Absolute angle measurement using a phase-encoded binary graduated disk

A new absolute angle measurement method using a phase-encoded binary graduated disk (PE-BGD) is presented. An absolute position binary code (APBC) is encoded by shifting the positions of binary patterns, and can be sub-divided by detecting their positions with sub-pixel resolution of a multi-element detector. Using an n-bit linear shift feedback register, we expressed a recursive APBC dividing the full circle by 2n − 1 angular positions. An experimental setup was constructed with a microscopic imaging system, a rotation stage having a precision angle encoder, and two kinds of PE-BGDs which employed 10-bit and 13-bit APBC. The resolution of the APBC, which equals to signal period of the PE-BGD, used in each disk is 0.352° and 0.044°, respectively. We evaluated its performance by comparing the readouts of the proposed system and the angle encoder, throughout the full circle range and for one signal period. In the full circle range, the differences between two measurement systems were less than 1/50 of the resolution of the APBC. We also proved that the absolute angle could be measured with small nonlinearity error, which was less than 1/600 of the signal period.