Principal Component Analysis for Spectral Mapping Data
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Solution Overview
Problem
Conventional mapping-data analysis methods using spectrometers only display a small part of the information from infrared spectra, relying on subjective peak assignment and failing to effectively differentiate defect characteristics due to overlapping peaks and incomplete spectral consideration.
Innovation Solution
A method and apparatus that perform principal component analysis on spectral data to create grouped maps, allowing for objective analysis by dividing the specimen surface into groups based on principal component scores, and optionally including scatterplot, similarity, concentration, physical-property, and thickness calculations to enhance data visualization and interpretation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If only specific peaks are extracted from infrared spectra for mapping display, then the map creation process is simplified, but most of the information in the measured spectra is discarded
Solution Approach 1:
The invention transforms the spectral data from peak-intensity parameters to principal component scores through mathematical transformation. This parameter change allows the entire spectrum to be utilized while maintaining a compact representation suitable for mapping display, thus preserving information while simplifying the display process.
Solution Approach 2:
The invention projects the high-dimensional spectral data onto a lower-dimensional space using principal component analysis. By displaying maps based on principal component scores rather than peak intensities, the system maintains comprehensive information while reducing the dimensionality suitable for visual mapping.
2Loss of information
If multiple peaks are considered in spectra analysis, then more information is retained, but it becomes difficult to assign peaks to functional groups due to overlapping peaks
Solution Approach 1:
The invention extracts the essential information from complex overlapping spectra by transforming them into principal component scores. This extraction process separates the meaningful variance from the overlapping noise, making it possible to analyze multiple peaks without the difficulty of individual peak assignment.
3Measurement precision
If the entire spectrum is considered for defect detection, then comprehensive feature information is obtained, but subjective analysis must still be relied upon for peak identification
Solution Approach 1:
The invention replaces the manual, subjective process of peak identification with an automated principal component analysis system. The mathematical transformation objectively processes the entire spectrum without requiring human interpretation of individual peaks, thus improving both accuracy and objectivity.
4Measurement precision
If principal component analysis is performed on spectral data, then comprehensive and objective analysis is enabled, but the complexity of data processing increases
Solution Approach 1:
The invention performs principal component analysis as a preliminary processing step before mapping display. By pre-calculating the principal component scores from the spectral data, the system reduces the complexity of subsequent mapping operations while maintaining the benefits of comprehensive spectral analysis.
Data Source
AI summary
It is an object of the present invention to provide a mapping-data analyzing method that can display a map in which sufficient information is extracted from the spectra of obtained mapping data to enable objective analysis. The mapping-data analyzing method of the present invention is used for analyzing mapping data obtained by measuring, with a spectrometer apparatus, spectra at a plurality of points on a specimen surface. The method comprises a principal-component calculating step and a grouped-map display step. In the principal-component calculating step, spectral data obtained at each point on the specimen surface is defined as an individual sample and principal component analysis, in which values at a plurality of wave numbers of each spectral data set serve as variables, is performed to calculate the scores of a plurality of principal components for each individual sample. In the grouped-map display step, the points on the specimen surface are divided into a plurality of groups based on the scores of a plurality of principal components calculated in the principal-component calculating step and a two-dimensional or three-dimensional map indicating to which group each point on the specimen surface belongs is displayed on a display device.