbulence framework with HV57 model for the height profile of the refractive index structure parameter. The numerical analysis demonstrated that both refractivity and turbulence could significantly impact both laser beam propagation and image formation and lead to noticeable anisotropic effects.
Backscattering enhancement (BSE) effect is due to the fact that both the initial and back-scattered waves propagate
through the same inhomogeneities of the refractive index. Mean value of the back-scattered intensity is higher than it
would be with the same obstacle but no inhomogeneities. This effect is named backscattering enhancement (BSE) effect. Numerical modeling of lidar that based on BSE effect was carried out in Rutov-Obukhov approximation in our work. The integral equation was considered which bundles up the distribution of turbulence intensity throughout the space between the source and a scatterer. Coefficient BSE was determined as ratio of relation dispersions of radiation intensity fluctuation that scattered straight back and at an angle. BSE coefficient does not depend on the nature of scatterings in cases of aerosol or molecular scatterers. As example variants of turbulence intensity distribution Cn2 between sources in form select layer or boundaries of half-space with enhanced turbulence intensity scatterers were considered. Possibility of detection the sort out the regions with enhanced turbulence intensity was showed in the case isotropic turbulence for molecular or aerosol scatterings. Inhomogeneous
distribution of turbulence intensity is reliably picked out on dependence of BSE coefficient on distance between source and probing laser beam. The lidar scheme for BSE measurements with space modulation of probing beam is suggested. It allows suppressing systematic errors. Lidar allows measure BSE coefficient along with the routine lidar sensing. The dependence of BSE coefficient on the line along propagation path has considered for finite receiving aperture and finite diameter of probing laser beam. The results of modeling demonstrate that BSE measurements make it possible to remotely sort out the regions with enhanced turbulence intensity at distances determined by the maximum sensing range.
Turbulence is one of the key factors responsible for light beam distortions while its propagation through randomly
inhomogeneous medium such as the atmosphere. Many common methods of turbulence study are based on the phase or
amplitude analyses of the lightwave that have passed through turbulent medium. The significant role of explicit account
of the inner and the outer scales in experimental data description is well known.
We propose an optical method of turbulence characteristic scales estimation using phase data from Shack-Hartmann
sensor obtained of a single laser beam. The method is based on the sequential analysis of normalized correlation
functions of Zernike coefficients. It allows the excluding of the structural constant of refractive index value from the
analysis and reduces the solution of a two-parameter problem to sequential solution of two single-parameter problems.
The method has been applied to analyze the results of measurements performed in a water cell with created turbulence. A
horizontal flow was induced to simulate turbulence driftage. It is shown that taking into account the inner scale is
necessary for fitting of correlations of the third-order Zernike modes in the experimental error limits for lm/D=0.5 or
higher values (lm - the inner scale, D- aperture diameter). Inner scale estimations did not depend on the flow or changes
in the temperature difference. We have shown also that taking into account the outer scale is necessary for fitting of
experimental correlations of the first-order Zernike modes in the experimental error limits when L0/D<50 (L0 – the outer
scale).
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