Description of diffractive optical elements with self-Fourier transform functions

In (synthetic) holography and diffractive optics, the optical field is often decomposed in a set of spherical or plane waves. This gives sometimes some problems in calculating the Fourier transform. Because Gaussian beams are their own Fourier transform, it seems to be more natural to use Gaussian beams as basis functions. However, because Gaussian functions are no complete set of basis functions, it is necessary to extend the idea and to use rather Gaussian-Hermite wave functions as an orthonormal basis set. Those ideas can also be applied to general Self-Fourier Transform functions.