The Doppler effect has inspired numerous applications since its discovery, initially enabling measurement of the relative velocity between a moving object and a wave source. In recent years, it has been found that scalar vortex beams with orbital angular momenta can produce the rotational Doppler effect, which can be used to measure the rotational speeds of rotating objects. However, in practice, only the absolute value of the rotational Doppler frequency shift can be obtained, and it is difficult to distinguish the direction of the object directly by a single measurement. This difficulty can be solved by using cylindrical vector beams with spatially varying polarization states. The cylindrical vector beam is formed by coaxial superposition of two vortex beams with opposite orbital angular momenta and orthogonal polarization states. By using two different polarization channels, the rotation direction can be directly recognized according to the relative phase difference between the two channels. In this paper, the scattering point model is employed to analyze the rotational Doppler effect of cylindrical vector beams, and a variety of cylindrical vector beams are generated by using vortex half-wave plates. The scheme can realize measurement of the rotational speed and direction simultaneously, and the system has simple construction, high accuracy of angular velocity measurement, and accurate direction identification.

We propose a method for detecting the symmetry of rotating patterns based on the rotational Doppler effect (RDE) of light. The basic mechanisms of the RDE are introduced, and the spiral harmonic distribution of rotating patterns is analyzed. By irradiating the rotating pattern using a superimposed optical vortex and analyzing the amplitude of the RDE signal, the spiral harmonic distribution of the pattern can be measured, and then its symmetry can be detected. We demonstrate this method experimentally by using patterns with different symmetries and shapes. As the method does not need to receive the scattered light completely and accurately, it promises potential application in detecting symmetrical rotating objects at a long distance.