Periodic error quantification for non-constant velocity motion

This paper describes a procedure for analyzing non-stationary (variable frequency content) periodic error signals obtained during accelerating or decelerating motion. This capability is important due to the recent interest in real-time compensation of periodic error for precision positioning systems. In order to apply the spatial Fourier transform to the non-stationary signal, the constant time interval signals are resampled by linear interpolation using a constant spatial interval. Numerical and experimental results are provided for constant acceleration and sinusoidal motion profiles.

► It is necessary to analyze non-constant velocity profiles for real-time compensation of periodic error in displacement measuring interferometry.
► Because periodic error is characterized by constant spatial periods, the signal is non-stationary for accelerating/decelerating motions.
► It is shown that a resampling of the data enables the spatial Fourier transform to be applied for determination of the residual periodic error magnitudes.