Efficient Fresnel-transform algorithm based on fractional Fresnel diffraction

Abstract

The efficient Fresnel-transform algorithm (EFTA) is a computational tool that facilitates diffracted field analysis. The computational improvement that is achieved with the EFTA relative to the conventional double fast-Fourier-transform (FFT) algorithm results from the properties of fractional Fresnel diffraction. Some programming simplicities are shown to appear at numerous locations along the propagation axis. The number of those locations is determined by the fractional order. Some computational aspects of the method are presented and compared with those of the FFT algorithm.