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The presence of practically unavoidable scatterers and background absorbers in turbid media such as biological tissue or cell suspensions can significantly distort the shape and intensity of fluorescence spectra of fluorophores and, hence, greatly hinder the in situ quantitative determination of fluorophores in turbid media. In this contribution, a quantitative fluorescence model (QFM) was proposed to explicitly model the effects of the scattering and absorption on fluorescence measurements. On the basis of the proposed model, a calibration strategy was developed to remove the detrimental effects of scattering and absorption and, hence, realize accurate quantitative analysis of fluorophores in turbid media. A proof-of-concept model system, the determination of free Ca(2+) in turbid media using Fura-2, was utilized to evaluate the performance of the proposed method. Experimental results showed that QFM can provide quite precise concentration predictions for free Ca(2+) in turbid media with an average relative error of about 7%, probably the best results ever achieved for turbid media without the use of advanced optical technologies. QFM has not only good performance but also simplicity of implementation. It does not require characterization of the light scattering properties of turbid media, provided that the light scattering and absorption properties of the test samples are reasonably close to those of the calibration samples. QFM can be developed and extended in many application areas such as ratiometric fluorescent sensors for quantitative live cell imaging.

Particle size distribution and compactness have significant confounding effects on Raman signals of powder mixtures, which cannot be effectively modeled or corrected by traditional multivariate linear calibration methods such as partial least-squares (PLS), and therefore greatly deteriorate the predictive abilities of Raman calibration models for powder mixtures. The ability to obtain directly quantitative information from Raman signals of powder mixtures with varying particle size distribution and compactness is, therefore, of considerable interest. In this study, an advanced quantitative Raman calibration model was developed to explicitly account for the confounding effects of particle size distribution and compactness on Raman signals of powder mixtures. Under the theoretical guidance of the proposed Raman calibration model, an advanced dual calibration strategy was adopted to separate the Raman contributions caused by the changes in mass fractions of the constituents in powder mixtures from those induced by the variations in the physical properties of samples, and hence achieve accurate quantitative determination for powder mixture samples. The proposed Raman calibration model was applied to the quantitative analysis of backscatter Raman measurements of a proof-of-concept model system of powder mixtures consisting of barium nitrate and potassium chromate. The average relative prediction error of prediction obtained by the proposed Raman calibration model was less than one-third of the corresponding value of the best performing PLS model for mass fractions of barium nitrate in powder mixtures with variations in particle size distribution, as well as compactness.