## 3 Results
### Determination of Optimal FOD Order  
To identify the best FOD order for modeling tea quality indices, the spectral data processed with FOD at different orders were input into CARS+PLSR models. The accuracy of the test set was used as the selection criterion, with each order being evaluated five times to avoid experimental bias. As displayed in Figure 7, for AA, the maximum R\({}^{2}\) for the test set was achieved at the FOD order of 0.7 (R\({}^{2}\) = 0.80). For TP, the best performance was observed at the FOD order of 0.1 (R\({}^{2}\) = 0.42). Different quality indices in fresh tea leaves exhibit varying spectral characteristics, and the FOD order that best highlights these characteristics differs for each compound. Figure 5: Correlation coefficient curves between fractional-order derivatives (orders 0.0–1.0) and AA content versus wavelength (nm). Figure 6: Correlation coefficient curves between fractional-order derivatives (orders 0.0–1.0) and TPs content versus wavelength (nm). As shown in Figure 8, panels (a) through (f) demonstrate the predictive capabilities of the CARS-PLSR models corresponding to AA's 0 th-, 0.7 th-, and 1 st-order derivatives, and  
Figure 7: Maximum R\({}^{2}\) values for AAs (**a**) and TPs (**b**) at different FOD orders. TP's 0 th-, 0.1 st-, and 1 st-order reflectance derivatives, respectively. The results demonstrate that the application of FOD improves model accuracy compared to raw spectra and integer-order derivatives. In particular, FOD more effectively captures the spectral features related to the biochemical compounds in tea leaves. Figure 8 shows the test results for predicting AAs and TPs in fresh tea leaves using CARS-PLSR models under different fractional-order derivative (FOD) preprocessing methods. For AAs, the 0.7 th-order derivative gave the best performance, with a relatively high R\({}^{2}\) of 0.8089 and the lowest RMSE of 0.2986, whereas the 0 th- and 1 st-order derivatives had lower R\({}^{2}\) values and higher RMSE values. In contrast, the best results for TPs were obtained with the 0.1 th-order derivative, which reached an R\({}^{2}\) of 0.4247 and an RMSE of 3.9064, although the overall accuracy for TPs was still lower than for AAs. These findings suggest that choosing the right fractional derivative order can help highlight the spectral features most relevant to each compound, but the optimal orders differ. Table 1 presents the inversion accuracy of two tea quality indicators, AAs and TPs, using different band selection algorithms. In the table, \(R_{\text{train}}^{2}\) and \(R_{\text{test}}^{2}\) represent the coefficient of determination for the training set and test set, respectively. Figure 8: Test results of the prediction model for AAs and TPs at different orders of FOD for tea fresh leaf spectra. **(a)** AAs with 0 th-order derivative, **(b)** AAs with 0.7 th-order derivative, **(c)** AAs with 1 st-order derivative, **(d)** TPs with 0 th-order derivative, **(e)** TPs with 0.1 st-order derivative, and **(f)** TPs with 1 st-order derivative using CARS-PLSR models. For the AA model, the CC+PLSR approach yielded an \(R^{2}_{\text{train}}\) of 0.67, with an RMSE of 0.51, in the training set, and an \(R^{2}_{\text{test}}\) of 0.63 with an RMSE of 0.47 in the test set. For the TP model, the \(R^{2}_{\text{train}}\) was 0.48, with an RMSE of 3.21, and the \(R^{2}_{\text{test}}\) was 0.39, with an RMSE of 4.57. The overall accuracy of CC+PLSR was relatively low, particularly for the TP model, where both the training and test R\({}^{2}\) values were below 0.5, indicating a weak predictive capability. In contrast, the CARS+PLSR method achieved higher accuracy for both AAs and TPs. For the AA model, the \(R^{2}_{\text{train}}\) was 0.86, and the \(R^{2}_{\text{test}}\) was 0.80, demonstrating robust model performance. For the TP model, the \(R^{2}_{\text{train}}\) reached 0.70, and the \(R^{2}_{\text{test}}\) was improved to 0.42, with lower RMSE values compared to the CC+PLSR method.