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摘要:
在扫描相位测量轮廓术中，需要先将不同位置的物体匹配到同一点，再根据相移算法提取相位信息，而像素匹配精度与相移算法均会影响测量精度。为此，采用显微系统，根据其远心光路特性实现物体移动量与像素移动量的等量转换；通过交替采集白场图像和条纹图像，由白场图像通过光流法实现精确的像素匹配，再根据物体匀速运动特点实现条纹图像的精确像素匹配；根据初始条纹周期选择基本符合满周期的
N 幅条纹图，由任意步数相移方法计算出截断相位分布，再通过概率密度函数搜索最佳条纹周期，进而得到准确的相位信息，完成物体形貌测量。实验表明，所提方法有效提高了测量精度，相移算法也适用于任意N (N ≥3)幅图，在模拟工业流水线场景中物体的三维测量时，RMSE (均方根误差)可达0.008 mm左右。Abstract:In scanning PMP, it is essential to first match different positions of the object to the same point, and then extract phase information using phase-shifting algorithms. Both pixel-matching accuracy and phase-shifting algorithms influence measurement precision. To address this, a microscopic system is employed, leveraging its telecentric optical path characteristics to achieve equal conversion between object displacement and pixel displacement. By alternately capturing white-field and fringe images, precise pixel matching is realized through optical flow in the white-field images, followed by accurate pixel matching of the fringe images based on the object's uniform motion. A set of
N fringe images, closely matching a full cycle based on the initial fringe period, is selected to compute the truncated phase distribution using an arbitrary step phase-shifting method. The optimal fringe period is then identified through a probability density function, leading to the accurate extraction of phase information and the completion of the object morphology measurement. Experimental results demonstrate that the proposed method significantly enhances measurement accuracy, with the phase-shifting algorithm applying to anyN ≥3 images, making it particularly suitable for 3D measurements of objects in industrial production lines, achieving an RMSE measurement accuracy of about 0.008 mm. -
Overview: In recent years, fringe projection profilometry has emerged as a powerful tool for measuring and inspecting the three-dimensional (3D) morphology of objects. Among them, phase measurement profilometry (PMP) has garnered significant attention due to its high precision. Traditionally, at least three deformed fringe images are required for phase retrieval. To achieve higher precision, even more deformed fringe images are typically needed. In industrial applications, such as inspections on production lines where new samples continuously flow in and out, or to measure large samples with a set of small fields of views for high precision. This necessitates a motion scheme to complete the inspection process. Therefore, it will be promising to integrate the phase-shifting process of PMP with lateral motion. This type of lateral scanning process has been validated in white light interferometry and structured illumination microscopy. This paper proposes a scanning microscopic PMP that combines phase shifting with object translation, reducing measurement complexity and enhancing measurement efficiency. In this design, the measuring unit is fixed and the measuring object is moved along the translation stage. The camera is synchronized with the translation stage and the switching of the white light and structured light illuminations. Then sequential images will be captured with one deformed image and one white light image continuously. The phase drilling process consists of two main steps. The first step is pixel matching, which is used to align the images captured at different positions. The white light images are used to find the amount of pixel shift by optical flow methods, which can reach a sub-pixel level precision via linear interpolation. Then the pixel matching of the fringe images will be fulfilled while we assume the translation is consistent. The second step is to decipher the phase with these matched fringe images. Here, an arbitrary N-step phase-shifting technique is adopted instead of the classical N-step phase-shifting approach. Moreover, a telecentric optical path system is employed to ensure consistency between the actual object movement and pixel shift. The initial phase shift is determined by the offset pixels and the initially estimated fringe period, which is optimized through a probability density function. The experiments in this paper compare static and dynamic results, with the static position fixed as the starting point for dynamic measurements to ensure consistent comparison. The results demonstrate the feasibility of the proposed method, achieving measurement accuracy comparable to traditional PMP systems, with a maximum measurement accuracy of 0.008 mm in planar validation experiments.
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图 2 不同周期计算的截断相位PDF曲线及其RMSE曲线。(a)不同周期计算的截断相位的概率密度分布；(b)标定的初始周期和最佳周期计算的结果对比；(c)不同周期计算结果的RMSE分布；(d)不同周期计算的截断相位与静态12步相移的RMSE
Figure 2. PDF distribution with different phase shift errors and their error curves. (a) The PDF of the wrapped phase calculated at different periods; (b) Comparison of the results of the period of calibration and the optimal period calculation; (c) RMSE distribution of calculation results at different periods; (d) RMSE between wrapped phase and static 12-steps phase-shift calculated at different periods
图 6 硬币测量结果。(a, g),(b, h),(c, i)静态3、6和12步相移；(d, j) ,(e, k),(f, l)所提方法3、6和12步扫描相移结果
Figure 6. The measurement result of a coin. (a, h),(b, i),(c, j)3, 6, 12-step of classic phase shift; (d, k),(e, l),(f, m) Proposed method 3, 6, 12-step scanning phase shift
图 7 不同扫描步数与静态相移的相位误差
Figure 7. Phase error of different scanning steps and static phase shift
表 1 光流法计算得到的匹配量与相移量
Table 1. The matching quantity and phase-shift quantity calculated by optical flow method
白场/第2k-1帧 1 3 5 7 9 11 13 15 17 19 21 23 匹配量/pixel [0 0] [2.4 0.1] [4.6 0.1] [7.2 0.2] [9.4 0.2] [11.6 0.2] [14.2 0.2] [16.5 0.2] [18.7 0.2] [21.3 0.3] [23.5 0.3] [25.8 0.3] 条纹场/第2k帧 2 4 6 8 10 12 14 16 18 20 22 24 相移量/rad 0 0.656 1.257 1.967 2.568 3.169 3.880 4.508 5.109 5.819 6.420 7.048 
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表 2 不同步数扫描截断相位
Table 2. RMSE of different steps scan wrapped phase
扫描步数RMSE/rad 参与计算的图像序号 硬币位置1 硬币位置2 3步 2, 8, 16 0.0457 0.0386 6步 2, 4, 6, 10, 14, 18 0.0319 0.0289 12步 全部 0.0296 0.0262
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表 3 不同高度平面的误差分析
Table 3. Error analysis of planes with different heights
0.4 mm 1.2 mm 2 mm m1/mm 0.3973 1.2002 1.9936 m2/mm 0.3967 1.1937 1.9907 RMSE1/mm 0.0095 0.0099 0.0087 RMSE2/mm 0.0120 0.0114 0.0116
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