Research on rotational velocity measurement performance enhancement based on an amplitude-phase joint modulation algorithm

To address the issue of increased measurement error caused by atmospheric turbulence in remote rotational velocity detection, we propose an amplitude-phase joint modulation phase retrieval (APJM-PR) algorithm that incorporates a dual optimization strategy combining gradient-based correction and random perturbation, effectively preventing convergence to local optima. Compared with the Gerchberg-Saxton (GS) algorithm, our method demonstrates superior performance in strong turbulence conditions through integrated frequency-domain constraints and spatial-domain nonlinear feedback, achieving satisfactory mode purity with significantly fewer iteration cycles and notable improvements in all key performance metrics. The superior compensation capability of APJM-PR overcomes the limitations of the GS algorithm's linear update mechanism, enabling significant enhancement in optical field and spectral performance metrics for complex turbulence distortion scenarios involving high-order orbital angular momentum (OAM) modes and long-distance propagation. Moreover, APJM-PR achieves the highest improvement rate over the GS algorithm at critical turbulence intensities. The proof-of-concept experiment results further validate the algorithm's exceptional performance, demonstrating a velocity measurement accuracy standard deviation of 10^-4 rad/s across varying turbulence intensities, with an average improvement of 0.02 rad/s in velocity measurement accuracy for different OAM modes compared to the GS algorithm. These findings confirm that the APJM-PR algorithm possesses superior turbulence compensation capability and shows the potential for improving the accuracy of remote rotational velocity measurement in the future.