## 2 Theoretical Analysis and Fabrication of Lens and Heatsink for the Seaport Luminaire  
### Theoretical Analysis and Fabrication of Optimized Optical Lens  
To investigate the optimal lens design for the seaport luminaire, the near field optical characteristics of a high-power LED PKG were analyzed. In the measurement, as shown in Figure 1a, Lumiides's Luxeon M LED PKG with 5 W power was used at the distance of 6 mm [24]. The viewing angle and luminous distribution curve of this LED PKG are shown in Figure 1b,c, respectively.  
Based on the viewing angle data of the LED PKG, various types of optical lens were designed using LightTools software, as shown in Figure 2a. After theoretical analysis of the light distribution of the LED PKG with an optical lens, four types of lens were selected as candidates for the seaport light source. According to the design of each lens, four types of optical lens were fabricated using a high-speed precision processing machine with PowerMill software, and then, the surface of the lens was polished for high transmittance, as shown in Figure 2b.  
Then, the real light distribution data of an LED PKG with an optical lens was measured by a gonio-photometer, as shown in Figure 2c. To verify the feasibility of seaport lighting application, light distribution was simulated using Relux software considering the requirements of seaport lighting application--for example, illuminated area, height of luminaire installation, and required overall uniformity. These boundaries and input conditions used in the simulation are listed in Table 1. The dimensions of the illuminated area are about 150 m by 150 m, as shown in Table 1. Figure 2d shows the simulated result of light distribution, and the expected overall uniformity is about 0.53. Overall uniformity is a measure of how evenly lit the road surface is, and it is calculated by dividing the minimum value of illuminance by the average illuminance [25].  
As the required minimum overall uniformity for the seaport lighting application was 0.7, three other types of lens were also investigated to meet the overall uniformity of 0.7.  
Figure 1: Photo of Lumiled’s Luxeon M LED PKG (**a**), measured viewing angle (**b**) and luminous distribution curve (**c**).  
Figure 2: Optical lens design using LightTools software (**a**), fabricated optical lens using high-speed precision processing machine (**b**), measured actual light distribution of LED PKG with an optical lens (**c**), and simulated light distribution considering a real dimension (150 m \(\times\) 150 m) of seaport installation (**d**).  
Figure 3 shows the simulation results of light distribution for four types of lens: A, B, C, and D. Among these four lens types, the light distribution with lens type D provides the best overall uniformity characteristics, as shown in Figure 3d.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Installation height of luminaire & 35 m \\ Dimension of illuminated area & 150 m \(\times\) 150 m \\ Minimum overall uniformity & 0.7 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The boundary and input conditions used in the simulation of seaport lighting.  
Figure 3: Design drawing, photo of fabricated optical lens, measured luminous intensity distribution, and simulated light distribution of lens type A (**a**), B (**b**) C (**c**), and D (**d**) (the parameters listed in Table 1 were used for the simulation of light distribution).  
The simulated overall uniformity for each of the four types of lens is summarized in Table 2, and the overall uniformity is 0.48 for lens type A, 0.53 for type B, 0.45 for type C, and 0.73 for lens type D, respectively. It means that only the type D lens meets the minimum overall uniformity requirement of 0.7. Thus, the type of optical lens was fixed as type D.