A sensor may simultaneously sense 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. The sensor may include a first and second disk, each having an annular pattern which alternates between two different levels of optical transparency. One disk may be coupled to the first rotatable member, the other disk may be coupled to the second rotatable member. A signal processing system may determine both angular positions based on sampling a consolidation of the first and the second annular patterns at locations that are not at a transition in the consolidated pattern.