The rotational Doppler effect (RDE), as a counterpart of the conventional well-known linear Doppler effect in the rotating frame, has attracted increasing attention in recent years for rotating object detection. However, the effect of the beam size on the RDE is still an open question. In this article, we investigated the influence of the size of the probe light; i.e., the size of the ring-shaped orbital angular momentum (OAM)-carrying optical vortex (OV), on the RDE. Both the light coaxial and noncoaxial incident conditions were considered in our work. We analyzed the mechanism of the influence on the RDE under the light coaxial, lateral misalignment, and oblique incidence conditions based on the small-scatterer model. A proof-of-concept experiment was performed to verify the theoretical predictions. It was shown that both the signal-to-noise ratio and the frequency spectrum width were related to the OV size. The larger the beam size, the stronger the RDE signal observed in the practical detection. Especially in the lateral misalignment condition, the large OV size effectively reduced the signal spreading and enhanced the signal strength. These findings may be useful for practical application of the optical RDE in remote sensing and metrology.

We reveal the mechanism of the noncoaxial rotational Doppler effect (RDE) of an optical vortex and report its application in discriminating the orientation of the rotating axis of the rotating body. In most cases of the RDE-based measurement, the beam axis must be aligned with the rotating axis of the rotational body to observe a good signal. Once the beam axis is not coaxial with the rotating axis, the RDE frequency shift would change related to the misalignment distance, which can be called the noncoaxial RDE. Here, we take the advantage of the misaligned RDE augment with precise light-field modulation and successfully realize the discrimination of the orientation of the rotating axis relative to the illuminating beam. We clarify the principle of noncoaxial RDE and explain why the incomplete optical vortex (OV) is sensitive to the position of the rotating axis. We switch the OV field into four quadrants synchronized with sampling by the data acquisition system, and conduct Fourier transformation of the signals. Combined with the fitting algorithm, the orientation of the rotating axis can be recognized directly. This method may find applications for the noncontact detection of rotating bodies in both industrial and astronomical scenarios.

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.

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.