Rotation and differential angle optical sensor with short optical sensing array

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 and which has a length which is not substantially greater than the width of the annular illumination pattern 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 which spans an angle that is less than or equal to the maximum displacement angle;
• 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.