Ultrahigh Precision Angular Velocity Measurement using Frequency Shift of Partially Coherent Beams

In the recent decade, the rotational Doppler effect has garnered considerable attention for stimulating the development of applications such as rotational Doppler velocity and topological charge measurements. Previous studies performed measurements under sources with one or multiple amplitude, phase, and polarization modulations. However, the applicability of these schemes is limited by the crucial factor of alignment between the source and object, especially if the magnitude of the source is greater than the object size. Therefore, this study proposes a partially coherent angular velocity measurement model that allows the rotational axes of targets to deviate from the source center and is even less susceptible to external jitters. Accordingly, a proof-of-principle experiment to determine the angular velocity under arbitrary alignment conditions is conducted. Tracing the rotational motion by rotating the coherent structure of the source results in a frequency shift—red shift for the same rotation and blue shift for a reverse rotation. The angular velocity vectors (both magnitude and direction) of two anisotropic sub-Rayleigh objects are successfully measured with ultrahigh precision. The lowest angular velocity is 0.001 r s−1. The average relative error is less than 0.05% with sufficient sampling. Thus, the present findings can be applied to velocity metrology and micromanipulation.