## 2 Module Design and Simulation
### Simulation: Illumination Performance and Tolerance Analyses  
LightToolsTM optical simulation software was used to simulate the structure of the proposed LED lighting system. The structure of the simulation system is shown in Figure 6. A square lighting shape was chosen as an example to investigate the performance of the designed lighting system. As described above, the LED lighting system consisted of a single LED, a commercial collimator lens, and a set of double linear Fresnel lenses to redistribute light on the receiver. A 5W, 630 nm COB LED was used in simulations with a luminous flux of 200 lm. Fresnel lenses and the collimator lens were made of poly methyl methacrylate (PMMA) material. Double Fresnel lenses produced a uniform distribution of illumination on a 2 m \(\times\) 2 m receiver. The receiver was located 2 m away from the light source. The simulation results of ray tracing of the collimator lens are shown in Figure 7. Figure 7a shows the illumination distribution in the receiver. With a lighting distance of 2 m, the distribution on the receiver area has a radius of 15 cm. Figure 7b shows the intensity distribution of the far-field receiver. It shows that the full width at half-maximum intensity angle was 1.2\({}^{\circ}\). The total flux was 198.4 lm. Figure 7c intuitively displays the rays passing through the collimator lens. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Design Parameters**} \\ \hline Type of LED & COB \\ Type of collimator & TIR \\ Refractive index of the Fresnel lens & 1.49 \\ Thickness of the Fresnel lens & 5 mm \\ Number of grooves of the Fresnel lens & 20 \\ Diameter of the Fresnel lens & 100 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The double Fresnel lenses design parameters. Figure 6: The simulation parameters using LighthoSLTM software. Simulation results of the optical distribution of the COB LED with the collimator and double Fresnel lenses are shown in Figure 8. It shows the illumination with a size of \(2\times 2\) m square on the target surface. The distribution formed a square radiation pattern with a size of \(1.8\) m\(\times\)\(1.8\) m at height of \(2\) m, which was in agreement with the expected shape. The uniformity of illumination on the target surface was 78% with a minimum intensity of 28 lux and maximum intensity is 48 lux. The efficiency was 77%. Illumination uniformity is calculated by Equation (2):  
\[u=\frac{I_{min}}{I_{agg}} \tag{2}\]  
where \(I_{min}\) is the minimum intensity value and \(I_{agg}\) is the averaged intensity value of all the pixels. To evaluate the losses in the system, we inserted two optical surface receivers in the simulation process, as shown in Figure 9. The system losses were from the loss of the collimator and the loss of the double Fresnel lenses. The loss of the collimator was from the material absorption and the Fresnel losses. The loss of the collimator was 1.56 Lux, as show in Figure 7b. The collimator losses are denoted by \(L_{1}\). Using LightTools(tm) software, \(L_{1}\) can be calculated by Equation (3):  
\[L_{1}=\frac{\mathit{Flux}\ \mathit{of}\ \mathit{LED}\ \mathit{source}-\mathit{ Flux}\ \mathit{on}\ \mathit{Receiver}\ 1}{\mathit{Flux}\ \mathit{of}\ \mathit{LED}\ \mathit{source}} \tag{3}\]  
Figure 8: Light distribution on an LED receiver using a collimator and double linear Fresnel lenses. Figure 7: Simulation performance of collimator lens: (**a**) light distribution of output beam; (**b**) viewing angle of LED with collimator at \(1.2^{\circ}\); and (**c**) ray tracing of LED with collimator. The loss of double Fresnel lenses was from the material absorption, the Fresnel losses, and the geometrical loss of the Fresnel lens. Geometrical loss of the Fresnel lens occurred when a non-ideal collimated beam was applied to this design. Although the theoretical design was optimized for an ideal parallel beam, this design still worked with a highly collimated beam, with a slight reduction in optical efficiency and uniformity.