Abstract
An important tool in optical pattern recognition, the joint
fractional transform correlator (JFTC), was introduced
recently. We analyze the peak properties of fractional correlation
(FC) by symbolic derivation and computer simulation. We show
that the FC has a maximum correlation peak when the second fractional
Fourier transform is reduced to the conventional Fourier
transform. We introduce nonlinear operations in a joint fractional
transform power spectrum and propose a differential JFTC and a binary
differential JFTC. Numerical simulations show that such nonlinear
JFTCs exhibit remarkable improvement in correlation peak intensity,
discrimination capability, and signal-to-noise ratio. An
optoelectronic setup that can implement such nonlinear JFTCs is also
proposed.
© 2001 Optical Society of America
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