The lensless joint transform correlator optically determines the relat
ive x-y position of two pinholes. The pinholes are placed in parallel
arms of a Mach-Zehnder interferometer. The Fraunhaufer diffraction pat
terns combine to form a joint transform plane. Because of the interfer
ence of the two signals, a Fresnel zone is formed in the joint Fraunha
ufer diffraction pattern. This is captured and used in a second stage,
just as the joint power spectrum is in a joint transform correlator.
The joint transform is illuminated with a plane wave, and the output t
aken in the focal plane of the Fresnel zone. As with the single-lens j
oint transform correlator, the lensless joint transform correlator exh
ibits magnification between the input displacement and the output peak
displacement. By using the third or fifth order focus of the Fresnel
zone, the output resolution can be improved by a factor of three or fi
ve in both the x and y dimensions, The output has very good peak-to-no
ise ratio and position resolution. A peak-to-noise ratio of 106 dB wit
h a resolution of 1.4 mu m are observed when using the fifth order foc
us of the Fresnel zone. (C) 1997 Society of Photo-Optical Instrumentat
ion Engineers.