Vortex phase-shifting digital holography for micro-optical element surface topography measurment
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摘要:
非接触、无损害的相移数字全息技术对微光学元件检测具有独特优势。因传统的相移数字全息技术需要对相移器进行精细控制和繁琐校准，同时其光路易受到机械振动干扰，导致全息再现像的质量降低。本文借助涡旋光特殊的相位分布，提出了一种基于涡旋相移数字全息的微光学元件表面形貌测量方法。该方法利用螺旋相位板调制涡旋相位，引入高精度相移。基于构建的涡旋相移数字全息显微实验装置，采用干涉极值法确定了相移干涉图之间的真实相移量，并对螺旋相位板的旋转角度与相移量的关系进行标定，实验验证了涡旋相移的可行性；对微透镜阵列进行了重复测量实验，将测试结果与ZYGO白光干涉仪的测试结果进行比较。结果表明：测量得到单个微透镜的平均纵向矢高为12.897 μm，平均相对误差为0.155%。所提方法可以实现对被测微光学元件表面形貌的高精度测量，具有易操作、稳定可靠、准确性高等优点。
Abstract:Non-destructive, non-contact phase-shifting digital holography technology has distinct advantages in identifying micro-optical components. As traditional phase-shifting digital holography technology requires fine control and cumbersome calibration of the phase shifter, furthermore, its optical path is susceptible to mechanical vibration interference, which reduces the quality of the holographically reproduced image. To solve the above problems, we propose a vortex phase-shifting digital holography for the micro-optical element surface measurement with the help of the special phase distribution of vortex light. The method utilizes a helical phase plate to modulate the vortex phase and introduce a high-precision phase shift. Based on the constructed vortex phase-shifting digital holographic microscopy experimental setup, the actual phase shifts between phase-shift interferograms were determined using the interferometric polarity method, the relationship between the rotation angle of the helical phase plate and the phase shift was calibrated, and the feasibility of the vortex phase shift was experimentally verified. Repeated measurement experiments were carried out on the micro-lens arrays, and the measurement results were compared with those of the ZYGO white light interferometer. The results indicate that a single micro-lens's average longitudinal vector height is 12.897 μm with an average relative error of 0.155%. The proposed method enables highly precise measurement of the surface topography of micro-optical elements. It offers the advantages of easy operation, high stability, and high accuracy.
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图 2 涡旋相移数字全息显微成像原理图
Figure 2. Schematic diagram of vortex phase-shifting digital holographic microscopy
图 3 涡旋相移数字全息显微成像实验装置
Figure 3. Experimental setup for vortex phase-shifting digital holographic microscopy
图 10 微透镜矢高与旋转角度误差之间的关系曲线
Figure 10. Relationship curves between micro-lens vector height and rotational angle error
表 1 相移全息图的实际相移量和相移误差
Table 1. Actual phase shift and phase shift error in phase shift holograms
No. Theoretical Phase
Shift/radActual Phase
Shift/radPhase Shift
Error/rad1 0 0 0 2 0.5π 0.4992π −0.0008π 3 π 0.9963π −0.0037π 4 1.5π 1.4876π −0.0024π 
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表 2 测量微透镜阵列纵向矢高实验结果
Table 2. Experimental results of the measured longitudinal vector height of micro-lens arrays
No. Vertical height of single
micro-lens/μmAbsolute
error/μmRelative
error/%1 12.906 0.011 0.085 2 12.917 0.000 0.000 3 12.920 0.003 0.023 4 12.898 0.019 0.147 5 12.921 0.004 0.031 6 12.875 0.042 0.325 7 12.897 0.020 0.155 8 12.860 0.057 0.441 9 12.871 0.046 0.356 10 12.903 0.014 0.108
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