Lensless joint transform correlator

TLDR: In this paper, a lensless joint transform correlator is used to determine the relative x -y position of two pinholes placed in parallel arms of a Mach-Zehnder interferometer.

Abstract: The lensless joint transform correlator optically determines the relative x -y position of two pinholes. The pinholes are placed in parallel arms of a Mach-Zehnder interferometer. The Fraunhaufer diffraction patterns combine to form a joint transform plane. Because of the interference of the two signals, a Fresnel zone is formed in the joint Fraunhaufer 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 taken in the focal plane of the Fresnel zone. As with the single-lens joint transform correlator, the lensless joint transform correlator exhibits 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 five in both the x and y dimensions. The output has very good peak-to-noise ratio and position resolution. A peak-to-noise ratio of 106 dB with a resolution of 1.4 µm are observed when using the fifth order focus of the Fresnel zone.