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.

Worked example

Encoder wheel diameter	50.8 mm
Pulses per revolution	500
Decoding multiplier	4
Calibration travel	500 mm
Scan axis resolution	1 mm
Wheel circumference	159.593 mm
Counts per revolution	2000
Counts per millimetre	12.532
Travel per count	0.0798 mm
Counts expected over the calibration travel	6265.9

A 50.8 mm wheel rolls π × 50.8 = 159.593 mm per turn. 500 pulses per revolution decoded in quadrature gives 2000 counts per turn, so 2000/159.593 = 12.532 counts per millimetre, or 0.0798 mm per count. Over a 500 mm verification the instrument should report 6265.9 counts.