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高阶截断误差的斜率和曲率混合型波前重构算法

ISSN号：1002-1582
期刊名称：光学技术
时间：2013.9.15
页码：450-455
分类：O439[机械工程—光学工程;理学—光学;理学—物理]
作者机构：[1]北京理工大学光电学院光电成像技术与系教育部重点实验室,北京100081
相关基金：国家自然科学基金重点项目（60938003）;国家科技重大专项;国家自然科学基金青年科学基金项目（61205164）;北京理工大学基础研究基金（20120442004）资助课题
相关项目：超大数值孔径正交位相光栅横向剪切干涉关键技术基础研究

关键词：光学测量, 混合型重构算法, 泰勒展开, 截断误差, optical measurement, hybrid reconstruction algorithm, Taylor expansion, truncation error

中文摘要：

研究了斜率和曲率混合型区域波前重构算法，提出了通过减小重构方程的截断误差来提高波前重构精度。利用泰勒展开推导了波前值、波前斜率和曲率值三者间的数学关系，得到了截断误差为相邻两波前测量点间距五次方的重构方程。将该方程用于波前重构中，提出了一种新的斜率和曲率混合型波前重构算法。通过重构仿真对比了该混合型算法与现有混合型算法的波前重构误差。结果表明，在忽略测量噪声的情况下，提出的算法将相对重构误差降低了约两个数量级；在考虑测量噪声的情况下，提出的算法在对高阶像差的重构时，具有更小的相对重构误差。提出的高阶截断误差的混合型波前重构算法较现有的混合型算法需要的计算量更小，更利于实时波前重构。

英文摘要：

Hybrid gradient and curvature zonal wave/font reconstruction algorithm is researched. It is proposed that wavefront reconstruction accuracy can be improved by reducing the truncation error of the reconstruction equation. The mathematical relationship for wavefront values, wavefront gradients and curvatures is calculated using Taylor expansion, obtaining the reconstruction equation whose truncation error is the 5th order of the two adjacent estimated points＇ inter val. Applying the obtained equation to wavefront reconstruction, a new hybrid gradient and curvature wavefront recon struction algorithm is proposed. The reconstruction error of the proposed algorithm and that of the algorithm published in the past are compared through simulations. It shows that the relative reconstruction error is reduced about two orders of magnitude by the algorithm proposed when measurement noise is ignored; when measurement noise is considered, the al gorithm proposed gives apparently smaller relative reconstruction error for the reconstructions of high-order aberrations. Moreover, less calculation is needed for the algorithm proposed, and the algorithm is more appropriate in real-time wave front measurement.

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