Statistical perspectives of self-calibration

Michael R. Raugh; James M. Minor

doi:10.1117/12.240147

21 May 1996 Statistical perspectives of self-calibration

Michael R. Raugh, James M. Minor

Proceedings Volume 2725, Metrology, Inspection, and Process Control for Microlithography X; (1996) https://doi.org/10.1117/12.240147
Event: SPIE's 1996 International Symposium on Microlithography, 1996, Santa Clara, CA, United States

Abstract

Positional self-calibration refers to the use of an imperfectly calibrated measurement gauge in an imperfectly calibrated measuring or manufacturing machine to simultaneously deduce improved positional accuracy in the calibrations of the gauge and the machine. The self- calibration function corrects the distortions in the image produced by a high-quality machine as it processes an object in its measurement field. The original derivation by Raugh (1984, 1985) focused on abstract mathematical/geometrical foundations of self-calibration. A later paper by Raugh (1991) dealt with the problem more concretely by showing how a patterned measurement gauge with suitable symmetry properties combined with near-linear comparisons could be used for self-calibration. This poster recasts self-calibration as a statistical problem. Hence, determination of the self-calibration function becomes a problem in statistical estimation, and specification of an optimal set of gauge positions and orientations for self- calibration becomes a problem in statistical design of experiment. This representation enables one to take advantage of established statistical methods for separating signal from extraneous effects and noise using stable and efficient techniques. An example of noise is measurement error. Extraneous effects include imperfections in the gauge and its positioning in the measurement field. The concepts are illustrated by a simple example.

Citation Download Citation

Michael R. Raugh and James M. Minor "Statistical perspectives of self-calibration", Proc. SPIE 2725, Metrology, Inspection, and Process Control for Microlithography X, (21 May 1996); https://doi.org/10.1117/12.240147

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