## 3 Verification
### Measurement of Atmospheric Turbulence Distribution  
Using SOAPY simulator, we generated open- and closed-loop data of multiple guide stars under two-layer turbulence. Open-loop data could be used to measure atmospheric turbulence parameters directly. For closed-loop data, pseudo-open loop reconstruction was used to obtain the corresponding open-loop data, and then the atmospheric turbulence parameters were measured.  
We varied the height of the upper turbulence to see if the measurements would follow the same pattern. The corresponding results are shown in Figure 7.  
Figure 6: Probability density function of a set of \(r_{0}\) measurement results. The blue bar chart and line represent the probability density function of the results using only one sub-aperture pair and one guide region, while the red vertical line represents the fitting \(r_{0}\) using all sub-aperture pairs and guide regions.  
To compare the S-DIMM+ and SLODAR methods, we used the same data and parameters to measure atmospheric turbulence intensity distribution using the S-DIMM+ method. Figure 8 shows the measurement results.  
We use the following quantification formula to analyze the measurement accuracy of the SLODAR method and the S-DIMM+ method.  
\[J=1-0.5\times\sum_{i}\lvert w_{i}^{m}-w_{i}^{a}\rvert, \tag{7}\]  
In the formula, \(J\) represents the proportion of correctly detected atmospheric turbulence intensity; \(i\) represents the \(i\)-th layer; \(w^{m}\) and \(w^{a}\) represent the proportion of intensity detected in each layer and the theoretically set proportion of intensity. The corresponding quantification results are shown in Table 2.  
Figure 8: Measurement results of S-DIMM+ method for same data and parameter. Each column in the figure represents a measurement result. The vertical coordinate indicates the height level measured, and the horizontal coordinate indicates the set height of the upper turbulence; **(a)** the result of open-loop data; **(b)** the result of pseudo-open-loop data.  
Figure 7: Measurement results of open-loop data and pseudo-open-loop data. Each column in the figure represents a measurement result. The vertical coordinate indicates the height level measured, and the horizontal coordinate indicates the set height of the upper turbulence; **(a)** the result of open-loop data; **(b)** the result of pseudo-open-loop data.  
Comparing the S-DIMM+ and SLODAR methods, it can be found that the SLODAR method can achieve better measurement results under the current parameter configuration. The accuracy of the SLODAR method is approximately 93%, while that of the S-DIMM+ method is 87%. From Figure 8, it can be observed that S-DIMM+ extends a layer of turbulence to nearby turbulence layers. When detecting the highest turbulence, the accuracy of the SLODAR method decreases; however, the S-DIMM+ method performs poorly in detecting turbulence in the middle layer. Compared to the S-DIMM+ method, using the SLODAR method can achieve better measurement results under the current GLAO parameter settings. This is also the reason why the measurement system utilizes the SLODAR method for calculations.  
Furthermore, the results show that using closed-loop data to calculate atmospheric turbulence is feasible. Compared to open-loop data, closed-loop data do not show a decrease in measurement accuracy when used for atmospheric turbulence measurement. This means that the measurement system can operate smoothly during the normal closed-loop operation of the GLAO system.