27 November 2002 Fractional correlation based on nonconventional joint transform correlator
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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.
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Sang-il Jin, Sang-il Jin, You-Seok Bae, You-Seok Bae, Soo-Young Lee, Soo-Young Lee, } "Fractional correlation based on nonconventional joint transform correlator", Proc. SPIE 4789, Algorithms and Systems for Optical Information Processing VI, (27 November 2002); doi: 10.1117/12.450842; https://doi.org/10.1117/12.450842


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