Self-Fourier-Fresnel Functions for 2D Transform Case

A function whose Fourier transform is itself is called a self-Fourier function. If the Fresnel transform of this function is also itself, then the function will be called a self-Fourier-Fresnel function (SFFrF). For studying SFFrF, a new formula of Fresnel transform is proposed. It is shown that SFFrF can be found. For the discrete transform case, the new formulae of Fourier transform and Fresnel transform are proposed, respectively. Then, SFFrF can also be found for the discrete transform case. These functions can be applied for the optical information processing.