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This article introduces two approximations that allow the evaluation of Fresnel integrals without the need for using numerical algorithms. These equations accomplish the characteristic of being continuous in the same interval as Fresnel. Both expressions have been determined applying the least squares method to suitable expressions. Accuracy of equations improves as x increases; as for small values of x, it is possible to achieve an absolute error less than 8×10-5. To probe the efficiency of the equations, two case studies are presented, both applied in the optics field. The first case is related to the semi-infinite opaque screen for Fresnel diffraction. In this case study Fresnel integrals are evaluated with the proposed equations to calculate the irradiance distribution and the Cornu spiral for diffraction computations of the Fresnel diffraction; obtained results show a good accuracy. The second case is related to the double aperture problem for Fresnel diffraction.

Approximation of Fresnel Integrals with Applications to Diffraction Problems