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
Original Manuscript: September 16, 1999
Revised Manuscript: October 30, 2000
Published: June 10, 2001
Banghe Zhu, Shutian Liu, Li Han, and Xueru Zhang, "Nonlinear joint fractional transform correlator," Appl. Opt. 40, 2836-2843 (2001)