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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 20, Iss. 11 — Nov. 1, 2003
  • pp: 2033–2040

Fractional free space, fractional lenses, and fractional imaging systems

Uygar Sümbül and Haldun M. Ozaktas  »View Author Affiliations


JOSA A, Vol. 20, Issue 11, pp. 2033-2040 (2003)
http://dx.doi.org/10.1364/JOSAA.20.002033


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Abstract

Continuum extensions of common dual pairs of operators are presented and consolidated, based on the fractional Fourier transform. In particular, the fractional chirp multiplication, fractional chirp convolution, and fractional scaling operators are defined and expressed in terms of their common nonfractional special cases, revealing precisely how they are interpolations of their conventional counterparts. Optical realizations of these operators are possible with use of common physical components. These three operators can be interpreted as fractional lenses, fractional free space, and fractional imaging systems, respectively. Any optical system consisting of an arbitrary concatenation of sections of free space and thin lenses can be interpreted as a fractional imaging system with spherical reference surfaces. As a special case, a system departing from the classical single-lens imaging condition can be interpreted as a fractional imaging system.

© 2003 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(080.0080) Geometric optics : Geometric optics
(080.2720) Geometric optics : Mathematical methods (general)

History
Original Manuscript: March 18, 2003
Revised Manuscript: June 25, 2003
Manuscript Accepted: July 18, 2003
Published: November 1, 2003

Citation
Uygar Sümbül and Haldun M. Ozaktas, "Fractional free space, fractional lenses, and fractional imaging systems," J. Opt. Soc. Am. A 20, 2033-2040 (2003)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-11-2033

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