Application of basic optics principles for the determination of effective limits of numerical diffraction methods

The range of application of the methods of angular spectrum and Fresnel-Fraunhofer transform to compute numerical diffraction is evaluated via the basic optics concepts of Babinet's principle and Frenel's zones number. Conventionally, such limit is determined by assessing the correct sampling of the impulse response of the free space for each method as it evolves from the aperture to infinity. In this paper we make combined use of Babinet's principle and Fresnel's zones number to determine the phase that an optical wave field must exhibit after being propagated a given distance; the deviation of the phase of the optical field from the forecasted value is the metric utilized for testing the validity of the propagation method. The results show that the limit of application of the methods angular spectrum and Fresnel-Fraunhofer transform must be revisited. We propose a new limit that accounts for the number of pixels utilized for the correct sampling of a phase jump.