Encoder resolution

A wheel encoder converts travel into counts. One revolution covers π·D of surface, and produces PPR pulses per channel. Instruments normally decode both channels on both edges, giving a quadrature multiplier of four, so the resolution is PPR × 4 / (π·D) counts per millimetre.

A 50.8 mm wheel with a 500 pulse encoder in quadrature gives about 12.5 counts per millimetre, or 0.08 mm per count - comfortably finer than any scan resolution in normal use. The rule is that the encoder step must be several times finer than the scan resolution, otherwise the position of each stored line jitters by a whole count.

Calculate the value, then calibrate it. Wheel diameter changes with wear and with the load pressing it onto the surface, and on a painted or scaled surface the wheel slips. Every procedure worth following requires the encoder to be verified over a known distance - typically 500 mm - before and after a scan, and the calculated value is only the starting point for that check.

circumference = π × D
counts per revolution = PPR × quadrature
counts per mm = PPR × quadrature / (π × D)