Double two-dimensional correlation analysis – 2D correlation of 2D spectra

Abstract

2D correlation analysis of 2D correlation spectra, i.e., double 2D correlation analysis, is carried out by a series of simple matrix multiplication operations. A new class of correlation spectra with higher selectivity and spectral resolution are generated. Quadrature 2D correlation enabled by the proper rescaling of double 2D correlation is especially useful for the analysis of the contravariant portion of spectral signals, which are 90 deg out of phase with the rest of data. The utility of double 2D correlation is most clearly demonstrated when it is applied to hetero-spectral or hetero-mode correlation analysis. Double hetero-correlation generates highly selective 2D spectra based on a portion of spectra which is projected onto a space spanned by other spectra or different spectral region. Illustrative examples are provided with Raman spectral monitoring of an emulsion polymerization process and a solution mixture undergoing compositional changes to show how double 2D correlation can be utilized.