光刻胶热熔法制备的非球面微透镜的设计方法
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摘要
为了进一步提高入射到光敏元上的光能,针对光刻胶热熔法制备的微透镜的非球面面形,提出了一种结合有限元光线追迹和拉格朗日乘子法的设计方法。给定焦距,用该算法可以自动计算出所需的微透镜面形。为了验证算法的精度,对圆形孔径的焦斑均方根半径进行了模拟和理论计算,二者较为吻合。对三次有限元光线追迹的点列图误差进行了估计。计算了会聚到320 pixel×256 pixel背照射紫外焦平面探测器光敏元上的能量集中度,比较了具有不同圆角半径的方形孔径蓝宝石微透镜的效率。结果表明,具有6μm圆角半径的方形孔径微透镜的能量集中度较高,为96%。
In order to further improve the light energy collected by the photo-sensitive area, a new design method for the aspheric microlens fabricated by the photoresist reflow method is proposed, which combines finite element ray tracing with the Lagrange multiplier method. Given the focal length, the needed aspheric surfaces can be computed automatically by the proposed method. In order to verify the accuracy of this algorithm, the RMS radius of the focal spot of the microlens with circular aperture is simulated and theoretically calculated, respectively, and both results are consistent. The approximation error of spot diagram of the cubic finite element ray tracing is estimated. The enclosed energy collected by the photo-sensitive area of 320 pixel×256 pixel ultraviolet photodetectors is computed and the efficiencies of microlens with square aperture shapes and different fillet radii are compared. The results show that the square aperture microlens with a 6 μm fillet radius has a relatively high energy concentration with an efficiency of 96%.
In order to further improve the light energy collected by the photo-sensitive area, a new design method for the aspheric microlens fabricated by the photoresist reflow method is proposed, which combines finite element ray tracing with the Lagrange multiplier method. Given the focal length, the needed aspheric surfaces can be computed automatically by the proposed method. In order to verify the accuracy of this algorithm, the RMS radius of the focal spot of the microlens with circular aperture is simulated and theoretically calculated, respectively, and both results are consistent. The approximation error of spot diagram of the cubic finite element ray tracing is estimated. The enclosed energy collected by the photo-sensitive area of 320 pixel×256 pixel ultraviolet photodetectors is computed and the efficiencies of microlens with square aperture shapes and different fillet radii are compared. The results show that the square aperture microlens with a 6 μm fillet radius has a relatively high energy concentration with an efficiency of 96%.
引文
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[2] Wang D Y, Xue C X, Li C, et al. Design of electronic endoscope optical system based on microlens array[J]. Acta Optica Sinica, 2018, 38(2): 0222003. 王丹艺, 薛常喜, 李闯, 等. 基于微透镜阵列的电子内窥镜光学系统设计[J]. 光学学报, 2018, 38(2): 0222003.
[3] Piotrowski J, Grudzien M, Nowak Z, et al. Uncooled photovoltaic Hg1-xCdxTe LWIR detectors[J]. Proceedings of SPIE, 2000, 4130: 175-185.
[4] Huang J, Zhou W H, Yin W T. Fabrication and evaulation of the CdZnTe microlens arrays[J]. Proceedings of SPIE, 2010, 7658: 76584G.
[5] Ke C J,Yi X J, Lai J J. Research on fused silica microlens arrays with high effective aperture ratio[J]. Semiconductor Technology,2004, 29(4): 52-55. 柯才军,易新建,赖建军. 高有效孔径比面阵石英微透镜阵列研究[J]. 半导体技术, 2004, 29(4): 52-55.
[6] Sun Y J, Leng Y B, Chen Z, et al. Square aperture spherical microlens array for infrared focal plane[J]. Acta Photonica Sinica, 2012, 41(4): 399-403. 孙艳军, 冷雁冰, 陈哲, 等. 用于红外焦平面的正方形孔径球面微透镜阵列研究[J]. 光子学报, 2012, 41(4): 399-403.
[7] He M, Yuan X C, Moh K J, et al. Monolithically integrated refractive microlens array to improve imaging quality of an infrared focal plane array[J]. Optical Engineering, 2004, 43(11): 2589-2594.
[8] Fossati C, Gagliano O, Commandre M, et al. Microlens design for CMOS image sensor[J]. Proceedings of SPIE, 2005, 5962: 596229.
[9] Nam H H, Park J L, Choi J S, et al. The optimization of zero-spaced microlenses for 2.2 μm pixel CMOS image sensor[J]. Proceedings of SPIE, 2007, 6520: 652034.
[10] Deguchi M, Maruyama T, Yamasaki F, et al. Microlens design using simulation program for CCD image sensor[J]. IEEE Transactions on Consumer Electronics, 1992, 38(3): 583-589.
[11] Schilling A, Merz R, Christian O, et al. Surface profiles of reflow microlenses under the influence of surface tension and gravity[J]. Optical Engineering, 2000, 39(8): 2171-2176.
[12] Liu X Y, Liu S J, Qiao H, et al. Fabrication and surface profile simulation of sapphire microlens array[J]. Proceedings of SPIE, 2014, 9522: 95221Q.
[13] Ortiz S, Siedlecki D, Remon L et al. Three-dimensional ray tracing on Delaunay-based reconstructed surfaces[J]. Applied Optics, 2009, 48(20): 3886-3893.
[14] Simon M C, Echarri R M. Ray tracing formulas for monoaxial optical components: vectorial formulation[J]. Applied Optics,1986, 25(12): 1935-1939.