Curve resolution of fluorescence data

Fluorescence spectroscopy is often used in analytical chemistry, food analysis, environmental analysis etc. It is a very sensitive spectroscopic technique which can be performed nondestructively and provides qualitative and quantitative information of diverse types of chemical analytes [Andersson Arndal 1999, Aubourg et al. 1998, Beltran et al. 1998a, Bright 1995, Bro 1999, Ferreira et al. 1995, Guiteras et al. 1998, Jensen et al. 1989, Jiji etal. 2000, Ross etal. 1991, Wolfbeis Leiner 1985], This application explains an example of estimating relative concentrations and pure analyte spectra from fluorescence measurements of chemical analytes in mixtures. Similar problems also arise frequently in other types of spectroscopy, in chromatography and other areas. Several names are used for this problem unmixing, curve resolution, source separation etc. Specifically, the application 

Curve resolution is the goal and as fluorescence data are known to approximately follow a PARAFAC model (see next), only PARAFAC models will be investigated. Hence, in this application, there will not be any investigation as to which model structure is preferred. 

In this particular problem, a set of 27 samples containing different amounts of L-phenylalanine, L-3,4-dihydroxyphenylalanine (DOPA), 1,4-dihydroxybenzene and L-tryptophan have been measured by fluorescence spectroscopy [Baunsgaard 1999, Riu Bro 2002], The data are important as a model system for many biological systems, e.g. in food and environmental analysis. The goal here is to develop a PARAFAC model of the measured data because a PARAFAC model will ideally resolve the pure spectra as well as the relative concentrations of the analytes [Bro 1997, Bro 1998, Bro 1999, Leurgans et al. 1993, Leurgans Ross 1992, Ross Leurgans 1995]. 

The parameter cif is linear in the concentration of analyte / and includes the quantum yield of the analyte. The parameter bg is specific to analyte / and expresses the fraction of photons emitted at wavelength j. Finally, the parameter holds the intensity of the incident light at excitation wavelength k multiplied by the absorption at wavelength k. 

This model of fluorescence data is based on the assumption that the total absorbance is small and that there is no energy transfer between analytes [Ewing 1985], If the model is extended to several (/) samples, it is identical to a PARAFAC model 

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