## 3 Results  
### Distribution of \(R_{total}\) Values for p-Waves Incident at \(\theta_{B}\)  
Based on the equation that relates Brix to the refractive index (n), which was provided by the International Commission for Uniform Methods of Sugar Analysis [22], an SSC of 14\({}^{\circ}\) Brix corresponds to \(n=1.354\). Therefore, the refractive index of medium 1 and medium 2 are n\({}_{1}=1.000\) and n\({}_{2}=1.354\), respectively. According to [PERSON]'s law of reflection, the angle of incidence that minimizes R\({}_{\mathrm{P}}\) (i.e., \(\theta_{\mathrm{B}}\)) is 53.55\({}^{\circ}\). Because the thickness of the skin of Indian jujube is only 0.1-0.15 mm and 700-1600 nm light is known to penetrate 3-4 mm of fruit flesh [23], it may be assumed that the skin's influence on reflectance is negligible and that all of the NIR light had penetrated into the fruits' flesh. P-waves and unpolarized light were used to probe the reflectance of Indian jujube fruits, with the angle of incidence being \(\theta_{\mathrm{B}}\). The resulting R\({}_{\mathrm{total}}\) values were then recorded. When these measurements are performed with p-waves and an angle of incidence of \(\theta_{\mathrm{B}}=53.55^{\circ}\), R\({}_{\mathrm{surface}}\) will be minimized (according to [PERSON]'s law, R\({}_{\mathrm{P}}=0\) and T\({}_{\mathrm{P}}=1\)), as shown in Figure 3. Therefore, all of the light will penetrate into the flesh of the Indian jujube fruits, thus maximizing the absorption of incident light by chemical bonds within the fruit, which will manifest in the reflectance signal measured by the NIR photodetector. To confirm that polarization affects transmittance, we examined whether R\({}_{\mathrm{total}}\) changed with the polarization of the light source while maintaining the angle of incidence at \(\theta_{\mathrm{B}}\). Indian jujube fruits with the same SSC (SSC = 14\({}^{\circ}\) Brix) were used in this experiment and R\({}_{\mathrm{total}}\) was measured using p-waves and nonpolarized waves, 30 times each. The resulting R\({}_{\mathrm{total}}\) values are shown in Figure 4a,b, which show that the nonpolarized waves and parallel-polarized waves resulted in R\({}_{\mathrm{total}}\) values of 0.42-0.67 and 0.47-0.57, respectively (all R\({}_{\mathrm{total}}\) values have been normalized). Because the R\({}_{\mathrm{total}}\) values that were obtained with p-waves are less scattered than those obtained with unpolarized waves, one may conclude that the use of p-waves at \(\theta_{\mathrm{i}}=\theta_{\mathrm{B}}\) can effectively reduce the interference caused by reflections from the Indian jujube fruits' skin. Figure 3: Transmittance and reflectance of p-waves at each angle of incidence. Correlation between the Vitamin C Contents of the Calibration Set and the Reflectances of the Characteristic Wavelength Combinations  
In the following experiment, the vitamin C content of Indian jujube was measured using a variety of wavelengths that were obtained using NIR bandpass filters. The r\({}_{\rm c}^{2}\) and RMSEC values of each wavelength with p-waves and nonpolarized waves are shown in Table 3.  
As shown in Table 3, the errors of the predictions based on p-waves are generally lower than those of nonpolarized waves. Hence, it may be inferred that the use of p-waves can effectively suppress the influence of surface reflections from the samples, which increases the strength of OH and CH\({}_{2}\) absorptions in the reflectance signal, thus improving accuracy and reducing the RMSEC [16; 17]. Figure 4: Comparison between the total reflection (R\({}_{\rm total}\)) of (**a**) non-polarized waves (NP) and (**b**) parallel-polarized waves (p-waves). Wavelengths whose reflectances correlate most strongly with the vitamin C contents of Indian jujube are 1200, 1400 and 1450 nm. This indicates that the chemical bonds of vitamin C absorb most significantly at these wavelengths, which resulted in high \(\mathrm{r_{c}^{2}}\) values.