## 2 Materials and Methods
### Materials
Second, the obtained conversion factor that was employed in (3) to obtain the \(PPF\) of the warm white LED of interest, \(PPF_{singleLED\_WW}\). \[PPF_{singleLED\_WW}=LF\cdot K_{LF\text{-}to\_PF}/1000 \tag{3}\]  
The obtained \(PPF\) values for each type of LED are summarized in Table 2.  
For each considered LED module, the overall \(PPF\), \(PPF_{module\_calc}\) can be easily obtained as shown in (4) combining the \(PPF_{singleLED\_HR}\), \(PPF_{singleLED\_DB}\) and \(PPF_{singleLED\_WW}\) reported in Table 2 and the LED's composition of the modules reported in Table 1.  
\[PPF_{module\_calc}=\#LED_{HR}.PPF_{singleLED\_HR}+\#LED_{DB}.PPF_{single LED\_DB}+\#LED_{WW}.PPF_{singleLED\_WW} \tag{4}\]  
where \(\#LED_{HR}\), \(\#LED_{DB}\), \(\#LED_{WW}\) are the number of hyper red, deep blue and warm white LEDs per module, respectively. The obtained \(PPF\) compositions for each considered LED module is shown in Table 3. For a given module, there is not a direct relationship between the percentage of PPF and the ratio between number of LEDs of a given type and total number of LED of the module. The reason is that the overall photon flux (\(PF\)), in umol/s, depends on the radiant flux (\(RF\)), in W, and is proportional to the light wavelength, \(\lambda\). Conversely, the energy per photon, \(E_{ph}\), is inversely proportional to \(\lambda\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**LED Type** & **Peak Emission** & **Spectral** & **Correlated Color** & **PPF [umol/s]** \\  & **Wavelength** & **Bandwidth at 50\%** & **Temperature** & **\(PPF_{singleLED\_WW}\)** \\ \hline HR & 660 nm & 25 nm & - & 2.01  & \(PPF_{singleLED\_HW}\) \\ DB & 451 nm & 20 nm & - & 2.26  \\ DW & - & - & 3000 K & 1.47  \\ \hline \hline \end{tabular}  
* \(PPF_{singleLED\_HR}\) obtained by (1). \({}^{2}\)\(PPF_{singleLED\_DB}\) obtained by (2). \({}^{3}\)\(PPF_{singleLED\_HW}\) obtained by (3).  
\end{table} 
Table 2: Main opto-electrical features of the considered single LED as result by combining data reported in datasheets and off-line computations. For each considered module, the comparison between the _PPF_ measured with the ETO integrating sphere, \(\mathit{PPF}_{\mathit{ETO}}\), and the \(\mathit{PPF}_{\mathit{module\_calc}}\), is shown in Table 4.  
Off-line computations \(\mathit{PPF}_{\mathit{module\_calc}}\) have a good match with direct measurements \(\mathit{PPF}_{\mathit{ETO}}\) with a maximum deviation of about 8%. In the first approximation, this evidence validates the procedures used to calculate \(\mathit{PPF}_{\mathit{singleLED\_HR}}\), \(\mathit{PPF}_{\mathit{singleLED\_DB}}\) and \(\mathit{PPF}_{\mathit{singleLED\_WW}}\), demonstrating that they provide an easy way to estimate the \(\mathit{PPF}\) of any custom LED light source, basically using only the data provided by the LED manufacturer and always reported in the LED's datasheet. From a practical point of view, this is important because for a given horticulture scenario, it allows to obtain a reliable \(\mathit{PPF}\) estimation at design time, without need for field tests on the real system. Consequently, it allows obtaining significant savings in terms of development time, costs, instrumentation needed and design software analysis. To verify the behavior of each LED module under the same working conditions, and to evaluate the effect of the distance among plants and LEDs in terms of PPF, three different distances, d, (60, 70 and 80 cm respectively) were considered. All the considered LED modules were experimental characterized by means of a low-cost spectral sensor (AS7341 from Ams, [36]). The measurements were conducted by reproducing the same test conditions used for the test with ETO integrating sphere, i.e., constant current flowing through the LEDs of 350 mA and temperature of the modules of 42 \({}^{\circ}\)C. Temperature and relative humidity of the surrounding air 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.