波面重构中非圆域Zernike正交基底构造方法

发布时间：2018-02-12 12:45

本文关键词： 光学测量波面拟合 Zernike多项式非圆域正交化系数矩阵　出处：《光学技术》2017年03期 　论文类型：期刊论文

【摘要】：针对非圆域波面拟合中Zernike多项式失去正交特性、拟合系数交叉耦合的问题,提出非圆域Zernike正交基底函数构造方法。以圆Zernike为基底,采用Gram-Schimdt正交组构造方法,线性表出单位正交基底。通过构造不同遮光比环形光阑下的正交基底与环Zernike多项式进行比较,验证了此方法的正确性。然后采用圆Zernike多项式和构造的新基底对矩形光阑下的波面进行了拟合,从拟合残余误差、各项基底系数的稳定性、传递矩阵的条件数等分析,结果表明针对特定的非圆域构造的新基底可靠性和抗扰动能力优于圆Zernike多项式。此方法不需要具体求出基底的解析表达式,不同非圆域仅是正交化系数矩阵发生改变,为非圆域正交基底构造提供了一种新途径。
[Abstract]:In order to solve the problem that Zernike polynomials lose their orthogonality and cross coupling of fitting coefficients in non-circular domain wave surface fitting, a method of constructing Zernike orthogonal base functions in non-circular domain is presented. The method of constructing Gram-Schimdt orthogonal group is used to construct the Zernike orthogonal base in non-circular domain. The orthogonal bases with different shading ratios are constructed and compared with the ring Zernike polynomials. The correctness of the method is verified, and then the wavefront under the rectangular aperture is fitted by using the circular Zernike polynomial and the constructed new substrate. The residual error of fitting, the stability of each base coefficient, the condition number of the transfer matrix, and so on are analyzed. The results show that the reliability and anti-disturbance ability of the new basement constructed in the specific non-circular domain is superior to that of the circular Zernike polynomial. This method does not need to obtain the analytical expression of the basement, and the different non-circular domains are only changed by the orthogonal coefficient matrix. It provides a new way for the construction of non-circular orthonormal basement.
【作者单位】：北京理工大学精密光电测试仪器及技术北京市重点实验室;哈药集团制药总厂;
【基金】：国家自然基金仪器专款(61327010)
【分类号】：O174.14;O436.1

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