1. ANALYTICAL HAZE SIMULATION OF OPTICAL FILMS WITH 2D PARABOLOIDAL MICROLENS ARRAY Jeng-Feng Lin, Chin-Chieh Kang, and Shih-Fu Tseng Department of Electro-Optical Engineering, Southern Taiwan University, Tainan, Taiwan E-mail:jengfeng@mail.stut.edu.tw, 97-EC-17-A-05-S1-114 ABSTRACT This paper describes haze simulation of optical films with 2D paraboloidal microlens array by analytical formulae and optical simulation software ASAP, respectively. Derivation of the analytical formulae assumes every paraboloidal lens is independent, i.e., we ignore the situation that outgoing rays from a paraboloidal microlens can hit nearby paraboloidal microlenses. Comparison between formulae calculation and ASAP simulation shows that they are close. INRODUCTION Under the pressure of cost down, multifunctional optical films, which combine light diffusion and luminance gain, have become key components in LCD backlight units. Most of multifunctional optical films are composed of regularly or randomly distributed conic microlenses [1, 2, 3, 4]. In this paper, first the behavior of normally incident rays inside the optical film is examined. Then formulae for haze calculation and haze simulation by ASAP are presented. The schematic diagram of the optical film with 2D paraboloidal microlens array is shown in Fig. 1. The substrate is PET with thickness of 180 mm and refractive index of 1.49. Above the PET there are a thin layer with thickness of 20 mm and microlens array, and both are made of cured UV resin with refractive index of 1.56. RAY TRACING For haze measurement light is essentially normally incident to the sample. Therefore, as shown in Fig. 2, we assume the light is normally incident to the left half of the paraboloidal microlens. Since the microlens is rotationally symmetric and the light is normally incident, we only need to do the ray tracing on a plane which contains the optical axis (z axis). We can express the parabola in Fig. 2 as z = x 2 /2r, where r is radius of curvature and is negative. Let R b denote the radius of the circular bottom of the microlens and define shape factor k as k = R b /|r|. As shown in Fig. 2, the incident ray is normally reflected back to the substrate after consecutive reflections at points A and B. Therefore, reflection at A and B can have three cases: (a) when x 2c <x 1 <x 1c, the incident ray is totally reflected at both A and B, (b) when x 1c <x 1 <0, the incident ray is refracted at A and totally reflected at B, (c) when x 1 <x 2c, the incident ray is totally reflected at A and refracted at B. CONCLUSIONS AND ACKNOWLEDGEMENT We have derive formulae for haze simulation under the assumption that outgoing rays from a paraboloidal microlens can hit nearby paraboloidal microlenses can be ignored. Comparison with ASAP simulation shows that results from both simulation are close. In addition, formula derivation indicates that shape factor is the structure parameter that affects haze, not radius of curvature or R b alone. To have a reasonable haze, the shape factor (k) should be away from 1.44. However, considering both haze and luminance gain, k>1.44 is required. This research is sponsored by the Ministry of Economic Affairs and the project ID is 97-EC-17-A-05-S1-114. REFERENCES [1] http://www.mntehch.co.kr [2] http://www.brightviewtechnologies.com [3] Shun-Ting Hsiao, Po-Hung Yao, and Chung-Hao Tien, “High gain diffuser film with surface relief of 2D paarboloidal lens array,” IDW Digest, pp619-633, 2007. [4] Joo-Hyung Lee, Jun-Bo Yoon, Joon-Yong Choi, and Sang-Min Bae, “ A novel LCD backlight unit using a light-guide plate with high fill-factor microlens array and a conical microlens array sheet,” SID’07 Digest, pp465-468, 2007. [5] ASTM Standard D 1003-07: Standard Test Method for Haze and Luminous Transmittance of Transparent Plastics, 2007. [6] Shih-Fu Tseng, Design and simulation of multi-functional optical films, Master Thesis, Southern Taiwan University, 2010. 180μm 20μm microlens cured UV resin Figure 1. Schematic diagram of the optical film with 2D paraboloidal microlens array. Figure 2. Ray tracing inside a paraboloidal microlens HAZE SIMULATION Figure 3 shows a schematic of hazemeter employed in the ASTM D1003 [5]. In haze simulation, as shown in Fig. 4, the integrating sphere and photodetector on it in the real hazemeter are replaced by an absorbing sphere, which totally absorbs any ray hit on it. In addition the incident beam is simplified as a collimated beam. According to ASTM D1003, the exit port subtends an angle of 8° at the center of the entrance port. Further more, we assume no light scattering due to the hazemeter when specimen of optical film is absent. Then haze is the percent of transmitted light that is scattered outside the exit port. Figure 3. Schematic diagram of hazemeter. Figure 4. Schematic for simulation of hazemeter. Derivation of the analytical formulae assumes every paraboloidal lens is independent, i.e., we ignore the situation that outgoing rays from a paraboloidal lens can hit nearby paraboloidal lenses. We assume the light is normally incident to the left half of the paraboloidal microlens. As mentioned above, reflection at the parabola has three cases. Therefore the derivation of the analytical formulae also has three cases. (a) k < 0.835 This is the case c for reflection at the parabola, i.e., the incident ray is refracted at A and totally reflected at B. Through some mathematical manipulations and numerical approximations, the haze can be expressed as, (1) (b) 0.835 < k < 1.44 where k is shape factor and ff is fill factor defined as the percent of the substrate that is occupied by the microlens. Apparently, haze is proportional to fill factor and increased with higher shape factors. Basically, when 1.44r<x 1 <x 1c, the incident ray is almost totally reflected to the substrate. Hence incident ray in this region can not contribute any diffused light and haze is decreased with higher shape factors. The haze can be expressed as, (2) (c) k > 1.44 When -R b <x 1 <1.44r, the power of the incident ray is almost refracted to the air. Hence incident ray in this region contributes diffused light and haze is increased with higher shape factors. The haze can be expressed as From the above derivation, we obtain two important observations: (a) shape factor is the structure parameter that affects haze, not radius of curvature or R b alone; (b) haze is always increased with higher fill factors. Assume R b = 25mm and ff = 81%. Haze versus various radius curvatures is shown in Fig. 5. Clearly, to have a reasonable haze, k should be away from 1.44. However, considering both haze and luminance gain, k>1.44 is required., (3) For R b = 30mm and ff = 81%, haze is simulated by analytical formulae and optical simulation software ASAP, respectively. Haze versus various radius curvatures is shown in Fig. 6. For simulation by ASAP, the microlenses are randomly distributed by a dedicated algorithm [6] and the situation that outgoing rays from a paraboloidal lens can hit nearby paraboloidal lenses is not ignored. Figure 6 shows simulation results from analytical formulae and ASAP are close. Figure 5. Haze simulation by analytical formulae (R b = 25mm and ff = 81%). Figure 6. Haze simulation by analytical formulae and ASAP (R b = 30mm and ff = 81%).