Estimation of Fat Globule Size Distribution in Milk Using an Inverse Light Scattering Model in the near Infrared Region

Abstract

The determination of particle characteristics from light scattering patterns is a challenging inversion problem and, not least, a demanding instrumentation problem. Despite the importance of the knowledge of size distribution in several technological dairy processes, often laser diffractometers and other instrumentation for particle size analysis are not available in dairy laboratories and, therefore, such information is not easily available, except for research purposes. Near infrared (NIR) instrumentation, instead, is largely available in dairy labs. Laser granulometers are based on the principle that particles scatter light from one or two laser beams with an angular pattern directly related to their size. Consequently, a suspension of particles forms an angular pattern of scattered light that is characteristic of its size distribution. In a similar manner, a NIR spectrometer in transmission mode can be considered as a tool for studying the behaviour of forward scattering at different wavelengths. In this work, a model based on an approximation of Mie scattering was developed for the calculation of scattering due to fat globules in the NIR transmission spectrum of milk. The inversion of the model was applied to raw milk spectra in the spectral regions from 1000 nm to 1360 nm and from 1580 nm to 1800 nm, free from strong absorption bands, in order to estimate the fat particle size distribution. More than 700 samples, collected monthly for two years from 50 Friesian–Holstein, 7 Jersey and 5 Brown cows, were analysed. Four hundred of these samples were also analysed using a laser granulometer. The correlation ( r2) between NIR and laser granulometric data was equal to 0.95 for the mean volume surface diameter ( d3,2) with a root mean square error ( RMSE) of 0.11 microns. A sub-class of Weibull distribution with only one freedom parameter proved to be sufficient in order to describe milk fat globule distribution and fit spectral data. The method developed in this work can be useful both for genetic selection and technological purposes and easily extended to the analysis of other dietary fat emulsions.