Fig. 2. Procedures of our approach for probing a turbulence distribution with three different turbulence regions.

a Three equal-length turbulence regions in simulation with each region having a different turbulence strength of $\left\{C_{n,j}^2,j=\mathrm{1,\; 2,\; 3}\right\}$. b Simulated beam widths ($D_{i,j}$ for each beam i in each region j) of the three beams designed for turbulence probing. c Simulated average modal spectrum for the three beams at the Rx under 200 turbulence realizations. The bars show the standard deviation for the simulation results. d Normalized average power remained on the $\mathcal{l}\mathcal{=}0$ for the three beams (e.g., $P_i\left(\mathcal{l}\mathcal{=}0\right)$ for Beam i) in the simulation. e Constructed equations for retrieving the turbulence distribution. f Probed turbulence distribution in simulation. The simulated relative probing error is ~4% (~0.2 dB from the original value) for this example of probing three turbulence regions.