Investigating the Quality of Milk using Spectrometry Technique and Scattering Theory

Milk is a dairy product that contains dissolved proteins, carbohydrates, fat, and many minerals. Milk enhances body growth and provides vital energy and fatty acids. Milk can turn bad after being kept at room temperature for several days. The endurance of milk could depend on its fat and protein composition. Our work aims to compare the quality of milk after being kept at room temperature for several days using spectroscopy methods. Modeling based on scattering theory is also provided to compare the light propagation in milk, water, and air. A VIS-NIR spectrometer was used to observe the light absorption, transmission, and reflectance whereas a modeling approach was applied to study the scattering, absorption, and extinction efficiencies. The milk samples consist of full cream milk kept at room temperature for 8 days, 11 days, 14 days, and 17 days. The results show that milk without fermentation has higher light absorbance and lower transmission compared to milk with fermentation, due to changes in milk composition after the fermentation process. Milk scatters more light compared to water and air due to its fat globule and protein ingredients. The output of this study can be used as a reference for studies involving bacteria or microorganisms in milk. It also can be used to compare the quality of milk with and without air exposure. Keywords-light propagation; absorbance; transmittance; reflectance; scattering; milk; spectroscopy


INTRODUCTION
It is crucial to monitor the quality of milk in order to ensure we gain sufficient nutrients and minerals and prevent the occurrence of diseases. Cow milk consists of water (87%), fat (4%), proteins (3.4%), lactose (4.8%), and minerals (0.8%) [1]. Fat composition is not similar in full cream milk and skimmed milk. A layer of cream forms on the milk's surface if it is exposed for several days. This cream consists of spheres of various sizes floating in milk surrounded by a fat globule membrane. The membrane is responsible for fat protection against enzymes and prevents any globule coalescing into butter grains [1]. The spectroscopy technique can be used to observe the optical properties of milk based on light absorbance, transmission and scattering. Mie scattering theory is used to compute the absorption coefficient (μ ), the scattering coefficient (μ ), and the phase function p(θ), where θ is the scattering angle [2]. Mie theory is used to calculate the spectral dependence for the extinction cross section of nanoparticle suspensions [3]. The pump source energy passes through the turbid media depending on optical properties such as the refractive index, scattering, anisotropic factor, and laser light absorption [4]. The optical properties of milk based on backscattering intensity can be used to study fat and protein concentrations [5]. The complex fluid of milk is made up of many components such as water, lipids, lactose and protein [6,8]. Spectroscopy is widely used to measure the optical properties of samples based on light propagation and fluorescence. Color spectroscopy is used to obtain information about the atoms and molecules [8][9]. The absorbance spectroscopy is a technique used to measure the amount of absorbed light [10,11] with the determination of solution concentration based on Beer's Law [12]. NIR spectrometer and VIS-NIR spectrometer with different wavelength ranges are used to determine the accuracy of the intensity spectrum in the spectroscopy analysis [13].
Many recent studies on light propagation in milk involve backscattering [5], external cavity-quantum cascade laser spectroscopy [6], and laser diffraction and centrifugation [7]. Authors in [8] introduced the simplified NIR spectroscopy in measuring the end of milk fermentation by transforming sugar to lactic acid. The key characteristic of the fermentation process is the pH end point value, in the range of 4.4-4.5 [8]. This technique is quite complicated and costly. To the best of our knowledge, no comparison has been conducted using milk after several days' exposure and water. The previous studies also do not provide a modeling approach on light scattering in milk. Our previous work [14] compared the optical properties of full cream and skimmed milk using different spectrometer types. We found that full cream milk has higher absorption due to its higher fat content. This research is continued in the current paper, which aims to study the light propagation in various milk samples for different exposure at room temperature durations based on spectroscopy techniques using Visible (VIS) and Near Infra-Red (NIR) spectrometers. The technique is simpler and cheaper than the ones used in previous studies as indicated in the experimental section. The output shows that the newly opened milk sample absorbs more light than the other samples. A modeling approach based on Mie theory was also provided to compare light scattering in milk, water, and air.

