Orthogonal Decomposition of Profile Data

In Section 10.1, it was stated that the basic steps of data evaluation are (a) removing of mean, (b) correlating the dominant trend, and (c) analyzing the residual scatter around the correlation. For the two-dimensional sheet process data MD/CD decomposition is essentially the implementation of step (a) in both the spatial and temporal modes. The resulting data com- 

Process data can be correlated or de-trended using a variety of functions. A computationally reliable approach is the use of orthogonal functions. Least squares fit of data with a simple reduced order function can provide valuable information about process performance in terms of dominant contributions to variability. 

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Principal components analysis (PC A) (see Section 3.1) provides a technique to define orthogonal basis functions that are directly constructed from process data, unlike Gram polynomials which are dependent on the data length only. PCA is also uniquely suitable for extracting the dominant features of two-dimensional data like the residual profile obtained after MD/CD decomposition, Yr. 

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