Fig. 4. Advances in Doppler metrology.

Doppler metrology technology has evolved from assessing the 2D rotational velocity to covering 3D velocity assessment, determination of rotational direction and acceleration, geometric symmetry analysis, and detection of axis orientation. 3D velocity trajectories of particles can be analyzed by revealing both translational and rotational velocities, including helical motions. The rotational axis and direction can be determined by using dynamic structured light, dual-frequency vortex beam, or vector RDE with oppositely polarized vortex beams. Time-frequency analysis dynamically tracks rotational velocity and obtains acceleration. RDE measurements exhibit high sensitivity to geometric symmetry and rotation axes of objects, enabling analysis of geometric symmetry and determination of rotation axes. References given in the insets