Polarimetric 360° absolute rotary encoder

Abstract Encoders of angle based on rotating polarizers suffer from 180° ambiguity due to their inherent twofold rotational symmetry. This restricts their applications in motor and machine controls. We show that the ambiguity can be resolved through a geometrical mapping from a plane to a conical surface. Seen from the local surface normal, one full rotation of the cone gives one half rotation of the polarizer axis. With appropriate transmission or reflective optics and multiphase detection, we build high resolution, moderate accuracy, absolute-angle encoders without 180° ambiguity. Polymer birefringent retarders can be used similarly.