The relation between light diffraction and the fractional Fourier transform

摘要

The relation between the diffraction integral and the fractional Fourier transform is analysed in detail from the geometrical and energy points of view. It is shown that the optical matrices associated with the two transformations in the geometrical approximation, although very different, are consistent with the simple relation between the respective integral transforms. Moreover, the meaning of the complex degree of fractionality of the fractional Fourier transform is found to be related to the energy variation of the beam. Its influence on the phase-space representation of the optical beam is shown to be different compared with the diffraction through an energy variant system. [References: 22]