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.

We propose a method for detecting the symmetry of rotating patterns based on the rotational Doppler effect (RDE) of light. The basic mechanisms of the RDE are introduced, and the spiral harmonic distribution of rotating patterns is analyzed. By irradiating the rotating pattern using a superimposed optical vortex and analyzing the amplitude of the RDE signal, the spiral harmonic distribution of the pattern can be measured, and then its symmetry can be detected. We demonstrate this method experimentally by using patterns with different symmetries and shapes. As the method does not need to receive the scattered light completely and accurately, it promises potential application in detecting symmetrical rotating objects at a long distance.

We demonstrated an efficient scheme of measuring the angular velocity of a rotating object with the detection light working at the infrared regime. Our method benefits from the combination of second-harmonic generation (SHG) and rotational Doppler effect, i.e., frequency upconversion detection of rotational Doppler effect. In our experiment, we use one infrared light as the fundamental wave (FW) to probe the rotating objects while preparing the other FW to carry the desired superpositions of orbital angular momentum. Then these two FWs are mixed collinearly in a potassium titanyl phosphate crystal via type II phase matching, which produces the visible second-harmonic light wave. The experimental results show that both the angular velocity and geometric symmetry of rotating objects can be identified from the detected frequency-shift signals at the photon-count level. Our scheme will find potential applications in infrared monitoring.

涡旋光是一种携带轨道角动量的空间结构光束，照射到旋转的平板物体表面时频率会发生移动，这一现象被称为光学旋转多普勒效应，通过测量光束频移可获得平板物体的旋转速率。频移受光束入射条件的影响，通过揭示入射条件影响规律，可实现任意入射条件下的旋转物体转速测量。首先，建立了速度投影模型，分析了光学旋转多普勒效应的产生机理。其次，通过理论推导得出了涡旋光任意入射条件下的旋转多普勒频移分布规律，并提出了提取物体旋转频率的理论方法。最后，搭建了旋转多普勒效应的实验装置，采用拓扑荷数为 $ \pm 18$的叠加态拉盖尔-高斯光束在四种不同入射条件下测量旋转多普勒频移谱，将实验频谱与理论频移曲线结合，测得物体的旋转频率，相对误差低于1%。

涡旋光束是一种携带轨道角动量且具有螺旋波振面的新型结构光场。自1992年Allen等首次证明了近轴条件下带有螺旋相位因子的光场具有轨道角动量以来，涡旋光束因其在光操控、光通信、光学测量和遥感等领域中的广泛应用而备受关注，特别是近年来涡旋光束在惯性测量领域的应用吸引了诸多学者的研究兴趣。文中主要涉及三个方面的内容：涡旋光束制备方法研究进展；涡旋光束在惯性测量领域中的关键应用，具体为基于涡旋光的旋转多普勒效应和量子陀螺；最后还就惯性测量对涡旋光束制备提出的新要求进行了讨论。

对于基于叠加态涡旋光和涡旋光零差探测等传统转速测量方式，光的远距离传输和发散等原因造成的信号光衰减会导致探测系统无法准确提取信号，而涡旋光平衡探测系统可以解决这一难题，但是以往的研究对该探测系统的精度和信噪比鲜有分析，这一定程度上限制了其工程化的进展。首先将零差探测系统作为对比项，通过分析不同转速下涡旋光平衡探测系统和零差探测系统测量精度的变化情况，证明了二者均可实现高精度测量，其次通过对比在不同信号光功率下二者的信噪比(SNR)，发现了在测量微弱信号时涡旋光平衡探测系统具有明显优势；最后，通过分析不同本振光功率对信噪比造成的影响，揭示了平衡探测信噪比和本振光功率之间的关系，阐明了信噪比随本振光功率变化的原因。