## 5 Discussion and Conclusions  
Dependence of the autocorrelation function \(B(\tau)\) and the variance of the TILAS received power signal \(\sigma_{J}^{2}\) on the atmospheric turbulence distribution, strength, and outer scale can serve for turbulence characterization. Sequential analysis of these quantities provides information about the turbulence properties along the laser beam propagation path. Analysis of the shape of the autocorrelation function allows distinguishing between homogeneous and inhomogeneous turbulence distributions, while estimation of the strength of homogeneous turbulence or localized layer can be performed based on the signal variance when the turbulence distribution is known. The procedure of finding the position and strength of a single turbulence layer based on the \(\tau_{\text{cor}}\) and \(\sigma_{J}^{2}\) quantities obtained using the TILAS received power signal measurements can be summarized by the following algorithm:  
1. The relative turbulence layer position \(z\)/\(L\) is estimated using the set of functions \(\tau_{\text{cor}}\) (\(z\)/\(L\)) computed for given TILAS parameters, known distance to the target and target speed, as well as various turbulence strengths of the layer \(C_{n}^{2}\), as in Figure 4a. Since the functions \(\tau_{\text{cor}}\) (\(z\)/\(L\)) are weakly dependent on the turbulence strength, the turbulence layer position will be estimated with some error due to the uncertainty of \(C_{n}^{2}\). 2. The turbulence layer strength is defined using the set of functions \(\sigma_{J}^{2}(C_{n}^{2})\) computed for the estimated interval of \(z\)/\(L\) values, as in Figure 5b. The error in the layer position will introduce the corresponding error in the turbulence layer strength estimates. To reduce the estimation errors, the algorithm can be iterated using the obtained turbulence strength interval as the initial \(C_{n}^{2}\) interval in Step 1 until the desired accuracy is achieved. To speed up the turbulence layer position and strength retrieval procedure, a set of functions \(\tau_{\text{cor}}\) (\(z\)/\(L\)) and \(\sigma_{J}^{2}(C_{n}^{2})\) can be precomputed. Three examples of the evaluation of the turbulence layer characteristics are given in Table 1. The first two columns show the input parameters used for simulations. The third and fourth columns contain the quantities computed using the TILAS power signal processing, which are used to estimate \(z\)/\(L\) and \(C_{n}^{2}\) of a single turbulence layer. The fifth and sixth columns show the intervals of values for the layer position and strength computed after the first iteration of the algorithm. Note that the identification of the layer position appears to be more accurate for layers located on the ends of the propagation path, while the estimation of the layer strength is more accurate for layers located in the middle of the optical path. The second iteration results in noticeable increase of the accuracy, as can be seen by comparing the estimates (last two columns) to the input parameters (first two columns). More rigorous analysis based on simultaneous evaluation of strength and positions of few layers performed with summarizing autocorrelation function with weight coefficients regarding their position and strength can potentially provide detailed information about complex turbulence distribution. Additional opportunities are related to the use of a multi-aperture TILAS transceiver system. Such a system can transmit several laser beams with different initial diameters, which would serve for estimation of the turbulence outer scale.