Rotation and differential angle optical sensor which does not require keyed installation

A sensor for simultaneously sensing the angular position of a first rotatable member relative to a frame of reference and the angular position of a second rotatable member relative to the first rotatable member up to a maximum displacement angle, the sensor comprising:

• a first disk having a first annular pattern which alternates between two different levels of optical transparency;
• a first coupling configured to couple the first disk to the first rotatable member;
• a second disk having a second annular pattern which alternates between two different levels of optical transparency and which has substantially the same radius as the first annular pattern, the second disk being configured such that the first and the second annular patterns may independently rotate about substantially the same axis while remaining substantially adjacent to one another;
• a second coupling configured to couple the second disk to the second rotatable member;
• an optical sensing array configured to provide signals indicative of an annular illumination pattern which is cast upon the optical sensing array;
• a lighting system configured to direct light toward the first and the second disks with an orientation that causes an annular illumination pattern to be cast upon the optical sensing array which corresponds to a composite of a portion of the first and the second annular patterns;
• and
• a signal processing system configured to generate an output that is indicative of both of the angular positions based on the signals from the optical sensing array,
• wherein the first and the second annular patterns are configured such that the angular displacement of the second rotatable member relative to the first rotatable member angle is accurately indicated by the output up to the maximum displacement angle, regardless of how the first annular pattern is aligned with respect to the second annular pattern at the time the couplings are coupled to their respective rotatable members.