## 1 Introduction
proposed an improved S-DIMM+ method that clearly shows the location of strong turbulent layers [18]. In 2021, [PERSON] et al. determined the relationship between the height of the atmospheric turbulence layer and the angular displacement by measuring the image jitter using the S-DIMM+ method [19]. DICM lidar uses a charge-coupled device (CCD) image plane to image two scattered light columns to obtain the coherent length and turbulence profile of the atmosphere. In 2014, [PERSON] et al. studied the detection performance of heterodyne lidar for turbulence [20]. DW lidar can invert the atmospheric turbulence profile by calculating the variance in the wavefront jitter of two light spots on the intensified charge-coupled device (ICCD). In 2021, [PERSON] et al. simulated and experimentally verified the performance of differential wavefront lidar in detecting atmospheric turbulence [21]. The above lidar basically uses the dither variance of the image light spot to detect the atmospheric turbulence profile. Mie-scattering lidar is an atmospheric lidar system designed based on the Mie-scattering theory proposed by [PERSON] [22]. Compared with the other lidar methods mentioned above, Mie-scattering lidar is smaller in size, simple in operation, cost-saving, and easy to move, with high spatial and temporal resolution and a strong return signal. It is generally used to measure the height of cloud bases, aerosol structures, or atmospheric visibility below 30 km. In the method proposed in this paper, due to the presence of turbulence, there are certain fluctuations in the optical power of the echo wave detected by Mie-scattering lidar, including aerosol particle fluctuations and turbulence fluctuations. By adding a small iris diaphragm to the telescope, the fluctuation information causedby turbulence can be extracted from the Mie-scattering lidar return signal, and the atmospheric turbulence can be detected by the intensity fluctuation in the return signal. \(C_{n}^{2}\) is a parameter that directly describes atmospheric turbulence; for Mie-scattering lidar, the \(C_{n}^{2}\) profile can be obtained from return signal fluctuations. This is different from the other lidar detection principles mentioned above. The Kolmogorov turbulence theory is a local isotropic turbulence theory, which is an idealized theory. It is widely used in the inversion of turbulence intensity in the process of detecting atmospheric turbulence with lidar. However, some experiment results show that the turbulence characteristics of the tropopause and the stratosphere are significantly different when using Kolmogorov theory [23; 24]. In this case, the turbulence is no longer uniform in three dimensions, so the Kolmogorov theory is no longer applicable. Therefore, it is necessary to study non-Kolmogorov turbulence profile theory, which is closer to the actual situation, to describe the actual turbulence state [25]. In 2018, [PERSON] et al. analyzed the light intensity distribution, beam propagation, and scintillation index of non-Kolmogorov turbulence in a double-passage lidar system through theoretical and simulation methods [26]. Therefore, this paper proposes a method to detect the intensity of non-Kolmogorov turbulence using Mie-scattering lidar. In this paper, based on residual turbulent scintillation (RTS) theory, a Mie-scattering lidar method suitable for measuring the atmospheric turbulence profile is proposed. The scintillation index of different heights was obtained by calculating the fluctuation in light intensity, and the atmospheric turbulence profile was calculated. Some experiments were performed. The turbulence theory was extended from the Kolmogorov theory to the non-Kolmogorov theory, and the atmospheric turbulence profiles under the two theories were obtained and compared with the \(C_{n}^{2}\) theoretical model of the Yinchuan region. The results show that it is feasible to use Mie-scattering lidar to detect non-Kolmogorov atmospheric turbulence.