## 2 Materials and Methods
### Construction and Reconstruction of the Initial Spectral Indices  
Under the stress of disease, the physiological and biochemical characteristics as well as the apparent morphology of crops varied, which in turn caused the changes in the spectral indices. Therefore, its spectral response could be regarded as a function of pigment, water, morphology, and structure changes [27; 28; 29]. SI formulated with the sensitive bands could reflect the fluctuation of the spectral response to realize the detection of the disease in light of the pathological mechanism [30; 31]. In this study, we constructed the SIs through two stages. The first stage was the construction of the initial SIs, where all possible combinations of six types of hyperspectral SIs were constructed to simplify the spectral detection of cotton aphid damage including three three-band SIs and three two-band SIs. These initial SIs were then reconstructed with the healthy samples in the second stage to evaluate the cotton aphid damage effectively. In the first stage, three types of two-band SIs including the differential spectral index (DSI), normalized difference spectral index (NDSI), and the ratio spectral index (RSI) were calculated for the construction of the two-band initial indices, and three types of three-band indices that improved the differential spectral index (IDSI), photochemical spectral index (PSI), and the ratio spectral index (IRSI) were constructed as the three-band initial indices based on the raw spectral response from the full band range. These were formulated as follows:  
\[DSI(\lambda_{i},\lambda_{j})=R_{\lambda_{i}}-R_{\lambda_{j}} \tag{2}\]  
\[RSI(\lambda_{i},\lambda_{j})=\frac{R_{\lambda_{i}}}{R_{\lambda_{j}}} \tag{3}\]  
\[NDSI(\lambda_{i},\lambda_{j})=\frac{R_{\lambda_{i}}-R_{\lambda_{j}}}{R_{ \lambda_{i}}+R_{\lambda_{j}}} \tag{4}\]  
\[IDSI(\lambda_{i},\lambda_{j},\lambda_{k})=R_{\lambda_{i}}-R_{\lambda_{j}}+R_{ \lambda_{k}} \tag{5}\]  
\[IRSI(\lambda_{i},\lambda_{j},\lambda_{k})=\frac{R_{\lambda_{i}}}{R_{\lambda_{ j}}+R_{\lambda_{k}}} \tag{6}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Grade** & **Grading Standard** \\ \hline
0 & Healthy \\
1 & Few aphids scattered over the plant. Foliage free from crinkling with no \\  & yellowing symptoms \\
2 & Crinkling and curling of few leaves in the upper portion of plant \\
3 & The most severely damaged leaves curl up to half circle or above, showing \\  & an arc \\
4 & The most severely damaged leaves are completely curled and spherical \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The grading criteria for cotton aphid infestation. \[PSI(\lambda_{i},\lambda_{j},\lambda_{k})=\frac{R_{\lambda_{i}}-R_{\lambda_{j}}}{R_{ \lambda_{i}}+R_{\lambda_{k}}} \tag{7}\]  
In Equations (2)-(4), \(\lambda_{i},\lambda_{j}\) were all possible two-band combinations in the range of 325-1075 nm; \(R_{\lambda_{i}}\) and \(R_{\lambda_{j}}\) were the reflectance values at \(\lambda_{i},\lambda_{j}\), respectively. In Equations (5)-(7), \(\lambda_{i},\lambda_{j},\lambda_{k}\) were all possible three-band combinations and \(R_{i},R_{j},R_{k}\) were the reflectance at \(\lambda_{i},\lambda_{j},\lambda_{k}\), respectively. Let \(m\) be the number of training samples. After the construction and calculation of the initial SIs for each training sample, we reconstructed them based on the SI difference between the sample \(x_{i}\) (\(1\leq i\leq m\)) and each healthy one in the training dataset to highlight their possible difference. The RISI, defined by the mean absolute value of the difference, is represented by Equation (8), where the higher the RISI, the greater the difference from healthy, and the more serious the disease, and vice versa. To some extent, the influence of illumination, canopy, and blade structure could be suppressed with the RISI. \[RISI=\frac{1}{\mu}\sum\limits_{t=1}^{\mu}|SI-SI_{t}| \tag{8}\]  
where \(SI_{t}\) is the \(SI\) of the healthy sample \(x_{t}\), and \(\mu\) is the number of healthy samples in the training dataset.