# Double-Sided Freeform Lens for Light Collimation of Light Emitting Diodes
## 1 Introduction  
Compared to the traditional UV mercury lamps used in conventional photolithography systems, ultraviolet (UV) light emitting diodes (LEDs) have the advantage of having a lower cost, a reduced electricity consumption, a longer lifetime, improved stability, and being more environmentally friendly. As a result, there has been growing interest in it being a potential light source for UV lithography processes. However, collimating the UV light without losing too much of the light energy represents a major challenge and requires the use of special lens designs. Both primary and secondary optics are commonly adopted to adjust the distribution of light so as to meet the overall specifications and create the desired beam pattern. Freeform surfaces, in particular, have been widely used to refract and/or reflect LED light. For example, the authors in [1; 2; 3] used lenses with a concave spherical surface on the LED side and a freeform refractive surface on the other side to achieve a uniform illumination intensity over a rectangular area. In contrast, the authors in [4; 5; 6] used double freeform surfaces to improve the optical performance by refracting the LED light twice. In many cases, the freeform lenses are intimately integrated with the LED packaging in order to achieve compactness [7; 8], or better angular color uniformity [9]. For LEDs with a wide radiation angle, more complex freeform surfaces are commonly employed to refract the light at a lower angle and reflect the light at a higher angle [10; 11; 12; 13; 14; 15; 16; 17]. The surface profiles in such lenses typically comprise of several discontinuities separating a small number of analog profile sections with different functions. The resulting freeform surfaces are generally designed using numerical schemes andcomputer algorithms. However, Fresnel surfaces have also been proposed for redistributing LED light on the reflection surface [18; 19]. Proposed freeform lens share the same purpose of many other lens designs, such as the positive meniscus lens [20], by minimizing the spherical aberration. However, conventional positive meniscus lenses consist of two spherical lens surfaces, and hence their light collimating capability is limited only to paraxial rays. In practice, most LEDs have a large radiation angle. Therefore, they cannot be easily collimated to a small collimating angle by a conventional meniscus lens without losing the majority of their light energy. Furthermore, most commercial positive meniscus lenses have a relatively long focal length of around 100 to 1000 mm and are therefore not easily integrated with LEDs. The majority of previous studies on the use of freeform surfaces for LEDs consider the problem of optical lighting, which generally requires a certain distribution of illumination intensity on a target area that is placed quite far from the LED. In such situations, the light collimating effect is not a significant concern, provided that the light beam has a limited viewing angle in the far field. As a result, when designing the lens, emphasis is placed mainly on the illumination uniformity and light efficiency. However, when applying UV-LEDs to photolithography applications, light collimation is a major concern since it has a direct effect on the dimensional accuracy of the developed photoresist (PR) microstructure. Furthermore, in photolithography, the UV light source is relatively close to the targeted PR layer, and hence the UV light should be collimated immediately after the freeform lens in the near field. However, the uniformity of the projected light intensity is less important than in general optical lighting applications since the UV patterned area is typically in the wafer size (up to 12\") or panel size (up to 28\") and hence illumination is generally achieved using an array of lens/LED units in which the overlapping exposures of the multiple units are controlled using a programmed scanning movement [16].