FFT calculation for Fresnel diffraction and energy conservation criterion of sampling quality

Abstract

Since Fresnel diffraction integral can be expressed in convolution form, it can be calculated by Fast Fourier Transform (FFf) method. It is regarded that the FFT diffraction calculation can be achieved only in the region of Fresnel diffraction. But in fact, Kirchhoff's formula and Rayleigh-Sommerfeld's formulae can be also rewritten in convolution form so that the diffraction problems can be calculated very accurately with FFT method. In this paper we will deduce the convolutional form of the formulas of Kirchhoff's and Rayleigh-Sommerfeld's diffraction calculation. Finally, according to the principle of conversation of energy, we present a criterion to judge whether the numbers of sampling for FFT diffraction calculation is reasonable.