Calibration of angle encoders using transfer functions

Classical approaches to the calibration of angle encoders typically make use of circle division by means of an auxiliary artefact and apply linear equation systems constrained by circle closure which are solved for the errors of the encoder and those of the artefact simultaneously. Lately, emphasis has been placed on Fourier methods, as Fourier approaches involving transfer functions have proved to be a powerful tool applicable to various high-precision measurement tasks. We present an in-depth treatment of the use of the Fourier approach including transfer functions for the calibration of angle encoders. Different weighting schemes for combining the measurements will be presented by which the uncertainty of the calibration of angle encoders can be substantially reduced. The method utilizes angle difference measurements and it can therefore also be applied to the calibration of angle encoders using suitable arrangements of multiple reading heads. The approach is used for calibrating an angle encoder in an experimental set-up by means of a five-sided calibration polygon with angle differences between the optical faces that are not integer fractions of the full circle. The calibration results, including an evaluation of the measurement uncertainty, are presented for different weighting schemes and it is shown that appropriate weighting leads to a reduction in the uncertainty up to a factor of 4.