激光与光电子学进展, 2018, 55 (10): 102202, 网络出版: 2018-10-14   

基于Zernike多项式光滑优化的均匀方斑透镜设计 下载: 551次

Design of Uniform Square Spot Lens Based on Smooth Optimization of Zernike Polynomials
作者单位
浙江工业大学理学院光电子智能化技术研究所, 浙江 杭州 310000
摘要
采用二次支撑面法(SQM)设计了一种均匀方斑透镜, 建立了Zernike正交多项式曲面插值重构算法。在初始基面上对每一个子面选择映射守恒点, 并按照相邻关系划分9点系统。针对9点系统, 利用多项式的低阶项建立了线性方程组, 并根据其唯一解构造了部分曲面。将所有部分曲面拼接, 得到了完整的连续光滑的优化曲面。该算法可在一定程度上简化SQM初始基面的后期优化, 得到良好的均匀方斑透镜设计效果。
Abstract
A uniform square spot lens is designed by the supporting quadratic method (SQM) and an algorithm for the interpolation and reconstruction of the curved surfaces based on the Zernike polynomials is developed. The mapping conservation points are chosen on the initial base surface for each sub-surface and the 9-point system is partitioned according to the adjacency relationship. As for this 9-point system, the linear equation group is established by using the lower order terms included in the polynomials and the partial curved surface is constructed with its unique solution. All the partial curved surfaces are spliced together and thus a complete and continuously smooth curved surface is obtained. This algorithm can simplify the later optimization of the initial base surfaces in SQM to a certain extent, which can ensure a good design effect of the uniform square spot lens.
参考文献

[1] 王进军, 王侠, 宁铎. 分区域多焦点叠加方形光斑均匀聚光菲涅耳透镜设计[J]. 光学学报, 2017, 37(3): 0322001.

    Wang J J, Wang X, Ning D. Design of Fresnel lens with square uniform concentration of sub-region multi-focus superposition[J]. Acta Optica Sinica, 2017, 37(3): 0322001.

[2] 张航, 吴梦荧, 马宇飞, 等. 矩形阵列LED均匀配光的对称性分析[J]. 激光与光电子学进展, 2015, 52(10): 102205.

    Zhang H, Wu M Y, Ma Y F, et al. Symmetrical analysis of uniform illumination design of rectangular arrayed light emitting diode sources[J]. Laser & Optoelectronics Progress, 2015, 52(10): 102205.

[3] 梁文跃, 李远兴, 龙拥兵, 等. 板上芯片型LED光源均匀照明自由曲面透镜设计[J]. 激光与光电子学进展, 2017, 54(1): 012202.

    Liang W Y, Li Y X, Long Y B, et al. Design of freeform surface lens with chip on board LED sources for uniform illumination[J]. Laser & Optoelectronics Progress, 2017, 54(1): 012202.

[4] Fournier F R, Cassarly W J, Rolland J P. Fast freeform reflector generation using source-target maps[J]. Optics Express, 2010, 18(5): 5295-5304.

[5] 丁毅, 顾培夫, 陆巍, 等. 利用微分方程数值解构造自由曲面反光器[J]. 浙江大学学报(工学版), 2007, 41(9): 1516-1518.

    Ding Y, Gu P F, Lu W, et al. Using numerical solutions of differential equations to form free reflector[J]. Journal of Zhejiang University (Engineering Science), 2007, 41(9): 1516-1518.

[6] Ding Y, Liu X, Zheng Z R, et al. Freeform LED lens for uniform illumination[J]. Optics Express, 2008, 16(17): 12958-12966.

[7] Oliker V I. Designing freeform lenses for intensity and phase control of coherent light with help from geometry and mass transport[J]. Archive for Rational Mechanics and Analysis, 2011, 201(3): 1013-1045.

[8] Ma Y F, Zhang H, Su Z Y, et al. Hybrid method of freeform lens design for arbitrary illumination target[J]. Applied Optics, 2015, 54(14): 4503-4508.

[9] 曹正林, 廖文和, 沈建新. Zernike多项式拟合人眼波前像差的一种新算法[J]. 光学 精密工程, 2006, 14(2): 308-314.

    Cao Z L, Liao W H, Shen J X. A new algorithm for human eye′s wave front aberration fitting with Zernike polynomial[J]. Optics and Precision Engineering, 2006, 14(2): 308-314.

[10] 叶井飞, 高志山, 刘晓莉, 等. 基于Zernike多项式和径向基函数的自由曲面重构方法[J]. 光学学报, 2014, 34(8): 0822003.

    Ye J F, Gao Z S, Liu X L, et al. Freeform surfaces reconstruction based on Zernike polynomials and radial basis function[J]. Acta Optica Sinica, 2014, 34(8): 0822003.

[11] 陈丽霞, 胡小川, 韩开, 等. Zernike多项式对空间高频相位拟合的改进方法[J]. 光学学报, 2016, 36(3): 0314001.

    Chen L X, Hu X C, Han K, et al. Improvement method for fitting high-frequency phase by Zernike polynomials[J]. Acta Optica Sinica, 2016, 36(3): 0314001.

[12] Chaves J. Introduction to non-imaging optics[M]. Boca Raton: CRC Press, 2008: 8-17.

张航, 陆建东, 刘锐, 马佩服. 基于Zernike多项式光滑优化的均匀方斑透镜设计[J]. 激光与光电子学进展, 2018, 55(10): 102202. Zhang Hang, Lu Jiandong, Liu Rui, Ma Peifu. Design of Uniform Square Spot Lens Based on Smooth Optimization of Zernike Polynomials[J]. Laser & Optoelectronics Progress, 2018, 55(10): 102202.

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