Freeform surface measurement method based on laser differential confocal with isoclinic line-based rapid focus tracking

XU Bei; TANG Yingqi; DONG Hangzhou; WANG Yun

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Freeform surface measurement method based on laser differential confocal with isoclinic line-based rapid focus tracking

Beijing Institate of Technology 85th Anniversary | 更新时间：2025-09-22

- Freeform surface measurement method based on laser differential confocal with isoclinic line-based rapid focus tracking
- OPTICAL TECHNIQUE Vol. 51, Issue 5, Pages: 541-548(2025)
- 作者机构：
  
  北京理工大学光电学院复杂环境智能感测技术工信部重点实验室，北京 100081
- 作者简介：
- 基金信息：
- DOI：
  CLC： TP394.1;TH691.9
- Received：12 April 2025，
  
  Revised：2025-05-25，
  
  Published：20 September 2025
- 稿件说明：
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徐蓓,唐颖奇,董航舟等.等倾角线快速跟焦的激光差动共焦自由曲面测量方法[J].光学技术,2025,51(05):541-548.

XU Bei,TANG Yingqi,DONG Hangzhou,et al.Freeform surface measurement method based on laser differential confocal with isoclinic line-based rapid focus tracking[J].OPTICAL TECHNIQUE,2025,51(05):541-548.
徐蓓,唐颖奇,董航舟等.等倾角线快速跟焦的激光差动共焦自由曲面测量方法[J].光学技术,2025,51(05):541-548. DOI：

XU Bei,TANG Yingqi,DONG Hangzhou,et al.Freeform surface measurement method based on laser differential confocal with isoclinic line-based rapid focus tracking[J].OPTICAL TECHNIQUE,2025,51(05):541-548. DOI：

摘要

针对逐点扫描测量自由曲面时法向倾角变化所引入的非线性误差导致精度变差的问题，提出了一种基于等倾角线快速跟焦的差动共焦自由曲面测量方法。方法利用改进的相干点漂移（CPD）配准算法，解算被测自由曲面（FSUT）的精确位姿，基于FSUT的精确位姿规划多条等倾角线；通过传感器轴向扫描获取不同等倾角线上光强与离焦量的关系，以轴向响应光强作为反馈沿等倾角线跟踪FSUT轮廓；利用归一化差动共焦轴向响应光强与离焦量之间的非线性误差对小角度变化不敏感的特性，通过沿等倾角线跟焦实现自由曲面快速扫描测量。实验结果表明，所提方法的等倾角线跟踪误差为±70nm，对离焦量计算精度的影响远小于差动共焦测量分辨力，相较于传统差动共焦测量方法效率至少提升至5倍；与ZYGO干涉仪数据点对点做差的面形峰谷（PV）值为9nm，均方根（RMS）值为1nm，实现了自由曲面的高精度、快速测量。

Abstract

To address the issue of measurement accuracy degradation caused by varying nonlinear errors induced by normal inclination angle changes during point-by-point scanning of freeform surfaces

an isoclinic line-based rapid focusing differential confocal method for freeform surface measurement was proposed. The method utilizes an improved Coherent Point Drift （CPD） registration algorithm to calculate the precise pose of the Freeform Surface Under Test （FSUT）. Based on the precise pose of the FSUT

multiple isoclinic lines are planned. By performing axial scanning with the sensor

the relationship between light intensity and defocus amount on different isoclinic lines is obtained. The axial response light intensity is used as feedback to track the contour of the FSUT along the isoclinic lines. Leveraging the characteristic that the non-linear error between the normalized differential confocal axial response light intensity and defocus amount is insensitive to small angle changes

fast scanning measurement of freeform surfaces is realized by focusing along isoclinic lines. Experimental results show that the tracking error of the isoclinic lines in the proposed method is ±70 nm

which has a negligible impact on the calculation accuracy of defocus amount compared with the differential confocal measurement resolution. Compared with the traditional differential confocal measurement method

the efficiency is increased to at least 5 times higher; the Peak-to-Valley （PV） value of the surface profile obtained by point-to-point subtraction with ZYGO interferometer data is 9 nm

and the Root Mean Square （RMS） value is 1 nm

achieving high-precision and fast measurement of freeform surfaces.

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