Optical correlators using the binarized joint power spectrum

Techniques for extending the performance and utility of the binary nonlinear joint transform correlator (BJTC) through Fourier plane processing are developed and demonstrated. It is shown that through use of frame subtraction, time modulation, or Fourier plane windowing, the PNR performance of the BJTC can be improved by a factor of four. Theoretical models are developed to described these techniques and the expected performance gain is verified through simulation and experimental demonstrations. These improvements make the BJTC practical for applications in pattern matching, target identification and tracking, fingerprint identification, security verification, precision part positioning and alignment, and component inspection. The techniques are compared as part of a fingerprint verification system. The concept of setting the threshold on the verification system to produce a constant false alarm rate is introduced. The results for the correlators are compared based on the probability of false pass with a given probability of false alarm for fingerprint verification. Two new correlators, the single lens joint transform correlator (SLJTC) with chirp-encoded inputs and the chirp-encoded lensless joint transform correlator (JTC), are developed. Both of these correlators are modifications of the chirp-encoded JTC. The joint power spectrum in the chirp-encoded JTC is shown to have the form of a Fresnel zone plate. In the SLJTC, the second transform lens is replaced by the Fresnel of the joint power spectrum to the zone plate focus. In the lensless JTC, pinholes are used as the input patterns, and their joint Fraunhaufer diffraction pattern replaces the joint transform signal. Both of these correlators are shown to allow a magnification of the output plane determined by the amount of chirp-encoding. It is also demonstrated experimentally that by using a shorter, higher order focus of the zone plate higher resolution than is possible for the BJTC can be achieved. Because of their potential for high speed, high resolution position determination, these correlators can potentially find application in industrial parts positioning and semiconductor mask alignment.