Abstract:The article elaborates on the latest research progress related to the rotational Doppler effect (RDE) technology associated with orbital angular momentum (OAM). The experiments employed OAM beams characterized by topological charges l=±2, ±4, ±6, achieving high-precision measurements of rotational velocity and frequency with an error margin of merely 1.23%. The congruence between our experimental findings and theoretical forecasts attests to the accuracy and dependability of the RDE methodology.To address the perturbations induced by atmospheric turbulence on OAM beam propagation, we formulated a probabilistic model delineating the discrepancy in the orbital angular momentum quantum numbers between received and emitted photons. Subsequently, the article engineered an experimental optical setup incorporating a random phase plate to emulate the perturbations of atmospheric turbulence. The experimental data corroborate the accuracy of the theoretical model, indicating that the probability distribution of quantum number differences for orbital angular momentum (OAM) beams in atmospheric transmission is in accordance with theoretical predictions.