Simple technique for the accurate internal measurement of a right angle with a polarization phase-shifting, lateral-shearing, cyclic path optical configuration

Abstract

A simple, new, self-referenced technique for the internal measurement of a right angle is presented. A polarization cyclic path optical configuration (CPOC) receives as the input beam a pair of laterally separated plane wave components, having angular separation of ψw = (π±4nδ), produced due to internal reflection of a linearly polarized plane wave on the surfaces enclosing the 90-deg (±δ) angle of a right-angled prism (where δ is the error in 90-deg angle and n is the index of refraction of the material of the prism). The CPOC is used to superpose the mutually inclined plane wave components by duplicating the input pair of plane wave fronts and introducing appropriate lateral shear between the identical pairs. The superposed inclined plane wave components interfere to produce two beam Fizeau fringes (FF), when brought to the same state of polarization. The error in the right angle can be calculated simply from the spacing of the resulting FFs or, more accurately, from the slope of the optical path difference variation obtained by applying polarization phase-shifting interferometry. Results obtained for a right-angled prism are presented.