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Fig. 3 | Plant Methods

Fig. 3

From: Non-invasive absolute measurement of leaf water content using terahertz quantum cascade lasers

Fig. 3

How the nonlinear relations between A, \(\tau\) and \(M_W\) can be used to improve the linear regression model. a Measured \(\tau\) versus A. We report only some of the experimental data points, for the sake of clarity, grouped in three set according to similar mass: the light green squares represent all the samples having \(M_W = 430 \pm 10\) mg, the emerald squares \(M_W = 610 \pm 10\) mg, and the dark green squares \(M_W = 1150 \pm 100\) mg. The dashed curves are obtained from Eq. (6), using the mean \(M_W\) of each data group. b Measured A versus \(M_W\). Referring to the data points of Fig. 2b, multiplication of \(\tau\) and \(M_{W} A^{-1}\) by A improves the linearity of the model. The specific nonlinear relation between A and \(M_W\) (b) spreads the data cloud horizontally, whereas the inverse proportionality between \(\tau\) and A (a) reduces the data fluctuations at given \(M_w\). c The process explained before results in the graph of \(\tau A\) as function of the water mass \(M_W\). In this case the linear best fit (red line) has two statistically significant parameters. The intercept \(C_1 = 14 \pm 3 \, \text {cm}^2\) (p value \(8.1 \times 10^{-7}\)) is ascribed to light scattering, whereas the slope \(C_2 = 413 \pm 6 \, \text {cm}^2 \, \text {g}^{-1}\) may be still related to an effective absorption coefficient of water. The linear regression best fit has a coefficient of determination \(R^2 = 0.95\), which means that our linear model explains \(95\%\) of the experimental data fluctuations

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