Simulation of spatial coherence of laser echo light field from random rough surface in turbulent atmosphere
Authors: Li Yan-Ling , Mei Hai-Ping , Ren Yi-Chong , Zhang Jun-Xin , Tao Zhi-Wei , Abdukirim Azezigul , Liu Shi-Wei ,   Key Laboratory of Atmospheric Optics, Anhui Institute of Optics and Fine Mechanics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China,   Science Island Branch, Graduate School of University of Science and Technology of China, Hefei 230026, China,   School of Environmental Science and Optoelectronic Technology, University of Science and Technology of China, Hefei 230026, China,   Advanced Laser Technology Laboratory of Anhui Province, Hefei 230037, China
Published: April 2022

According to the generalized Huygens-Fresnel principle, we derive the analytical formula for the complex degree of coherence of the echo light field under the von Karman atmospheric turbulence spectrum condition. Based on split-step beam propagation method of the turbulent phase screen and the target surface model, the fold pass propagation simulation of the laser in the turbulent atmosphere is realized. The dynamic speckle characteristics on the image plane are consistent with the experimental phenomenon. Firstly, the simulation results of the complex degree of coherence and phase structure function of the mirrored reflection echo light field are compared with the theoretical values, which verifies the correctness of the algorithm. Based on this, the complex degree of coherence of the echo light field reflected by the optical rough surface is calculated and analyzed. The results show that on a double-path turbulent flow path of 1.1 km, in other words, it transmits 2.2 km in unfolded mode, the spatial coherence of the echo light field is very sensitive to the root mean square value of height. When the root-mean-square value of height is close to the wavelength, the coherence is seriously degraded. When the correlation length of the target surface is much larger than the atmospheric coherence length, the coherence length of the echo light field is relatively close to the set spatial coherence length. When the correlation length of the target surface is close to the atmospheric coherence length, the influence of the rough surface of the target on the beam coherence cannot be ignored. When the correlation length of the target surface is much smaller than the atmospheric coherence length, the target surface characteristics have a dominant influence on the echo coherence, the spatial coherence of the light field is seriously degraded, and the echo is close to incoherent light. Considering the smooth target reflection surface, the greater the strength of turbulence, the faster the complex coherence decreases with space. The atmospheric coherence diameter <inline-formula><tex-math id="M1">\begin{document}${r_0}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20212420_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20212420_M1.png"/></alternatives></inline-formula> can be calculated further according to the complex degree of coherence. For the Pearson correlation coefficient the simulation value and theoretical value are both 0.998, which indicates that the atmospheric coherence diameter calculated by the complex degree of coherence has a high correlation with the theoretical value. This research provides a theoretical basis for the coherent detection scheme of echoes from rough surfaces in the turbulent atmosphere. The simulation algorithm extracts the target surface features by analyzing the variation of the complex coherence of laser echo signals in the turbulent atmosphere with the spatial distance, and also provides a method of using the known target surface to obtain path turbulence information.