Abstract

Fresnel integrals continue to find new applications in various areas of human activity, including technology and music. However, performing calculations with them is often hindered by a mathematical peculiarity of these integrals, which is the rapidly oscillating functions of the basic variable. This circumstance complicates the numerical calculations when these integrals need additional integral transformation: convolution, Fourier transform, etc. The suggested solution of the problem consists of replacement of the complex Fresnel integral by a single rational function that simulates this integral in the entire area of its existence with an accuracy up to ${10}^{-6}$. The advantages of the suggested approach are confirmed by the concrete example.

© 2006 Optical Society of America

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