# Double-Sided Freeform Lens for Light Collimation of Light Emitting Diodes
## 3 Lens Design and Simulation with UV-LED  
The goal of the present study is to design a collimating lens for UV-LEDs for use in proximity/contact UV photolithography applications, in which highly-collimated UV light is required. Once the UV light is collimated, a uniform distribution of the UV dosage over the wafer/substrate surface area can be achieved by overlapping the UV exposures of multiple LED/lens units arranged in the form of an array using a pre-programmed mechanical scanning movement. In the method proposed in Section 2, only three parameters are required to complete the lens design, namely \(r_{o}\), \(\xi\), and \(\theta_{B}\). However, since there is only one characteristic length (\(r_{o}\)) involved in the analysis, \(r_{o}\) can be set equal to one such that all of the other dimensions become normalized with respect to \(r_{o}\). As a result, only two parameters, i.e., \(\xi\) and \(\theta_{B}\), were actually needed for the lens design under a point-source assumption. In real applications based on the use of true LEDs as the light source, the light is actually emitted from a finite size area with a dimension of \(d\). The larger the ratio of \(r_{o}\) to \(d\), the better the point source assumption is, and hence the better the light collimating effect achieved by the proposed double freeform lens. Regarding the two design parameters, \(\xi\) dominates the shape of the lens profile and the Fresnel losses, while \(\theta_{B}\) determines the total light collection angle from the LED and therefore governs the energy efficiency of the collimated LED light. The present study used an NCSU276A UV-LED (Nichia Inc., Tokushima, Japan) for illustration purposes. As shown in Table 1, the main features of the UV-LED include a peak wavelength of 365 nm, an optical power of 780 mW, and a radiation angle of 130\({}^{\circ}\) (full angle at half intensity). The analysis was performed using commercial Zemax optical design software (OpticStudio, Kirkland, WA, USA). Figure 2a,b show the angular distribution of the illumination intensity of the NCSU276A UV-LED, as simulated using the source model file provided by Nichia Inc. [21]. The results confirmed that the full angle of divergence measured at half the maximum intensity was indeed around 130\({}^{\circ}\). Furthermore, the light emitting area size is around \(1\times 1\) mm\({}^{2}\). \begin{table}
\begin{tabular}{c c} \hline \hline
**Model No.** & **NCSU276A** \\ \hline Peak Spectrum & 365 nm \\ Typical Optical Power & 780 mW \\ Forward Voltage (\(V_{F}\)) & 3.8 V (Typ.) \\  & 4.4 V (Max.) \\ Directivity (\(2\theta\), Half Max.) & 130\({}^{\circ}\) \\ Forward Current (\(I_{F}\)) & 500 mm \\ LED Size & \(3.5\times 3.5\times 2.0\) mm\({}^{3}\) \\ Light Emitting Area & \(1.0\times 1.0\) mm\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main features of NCSU276A UV-LED (Nichia Inc., Tokushima, Japan). The UV-LED collimating lens designed in this study was manufactured using an injection molding technique since it can precisely control the lens surface profiles and enables the mass production of the lens with a high throughput and low cost. The lens was manufactured in PLEXIGLAS(r) 8012 (Evonik Performance Materials GmbH, Essen, Germany), which is a poly(methyl methacrylate) (PMMA) material suitable for making lenses with a working UV-A spectrum of 365-395 nm and has an optical refraction index (\(n\)) of 1.51 - @365 nm [22]. Figure 3a,b show the calculated optical transmission coefficients of the chosen material at the air/lens and lens/air interfaces, respectively, as a function of the incident angle (note that the calculated coefficients are used in the later lens design process). As shown in Figure 3b, the total reflection angle at the PMMA/air interface was around 41\({}^{\circ}\). Using the method described in Section 2, several double freeform lenses were designed with \(\xi\)-parameter values ranging from 0.1 to 0.9.