Reflection Lau Imaging And Its Application To Displacement Sensing

The interference fringe known as the Lau image is produced at the infinite image plane when two transmission gratings are located in tandem and are illuminated incoherently. We have studied this imaging by analyzing the optical arrangement in which the second transmission grating is replaced by a reflection grating. Unlike the transmission Lau imaging, the new set of fringes become changeable in their profile when one of the gratings is subjected to an inplane translatory motion in the direction perpendicular to the grating lines. The phenomenon is investigated theoretically and experimentally from the viewpoint of displacement sensing. Using the combination of the binary gratings having duty cycle of 1/2, two fringe maxima with different intensities are obtained in a single period of the fringe pattern. Introducing the lateral displacement of the grating, one of the maxima decreases in its intensity while the other increases. The change of the fringe profile has been used for an alignment method. Using 25pm gratings and an automatic alignment system with piezo-electric actuators, alignment precision of about ±50nm has been obtained.