## Random fractional Fourier transform: stochastic perturbations along the axis of propagation

JOSA A, Vol. 16, Issue 8, pp. 1986-1991 (1999)

http://dx.doi.org/10.1364/JOSAA.16.001986

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### Abstract

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

**OCIS Codes**

(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

**History**

Original Manuscript: August 25, 1998

Revised Manuscript: March 23, 1999

Manuscript Accepted: March 23, 1999

Published: August 1, 1999

**Citation**

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)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-8-1986

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