Precise characterization of atmospheric turbulence is fundamental to free-space optical communications and imaging. While vortex beams are effective turbulence probes, existing sensing methods rely on a spatially integrated one-dimensional (1D) orbital angular momentum (OAM) spectrum, which obscures the heterogeneous nature of atmospheric distortions. Via numerical simulations, here we introduce radially resolved two-dimensional (2D) OAM spectroscopy, P(m, n), which resolves the azimuthal OAM spectrum (topological charge m) across discrete radial annuli (index n). This framework captures the spatially dependent beam-turbulence interactions of complex structured probes, such as multi-ringed Bessel–Gaussian beams. Coupled with a Support Vector Machine classifier, this method achieves a median classification accuracy of 86% across 25 distinct turbulence conditions, a 23% improvement over conventional 1D techniques. Additionally, we establish a targeted feature-selection protocol to mitigate peripheral noise. Our proposed technique to co-design the probe field is of immediate use in optical sensing as it can enable high-fidelity environmental characterization. Accurately sensing atmospheric turbulence is vital for optical communications, yet standard methods often obscure the spatial nature of these distortions. Via numerical simulations, the authors show that two-dimensional orbital angular momentum spectroscopy resolves turbulence across radial dimensions, enhancing the accuracy of environmental sensing.
Jiang et al. (2026) studied this question.