## 1 Introduction
Consequently, it is imperative to explore additional spectral bands associated with ChIF parameters and to develop and validate more universal methods. In comparison, partial least squares regression (PLSR), an advanced form of multivariate linear regression, has become a straightforward yet effective method for handling complex data [12]. This is attributed to its ability to manage high-dimensional variables with high accuracy, ease of application, and interpretability. PLSR is particularly popular for retrieving plant properties from hyperspectral data. Studies have demonstrated its strong predictive ability for leaf photosynthetic capacity [13], evapotranspiration [14], and various biophysical and biochemical properties [15; 16]. However, the efficacy of PLSR in estimating ChIF parameters has not been extensively investigated. In this regard, the potential of PLSR has been suggested by a limited body of research. For instance, one study reported that a PLSR model utilizing reflectance in the 600-900 nm range could predict PSII\({}_{\mathrm{max}}\), NPQ, qL, and \(\Phi\)P in date palms [17]. Similarly, a study by [PERSON] et al. [18] on tobacco found PLSR to be effective in predicting PSII\({}_{\text{max}}\), NPQ, and \(\Phi\)P. These studies are limited to specific species, and the applicability of PLSR to more complex datasets requires further investigation. The connection between hyperspectral reflectance and ChIP parameters extends over the visible (VIS), red-edge, near-infrared (NIR), and shortwave infrared (SWIR) regions [19]. This phenomenon can be attributed to the significant impact of various leaf traits on ChIP parameters [20], as changes in these traits are reflected in the spectral signatures across these regions. Therefore, for PLSR to accurately predict ChIP parameters, it must be driven by high-dimensional spectral information that encompasses these spectral regions. However, high-dimensional data frequently contain irrelevant or redundant information, which can compromise the generality and robustness of PLSR models [21]. Consequently, the selection of informative spectral features and the utilization of relevant bands to drive PLSR models are essential to improve model performance [22]. Earlier studies have demonstrated that selecting appropriate bands enhances the estimation of leaf traits [23; 24; 25]. Further research is needed to compare different feature selection methods and assess their effectiveness in optimizing PLSR models for ChIP parameter estimation. On the other hand, in situ hyperspectral reflectance has been demonstrated to capture subtle responses of leaves with high precision. However, factors such as sample humidity, the roughness of the leaf surface, and experimental conditions, including light intensity, temperature, and measurement angle, have been found to affect spectral reflectance [26]. Applying appropriate spectral transformations to the original reflectance has been identified as an effective approach to enhancing spectral signals and reducing background noise [27]. First- and second-order integer derivatives are among the most widely used preprocessing techniques, as they effectively improve the signal-to-noise ratio of reflectance signals. A previous study illustrated that spectral indices derived from first-order derivative spectra provided better estimates of ChIP parameters in comparison to those derived from the original reflectance [10]. However, the capability of first- and second-order derivatives to extract valuable information remains constrained. In cases where the slope or curvature of reflectance undergoes gradual changes, integer-order derivatives may not effectively capture meaningful variations, resulting in information loss in the original spectra [28]. This limitation has led to the development of fractional-order derivatives (FODs), which are now widely accepted as the best solution for extracting weak but meaningful reflectance features to capture leaf biochemical traits [29; 30] and photosynthetic capacity parameters [31].