A nonlinear joint transform image correlator is investigated. The Fourier transform interference intensity is thresholded to provide higher correlation peak intensity and a better defined correlation spot. Analytical expressions for the thresholded joint power spectrum are provided. The effects of nonlinearity at the Fourier plane on the correlation signals at the output plane are investigated. The correlation signals are determined in terms of nonlinear characteristics of the spatial light modulator (SLM) at the Fourier plane. We show that thresholding the interference intensity results in a sum of infinite harmonic terms. Each harmonic term is envelope modulated due to the nonlinear characteristics of the device and phase modulated by m times the phase modulation of the nonthresholded joint power spectrum. The correct phase information about the correlation signal is recovered from the first-order harmonic of the thresholded interference intensity. We show that various types of autocorrelation signal can be produced simply by varying the severity of the nonlinearity and without the need to synthesize the specific matched filter. For example, the autocorrelation signal produced by a phase-only matched filter can be obtained by selecting the appropriate nonlinearity.
© 1989 Optical Society of America
Original Manuscript: July 18, 1988
Published: June 15, 1989
Bahram Javidi, "Nonlinear joint power spectrum based optical correlation," Appl. Opt. 28, 2358-2367 (1989)