## 2 Three-Layer Altitude Spectrum Model of Refractive-Index Fluctuations  
Increasing measurements of the atmosphere have shown that the turbulence statistical characteristics in the atmosphere varies with altitude. Up until now, the experimental results have shown that the boundary layer (up to \(\sim\)2-3 km) had Kolmogorov turbulent characteristics and the free troposphere (up to \(\sim\)8-10 km) and the stratosphere showed different non-Kolmogorov turbulent characteristics. Based on this, [PERSON] et al. [24] suggested a three-layer altitude spectrum model that is more accurate, in which the first layer corresponds to the boundary layer with Kolmogorov turbulence (with spectrum exponent value of \(11/3\)); the second one corresponds to the free troposphere with non-Kolmogorov turbulence (with spectrum exponent value of \(10/3\)), and the third layer where non-Kolmogorov turbulence spectrum has a slope 5. The values of the refractive index structure constant for the free tropospheric turbulence and stratospheric one are given, respectively, \(A(\alpha=10/3)=0.015\) and \(A(\alpha\longrightarrow 5)=0.0024\). As mentioned above, the conclusions developed by [PERSON] et al. can present a reasonable theoretical basis. Since the turbulence is developed in the boundary layer and the Kolmogorov turbulence appears, the difference in the sizes of primary vortices of different coherent structures is small in the area under study and the sum of the spectra of different coherent structures is close to a Kolmogorov power dependence. On the contrary, the turbulence is undeveloped in the free troposphere and the stratosphere and coherent turbulence appears, so the difference in the sizes of primary vortices of different coherent structures is high, and the sum of the spectrum shows a rapid power decrease, corresponding to non-Kolmogorov power dependence [17; 18]. Here, a three-layer altitude-dependent turbulent spectrum model of refractive-index fluctuations for a vertical/slant path is proposed to describe the variations of turbulent statistical characteristics with altitudes in the aerospace in Reference [22], which is equal to the sum of refractive-index fluctuation power spectra in the boundary layer, the free troposphere, and the stratosphere. It is shown that the turbulence is characterized by the conventional Kolmogorov model in the boundary layer and the refractive-index fluctuations power spectrum has the following form,  
\[\Phi_{nB}(\kappa,z)=0.033\ C_{n}^{2}(z)\ \kappa^{-11/3}, \tag{1}\]  
where \(\kappa\) is the magnitude of the spatial frequency vector in units of rad/m, \(z\) is a propagation distance that varies between \(z=0\) and \(z=L\), and \(C_{n}^{2}(z)\) is the conventional Kolmogorov turbulent index-of-refraction structure parameter in the boundary layer that is dependent on the altitude and has units of m\({}^{-2/3}\). The turbulence exhibits non-Kolmogorov characteristics in the free troposphere and the refractive-index fluctuations power spectrum has the following form,  
\[\Phi_{nF}(\kappa,z)=0.015\widetilde{C}_{nF}^{2}(z)\ \kappa^{-10/3}, \tag{2}\]  
where \(\widetilde{C}_{nF}^{2}(z)\) is non-Kolmogorov index-of-refraction structure parameter in the free troposphere that depends on the altitude and has units of m\({}^{-1/3}\). The turbulence exhibits another non-Kolmogorov characteristics in the stratosphere above them and the refractive-index fluctuations power spectrum has the following form,  
\[\Phi_{nS}(\kappa,z)=0.0024\widetilde{C}_{nS}^{2}(z)\ \kappa^{-5}, \tag{3}\]  
where \(\widetilde{C}_{nS}^{2}(z)\) is non-Kolmogorov index-of-refraction structure parameter in the stratosphere that is dependent on the altitude and has units of m\({}^{-2}\)[22].