## Fractionalization of the linear cyclic transforms

JOSA A, Vol. 17, Issue 12, pp. 2330-2338 (2000)

http://dx.doi.org/10.1364/JOSAA.17.002330

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### Abstract

In this study the general algorithm for the fractionalization of the linear cyclic integral transforms is established. It is shown that there are an infinite number of continuous fractional transforms related to a given cyclic integral transform. The main properties of the fractional transforms used in optics are considered. As an example, two different types of fractional Hartley transform are introduced, and the experimental setups for their optical implementation are proposed.

© 2000 Optical Society of America

**OCIS Codes**

(070.0070) Fourier optics and signal processing : Fourier optics and signal processing

(070.2590) Fourier optics and signal processing : ABCD transforms

(070.6020) Fourier optics and signal processing : Continuous optical signal processing

**History**

Original Manuscript: February 22, 2000

Revised Manuscript: June 21, 2000

Manuscript Accepted: June 23, 2000

Published: December 1, 2000

**Citation**

T. Alieva and M. L. Calvo, "Fractionalization of the linear cyclic transforms," J. Opt. Soc. Am. A **17**, 2330-2338 (2000)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-12-2330

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