Fast numerical calculation of Fresnel patterns in convergent systems

Abstract

In this communication, the authors study diffraction patterns calculation under convergent illumination. We analyze known fast algorithms using the Fourier transform and the fractional Fourier transform (FRT). We show that interference between convergent phase factor and the kernel of the different numerical Fresnel transformation may impose serious restrictions on the range of distances, where diffraction patterns can be accurately calculated. We review free space diffraction patterns calculation algorithms. In that case, the FRT provides a unified algorithm for the calculation of amplitude patterns in all the range of distances. On the contrary, we show below that, when convergent illumination is used, none of the algorithms is capable of providing a unified framework of calculation for the entire region of interest from object to focus.