The Calculating Formulas of the Fresnel Integral and Its Application

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.