Detection of angular acceleration based on optical rotational Doppler effect

Several parameters are derived and utilized in the design analysis and development of rotational bodies. They include angular momentum, angular velocity, and angular acceleration among others. In particular, angular acceleration describes the rate of change of angular velocity and can be categorized into a spin and orbital angular acceleration. The measurements of angular acceleration play a significant role in physics and engineering. Owing to the technological advancement, several sensors have been developed for detection and measurement of angular acceleration. Fiber optic gyroscope is a good example of such sensors. Unfortunately, the detection of angular acceleration based on the optical rotational Doppler effect has not been fully explored.

The rotational Doppler effects are generally induced by a body undergoing rotational motion and orbital angular momentum (OAM). Pioneered by Nienhuis, it has continuously attracted significant attention from researchers. This has led to various studies on induced Doppler frequency shift in OAM beams as well as the physical mechanisms and relationship between the rotational and linear Doppler shifts taking into consideration the momentum and energy conservation.

Recently, Beijing Institute of Technology researchers; Yanwang Zhai (PhD candidate), Shiyao Fu, Ci Yin, Heng Zhou, and led by Professor Chunqing Gao explored the detection of angular acceleration based on the optical rotational Doppler effect. This approach is fundamentally based on a remote sensing scheme. The work is currently published in the research journal, Optics Express.

Before this work, orbital angular momentum has been widely used in the detection of angular velocity. Despite their good performance, the effects of the misalignments between the light and rotational axes is still a big challenge. Several mitigation measures including the use of anti-shake devices and balancing the frequency and time resolutions have been proposed. The authors analyzed the beat frequency signals of the orbital angular momentum beams of a non-uniform spinning body to detect angular acceleration. The object was probed with Laguerre-Gauss beams to produce the rotational Doppler frequency shifts. The detection system was constructed to collect the beating signals produced by the Laguerre-Gauss beams back-scattered from the spinning body.

Beat frequency signals of different kinds were analyzed in both time and frequency domains. Even though the angular velocity of a rotational body is time-dependent, the orbital angular momentum components in the scattered light were never affected by the change in time. As such, the change rate of the frequency shift was observed to be proportional to the angular acceleration of the body. By employing different angular accelerations of the rotor as well as different modes of the probe beams, the evolution of the angular velocity in time was investigated. The obtained results were consistent with the theoretical estimations. This enabled investigation of the measurement errors of different probes with different topological charges.

In summary, Beijing Institute of Technology scientists successfully demonstrated the use of the rotational Doppler frequency shift of the returned signals to predict the angular acceleration of a spinning object for the first time. The study will, therefore, lead to the development of advanced angular acceleration measurements and detection techniques for application in various disciplines.