4D fourier transform of wave function and reinvention of holography

Fourier Transform is well known the fundamental theory for information processing. It has been successfully adopted in the whole IT industries respectively with 1D for signal communication, 2D for image processing, and 3D for color recognition. In this paper, we propose to make four dimensional Fourier Transform of wave function (or the probability amplitude) f(x, y, z, t) of the quantized energy probability distribution I(x, y, z, t) of this nature to bring up a new description of light with its two kinds of spectra— temporal spectrum and spatial spectrum. We shall expand the concept of spatial frequency in nowadays imaging system as the spatial spectrum owned by the nature itself while the reconstruction of a complicated wavefront (i.e. both amplitude and phase ) in holography into the recovering of spatial and temporal spectra of the nature itself. Real time holographic display for holographic video is also demonstrated as the application of this theory.