Identification of Zernike-Polynomial Systematic Pattern with Spatial Variation Spectrum
Date Issued
2009
Date
2009
Author(s)
Hsueh, Han
Abstract
Zernike polynomials are commonly used to characterize and model systematic patterns of observed circular-shaped topography, such as wafer topography in semiconductor fabrication and corneal aberration in biomedical engineering. However, the infinite number of Zernike polynomials leads to difficulties in modeling the observed topography. Conventional Zernike polynomials selection methods either select the Zernike polynomials in sequence without considering the similarity between the observed topography and the Zernike polynomials or use the bootstrap method, which demand great simulation and computation time on all possible Zernike-polynomials combination models to find the best-fit model.n this research, we propose a Zernike polynomials selection method based on the characteristics of circular topography. The objective is to analyze observed topography and select the Zernike polynomials with similar spatial variation patterns for modeling, without attempting all possible model combinations.patial moving variance and radial moving variance are used to characterize the systematic variation over the frequency spectrum. The Zernike polynomials will be classified into groups based on their spatial variation pattern and prediction models will be established for each group. Using the prediction models, a forward selection algorithm will be proposed to select the Zernike polynomials, with systemic variation patterns similar to the observed topography, into the model.o validate, the proposed method is compared with other conventional selection methods via simulated data and real cases. It is shown that the same or better modeling results can be obtained through the proposed methods.
Subjects
Zernike polynomials
model selection
spatial variation
spatial moving variance
spatial spectrum
radial variation
radial spectrum
systematic variation
Type
thesis
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