Capabilities and limitations of the self-calibration of angle encoders

At the Physikalisch-Technische Bundesanstalt (PTB), a self-calibration method for the fast and precise in situ calibration of angle encoders without recourse to external reference standards has been developed. It relies on a suitable geometric arrangement of multiple reading heads which read out the radial grating of the angle encoder at different angular positions. Fourier-based algorithms are used to analyse the measurement differences of pairs of heads to recover the graduation error of the grating. A comprehensive overview, both theoretical and experimental, of the capabilities and limitations of the self-calibration method is presented, including experimental data obtained with the high-precision primary angle standard of PTB. The evaluation and, where it is possible, correction of error influences due to lateral shifts of the centre of the encoder's grating during its rotation, including its eccentricity, the reading heads' angular positions, and their non-uniform response, are discussed in detail, as well as the resulting uncertainty budget.