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 \(\{{C}_{n,\,j}^{2},\,{j}={{{{\mathrm{1,2,3}}}}}\}\). 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 \({{{{{\mathscr{l}}}}}}{{{{{\mathscr{=}}}}}}0\) for the three beams (e.g., \({P}_{i}\left({{{{{\mathscr{l}}}}}}{{{{{\mathscr{=}}}}}}0\right)\) 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.