## 2 Materials and Methods
### Data Analysis
#### 2.3.3 Statistical Analysis  
Pearson's correlation coefficient (R) [46; 47], which is calculated with Equation (3), was used to analyze the correlation between SAPD, LAI, and the spectral parameter. A strong correlation between SPAD, LAI, and the spectral parameter could be observed if the absolute value of \(R\) was high. \[R=\frac{\sum_{i=1}^{m}(x_{i}-\overline{x})(y_{i}-\overline{y})}{\sqrt{\sum_{i=1 }^{m}(x_{i}-\overline{x})^{2}}\sqrt{\sum_{i=1}^{m}(y_{i}-\overline{y})^{2}}} \tag{3}\]  
where \(x_{i}\) is a spectral parameter, which includes the spectral reflectance, red-edge parameters, and absorption features parameters. \(\overline{x}\) is the average of all spectral parameters. \(y_{i}\) is the rice physiological indices, which include SPAD and LAI. \(\overline{y}\) is the average value of the rice physiological indices. \(m\) is the sample size. For the Pearson's correlation coefficient, we focused on statistical inference with the aim to test the null hypothesis, through which the true correlation coefficient \(\rho\) is equal to 0, based on the value of the sample correlation coefficient R [46]. Then, we used the exact distribution to calculate the \(p\)-value--namely, when the samples x and y follow the normal distribution, the probability density function of the correlation coefficient R distribution can be calculated by Equation (4), while the \(p\)-value can be estimated using Equation (5). Generally, the smaller the \(p\)-value is, the more significant the correlation is. In this paper, 0.05 was used as the standard for significant correlation. \[f(R)=\frac{\left(1-R^{2}\right)^{(m/2-2)}}{B\left(\frac{1}{2},\frac{m}{2}-1 \right)} \tag{4}\]  
\[P=\int\limits_{-|R|}^{|R|}f(R)dR \tag{5}\]  
where \(R\) is the correlation coefficient, \(m\) is the sample size, and B represents the Beta distribution. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Description** & **Calculation Methods** \\ \hline A1 & The area of the left part of the first absorption band & \(\lambda_{c}^{1}-\lambda_{s}^{1}-\int_{\lambda_{c}^{1}}^{\lambda_{c}^{1}}Rn( \lambda)d\lambda\) \\ A2 & The area of the right part of the first absorption band & \(\lambda_{c}^{1}-\lambda_{c}^{1}-\int_{\lambda_{c}^{1}}^{\lambda_{c}^{1}}Rn( \lambda)d\lambda\) \\ A3 & The area of the left part of the second & \(\lambda_{c}^{2}-\lambda_{c}^{2}-\int_{\lambda_{c}^{2}}^{\lambda_{c}^{2}}Rn( \lambda)d\lambda\) \\ D2 & The depth of the second absorption band & \(Rn(\lambda_{c}^{2})\) \\ A4 & The area of the right part of the second & \(\lambda_{c}^{2}-\lambda_{c}^{2}-\int_{\lambda_{c}^{2}}^{\lambda_{c}^{2}}Rn( \lambda)d\lambda\) \\ A5 & The area of the left part of the third absorption band & \(\lambda_{c}^{3}-\lambda_{c}^{3}-\int_{\lambda_{c}^{3}}^{\lambda_{c}^{3}}Rn( \lambda)d\lambda\) \\ D3 & The depth of the third absorption band & \(Rn(\lambda_{c}^{2})\) \\ A6 & The area of the right part of the third & \(\lambda_{c}^{3}-\lambda_{c}^{3}-\int_{\lambda_{c}^{3}}^{\lambda_{c}^{3}}Rn( \lambda)d\lambda\) \\  & absorption band & \(\lambda_{c}^{3}-\lambda_{c}^{3}-\int_{\lambda_{c}^{3}}^{\lambda_{c}^{3}}Rn( \lambda)d\lambda\) \\ \hline \hline \end{tabular}  
* Rn is the normalized spectral reflectance curve, and \(\lambda\) is the wavelength (350–1350 nm). \(\lambda_{s}^{1}\), \(\lambda_{c}^{1}\), and \(\lambda_{c}^{1}\) are the start position (the average of all data is 553 nm), the deepest absorption position (673 nm), and the end position (788 nm) of the first absorption band; \(\lambda_{s}^{2}\), \(\lambda_{c}^{2}\), and \(\lambda_{c}^{2}\) are the start position (874 nm), the deepest absorption position (969 nm), and the end position (1072 nm) of the second absorption band; \(\lambda_{s}^{3}\), \(\lambda_{c}^{3}\), and \(\lambda_{c}^{3}\) are the start position (1072 nm), the deepest absorption position (1192 nm), and the end position (1257 nm) of the third absorption band.  
\end{table} 
Table 2: The description and calculation method of each absorption band parameter.