The fractional Fourier transform (FRT) is known to be optically implementable with use of a medium with a perfect radial quadratic-index profile. Using the quantum-mechanical operator formalism, we examine the effects on the FRT action of such a medium that are due to small random inhomogeneities in the longitudinal direction, the direction of propagation, and we formulate the random fractional Fourier transform (RFRT). Applying the RFRT to a self-fractional Fourier function, a Gaussian function, we discuss both the total power and the variance. The random Fourier transform is examined as a special limiting case.
© 1999 Optical Society of America
(000.5490) General : Probability theory, stochastic processes, and statistics
(030.4280) Coherence and statistical optics : Noise in imaging systems
(070.2590) Fourier optics and signal processing : ABCD transforms
(270.2500) Quantum optics : Fluctuations, relaxations, and noise
Sumiyoshi Abe and John T. Sheridan, "Random fractional Fourier transform: stochastic perturbations along the axis of propagation," J. Opt. Soc. Am. A 16, 1986-1991 (1999)