FRACTIONAL FOURIER OPTICS

There exists a fractional Fourier-transform relation between the ampli tude distributions of light on two spherical surfaces of given radii a nd separation. The propagation of light can be viewed as a process of continual fractional Fourier transformation. As light propagates, its amplitude distribution evolves through fractional transforms of increa sing order. This result allows us to pose the fractional Fourier trans form as a tool for analyzing and describing optical systems composed o f an arbitrary sequence of thin lenses and sections of free space and to arrive at a general class of fractional Fourier-transforming system s with variable input and output scale factors.