# Color Recognition of Transparent Plastic Based on Multi-Wavelength Transmission Spectrum
## 3 Results and Discussion  
### Characteristics of Transmission Spectrum  
The color of the transparent plastic depends on the wavelength of the light that is passing through the plastic [26; 27; 28], as shown in Figure 2e-h, the plastics of the four colors possess different transmission spectra at a same transmission light source. However, because the four colors of the plastics are similar, the transmission spectra of the plastics may also be similar at certain wavelengths of light source. The ratios of the \(R\), \(G\) and \(B\) wavebands can magnify the difference in the transmission spectra, and furthermore, the ratios are stable for a certain color because they are only related to the color and are not affected by other factors such as light intensity. Therefore, the ratios of the \(R\), \(G\) and \(B\) wavebands were used as color parameters to describe the difference in the transmission spectra of transparent plastics with different colors. The ratios of the \(R\), \(G\) and \(B\) wavebands, that are \(BG\), \(GR\) and \(RB\), were calculated using Equations (1)-(3). Each transmission spectrum contributes a set of color parameters \(BG\), \(GR\) and \(RB\). \[BG=\frac{(B/G)_{plastic}}{(B/G)_{light}} \tag{1}\]  
\[GR=\frac{(G/R)_{plastic}}{(G/R)_{light}} \tag{2}\]  
\[RB=\frac{\left(R/B\right)_{plastic}}{(R/B)_{light}} \tag{3}\]  
where (\(B\)/\(G\))\({}_{plastic}\), (\(G\)/\(R\))\({}_{plastic}\) and (\(R\)/\(B\))\({}_{plastic}\) are calculated from the transmission spectrum of the plastic, and (\(B\)/\(G\))\({}_{light}\), (\(G\)/\(R\))\({}_{light}\) and (\(R\)/\(B\))\({}_{light}\) are calculated from the spectrum of the light source that is acquired by the camera when there is no plastic sample. By dividing the parameters calculated from the light source spectrum, the influence of the light source can be eliminated in the color parameter calculation. For each sample, the color parameters \(BG\), \(GR\) and \(RB\) were calculated from the transmission spectra that were obtained at the 381 nm, 439 nm, 620 nm and white transmission light sources. As described in Section 2.2, for each color of plastic, there were 40 samples, thus there were 40 sets of color parameters \(BG\), \(GR\) and \(RB\) at each wavelength of transmission light source. The mean values of the 40 sets of color parameters were, respectively, calculated for each color of plastic at each wavelength of transmission light source, as shown in Table 1 and Figure 3. \begin{table}
\begin{tabular}{c c c c c c} \hline  & & **Colorless** & **Light Blue** & **Light Green** & **Apple Green** \\ \hline \multirow{4}{*}{**381 nm**} & \(BG\) & 1.011 & 1.045 & 0.848 & 0.913 \\  & \(GR\) & 0.900 & 1.101 & 0.802 & 1.061 \\  & \(RB\) & 1.102 & 0.879 & 1.476 & 1.036 \\  & \(BG\) & 1.020 & 1.022 & 1.180 & 1.127 \\
**439 nm** & \(GR\) & 1.082 & 1.089 & 1.700 & 1.485 \\  & \(RB\) & 0.913 & 0.905 & 0.503 & 0.602 \\  & \(BG\) & 0.571 & 0.571 & 0.568 & 0.547 \\
**620 nm** & \(GR\) & 1.893 & 1.764 & 1.806 & 1.636 \\  & \(RB\) & 0.928 & 0.993 & 0.975 & 1.117 \\  & \(BG\) & 1.014 & 1.033 & 0.931 & 0.935 \\
**white** & \(GR\) & 1.009 & 1.048 & 1.012 & 1.118 \\  & \(RB\) & 0.978 & 0.924 & 1.062 & 0.957 \\ \hline \end{tabular}
\end{table} 
Table 1: The mean values of the color parameters \(BG\), \(GR\) and \(RB\) of the colorless, light blue, light green and apple green plastics at 381 nm, 439 nm, 620 nm and white transmission light sources. As can be seen from Figure 3, on the whole, the color parameters \(BG\), \(GR\) and \(RB\) of the transparent plastics of the four colors show differences both in patterns and values at each light source. Therefore, color parameters \(BG\), \(GR\) and \(RB\) can be used for color recognition of transparent plastic. However, it should be pointed out that at 439 nm light source, the color parameters of the colorless and light blue transparent plastics were almost the same (Figure 3b), and at 620 nm light source, the color parameters of light blue and light green had little difference (Figure 3c).