Coupled turbidity and spectroscopy problems: A simple algorithm for the volumetric analysis of optically thin or dilute two-phase systems

We report an algorithm for measuring the phase volume fraction and solute concentration of a two-phase system, applicable to either optically thin or optically dilute spatially homogeneous systems. Probing light is directed into the sample, and the elastically scattered light (EE) is collected as one signal and the inelastically scattered light (IE) collected as another signal. The IE can be pure fluorescence or Raman or an unresolved combination of the two. As the IE and the EE are produced by fundamentally different processes, they are independent. The algorithm, derived from radiation transfer theory, shows that phase volume and concentration are linear functions of the EE and IE. The parameters are derived from a training set. We present examples of how the algorithm performs when the assumption of spatial homogeneity is violated and when light-induced photochemistry causes changes in the IE. Although this is a generally valid algorithm with many potential applications, its use is discussed briefly in the context of blood and tissue analysis since the algorithm was originally designed for noninvasive in vivo probing of human skin.