3.1. Distribution of Rtotal Values for p-Waves Incident at θB
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° Brix corresponds to n
= 1.354. Therefore, the refractive index of medium 1 and medium 2 are n1
= 1.000 and n2
= 1.354, respectively. According to Fresnel’s law of reflection, the angle of incidence that minimizes Rp
) is 53.55°. 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 θB
. The resulting Rtotal
values were then recorded. When these measurements are performed with p-waves and an angle of incidence of θB
= 53.55°, Rsurface
will be minimized (according to Fresnel’s law, Rp
= 0 and Tp
= 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 Rtotal changed with the polarization of the light source while maintaining the angle of incidence at θB. Indian jujube fruits with the same SSC (SSC = 14° Brix) were used in this experiment and Rtotal was measured using p-waves and nonpolarized waves, 30 times each.
The resulting Rtotal
values are shown in Figure 4
a,b, which show that the nonpolarized waves and parallel-polarized waves resulted in Rtotal
values of 0.42–0.67 and 0.47–0.57, respectively (all Rtotal
values have been normalized). Because the Rtotal
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 θi
can effectively reduce the interference caused by reflections from the Indian jujube fruits’ skin.
3.2. 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
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 CH2
absorptions in the reflectance signal, thus improving accuracy and reducing the RMSEC [16
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 values. The 1300, 1350 and 1650 nm wavelengths correlate more poorly with vitamin C content; this is because the chemical bonds of vitamin C do not absorb significantly at these wavelengths, thus resulting in low values.
Characteristic wavelengths that have the largest correlation coefficients were selected to form combinations of wavelengths and were then used to determine the vitamin C content of Indian jujube. Once the reflectance signals at these wavelengths were acquired by the NIR photodetector, the PLS algorithm was used to quantify the vitamin C content of each fruit. The correlation of each wavelength combination was then calculated. The
and RMSEC values of each wavelength combination (which comprises the most strongly correlated wavelengths) are shown in Table 4
The results of the PLS calculations indicate that the and RMSEC of combination A were 0.86 and 1.44 mg/100 g, respectively. Combinations B and C (N = 4) resulted in of 0.87 and 0.86, respectively, as well as RMSEC values of 1.39 mg/100 g and 1.42 mg/100 g, respectively. Although combinations B and C have similar values, the RMSEC of combination B was slightly lower. Therefore, another wavelength was added to combination B to form five-wavelength combinations (N = 5). Among combinations D, E and F (N = 5), D has the highest ( = 0.89) and lowest RMSEC (1.31 mg/100 g). Because the correlation of 1600 nm with vitamin C content is rather low ( = 0.55), the inclusion of this wavelength failed to enhance the accuracy of combination E and F. Another wavelength was added to combination D to form N = 6 combinations, thus forming combinations G, H and I, which all have slightly higher values than the N = 5 combinations. However, upon further analysis, it was discovered that the and RMSEC values of the N = 6 combinations were slightly better than those of the N = 5 combinations. We speculate that this is because the values of 1050 nm and 1150 nm are relatively low (0.70 and 0.68, respectively); therefore, the inclusion of these wavelengths in a wavelength combination did not significantly improve the of the combination.
The wavelengths of combination D (1200, 1400, 1450, 1500 and 1550 nm) correlated strongly with OH and CH2
absorptions. This result is consistent with the NIR absorptions of OH and CH2
that were observed by López et al. [24
], Aenugu et al. [25
], Fox et al. [26
], Rajan et al. [27
] and Bento et al. [28
Based on these results and the practical requirements of actual detection systems (e.g., size, cost and performance), we decided to use combination D (N = 5) in our detection system, whose
and RMSEC are 0.89 and 1.31 mg/100 g, respectively. The results obtained using combination D are shown in Figure 5
. This combination was then used to measure the vitamin C contents of the prediction set. The corresponding
and RMSEP values were then calculated.
3.3. Analyzing the Predicted Vitamin C Contents of the Prediction Set
Combination D (1200, 1400, 1450, 1500 and 1550 nm), which is the optimal combination of wavelengths for the calibration set, was used to predict the vitamin C contents of the prediction set. After nondestructive measurements and destructive HPLC analysis were performed on the 60 Indian jujube samples of the prediction set, the
and RMSEP values of the predicted values were calculated, as shown in Table 5
and RMSEP of combination D were are 0.84 and 1.65 mg/100 g for the prediction set, respectively. These values are similar to the
and RMSEC values of this combination with the calibration set. The correlation between the predicted and measured vitamin C values is illustrated in Figure 6
. Here, it is shown that our detection system and predictive model performs excellently and is highly robust, as it has a high
value and low RMSEP.