Theoretical analysis of errors in correction algorithms for periodic nonlinearity in displacement measuring interferometers

Journal article (2011)

Authors

J.D. Ellis Mechatronic Systems Design - Mechanical, Maritime and Materials Engineering
M Baas External organisation
K Joo Mechatronic Systems Design - Mechanical, Maritime and Materials Engineering
J.W. Spronck Mechatronic Systems Design - Mechanical, Maritime and Materials Engineering
Research Group
Mechatronic Systems Design (Mechanical, Maritime and Materials Engineering) (TU Delft)
More Info
expand_more

Published Date

2011

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Mechanical, Maritime and Materials Engineering

Department

Precision and Microsystems Engineering

Research Group

Mechatronic Systems Design

Abstract

Two different measure- and-correct algorithms, the Chu-Ray algorithm and the Eom algorithm, were simulated to estimate their effectiveness for correcting periodic nonlinearity applied a simulated wafer positioning system. Both algorithms, which demonstrated no periodic nonlinearity in some example constant velocity and constant acceleration datasets, and their specific implementations are described in detail. The algorithms were tested for both slit and scan directions using estimated wafer stage trajectories for ramping up to a constant scanning velocity with no velocity in the slit direction. Three different heterodyne frequencies and three different sampling frequencies were simulated to estimate the optical system and data acquisition parameters. The initial phase offset was also considered in the simulations and had a significant effect on both the scan and slit offset errors. The offset error appears to increase for certain initial phase values which manifests from compensating the periodic errors combined with the high stage dynamics. High noise levels and displacement jumps were observed when high velocity changes during a correction period suggesting increasing the minimum velocity threshold and limiting the maximum acceleration can improve the effectiveness of these algorithms.