Enhancing the accuracy of rotational velocity measurement for vortex beams within the optimal ability of phase retrieval algorithm

The measurement of the rotational velocity using the rotational Doppler effect (RDE) of a vortex beam is easily affected by atmospheric turbulence, leading to dispersed orbital angular momentum (OAM), and reduced measurement accuracy. This study investigates the optimal ability of the Gerchberg-Saxton (GS) phase retrieval algorithm to compensate for the optical field and enhance the velocity measurement accuracy within the optimal range of intrinsic parameters, such as the number of GS iterations, and extrinsic parameters, such as the atmospheric turbulence intensity and beam properties. Through detailed theoretical and simulation analyses, we demonstrate the outstanding effectiveness of the GS algorithm in improving the velocity measurement accuracy. Simulations conducted for a system-target distance of zS-T = 500 m show a 29.88% improvement in the velocity measurement accuracy and a 1.03-fold increase in the spectral signal-to-noise ratio (SSNR) within the optimal range. It showcases advantages that set it apart from other methods. This study reveals the threshold of the ability of GS algorithm to significantly enhance the rotational velocity measurement accuracy, providing valuable insights to precision measurements of rotational velocities in free-space applications.