Calculation of diffraction patterns on a spatial surface

An approximated formulation of the Fresnel function is put forward and is used in the approximate evaluation of the Fresnel diffraction integral. By comparing the approximate formulation with the experimental measurements and calculations in the fast Fourier transform (FFT) method of the diffraction integral, we demonstrate that the proposed method is sufficiently accurate for calculating the Fresnel diffraction. For the diffraction field calculation on a spatial surface, the calculation speed of this method is usually higher than that of the FFT method.