Rotational object detection at noncoaxial light incidence based on the rotational Doppler effect

The rotational Doppler effect (RDE) of optical vortex which can be used to detect the rotation speed, has become a well-known phenomenon and a hot topic of research in recent years. However, because the beam axis must be coaxial with the rotational axis of the object, it can only be used to detect cooperative targets in practical application. Here, we provide a novel approach for measuring rotational speed under light non-coaxial incidence relative to the rotating axis that uses the adjacent frequency difference of rotational Doppler shift signals. Theoretically, the rotational Doppler shift is proportional to the OAM mode of the incident beam, and the nature of the OAM carried by each photon is a discrete or quantized quantity under off-axis conditions leading to the discrete distribution of the Doppler shift signals. Experimentally, by extracting the difference between two adjacent Doppler shift signals, the rotating speed of the object can be determined. Based on our method, the rotational speed of the object can be measured precisely without the pre-known information about the position of the rotating axis. Our work supplies a significant complement to the conventional RDE theory and we believe it may promote the realistic application of the optical RDE-based metrology.