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.

中文翻译：

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基于拼接叠加光学涡旋旋转多普勒效应的旋转轴测量

在大多数旋转多普勒效应 (RDE) 测量中，需要对准物体的光轴和旋转轴。但在旋转检测的实际应用中，该条件很难达到，严重影响了接收信号。此外，在从制造到物理实验的应用中，有必要将光束聚焦在旋转表面的旋转轴上。例如，衍射光学元件的制造需要将光束对准主轴的旋转轴。因此，如何确定旋转轴的方位角成为亟待解决的问题。基于一种新型的具有多个拓扑电荷 (TC) 的叠加涡旋光束，我们报告了一种仅通过单次 RDE 测量来确定旋转轴位置的新方案，大大提高了测量效率。根据模式分解和角动量和能量守恒，我们揭示了称为拼接叠加光学涡旋 (SSOV) 的新型结构光束的 RDE 机制，并解释了为什么具有不对称缺陷的 SSOV 对物体的旋转轴敏感。此外，为了证明该方法的有效性，进行了概念验证实验以检测物体旋转轴在八个方位角范围内的位置，即[iπ/4, (我+ 1)π/4](我= 0、1、2、3、4、5、6、7）。在这项研究中打破光学涡旋（OV）的对称性并添加额外参数的想法可能在光学操纵和通信中具有巨大的应用潜力。最后，考虑到不完整OV和SSOV的轨道角动量(OAM)模式纯度和质量在远场传播过程中会降低，本研究提出了一种新的SSOV预校正方法，克服了影响。在一定程度上是由 Gouy 相移和衍射引起的。结合惯性导航，上述方法还可应用于遥感、制造、物理实验等领域。