# Study on the Performance of Optical Lenses under High Fluxes of Solar Radiation
## 2 Materials and Methods
### Irradiation Tests
#### 2.2.1 Irradiation with a Solar Simulator Using Xenon Arc Lamp  
Irradiation tests using a xenon arc lamp projector (see Figure 4) as high-flux solar simulator were conducted at the Unit of High-Temperature Processes of IMDEA Energy Institute (Mostoles, Madrid, Spain) [16]. The lenses were tested separately i.e., one by one. By default, the duration of exposure of each lens to the concentrated radiation was 60 min. The irradiation tests were stopped before 60 min only in the case of fracture of the lens. The lenses were appropriately positioned so that the power applied on the exposed surface of each lens could be calculated with reasonable accuracy. The test methodology for performing this calculation will be explained further on. A computer controlled XYZ table was used for the correct positioning of each lens. The xenon arc lamp that was used is manufactured by OSRAM GmbH (Munich, Germany) with the reference XBO 7000 W/HS XL OFR. These lamps of the XBO series are generally used for classic cinema 35 mm film projection. The radiation generated by the lamp has almost the same blackbody temperature that is attributed to the solar radiation entering the Earth's atmosphere (i.e., approx. 6000 K). The lamp belongs to the OFR class (ozone-free version) which means that during its operation it does not produce ozone. This is possible because the quartz alloy used in these xenon lamps is typically doped with \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Designation**} & \multirow{2}{*}{**Material**} & \multirow{2}{*}{**Diameter**} & \multicolumn{2}{c}{**Thickness**} & \multirow{2}{*}{**Focal Length**} \\  & & **(mm)** & & **Board (mm)** & & **Center (mm)** \\ \hline DB100 & Borosilicate glass & 50.8 & 9.0 & 2.0 & \(-100\)\({}^{1}\) \\ DB150 & Borosilicate glass & 50.8 & 7.7 & 3.5 & \(-150\)\({}^{2}\) \\ DB200 & Borosilicate glass & 50.8 & 6.7 & 3.5 & \(-200\)\({}^{2}\) \\ DB250 & Borosilicate glass & 50.8 & 5.0 & 2.0 & \(-250\)\({}^{1}\) \\ DS151 & Silica glass & 50.8 & 8.4 & 3.5 & \(-150\)\({}^{2}\) \\ DS201 & Silica glass & 50.8 & 7.1 & 3.5 & \(-200\)\({}^{2}\) \\ \hline \hline \end{tabular}  
\({}^{1}\): at 589 nm. \({}^{2}\): at 546.1 nm.  
\end{table} 
Table 1: Diverging (biconcave) lenses tested in this work. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Designation**} & \multirow{2}{*}{**Material**} & \multirow{2}{*}{**Diameter**} & \multicolumn{3}{c}{**Thickness**} & \multirow{2}{*}{**Focal Length**} \\  & & & **(mm)** & & **Center** \\ \hline CB100 & Borosilicate glass & 76.2 & 2.5 & 19.3 & \(100\)\({}^{1}\) & 87.2 \({}^{1}\) \\ CS100 & Silica glass & 76.2 & 2.4 & 22.9 & \(100\)\({}^{1}\) & 84.2 \({}^{1}\) \\ \hline \hline \end{tabular}  
\({}^{1}\): at 589 nm. \({}^{2}\) BFL: back focal length.  
\end{table} 
Table 2: Converging lenses (plano-convex) tested in this work. certain compounds or titanium dioxide to absorb ultraviolet wavelengths that serve to generate ozone during operations [17]. If it was not doped the silica glass would allow the light to pass through with very small wavelengths up to 180 nanometers (nm), but by using doped glass the xenon arc lamp will emit radiation with wavelengths larger than 220 nm. Details of experimental setup of the irradiation tests using xenon arc lamp are presented in Figure 5. Since the xenon arc lamp emits a constant (non-adjustable) radiation flux, metallic grids have been used as attenuators to change the radiation flux (see Figure 5a). The temperature in the vicinity of each lens was assessed by using K-type thermocouples (TC Ltd., Uxbridge, UK) and, additionally, a thermal imaging infrared camera was used (see example in Figure 6). Measurements of radiation flux were performed with a Gardon-type radiometer (Vatell Circular-Foil Heat Flux Transducer TG100-1, Vatell Corporation, Christiansburg, VA, USA) with sensitivity of 0.022 mV/(W\(\cdot\)cm\({}^{-2}\)); working range 0-445 W\(\cdot\)cm\({}^{-2}\); coated with colloidal graphite.