For one fluorophore (in essence one analyte) the emission intensity at a specific wavelength, j, when excited with light at a wavelength k, can be described:
xjk = abjck
where xjk is the intensity of the light emitted at emission wavelength
j and excitation wavelength k, a is the concentration of the analyte, bj is the relative emission emitted at wavelength j, and ck is the relative amount of light absorbed at the excitation wavelength k.
This relation holds approximately for diluted solutions (Ewing 85), and it further holds that bj is independent of ck. If several, F, analytes are present in a sample a similar relation for the intensity can be written:
Implying that the contribution to the emission from each analyte is independent of the contributions of the remaining analytes.
In the above equation the relative emission of analyte f at emission j is bjf and the relative absorption at excitation k is ckf, and the concentration of analyte f is af. For several samples, and aif being the concentration of the f ‘th analyte in the i ‘th sample, the model becomes
Hence the three-way PARAFAC model.
Galen W. Ewing. Instrumental methods of chemical analysis, New York:McGraw-Hill Book Company, 1985.