A Phase-Step Position Encoder with Nanometre-Scale Computed Resolution and a Full Accuracy Budget

Resolution is the cheapest specification in position encoding and accuracy is the expensive one; data sheets quote the first and bury the second. This paper specifies a position encoder whose readout follows the transit phase-step structure, subdividing a forty-micrometre scale pitch into 8192 phase steps, and it reports both numbers with equal prominence. The computed resolution is 4.88 nanometres. The computed accuracy over a half-metre travel, dominated by the thermal expansion of the steel scale at 575 nanometres for a tenth-kelvin temperature uncertainty, is 575 nanometres; interpolation error contributes only 0.024 nanometres. Maximum traverse speed at the two-megahertz sampling rate is 40.000 metres per second. SIMULATED, NOT MEASURED: all figures are computed from stated assumptions.