Correlation analysis of spectroscopic data

A method of correlation analysis of spectroscopic data is developed that allows the determination of patterns in experimental results with and without the application of a functional physico-mathematical model. In the latter case the method of correlation analysis allows to determine the regression values that occur in a physico-mathematical model. The method is applicable if the result of an experiment is the relationship between one physical variable and two or more parameters. The key idea of the method is search for particular measuring ranges of one of the parameters, where functional relationships of the physical value and one of the other parameters are either similar to each other or similar to some theoretical relationship. The ranges are found using the maximum of the cosines between two experimental data vectors or between the experimental data vector and the functional physico-mathematical model vector. The concept of a correlation spectrum that plays the major part in the correlation analysis of the experimental relationships between physical values and length or frequency of waves is introduced. The possibilities of the method are illustrated using the correlation analysis of the up-converted luminescence spectra of the YF3:Yb3+ (20 at.%), Tm3+(1 at.%) crystal that were captured at 13 equidistant power values of a laser diode stationary emission: P∈(Pmin,Pmax), Pmin=253.3mW, Pmax=1108mW, λex=934nm. Using the correlation spectra a strong correlational relationship is determined between P23 and D21 energy levels populations of the Tm3+ ion as well as weak spectrum line of Tm3+(P23→D21) that is not visible in a regular luminescence spectrum was determined. The properties of the correlation spectrum allows to assert that this line is determined by stimulated emission.