Scale corrections for faster evaluation of convergent Fresnel patterns

Abstract

Numerical calculation of Fresnel patterns through fast Fourier transforms usually requires an extremely large number of samples in order to fulfil the Nyquist sampling condition. In many applications, the cut-off frequency of the system is much below the limit fixed by our calculations. As a consequence of this, correct sampling may result in heavy processes that produce results of useless accuracy. Unfortunately, subsampling may introduce aliasing that may distort the final appearance of the diffracted pattern. In this paper, we present a simple method that permits subsampling the Fresnel pattern while maintaining the Nyquist condition, and thus preventing the appearance of aliasing effects in the calculation. Secondary effects of the subsamplings are rescaling the illuminating wavelength and the introduction of an effective low-pass filter. Some applications relative to the propagation of the light inside the human eye are also suggested in the text.