Rotating axis measurement based on rotational Doppler effect of spliced superposed optical vortex

In most rotational Doppler effect (RDE) measurements, the optical axis and the rotating axis of the object are required to be aligned. However, the condition is very difficult to achieve in practical applications of rotation detection, which seriously affects the received signal. Moreover, it is necessary to focus the beam on the rotating axis of a rotating surface in applications ranging from manufacturing to physical experiments. For example, the manufacture of diffraction optical elements requires aligning the beam to the rotating axis of the spindle. Therefore, how to determine the azimuth of the rotating axis has become an urgent problem to be solved. Based on a new type of superposed vortex beam with multiple topological charges (TCs), we report a new scheme for determining the position of rotating axis by only single RDE measurement, which greatly improves the measurement efficiency. According to the mode decomposition and conservation of angular momentum and energy, we reveal the RDE mechanism of the new structured beam named spliced superposed optical vortex (SSOV) and explain why the SSOV with asymmetrical defect is sensitive to the rotating axis of the object. In addition, in order to prove the effectiveness of the method, a proof-of-concept experiment is conducted to detect the position of object’s rotating axis in eight azimuth ranges, i.e., [iπ/4, (i + 1)π/4](i = 0, 1, 2, 3, 4, 5, 6, 7). The idea of breaking the symmetry of the optical vortex (OV) and adding additional parameters in this study may have great potential for applications in optical manipulation and communication. Finally, considering that the orbital angular momentum (OAM) mode purity and quality of the incomplete OV and the SSOV will decrease during the far-field propagation, a new method for pre-correction of SSOV is proposed in this research, which overcomes the effects caused by Gouy phase shift and diffraction to some extent. Combined with inertial navigation, these methods above can also be applied to remote sensing, manufacturing, and physics experiments.