光学学报, 2018, 38 (2): 0212002, 网络出版: 2018-08-30   

透射波前Zernike系数与波长的函数关系研究 下载: 1586次

Study on Functional Relationship between Transmitted Wavefront Zernike Coefficients and Wavelengths
作者单位
1 长春理工大学光电工程学院, 吉林 长春 130022
2 上海理工大学光电信息与计算机工程学院, 上海 200093
3 苏州慧利仪器有限责任公司, 江苏 苏州 215123
摘要
波前像差可以很好地反映光学系统的性能,波前检测结果通常用一组Zernike多项式线性组合表示。透射式光学系统波前需要在特定波长下检测,由于检测仪器的限制,目前只有少数波长的波前可以得到准确检测。提出一种新的思路,通过分析透射波前Zernike系数与波长的函数关系,间接反映波前随波长的变化规律,从而实现任意波长波前的检测。利用Zemax对光学系统建模,采集光学系统在不同波长时的波前Zernike系数,通过Matlab曲线拟合工具寻找Zernike系数与波长曲线可能存在的函数形式,并最终确定了Conrady-Zernike公式。模拟的光学系统使用这种解析式计算所得Zernike系数的最大误差在1%以内。结果表明透射式光学系统的波前Zernike系数与波长之间基本符合Conrady-Zernike公式的关系。
Abstract
Wavefront aberration can well reflect the performances of optical system. The test result of wavefront is usually expressed in a linear combination of Zernike polynomials. The wavefront of the transmission optical system needs to be tested at specific wavelengths. From now on, only a few wavelength wavefronts can be accurately tested because of the limitation of detection instrument. A new idea is put forward in this paper, the wavefront can be tested at any wavelength by analyzing the functional relationship between transmitted wavefront Zernike coefficients and wavelength, which can indirectly reflect the variation of the wavefront with the wavelength. The optical system is modeled by Zemax. The wavefront Zernike coefficients of the optical system at different wavelengths are collected. Then the possible function form of the curve of the Zernike coefficients and the wavelength are fitted by Matlab curve fitting tool. Finally, the Conrady-Zernike formula is determined. The maximum error of the calculated Zernike coefficients is within 1%, which is calculated by the Conrady-Zernike formula in the simulated optical system. The results show that the wavefront Zernike coefficients and the wavelength of transmitted optical system are basically consistent with the Conrady-Zernike formula.

张齐元, 韩森, 唐寿鸿, 罗春华, 付跃刚. 透射波前Zernike系数与波长的函数关系研究[J]. 光学学报, 2018, 38(2): 0212002. Qiyuan Zhang, Sen Han, Shouhong Tang, Chunhua Luo, Yuegang Fu. Study on Functional Relationship between Transmitted Wavefront Zernike Coefficients and Wavelengths[J]. Acta Optica Sinica, 2018, 38(2): 0212002.

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