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We construct a nonlinear equation between the return signal and the boundary value of extinction coefficient according to the lidar equation. And according to the nonlinear equation, we put forward a new method to solve the nonlinear equation by using Broyden algorithm. The Broyden algorithm is a concrete application of the quasi-Newton method. It has faster convergence and less iteration times, and does not need to calculate the derivative value. After choosing a suitable initial value, the boundary value can be obtained through the algorithm. A 532 nm single-band Mie scattering imaging lidar system is developed in Hefei, Southern China, for real-time atmospheric aerosol/particle remote sensing. Atmospheric measurement has been performed in Science Island during night time, and the time-range distribution of atmospheric backscattering signal was recorded on April 6, 2017, by employing the imaging lidar system. Then, the boundary values are achieved based on the Broyden algorithm and the least square algorithm. It adopts the Klett backward integration method to retrieve the horizontal distribution of extinction coefficients in a range of 1 km after the acquisition of the signal by changing the distance, then the horizontal atmospheric transmittance can be achieved based on the path integral. We also conduct a contrast experiment with the one-way transmission of the horizontal light near the ground within the range of 1 km at the same time. The initial site is situated in the experimental room besides the Dongpu reservoir and the end site is located on the second floor of our office building. The important things in this experiment are that the light reaching the target surface must be fully received and the laser power should be monitored at the double-end. Then we can obtain the transmittance by the direct method. By comparing the transmittance from the direct method with the transmittance from imaging lidar between the two different ways, i.e., Broyden algorithm and least square algorithm, then the correlation coefficients are obtained to be both over 0.95 in the period. And the method introduced in this paper is a little better than the least square algorithm with a value of 0.968. Besides, the average relative errors between the two inverse methods and the direct method are 4.66% and 9.10%, respectively. The average relative errors obtained by using the least square algorithm is about twice that by using the Broyden algorithm. It can be concluded that the algorithm introduced in this paper is effective and has certain advantages for the inverse problem.

In this article, a theoretical method based on the fluctuation of gradient tilt (G-tilt) of active light source is proposed to estimate the horizontal profiles of atmospheric optical turbulence (Cn2) and transverse wind. The G-tilt, related to the average phase gradient, is in the same direction as the average ray direction. And G-tilt angle is considered to be equal to the ratio between the centroid position offset and the focal length. In this method, a theoretical model based on lidar system is set up, in which forward scatter light beams at different distances are taken as beacons. These beacons are detected by a two-aperture telescope. And two light columns, from which we can obtain the information about G-tilt angle, are imaged by these beacons. In order to obtain the turbulence intensity and wind velocity from G-tilt angle with our theoretical model, the differential cross-correlation expressions of G-tilt angle and its derivative are derived in detail. These two expressions are based on the spatial cross-correlation function obtained from Rytov approximation and Taylor's frozen-flow hypothesis for Kolmogorov turbulence. Simultaneously, path weighting functions of Cn2 and wind velocity are derived, and the effects of path weighting functions on the calculation of our method are analyzed. Based on such an analysis, to realize the inversion of turbulence intensity and transverse wind, the matrix transformation algorithm is proposed. We ignore some minimal values of the path weighting functions in our algorithm so that the ill-conditioned matrix is avoided. Besides, numerical simulation is used for preliminarily validating this method. In our simulation, Cn2 varies randomly between 10-15 m-2/3 and 10-14 m-2/3 while wind velocity ranges from -5 m/s to 10 m/s. The sign of the wind velocity represents the direction of wind. According to the simulation results, the horizontal profiles of atmospheric optical turbulence and transverse wind calculated are consistent with their theoretical values no matter whether there exists Gaussian noise. When the ratio between the standard deviation of Gaussian noise we added and the original signal is 0.2, the maximum relative error of logarithmic Cn2 is 3.4%, and the correlation coefficient between the calculated results and theoretical values for Cn2 is 0.8. Besides, the maximum absolute error of wind velocity is 1.82 m/s, and the correlation coefficient between the calculated results and theoretical values for wind velocity is 0.9. Even if the horizontal profiles of atmospheric optical turbulence and transverse wind vary largely, the calculation results of our method remain stable. Therefore, a new idea is provided for measuring atmospheric turbulence and wind.

We report the basic theory and first horizontal results of a method called two-aperture differential scintillation method which is aimed at monitoring the vertical profile of atmospheric optical turbulence strength. The method is based on irradiance fluctuation of active light source, but can extract the optical turbulence information in the single-passage path. In this paper, the theoretical principle of two-aperture differential scintillation method is derived in detail. A concise expression is proposed for irradiance fluctuation structure function with differential aperture in the Rytov approximation under a weak fluctuation regime based on the cross-path theory. The mathematic relationship between irradiance fluctuation structure function and atmospheric optical turbulence strength is then developed. The effects of beacon aperture and beacon altitude on path weighting function of this method are analyzed for Kolmogorov turbulence. In order to test the validity of the new method, the experiments are conducted to compare the two-aperture differential scintillation method and single-aperture scintillation method in atmospheric boundary layer over 2 km horizontal single-passage path. In this arrangement, we employ a differential image motion monitor system to measure differential scintillation. Simultaneously, a large aperture scintillation instrument is placed 5 m away at the same altitude to measure the single-aperture scintillation. It is shown that the results of atmospheric refractive index structure constant deduced from the two methods are in good agreement. The measurements of atmospheric coherence length for spherical wave corresponding to the two methods indicate a linear correction factor (R2) of 0.96, in a slope of 0.98 with an offset of -0.09 cm. Feasibility and effectiveness of two-aperture differential scintillation method are thus verified experimentally. The novel method can separate single-passage scintillation information of active beacon double-passage propagation, thereby providing an accurate technique for measuring the atmospheric turbulence of active beacon.