Single-frame far-field intensity diagnostics for joint estimation of OAM mode fidelity and turbulence strength in free-space optical channels

Vortex beams carrying orbital angular momentum (OAM) underpin emerging free-space optical (FSO) communication and remote sensing architectures, yet their mode-space integrity is severely compromised by atmospheric turbulence, which couples the launched vortex into neighboring topological charges and degrades both link capacity and bit-error rate. Real-time diagnosis of this degradation requires simultaneous knowledge of two physical quantities: the instantaneous OAM mode fidelity η , governing inter-channel crosstalk, and the integrated turbulence strength D / r 0 , characterizing the propagation channel. Conventional approaches depend on Shack–Hartmann wavefront sensors or long temporal scintillation records, neither of which is compatible with compact or moving platforms. Here we show, in a numerical simulation study, that the single-frame far-field intensity distribution of a Kolmogorov-distorted Laguerre–Gaussian beam contains sufficient information to invert both η and D / r 0 jointly, provided the vortex order ℓ is known. A compact convolutional regressor ( ≈ 0.8 M parameters) with two physics-motivated output heads serves as the inversion operator, trained with a fidelity-weighted L1 objective that emphasizes the most ambiguous regime η ∈ [ 0.3 , 0.7 ] . On 6156 held-out samples spanning ℓ ∈ { 3 , 5 , 8 , 10 , 15 , 20 } and D / r 0 ∈ [ 0.1 , 15 ] ( ≈ 2.2 decades), the proposed diagnostic achieves an η mean absolute error of 0.0305 ( R 2 = 0.984 ) and a D / r 0 R 2 of 0.989 with a mean relative error of 6.1 % . Without retraining, the model remains stable under peak-SNR-defined detector noise down to 30 dB ( η MAE ≤ 0.035 ) and degrades gracefully at stronger, firmly out-of-distribution noise levels; it also retains η R 2 ≥ 0.86 in a zero-shot evaluation on eight multi-screen split-step channel configurations with distributed or axially concentrated turbulence. Inference requires ≈ 2 ms per frame on a single consumer GPU and ≈ 4 ms on one CPU thread. These results establish single-frame far-field intensity sensing, in simulation, as a computationally lightweight route to per-channel OAM link monitoring; extensions to simultaneously multiplexed OAM channels and experimental validation on physical links are identified as future work.