Calculation of Fresnel diffraction from 1D phase step by discrete Fourier transform

When a part of an optical wave-front experiences a sharp change in its phase, Fresnel diffraction becomes appreciable. Sharp change in phase occurs as a wave-front strikes with a phase step. The intensity distributions of diffraction patterns of the phase step is formulated by applying Fresnel-Kirchhoff integral. For while the incident light on the step is coherent, the Fresnel-Kirchhoff integral can be solved by using familiar Fresnel integrals. But, when the incident light is partially coherent, one can not express the diffraction integral as the Fresnel integrals and the problem is summarized in solving some unusual integrals. In this report, we propose Fourier transform method for solving the Fresnel-Kirchhoff integral. In this regard we use discrete Fourier transform method and calculate Fresnel diffraction from the 1D phase step by FFT-based algorithms. This method does not have any restriction on the coherence and profile shape of the incident light. We show that the method have appropriate solutions for coherent and partially coherent lights. For the case of the coherent light illumination of the step, the obtained results are in good agreement with the calculated results by using the Fresnel integrals in reported literatures.