哈特曼法焦度测量模型的误差分析及修正

杨金龙; 贾宏志; 金涛; 项华中; 张大伟; 庄松林

doi:10.12086/oee.2021.200238

哈特曼法焦度测量模型的误差分析及修正

doi: 10.12086/oee.2021.200238

详细信息

作者简介:
杨金龙(1990-)，男，硕士研究生，主要从事焦度计与旋光仪的研究。E-mail: 870015801@qq.com

通讯作者:
金涛(1985-)，男，博士，副教授，主要从事精密测量的研究。E-mail: jintao@usst.edu.cn

中图分类号: TN29
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出版历程
- 收稿日期: 2020-06-28
- 修回日期: 2020-09-18

Error model analysis and correlation correction of Hartmann's focimeter

More Information

Corresponding author: Jin Tao, E-mail: jintao@usst.edu.cn

摘要

摘要: 为了减少屈光度测量误差，提高精度。本文针对哈特曼法焦度测量建立了较详细的误差模型，着重分析了光源的色散误差、入射光与透镜未垂直、光电探测器中心定位不准、透镜倾斜、光源光线主轴与透镜主轴未重合所引起的屈光度测量误差。结果表明，得出由于光电探测器上中心提取的不准确，会对最终的结果产生较大的误差。并由此提出了双重双线性插值结合拟合法来求取中心的方法，并证明了其有效性和准确性。
- 哈特曼光阑 /
- 焦度测量 /
- 误差模型 /
- 图像处理 /
- 中心定位
Abstract: In order to reduce the error and improve the measurement accuracy, a more detailed error model is established for the Hartmann method of focal power measurement in this paper. It focuses on the analysis of several problems that cause the error of refraction problems, including the dispersion error of the light source, the inaccurate of the photodetector's central positing, the tilt of lens, misalignment between incidence axis and main axis of lens, and the incident light and the lens are not perpendicular. At last, it is concluded that the inaccuracy of the center extraction on the photodetector will cause a large error to the final result. For all these reasons, a method of dual bilinear interpolation combined with a fitting method to find the centroid is proposed, proving its effectiveness and accuracy.
- Hartmann diaphragm /
- focimeter /
- error model /
- image processing /
- centroid calculation

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图 1 哈特曼法测量模型

Figure 1. Measuring model for the Hartmann method

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图 2 透镜与光阑的实际位置关系图

Figure 2. Actual position diagram of the lens and diaphragm

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图 3 L₁所引起的屈光度误差曲线

Figure 3. Curves of diopter error caused by neglecting L₁

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图 4 透镜倾斜的测量模型

Figure 4. Measurement model of lens tilt

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图 5 透镜角度偏转导致的屈光度误差变化

Figure 5. Variation of diopter error caused by lens deflection

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图 6 主轴外光点射入透镜模型

Figure 6. A lens model for an external light spot of spindle

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图 7 光轴与透镜主轴的偏转角度导致的误差变化曲线

Figure 7. Error curve caused by the deflection angle between the optical axis and lens axis

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图 8 像素差导致的屈光度误差变化曲线

Figure 8. Diopter error curve caused by pixel difference

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图 9 算法的流程框图

Figure 9. Flow chart of the whole algorithm

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图 10 高斯光斑所对应的灰度图像

Figure 10. Gray image corresponding to the Gaussian spot

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图 11 高斯光斑所对应的二值化图像

Figure 11. Binary image corresponding to the Gaussian spot

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图 12 双线性插值算法示意图

Figure 12. Schematic diagram of the bilinear interpolation algorithm

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图 13 (a) 插值前高斯曲面图；(b) 插值前高斯曲面图

Figure 13. (a) Gauss surface figure before interpolation; (b) Gauss surface figure after interpolation

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图 14 (a) 插值前的图像边缘信息图；(b) 插值后的图像边缘信息图

Figure 14. (a) Image edge information before interpolation; (b) Image edge information after interpolation

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表 1 中心坐标及误差

Table 1. The results for centroid coordinates and error

插值位置间距	中心坐标	中心定位误差d_i
0.35	(59.681，59.655)	0.471
0.3	(59.892，59.857)	0.180
0.25	(59.878，59.860)	0.186
0.2	(59.877，59.841)	0.201
0.15	(59.969，59.967)	0.045
0.1	(59.928，59.887)	0.134
0.05	(59.890，59.854)	0.183

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