Identification of Zernike-Polynomial Systematic Pattern with Spatial Variation Spectrum

• Main Authors: Han Hsueh, 薛翰
• Other Authors: 陳正剛
• Format: Others
• Language: en_US
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/76970147627301487925

碩士 === 國立臺灣大學 === 工業工程學研究所 === 97 === 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. In 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. Spatial 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. To 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.