User:McAsf/SF

Spectra Fitting
Spectra Fitting is closely related to Multi-Componet Quantitative Analysis (MCQA). It may be considered as a graphical representation of MCQA. Though it can not be applied to every data that MCQA can be applied to, it also provides same extra functionalities that would be impossible with standard approach to MCQA.

A formal specification of a multi-component quantitative analysis problem has been formulated and presented. Many analysis methods dealing with spectra of mixtures and not just single components have been developed. Incomplete, deficient, curtailed and even imperfect data has been taken into consideration to ensure that maximum possible extent of the methods is being provided. As a straightforward extension of single component analysis K-matrix method (Classic Least Squares) has been presented, providing much better tolerance of distorted data owing to utilization of full spectra instead of single points. Even bigger improvement has been gained by engagement of PCR into analysis (Principal Component Regression) and treating absorbance as independent variable (Inverse Least Squares) which has led to development of Q-matrix method, capable of concentrations estimation based on incomplete calibration data. A graphical presentation of estimation as well as confirmation of its correctness is delivered by spectra fitting method. Spectra fitting enables also unexpected components detection and recognition. The key for the robustness of estimations is combining rank and range concepts with R2 criterion. The rank let us know if analysed spectrum is in range of a calibration data while a R2 criterion ensures that L-B law is sustained and absorbance is bounded with concentrations with linear dependence. The above methods has been integrated by the rules to a form of a consistent expert system. The system takes concentrations C and spectra a, A, and returns estimated concentrations c along with comments, explanations, graphical presentation or even instructions what to do in case estimation was not possible.