# 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
Figure 4: General layout of the solar radiation simulator/projector by xenon arc lamp, and the XYZ coordinate table. Initially, the measurements of flux were uniquely dedicated to determining the position of the focal zone, which corresponds to the x,y,z coordinates where the maximum value of radiation flux is registered. For that, the radiometer was moved along the three axes, in 1 mm steps (increments). After knowing the focal zone location, the second phase consisted in carrying out flux measurements after insertion of the radiation attenuators. Table 3 shows the values of radiation flux measured at the focal zone (typically named \"focus\") and the corresponding attenuation factor. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Attenuator** & **Radiation-Flux in the Focal Zone** & **Attenuation Factor** \\  & **(W cm\({}^{-2}\))** & **Attenuation Factor** \\ \hline Without attenuator & 316 & 1 \\ Attenuator no. 1 & 249 & 0.788 \\ Attenuator no. 2 & 221 & 0.699 \\ Attenuator no. 3 & 193 & 0.611 \\ Attenuator no. 4 & 162 & 0.513 \\ Attenuator no. 5 & 130 & 0.411 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Radiation-flux attenuation factors obtained with five different attenuators. Figure 5: Details of experimental setup for the irradiation tests using xenon arc lamp projector. (**a**) Photo of an irradiation test showing a metallic grid used as radiation attenuator (at the left) and irradiated lens (at the right); (**b**) lens (of 76.2 mm diameter) being irradiated, simply surrounded by alumina foam; (**c**) for confining the radiation beam, in some tests we have used a mask made of alumina felt with a circular aperture of 1 inch (25.4 mm) diameter; the Gardon-type radiometer is on the right protected by alumina foam; (**d**) fractured lens (of 50.8 mm diameter) mounted in metallic holder. The third phase of radiation-flux measurements consisted of obtaining radiation-flux values at positions around the \"focus\". The objective of these measurements is to estimate the total power incident on a plane perpendicular to the optical axis (X axis). This series of measurements was carried out with attenuator no. 5. Due to the dimensions of the radiometer used in this work, the measured values of radiation-flux are attributed to circles with 5 mm diameter. Thus, as is schematically shown in Figure 7a, 21 measurements of radiation-flux were performed at the positions represented in Figure 7a, all of them symmetrically distributed (at positions: north, south, east, west) inside a circular area with 55 mm diameter. This circular area has been chosen because the flux measured outside this area revealed very low values. For each of the circular crowns represented in Figure 7b we have calculated the average value of the four radiation-flux measurements that we took inside the circular crown (north, south, east, west) and then we multiplied this average value by the area of the corresponding circular crown, thus obtaining an estimate of the irradiation power received in each circular crown. These estimated values (in W) for each of the zones are shown in Figure 7b. By summing up the power received at each of the zones we obtain an estimate of the total power incident on a plane perpendicular to the optical axis. In the case shown in Figure 7b, the sum is \(29+149+172+105+82+70=607\) W. As in this case we have used the attenuator no.5, that has attenuation factor of 0.411, we may say that without attenuator the total power incident in a plane perpendicular to the optical axis would be 607/0.411 = 1477 W.  
Figure 6: Image provided by the infrared camera software during a test with a biconcave lens DS151, showing the temperature distribution. In this test, the irradiation power incident on the exposed surface of the lens is 180 W, because a mask made of alumina felt with a circular aperture of 1 inch (25.4 mm) diameter is used (facing directly towards the xenon lamp projector).