Estimation of particle size distribution from Vis/NIR scattering measurements

The quality of colloid systems, such as suspensions and emulsions, is determined by the chemical composition of the medium and dispersed particles, as well as the physical characteristics of the particles. The particle size distribution (PSD) and volume fraction of particles (VF) have an important effect on the product properties such as viscosity1, perception of creaminess of food emulsions2, etc. Therefore, PSD monitoring during production and storage of these colloids could promote early detection of an altering product quality. Optical measurements such as Vis/NIR spectroscopy have already found their way to the food industry for (on-line) process monitoring on a variety of products3, but the number of studies aiming at PSD monitoring is still very limited. For PSD estimation, the link between particle size and light scattering can be used instead of e.g. light absorption. In case of spherical particles, the relationship between bulk scattering properties (scattering coefficient μs, anisotropy factor g) and particle size is described by Mie theory. In case of a known PSD, the bulk optical properties and light propagation can be simulated, as was shown by Aernouts et al. for polydisperse systems4, 5, 6. However, in most cases the inverse problem is of interest, to derive the PSD from non-destructive optical measurements. In literature, inverse PSD estimations are often starting from simulated or measured optical density7,8,9. It is an ill-posed problem that needs regularization to select the solution that corresponds to a physically possible PSD and is consistent with literature knowledge. Depending on the assumptions about PSD shape, estimation methods can be divided in shape dependent and shape independent methods. The former assume a parametrized distribution form, while the latter impose conditions to the smoothness of the PSD8. In this study, both a shape dependent and a shape independent estimation method are elaborated. Their performance in estimating the PSD and volume fraction of milk fat globules in raw and homogenized milk based on the measured Vis/NIR bulk scattering coefficient profile is evaluated. The size of colloidal particles is an important quality characteristic of emulsions and suspensions as it is related to the stability and the general perception of the product. To monitor this physical quality property during production or storage, a measurement technique is required which can quantify the particle size distribution (PSD) in a rapid and non-destructive way. As such colloidal particles typically have a different refractive index than the surrounding medium, they scatter light. Therefore, the possibility to estimate the PSD and volume fraction of scattering particles from measured Vis/NIR scattering coefficient profiles was investigated in this study. Both a shape dependent and a shape independent PSD estimation method were elaborated and applied to estimate the PSD of the fat globules in milk. The shape dependent method approximates the PSD by a probability density function (e.g. Weibull). In case of a correct choice of the probability density function, this method results in good and robust estimations. In case of the shape independent method, the PSD is approximated by a weighted combination of B-splines. This provides extra flexibility, but can result in oscillations and artefact peaks in the estimated PSD if the regularization in not sufficient.