II. THEORETICAL FRAMEWORK
For the computation of Mie efficiencies, there are two input parameters which are the complex refractive index m and the parameter size x as shown in (1) and (2) [12].
= ' + " (1) where ' is the real refractive index, " is the imaginary refractive index, is wave number in the ambient medium, and is the sphere radius.
The key parameters of Mie theory are the computed amplitudes of the scattered field. The coefficients and are required to obtain the Mie efficiency using Spherical Bessel function n (n=1, 2, …) of higher order and work well in the wider range of size parameters [15].
The efficiency of extinction and scattering can be identified in forward-scattering theorem and in the integration of the power scatters in all directions. The absorption efficiency can be identified with the equation of energy conservation [16]. Meanwhile, the backscattering efficiency is applicable to monostatic radar [15]. Equations for absorption, scattering and backscattering efficiency are: where x is the parameter size and n is the spherical Bessel function order n.
The efficiency of radiation pressure can be proven by the Two-Stream Model and correlates with the asymmetry parameter [17].
where is the scattering angle.
Amplitude functions 1 and 2 indicate the scattering properties or the scattering of an electromagnetic wave from a spherical particle. The scattering function is required for the far field scatterer [16]:

III. METHODOLODGY
The research is conducted using experimental and theoretical methods. The light absorption and scattering analysis in milk are based on Mie scattering theory. The scattering, absorption, extinction, and backscattering efficiencies are analyzed in a homogeneous dielectric sphere and its angular scattering using MATLAB. The analysis is also repeated for water and air.

A. Modeling Approach
The modelling part is used to determine the characteristics of light in a disordered medium using MATLAB. The light propagation efficiency with the justification of Mie coefficient matrix is computed. The angular functions are also computed to produce the Mie angular efficiency. Figure 1 shows the flowchart of the constructed modeling approach. the light propagation in milk, water and air. The modeling analysis uses Mie theory to compute the efficiency of scattering, absorption, extinction, backscattering, asymmetry parameter, and radiation pressure whereas the experimental section shows the output in terms of absorbance, transmission, and reflectance. The output from the theoretical and experimental study are analyzed and discussed thoroughly in this section.

A. Modeling based on Mie Scattering Theory
The measurements of scattering, extinction and absorption efficiency based on Mie theory were conducted in MATLAB. The input parameters were the complex refractive index and the parameter size x [18]. Modeling was done for milk, water, and air. Figures 5 and 6 summarize the modeling results. Equations (3) to (7) were used in Figure 5. Figure 6 is plotted based on (8)- (9). The extinction, forward scattering, absorption, and backscattering efficiencies are represented by Q ext , Q sca , Q abs and Q b respectively. Figure 5 shows clearly that milk has better scattering efficiency than water and air. At parameter size 2, the scattering efficiency in milk (Figure 5(a)) reaches 0.6, while the scattering efficiency in water ( Figure  5(b)) and air ( Figure 5(c)) are 0.7 and 5×10 -7 respectively, prooving that the least light scattering occurs in the air, whereas milk and water consist of particles which can scatter the light. We presume that the light scattering and absorption are affected by the size and concentration of the particles, the incident light wavelength, and sample size [19]. Milk depicts the highest efficiency of light absorption due to its composition of fat globules and proteins. Figure 5 also shows that the forward scattering is more efficient compared to the backscattering for all samples due to the larger particles size of the samples. Figure 6 shows the scattering angle of milk, water and air respectively. We observe that milk has larger value of angular scattering than water and air. It is clearly shown that milk has higher scattering effect. We attribute that to the milk contents which mostly consist of fat and proteins which can scatter light [20].    Figure 4 lk is gradual creases due to   Figure 7(c) shows the reflectance spectra of the milk samples. The reflectance of newly opened milk is higher than the fermented milk's. The low reflectance values for fermented milk are recorded due to its high water absorption [25]. Hence, we suppose that the presence of fat globules and protein micelles in milk affect the light reflectance. The reflectance intensity decreases over the fermentation process due to the changes of protein and fat globules [26]. Figure 8 shows the spectra comparison of milk samples and water. Figure 8(a) shows that water absorbs most of the light at 600nm whereas the absorption peak of milk is at 700nm. Milk and water depict similar transmission peaks at ~ 650nm ( Figure  8(b)). Water sample shows higher transmission spectrum as it is more transparent than milk. Newly opened milk samples have higher reflectance than water due to their fat and protein composition. The size and shape of particles, the composition, and the concentration of the tested samples can affect the absorption, transmission, and reflectance of the samples respectively [26]. Newly opened milk samples consist of various particle compositions whereas the fermented milk samples have experienced physical state changes.

V. CONCLUSION
In conclusion, this research investigates the quality of milk for samples freshly opened and after being kept at room temperature for several days using spectroscopy and scattering theory. The optical properties of milk samples were investigated using VIS and NIR spectrometers. Newly opened milk samples have higher light absorbance and lower light transmission compared to the fermented milk, due to the aggregation of the fat and protein particles in milk during the fermentation process. Besides that, modeling based on scattering theory was done to compare the light propagation in milk, water, and air. The modeling shows that milk scatters more light compared to water and air due to the presence of fat globule, protein, and minerals. The outcome of the study shows that the quality of milk is reduced when it is kept at room temperature for several days. This is proved by both naked eye observation and spectroscopy. The outcome of this study can be useful in supporting future analysis studies on dairy products.