*3.1. Optical Properties of Milk in a Wide Spectral Range*

Attenuation of optical radiation propagating through a medium is a consequence of two fundamental physical phenomena of light-matter interaction—absorption and scattering; according to the Beer-Lambert law the intensity of radiation *I*λ decreases exponentially [45]:

$$I\_{\lambda} = I\_{0\lambda} \exp[-\mu\_{\text{e}} \cdot d] = I\_{0\lambda} \exp[-(\mu\_{\text{a}} + \mu\_{\text{es}}) \cdot d],\tag{1}$$

where *I*0<sup>λ</sup> is the intensity of incident radiation; μ<sup>a</sup> is the bulk absorption coefficient; μ<sup>s</sup> is the bulk scattering coefficient; μ<sup>e</sup> = μ<sup>a</sup> + μ<sup>s</sup> is the extinction coefficient, which includes both absorption and scattering; *d* is the thickness of an optical layer. The absorption and scattering coefficients μ<sup>a</sup> and μs, along with the refractive index n and the scattering anisotropy factor *g* [46] are referred to as bulk optical properties of a medium [47]. For highly turbid media, where multiple scattering events take place on the optical path, more sophisticated mathematical description of radiative transfer than the classical Beer-Lambert law may be needed [48,49].

For the purpose of optical radiation transfer analysis, milk can be represented as a three-phase inhomogeneous composite liquid medium consisting of the serum, the fat globules, and the casein micelles [50]. The serum (or whey) is an aqueous solution of whey proteins, lactose, vitamins, electrolytes, and other water-soluble components of milk. The fat globules are spherical lipid droplets, which form a stable emulsion in the serum, the size of the droplets in raw milk lies in the wide range from a few hundred nanometers up to 10 μm [51], but it can be sufficiently reduced and uniformed in the process of homogenization [52]. The casein micelles are solid spherical formations dispersed in the serum; they are formed of the insoluble casein proteins which represented up to 80% of all proteins in milk. These micelles vary in sizes from 50 nm to 680 nm (the mean diameter is about 200 nm) which are smaller than the diameter of fat globules [50].

The milk serum may be slightly opaque, but elastic scattering of photons occurs mainly on the fat globules and casein micelles. Taking into account that the sizes of these spherical particles P are comparable with the wavelengths of radiation λ in a considerable part of the optical region 0.1λ < P < λ, the Mie theory should be applied to analyze elastic light scattering in milk [51]. It is a highly turbid medium because the fraction of the scattering particles is very substantial: the concentration of fat in raw milk can achieve 8%, casein content can be as high as 3% [50]. In molecular absorption spectroscopy (spectrophotometry) the main challenges when dealing with such samples are distinguishing and separating absorption and scattering effects in the experimental data (usually reflectance and transmittance spectra), and subsequent recovering of the bulk optical properties [47]. For raw milk, this task is even more complicated because the distribution of scattering particle by size is not known beforehand and depends on many factors [51].

Alongside with the fat globules and casein micelles, somatic cells (primarily leucocytes with the diameter of 8.5–10 μm, which should be considered as an additional type of scattering particles) are always present in relatively small amounts even in normal milk. In case of inflammation (cow mastitis) the concentration of these cells is elevated; in the process of milk quality assessment it is necessary to control that it is below a certain threshold. This can be done by optical methods because somatic cells influence milk scattering properties [53].

In the Table 4 the wavelengths (wavenumbers) of the characteristic absorption of several important milk constituents are summarized; the strongest absorption bands, which are often used for quantitative spectral analysis, were selected in a wide spectral range (0.2–25 μm).


**Table 4.** The wavelengths/wavenumbers of the main milk constituents' characteristic absorption in a wide spectral range.

The diagram in the Figure 3 shows the most practically significant optical spectroscopic techniques for milk analysis; molecular absorption spectroscopy (spectrophotometry) is dominant among them for the purpose of the qualitative determination of the main milk constituents and some adulterants in routine milk testing.

**Figure 3.** Optical spectroscopic techniques for milk quantitative and qualitative analysis.

Despite similarity in the background physical principles, analytical approaches, methods, and equipment for the spectral analysis of milk strongly differ in different spectral regions (UV, visible, NIR, MIR) and should be discussed separately.
