Optical RDE-based detection of the rotating objects free of obstructions

Abstract

Rotational Doppler effect (RDE), as a counterpart of the conventional linear Doppler effect in the rotating frame, has attracted increasing attention in recent years on rotational object detection. In practical applications, it is common to see the condition that the beam is obstructed or not fully illuminated on the object, especially in long-rang detection conditions. For example, the fan blades are always wrapped inside the frame, the rotors of engines are arranged inside the machine, to name a few. How to realize the rotational speed measurement when the OV cannot fully illuminate the rotating target is a significant issue for the application of the RDE metrology. However, the principle of the RDE of fragmental optical vortex (FOV) has not been investigated yet. Here, we investigate the RDE of the fragmental optical vortex for the first time. Based on the orbital angular momentum (OAM) mode expansion technique, we establish the relationship between the OAM spectrum and the RDE frequency shift of FOV. The mechanism of the rotational speed extraction is analysed and validated by the numerical simulation and experiments. Further, a dual Fourier transformation method is proposed to accurately obtain the rotational speed which successfully overcome the problem of the discrete distribution of the RDE signals. Our work may be useful for practical remote sensing based on the optical RDE metrology.