## 2 Materials and Methods
### Materials
Light-to-frequency converters embedded into the sensor are used to convert the analog optical channel's output of the photodiodes to dimensionless digital output values of the sensors indicated as basic counts. Concerning the growth of plants one of the most important parameters is the Photosynthetic Photon Flux (PPF) emitted by the light source used (i.e., the LED modules in our case). PPF refers only to the photons with wavelengths in the range 400-700 nm,  
Figure 1: Comparison of the qualitative light spectrums for the considered modules: 3 HR:1 DB, 1 HR:1 DB, and 1 HR:3 DB, obtained using the low-cost AS7341 spectral sensor. Each curve is obtained by the interpolation of the dimensionless output values of the eight optical channels of the sensor with filters centered at wavelengths of 415, 445, 480, 515, 555, 590, 630, and 680 nm, respectively (marker dots). DB: deep blue, HR: hyper red. \begin{table}
\begin{tabular}{c c c} \hline \hline
**LEDs Ratio** & **Number of HR LEDs** & **Number of DB LEDs** \\ \hline
3 HR:1 DB & 9 & 3 \\
1 HR:1 DB & 6 & 6 \\
1 HR:3 DB & 3 & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Hyper red–deep blue light-emitting diodes (LEDs) ratio for the considered light recipes. because they are the only photons that contribute to the photosynthesis of the plants. Consequently, qualitative light spectrums shown in Figure 1 have been obtained by the interpolation of only the sensor output data provided by the 8 optical channels covering the visible spectrum. It is important to note that the photosynthetic photon flux (PPF) composition does not reflect the number of LEDs per type ratio of the light recipes. The reason is that the overall photon flux (_PF_), in \(\mu\)mol/s, depends on the radiant flux (_RF_), in W, and is proportional to the light wavelength, \(\lambda\), (1). Consequently, for a given _RF_, the number of photons generated by an HR LED is higher than the one of a DB LED. Vice versa, since the energy per photon, \(E_{ph}\), is inversely proportional to \(\lambda\), (2), DB LEDs have a higher _PF_ than HR LEDs for a given number of photons. \[PF=RF\cdot\lambda\cdot 0.00836 \tag{1}\]  
\[E_{ph}=h\cdot(c/\lambda) \tag{2}\]  
where the coefficient \(0.00836=1/(h\cdot c\cdot N)\), \(h\) is Planck's constant, \(c\) is the speed of light, and \(N\) is the number of Avogadro. In addition, both RF and PF depend on the current flowing through the LEDs. For all the considered modules, all the embedded LEDs were connected in series; therefore, they were driven by the same current and this means that HR and DB LEDs provide a different contribution to the total PPF, as shown in Table 3. The data shown in Table 3 were calculated combining the measurements carried out with the low-cost spectral sensor, direct measurements of power supply voltage and current of the LED modules carried out with digital multimeters, and the data reported in the datasheets of the modules [30] and the datasheet of the LEDs embedded into the modules [32; 33]. Temperature and relative humidity were recorded using wireless sensors with accuracy equal to \(\pm 1\)\({}^{\circ}\)C (resolution: 0.1 \({}^{\circ}\)C) for temperature and \(\pm 5\%\) (resolution: 1%) for humidity.