Conventionally, a component included in a sample is generally analyzed by using multivariate curve resolution (MCR) (for example, see Patent Documents 1 and 2). Resolution spectral data about respective components included in the sample is obtained by using the multivariate curve resolution, and the components can be discriminated based on each pieces of the resolution spectral data.
At the time of an analysis, for example, a spectrum is detected at a plurality of measurement points on a sample surface, and a measurement data matrix D is obtained based on the spectrum at each of the measurement points. The following relational expression (1) is established for this measurement data matrix D. A symbol C is a concentration matrix presenting concentration of the components at each of the measurement points, a symbol ST is a transposed matrix of a spectral matrix S where spectra of the components are arranged, and a symbol E is a matrix of noise components included in the measurement data matrix D.D=CST+E  (1)
In the multivariate curve resolution, C and ST are calculated based on the measurement data matrix D so that a sum of squares of the E component in the expression (1) is minimum. Such a process can be executed by using a publicly-known algorithm such as an Alternative Least Square (ALS). The spectra of the respective columns of the spectral matrix S obtained by the calculated ST compose the resolution spectral data of the components obtained by the multivariate curve resolution.
In the multivariate curve resolution, a number of components to be resolved should be set in advance. When k-number of components is assumed to be included in a sample, a resolved result of a data matrix can be expressed as the following expression (2) by using a concentration matrix Ck and a spectral matrix Sk obtained by the multivariate curve resolution. A symbol SkT is a transposed matrix of the spectral matrix Sk, a symbol Ek is a residual matrix. At this time, when the assumed number of the components k is different from the number of existent components, spectra and concentration distribution of the components obtained by the concentration matrix Ck and the spectral matrix Sk are different from spectra and concentration distribution of the components existent in the sample. For this reason, in order to obtain an appropriate resolved result, the multivariate curve resolution should be carried out after the number of components existent in the sample is set.D=CkSkT+Ek  (2)