Multi-Reflectance-Spectroscopy,Part I: Theory and Calculations Using Simulated Milk Samples

Abstract

Optical methods are appropriate for monitoring of constituents in suspensions and emulsions. A simple multi-wavelength, multi-reflectance spectroscopic technique, called MRS-Technology, is introduced. Two different signals of a sample are measured: the reflectance from a small and from a large measuring volume corresponding to the reduced scattering coefficient ${\mathrm{\mu }}_{\text{SCA}}^{\prime }$ and to the sum of ${\mathrm{\mu }}_{\text{SCA}}^{\prime }$ and the absorption coefficient μ_ABS, respectively. Analytical relations between the MRS reflectance and μ_ABS as well as ${\mathrm{\mu }}_{\text{SCA}}^{\prime }$ are derived. The investigations on MRS method are carried out using milk as an example. For this purpose “virtual” milk samples are defined. μ_ABS and ${\mathrm{\mu }}_{\text{SCA}}^{\prime }$ are calculated by means of the Mie scattering theory in the ultraviolet–visible–shortwave near-infrared (UV-Vis-SWNIR) spectral range. Using this data analytical reflectances can be calculated based on MRS theory as well as numerical reflectances obtained by Monte Carlo (MC) simulation. Analytical and numerical results are compared and investigated. The spectral behavior of the analytical reflectances is very similar to that of the numerical MC reflectances in the case of medium and low absorptions. By means of simple multilinear regression techniques (MLR), simple correlations between fat and protein volume fractions and reflectances could be generated with acceptable root mean square error (RMSE) values. Each correlation shows that best results will be achieved by using reflectances at sample-specific wavelengths for small and large measuring volumes of a sample indicating the potential of the MRS-Technology.

Graphical Abstract