引用本文: 曹庆源. 菲涅耳积分计算公式及其应用[J]. 武汉大学学报 ( 信息科学版), 1986, 11(2): 57-64.
Cao Qingyuan. The Calculating Formulas of the Fresnel Integral and Its Application[J]. Geomatics and Information Science of Wuhan University, 1986, 11(2): 57-64.
 Citation: Cao Qingyuan. The Calculating Formulas of the Fresnel Integral and Its Application[J]. Geomatics and Information Science of Wuhan University, 1986, 11(2): 57-64.

## The Calculating Formulas of the Fresnel Integral and Its Application

• 摘要: 菲涅耳积分是物理光学、微波技术与天线等多学科共用的特殊函数,其形式为上限可变而又不能积出的两个定积分,通常将其按变量u的不同区间分别用正或负幂级数计算。本文在原有公式的基础上研究出了简单、精密且变量复盖实数域的计算公式及其计算机程序。内容包括:(1)最佳分区点u1的选择;(2) u≤ut时菲涅耳积分的变比级数表达式;(3) u>u1时菲涅耳积分的三角函数表达式;(4)程序流程图;(5)抽样运行数据及检验结果。

Abstract: The Fresnel integral is a particular function in physical optics, especially in the application of the theory of diffraction, such as the diffraction of light, microwave technique, antenna, etc. The Fresnel integral may be calculated in the series which has positive powers when the variable is smaller or negative powers when the variable is greater. In this article a new calculated formula, which is simple and strict, is proposed. The article deals with. (1) the expressions of Fresnel integral used in a series which has a changeable ratio when u≤u_1; (2) the expressions used in trigonometric function when uu_1 (3) the determination of the optimal demarcating point u_1; (4) flow process diagrams; (5) the examination of the confidence of formulas, etc.

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