Enhanced Measurement of Vortex Beam Rotation Using Polarization-Assisted Particle Swarm Optimization for Phase Retrieval

In detecting the rotation velocity of an object employing the rotational Doppler effect of vortex beams, atmospheric turbulence can easily cause phase distortion and spiral spectrum dispersion, consequently reducing velocity measurement accuracy. This study combines adaptive optical intelligence algorithms with polarization compensation information to propose a novel approach, the Stokes–Particle swarm optimization Gerchberg–Saxton (Stokes-PSO GS) algorithm, which integrates Stokes polarization information assistance and PSO for GS phase retrieval. The algorithm adjusts the phase and amplitude of the pre-compensated phase screen of the GS algorithm utilizing Stokes information of polarized vortex beam (with l_L = 5 and l_R = −5) before and after distortion. The PSO is then employed to optimize the pre-compensated phase screen and perform compensations. Simulation results at z_S-T = 200 m and $C_n^2$ = 1 × 10⁻¹⁴ m^−2/3, demonstrate that the Stokes-PSO GS algorithm exhibits strong stability (small angular spectrum purity deviation, σ_{p, Stokes-PSO GS} = 0.005675% < σ_{p, GS} = 11.62%), superior optical field recovery (well-recovered Stokes optical field, up to 33.76% improvement in angular spectrum purity), and high-velocity measurement accuracy (25.93% improvement) compared to the GS algorithm. This approach enables precise measurement of the rotation velocity of the vortex beam, demonstrating its potential in practical applications.