Reagent-less spectroscopy towards NPK sensing for hydroponics nutrient solutions

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.