Frequency-Domain Properties of Moving Average and Moving Standard Deviation with Application to Stage (Motion) Control

In wafer scanners, moving average and moving standard deviation constitute time-domain measures that quantify scanning stage performance in terms of overlay and imaging. Though for control design a frequency-domain interpretation would be desirable to have, for moving standard deviation such an interpretation is not easily found. As a practical solution, an analytical expression for the response to single sinusoidal input will be derived. For data from an industrial scanning stage the usefulness of such an expression and the insights obtained from it will be discussed.