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Proceedings Paper

Fractional correlation based on nonconventional joint transform correlator
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Paper Abstract

Fractional correlation is an extension of the conventional correlation. It employs fractional Fourier transform (FRFT) that includes the conventional Fourier transform as a special case where the order of the FRFT equals one. Because of the FRFT's lack of the shift-invariant property, the FRFT is not applicable to the conventional joint transform correlator, but to the nonconventional joint transform correlator (NJTC) that have been proposed by F. T. S. Yu et al., in which separate lenses transform the input signals and their spectral distributions overlap on the square-law detector. This provides an optical implementation of the fractional correlation. The conventional Fourier transform generally yields a high peak at the center of the spectral plane. But the FRFT gives a spectral distribution with no high peak, which is desirable because the square-law detector has a finite dynamic range for the linearity. Moreover, we prove that the fractional correlation produces a narrower output distribution and has the same correlation value at the center of the output plane as the conventional correlation. The conventional correlation has the shift-invariant property, but the fractional correlation has not.

Paper Details

Date Published: 27 November 2002
PDF: 9 pages
Proc. SPIE 4789, Algorithms and Systems for Optical Information Processing VI, (27 November 2002); doi: 10.1117/12.450842
Show Author Affiliations
Sang-il Jin, Korea Advanced Institute of Science and Technology (South Korea)
You-Seok Bae, Hunno Technologies Inc. (South Korea)
Soo-Young Lee, Korea Advanced Institute of Science and Technology (South Korea)

Published in SPIE Proceedings Vol. 4789:
Algorithms and Systems for Optical Information Processing VI
Bahram Javidi; Demetri Psaltis, Editor(s)

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