Abstract
Nutrient quantification in hydroponic systems is essential. Reagent-less spectral quantification of nitrogen, phosphate and potassium faces challenges in accessing information-rich spectral signals and unscrambling interference from each constituent. Herein, we introduce information equivalence between spectra and sample composition, enabling extraction of consistent covariance to isolate nutrient-specific spectral information (N, P or K) in Hoagland nutrient solutions using orthogonal covariance modes. Chemometrics methods quantify nitrogen and potassium, but not phosphate. Orthogonal covariance modes, however, enable quantification of all three nutrients: nitrogen (N) with R = 0.9926 and standard error of 17.22 ppm, phosphate (P) with R = 0.9196 and standard error of 63.62 ppm, and potassium (K) with R = 0.9975 and standard error of 9.51 ppm. Including pH information significantly improves phosphate quantification (R = 0.9638, standard error: 43.16 ppm). Results demonstrate a direct relationship between spectra and Hoagland nutrient solution information, preserving NPK orthogonality and supporting orthogonal covariance modes. These modes enhance detection sensitivity by maximizing information of the constituent being quantified, while minimizing interferences from others. Orthogonal covariance modes predicted nitrogen (R = 0.9474, standard error: 29.95 ppm) accurately. Phosphate and potassium showed strong interference from contaminants, but most extrapolation samples were correctly diagnosed above the reference interval (83.26%). Despite potassium features outside the knowledge base, a significant correlation was obtained (R = 0.6751). Orthogonal covariance modes use unique N, P or K information for quantification, not spurious correlations due to fertilizer composition. This approach minimizes interferences during extrapolation to complex samples, a crucial step towards resilient nutrient management in hydroponics using spectroscopy.

Abstract
Early diagnosis of plant diseases is needed to promote sustainable plant protection strategies. Applied predictive modeling over hyperspectral spectroscopy (HS) data can be an effective, fast, cost-effective approach for improving plant disease diagnosis. This study aimed to investigate the potential of HS point-of-measurement (POM) data for in-situ, non-destructive diagnosis of tomato bacterial speck caused by Pseudomonas syringae pv. tomato (Pst), and bacterial spot, caused by Xanthomonas euvesicatoria (Xeu), on leaves (cv. cherry). Bacterial artificial infection was performed on tomato plants at the same phenological stage. A sensing system composed by a hyperspectral spectrometer, a transmission optical fiber bundle with a slitted probe and a white light source were used for spectral data acquisition, allowing the assessment of 3478 spectral points. An applied predictive classification model was developed, consisting of a normalizing pre-processing strategy allied with a Linear Discriminant Analysis (LDA) for reducing data dimensionality and a supervised machine learning algorithm (Support Vector Machine - SVM) for the classification task. The predicted model achieved classification accuracies of 100% and 74% for Pst and Xeu test set assessments, respectively, before symptom appearance. Model predictions were coherent with host-pathogen interactions mentioned in the literature (e.g., changes in photosynthetic pigment levels, production of bacterial-specific molecules, and activation of plants' defense mechanisms). Furthermore, these results were coherent with visual phenotyping inspection and PCR results. The reported outcomes support the application of spectral point measurements acquired in-vivo for plant disease diagnosis, aiming for more precise and eco-friendly phytosanitary approaches.

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