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:

*x*_{jk} = *ab*_{j}c_{k}

where *x*_{jk} is the intensity of the light emitted at emission wavelength*j *and excitation wavelength *k*, *a* is the concentration of the analyte, *b*_{j} is the relative emission emitted at wavelength *j*, and *c*_{k} 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 *b*_{j} is independent of *c*_{k}. 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 *b*_{jf} and the relative absorption at excitation *k* is *c*_{kf}, and the concentration of analyte *f* is *a*_{f}. For several samples, and *a*_{if} 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.