High-resolution of rotary encoder analog quadrature signals

The paper describes a software technique to provide high-resolution absolute angular measurements from the analog quadrature signals of a rotary encoder. The method uses digitized samples of the sinusoidal quadrature signals and the output of a divide-by-four counter circuit. Dynamic measurements on an external trigger signal are possible allowing instantaneous up-to-date angular readings even at high speed. The resolution and hysteresis errors are only dependent on the encoder itself and the bandwidth and resolution of the sampling circuitry. The scheme allows up to 135 degrees of counter hysteresis and delay without loss of precision, thus also affording excellent noise immunity. The theoretical resolution for a 12-bit digital conversion of the analog signals is 1/3360 of a pitch. Experimental results on an encoder built into a laser-tracking measurement system and using 81000 pitches show a unidirectional precision of 0.3 arcsec (rms), a mean bidirectional hysteresis of about 1 arcsec and a worst case variation for a stationary encoder shaft of 0.06 arcsec