## 4 Conclusions  
Based on RTS theory, Mie-scattering lidar technology was designed and built for the detection of atmospheric turbulence, and the vertical atmospheric refractive index constant profiles of Kolmogorov turbulence and non-Kolmogorov turbulence were detected and calculated, respectively. The return light intensity signal on the vertical path was analyzed statistically, and the actual probability distribution of the light intensity was fitted. The results show that the actual probability density distribution of logarithmic light intensity on the vertical path roughly obeys the normal distribution under weak fluctuations. The atmospheric turbulence was classified into Kolmogorov turbulence and non-Kolmogorov turbulence, and the inversion of the \(C_{n}^{2}\) profile was carried out. For Kolmogorov turbulence, the scintillation index profile was obtained by a return signal, and the \(C_{n}^{2}\) profile was obtained by hierarchical iterative inversion. By changing the iris diaphragm diameter, \(d_{0}\), it was found that the smaller the iris diaphragm diameter, \(d_{0}\), the larger the scintillation index, which is due to the existence of the aperture-smoothing effect. In addition, the atmospheric turbulence intensity under different weather conditions was also compared. The results show that the turbulence intensity under cloudy weather conditions was approximately one order of magnitude smaller than that under sunny weather conditions. For non-Kolmogorov turbulence, the detection method was the same as that for Kolmogorov turbulence; by changing the value of the spectral power law, \(\alpha\), it was found that the larger the value of spectral power law, \(\alpha\), the smaller the intensity of non-Kolmogorov turbulence. Moreover, the detection results of Mie-scattering lidar were compared with the HV-night model in the Yinchuan area. The results show that the Kolmogorov turbulence and non-Kolmogorov turbulence intensity profiles were consistent with the variation trend of the HV-night model, and the detected turbulence intensity fluctuated around the model. The reasons for this phenomenon can be summarized as two aspects: one is that the parameter selection in the model is not accurate enough, and the other is that the turbulence has internal and external scale changes. However, in general, it is feasible to use Mie-scattering lidar to detect atmospheric turbulence. In the future, the influence of the internal and external scales of turbulence varying with height should be taken into account, and more accurate and applicable inversion algorithms for the \(C_{n}^{2}\) profile should be selected to further improve the inversion accuracy from the scintillation index to the structure constant of the atmospheric refractive index \(C_{n}^{2}\). Conceptualization, J.M. ; Methodology, J.M. ; Software, Y.Z. ; Validation, J.L. ; Formal analysis, X.G. ; Resources, J.M. and H.Z. ; Writing--original draft, Y.Z. ; Writing--review & editing, Z.R. ; Supervision, J.M. ; Project administration, J.M. ; Funding acquisition, J.M. All authors have read and agreed to the published version of the manuscript. This work was supported by the National Natural Science Foundation of China (Nos. 42265009 and 42005103), the Natural Science Foundation of Ningxia Province (No. 2021 AAC02021), the Plan for Leading Talents of the State Ethnic Affairs Commission of the People's Republic of China, Innovation Team of Lidar Atmosphere Remote Sensing of Ningxia Province, the high-level talent selection and training plan of North Minzu University, the special funds for basic scientific research business expenses of central universities of North Minzu University (No. FWN20), Graduate Student Innovation Project of North Minzu University (No. YCX22114), and the Ningxia First-Class Discipline and Scientific Research Projects (Electronic Science and Technology) (No. NXYLX2017A07). Not applicable. Data Availability Statement: The relevent data used to support the findings of this study are available from the corresponding author upon request.