Improving the accuracy of vortex beam rotational velocity measurement based on phase recovery and polarization...

In remote rotational velocity measurements, atmospheric turbulence-induced phase distortion of the vortex beam increases velocity measurement error (VME). Previous studies overlooked the reference to new dimensional information for measurement error analysis and accuracy enhancement. Our work proposes the Optimal Joint Reference VME (OJR-σ) method as a, to our knowledge, novel error optimization method; it references the measurement error information from the left- and right-handed polarized components (LP and RP) of the polarized vortex beam and optimizes the velocity measurements values weights of LP and RP in the result to minimize the VME. Combined with the GS phase recovery algorithm, this method effectively reduces system VME, enabling distortion compensation and optimal VME mode distribution evaluation. The results indicate that the OJR-σ method achieves a lower VME advantage across all modes compared to both the General Joint Reference VME (GJR-σ) and General VME (G-σ) methods, with maximum VME decreases of 29% and 71% for the High VME decline rate modes, respectively. Additionally, the OJR-σ method exhibits fewer High VME modes, resulting in an average VME of 83.6% and 71.0% compared to the other two methods. After GS compensation, the VME of High VME modes decreases by 6.12%, 4.7%, and 6.78% for the three error methods, respectively. Furthermore, the OJR-σ method proves more effective than GJR-σ in reducing the VME for high topological charge modes, achieving a decline reaching 69.9%. Our work combines the phase recovery algorithm with the reference of measurement error information from both polarization dimensions, significantly reducing VME and demonstrating the potential of polarized vortex beams in high-precision applications. This innovatively provides, to our knowledge, a novel method and theoretical support for further enhancing the accuracy of free-space rotational velocity measurements.