Measurement of displacement and distance with a polarization phase shifting folded Twyman Green interferometer.

Abstract

A Sagnac interferometer (SI), consisting of a polarization beam splitter (PBS), along with two equally spaced plane mirrors that are inclined at 45° to each other, is transformed into a folded Twyman Green interferometer (TGI) by placing a mirrored parallel plate (MPP) into the hypotenuse arm of the SI. The converging input beam produced by a telescope objective (TO) is split into reflected (s-polarized) and transmitted (p-polarized) components by the PBS. The p- and s-polarized focal spots are made to fall on the mirrored end surfaces of the parallel plate (PP). The retroreflected p- and s-polarized beams become collimated after passing through the TO. A linear shift of the PP in either (longitudinal) direction alters the positions of the p- and s-polarized focal spots and results in a set of converging and diverging spherical wavefronts that interfere to form concentric circular fringes. We applied polarization phase-shifting interferometry to obtain the optical path difference (OPD) variation of the interference field. The displacement is calculated from the OPD variation. A validation experiment has been carried out by introducing known shifts to the PP. The setup can be used for displacement as well as distance measurement.