相干扫描干涉仪（CSI）被广泛应用于微纳米级别的表面轮廓测量、定量相位成像和相干光学层析术等领域。然而，CSI需要以较小的采样间隔捕获大量干涉图像实现重构，导致其较低的测量速度以及对环境干扰的高敏感性。近年来，光学频率梳（光频梳）独特的相干性质使其成为大视场CSI光源的理想选择，可溯源至原子钟的脉冲对准技术有望赋予CSI更高的精度。但采样对CSI测量速度的限制仍未得到有效解决。本文针对这一问题，在研究了基于光频梳的高精度脉冲对准算法的基础上，提出了降采样方法和基于外差干涉的相位补偿方法，构建了基于扫描重复频率的相干扫描干涉系统，将其应用于三维表面形貌的高精度快速检测，并进一步将该系统扩展至位姿测量领域，实现对非合作平面的快速三自由度测量。首先，本文研究了基于扫描光频梳重复频率的相干扫描干涉原理，对实验系统噪声、色散等基本参数进行了标定，并提出了一种基于分析傅里叶变换光谱相位的脉冲对准算法，实现了高精度、可溯源的相干测量。接着，针对CSI测量速度受限的问题，研究了降采样原理。由于相机带宽的限制，直接对CSI信号降采样会出现干涉对比度下降的现象，为此提出了两种解决方案：步进扫描重复频率同步曝光方法和基于外差干涉的相位补偿方法。第一种方法基于精确的重复频率控制，使扫描移相系统在每个需要曝光的采样点处停留一段时间用于曝光，从而解决了在线性扫描中，相机无法响应快速变化的干涉信号的问题。同时，还仿真分析了多项因素耦合对测量精度的影响，为降采样的实施提供了理论指导，并通过重构MEMS器件表面形貌验证了方法的可行性。考虑到步进扫描的速度受限于伺服控制响应，本文提出了第二种方法：通过声光调制器给干涉仪增加一个外差信号，降低原本线性移相中的高频载波相位，使其能够适配相机的测量带宽。实验表明，对于平面镜样品，该方法可以在每帧6.4 μm的扫描速度下实现2 nm的测量重复性。最后，基于这种全场式外差干涉仪，提出利用低相干空间干涉图来求解三自由度的方法，并应用于光滑或粗糙平面的三自由度测量。这种方法通过单光束即可实现快速、精密的多自由度测量。实验表明，该方法在100 Hz的刷新速度下，垂直距离的重复精度优于0.1 μm，俯仰角和偏摆角的重复精度优于1″。
Three-dimensional imaging systems play an extremely pivotal role in scientific research and industrial manufacturing. In order to obtain three-dimensional images at the micro-nanometer level, Coherent Scanning Interferometer (CSI) has been proposed and widely applied in fields such as surface profile measurement, quantitative phase imaging, and coherent optical tomography. However, CSI requires the capture of a large number of interference images at a small sampling interval for reconstruction, leading to a lower measurement speed and high sensitivity to environmental disturbances. In recent years, the advent of Optical Frequency Combs (OFCs) has brought revolutionary progress to the field of precision measurement. The unique coherence property of OFCs makes them an ideal choice for CSI light sources in large field of view, and pulse alignment technology that can be traced back to atomic clocks is expected to grant CSI with higher accuracy. Nevertheless, the limitation of sampling on CSI measurement speed has not been effectively solved. This dissertation targets this issue, proposes undersampling method and phase compensation method based on heterodyne interference based on the study of high-precision pulse alignment algorithms based on OFCs, constructs a CSI system based on scanning repetition frequency, applies it to surface topography inspection, and further extends the system to the field of pose measurement, realizing rapid three-degree-of-freedom measurement of non-cooperative planes.Firstly, this dissertation studies the principle of CSI based on scanning OFC repetition frequency, calibrates basic parameters such as system noise and dispersion, and proposes an efficient weighted least squares phase solving algorithm that is consistent with the system characteristics, achieving high-precision, traceable pulse alignment. The measurement algorithm is validated by measuring a step structure composed of gauge blocks.Next, facing the problem of limited CSI measurement speed, the undersampling principle is studied, the problem of contrast reduction faced by CSI when undersampling is directly applied is analyzed, and two solutions are proposed: stepped scanning repetition frequency synchronous exposure method, and phase compensation method based on heterodyne interference.The first method, based on precise repetition frequency control, allows the scanning phase shifting system to pause at each required exposure sampling point for a period of time for exposure, thus solving the problem in linear scanning where the camera cannot respond to rapidly changing interference signals. At the same time, the effects of factors such as vertical scanning step length, light source spectral width, temporal signal subdivision capability of the camera, and dynamic range of interference signal intensity on measurement accuracy are simulated and analyzed, providing theoretical guidance for the implementation of undersampling. The feasibility of the undersampling method is validated by measuring a MEMS device surface in an experiment.However, in stepped scanning, each sampling point needs to wait for about 20 ms of stabilization time before exposure, which also limits the measurement speed. Therefore, the second method proposed in this dissertation maintains the system in a linear phase shift scanning state, adds an extra heterodyne signal to the interferometer through an acousto-optic modulator, thereby compensating for the high-frequency carrier phase in the original linear phase shift. In this way, the carrier frequency can be customized without reducing the scanning speed, allowing it to adapt to the measurement bandwidth of the camera. The influences of different parameters on the measurement results are analyzed experimentally. For a plane mirror sample, a measurement repeatability of 2 nm can be achieved at a scanning speed of 6.4 μm per frame. Measurement results of a three-step sample and a Beijing Winter Olympics commemorative coin sample are demonstrated.Lastly, based on a full-field heterodyne interferometer, a method of using low-coherence spatial interference maps to solve three degrees of freedom is proposed and applied to the three-degree-of-freedom measurement of smooth or rough planes. This method can achieve fast, precise multi-degree-of-freedom measurement with a single beam, which is a novel approach not yet reported in the field of multi-degree-of-freedom measurement. The system‘s refresh speed of 100 Hz, the repeatability accuracy better than 0.1 μm for vertical distance, and the repeatability accuracy better than 1″ for pitch and yaw angles are validated through three-degree-of-freedom static tests and two-angle-coupled dynamic tests.
