| 基于Mathematica5.0的环域Zernike多项式符号计算方法 |
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| 引用本文： | 侯溪,伍凡,吴时彬,陈强.基于Mathematica5.0的环域Zernike多项式符号计算方法[J].四川大学学报(自然科学版),2005,42(2):305-310. |
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| 作者姓名： | 侯溪 伍凡 吴时彬 陈强 |
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| 作者单位： | 中国科学院光电技术研究所,成都,双流,610209;中国科学院研究生院,北京,100039;中国科学院光电技术研究所,成都,双流,610209 |
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| 基金项目： | 国家863高技术资助基金 |
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| 摘 要： | 在中心遮拦光学元件的波面拟合中，环域Zernike多项式具有优良的性能．该多项式在圆Zernike多项式的基础上，引入新的变量ε-遮拦比，进行Gram-Schimdt正交化得到．且部分项以递推公式形式表示，使得基函数表达式形式异常复杂，推导困难．基于Mathematica5．0强大的符号计算功能，用符号计算方法实现了计算．给出了具体的计算步骤和程序流程，计算结果较准确可靠．
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| 关 键 词： | 环域Zernike多项式 符号计算 波面拟合 中心遮拦 |
| 文章编号： | 0490-6756(2005)02-0305-06 |
Symbolic Algorithm of Zernike Annular Polynomials Based on Mathematica5.0 |
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| HOU Xi,WU Fan,WU Shi-bin,CHEN Qiang.Symbolic Algorithm of Zernike Annular Polynomials Based on Mathematica5.0[J].Journal of Sichuan University (Natural Science Edition),2005,42(2):305-310. |
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| Authors: | HOU Xi WU Fan WU Shi-bin CHEN Qiang |
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| Abstract: | Annular Zernike polynomials have advantages in wavefront fitting with central obscuration. Through introducing new variable-obscuration ratio, Annular Zernike polynomials are obtained on the basis of standard Zernike circle polynomials using Gram-Schmidt orthogonalization procedure, but many terms are given in recurrence formula, which make them very complicated and hard for use. With Mathematica5.0's strong symbolic calculation, the polynomial term expressions are inferred, program flow is presented,and results have been proven to be accurate and dependable. |
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| Keywords: | annular Zernike polynomial symbolic calculation wavefront fitting central obscuration |
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