张超, 袁群, 张佳乐, 冀翼, 高志山, 闫钧华. 白光显微干涉三维形貌测量中的移相误差校正方法[J]. 红外与激光工程, 2022, 51(7): 20220050. DOI: 10.3788/IRLA20220050
引用本文: 张超, 袁群, 张佳乐, 冀翼, 高志山, 闫钧华. 白光显微干涉三维形貌测量中的移相误差校正方法[J]. 红外与激光工程, 2022, 51(7): 20220050. DOI: 10.3788/IRLA20220050
Zhang Chao, Yuan Qun, Zhang Jiale, Ji Yi, Gao Zhishan, Yan Junhua. Calibration method of the phase-shifting error for the topography measurement utilizing white light interferometric microscopy[J]. Infrared and Laser Engineering, 2022, 51(7): 20220050. DOI: 10.3788/IRLA20220050
Citation: Zhang Chao, Yuan Qun, Zhang Jiale, Ji Yi, Gao Zhishan, Yan Junhua. Calibration method of the phase-shifting error for the topography measurement utilizing white light interferometric microscopy[J]. Infrared and Laser Engineering, 2022, 51(7): 20220050. DOI: 10.3788/IRLA20220050

白光显微干涉三维形貌测量中的移相误差校正方法

Calibration method of the phase-shifting error for the topography measurement utilizing white light interferometric microscopy

  • 摘要: 白光显微干涉术通过驱动干涉显微物镜垂直扫描移相,采集低相干干涉图序列,定位干涉包络中的零光程差位置,获取待测表面的三维形貌。微观形貌的计算由获取粗略形貌的垂直扫描(VSI)算法和获取精细形貌的移相(PSI)算法两部分组成。通常情况下,设置垂直扫描移相的步长为八分之一中心波长,但移相器误差和干涉显微物镜数值孔径效应等都会使得移相量偏离π/2。文中采用基于对比度变化重心提取的VSI算法,4M幅法和7幅法两种PSI算法,分别讨论了两种类型移相误差对形貌计算的影响。理论和数值分析结果表明,在宽带光作用下,7幅法仍对移相误差不敏感,4M幅法产生的精细相位误差形式恰好与干涉物镜数值孔径效应对条纹展宽的影响相一致,在从精细相位转换为精细形貌时相互抵消。因而,采用基于对比度变化重心提取的VSI算法和4M幅PSI算法计算形貌数据,干涉物镜数值孔径效应造成的移相误差无影响,移相器误差造成的形貌复原误差可以通过预先测量已知高度的标准台阶进行标定去除。应用上述移相误差校正方法测量了高度为460 nm的台阶,形貌测试结果正确且鲁棒。

     

    Abstract: Sequence of low coherence interferograms were captured during the vertical scanning of the interferometric microscope in the measurement procedure of the white light interferometric microscopy, and thus the topography of the surface under test was retrieved through determining the locations where the optical path difference (OPD) was zero in the envelope of the correlogram. The calculations of the topography for the micro-structures were composed of the vertical scanning interferometric (VSI) algorithm determining the coarse map and the phase-shifting interferometric (PSI) algorithm retrieving the fine map. Usually, the vertical scanning step was set as one eighth of the central wavelength, but the phase-shifting departures from π/2 inevitably due to the phase shifter error as well as the numerical aperture (NA) effect of the interferometric microscope. In this manuscript, the center-of-gravity solving of the visibility curves was adopted as VSI algorithm, and the 4M-frame method as well as the 7-frame method were both utilized as PSI algorithm respectively. The effect of the phase-shifting error on the topography measurement adopting the three above mentioned methods was discussed. Both theoretical derivations and simulation analysis demonstrate that the 7-frame method was insensitive to phase-shifting errors even under the low coherence illuminations. The fine phase error induced by phase-shifting error utilizing the 4M-frame method was by lucky coincides the form of the NA effect increasing the fringe spacing, and they were cancelled out during the transform from the fine phase to the topography. Therefore, adopting the center-of-gravity method as VSI algorithm and the 4M-frame method as the PSI algorithm, the phase-shifting errors arising from NA effect can be ignored, and the topography can be calibrated confronting the phase shifter error through measuring a certificated step standard in advance. A step height of 460 nm was measured utilizing the proposed method, and the topography demonstrate that it was both accurate and robustness.

     

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