Fractional Fourier optics

There exists a fractional Fourier-transform relation between the amplitude distributions of light on two\nspherical surfaces of given radii and separation. The propagation of light can be viewed as a process of\ncontinual fractional Fourier transformation. As light propagates, its amplitude distribution evolves through\nfractional transforms of increasing order. This result allows us to pose the fractional Fourier transform as a\ntool for analyzing and describing optical systems composed of an arbitrary sequence of thin lenses and sections\nof free space and to arrive at a general class of fractional Fourier-transforming systems with variable input\nand output scale factors.