| 面光源矩形匀光照明反射器数学建模分析 |
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| 引用本文： | 高培丽,李潇,黄逸峰,钱维莹,刘诚,高淑梅.面光源矩形匀光照明反射器数学建模分析[J].应用光学,2016,37(1):136-142. |
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| 作者姓名： | 高培丽 李潇 黄逸峰 钱维莹 刘诚 高淑梅 |
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| 作者单位： | 1.江南大学 理学院 江苏省轻工光电工程技术研究中心,江苏 无锡 214000 |
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| 基金项目： | 国家自然科学基金（61178032） |
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| 摘 要： | 通常反射器照明器件结构对面光源出射光线难以有效控制，用透镜又存在不可避免的色散问题。采用面光源置于反射器杯口，出光面背对目标面的结构，提出一种分点、分区控制光线的自由曲面反射器的设计方法。利用有限元法划分面光源，将微面光源视为点光源，根据矩形匀光照明配光条件，建立面光源与目标面的能量对应关系。根据微分几何理论和Snell定律，建立反射器的数学模型，只要给定参数，无需进行反馈优化，即可用Matlab软件给出自由曲面反射器的数值解。以台灯照明为例，用光学设计软件对其性能进行了模拟应用分析，结果表明，在有效照明区域内均匀度可达到80%以上，光能利用率达到90%。
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| 关 键 词： | 光学设计 自由曲面反射器 有限元法 矩形均匀照明 LED面光源 |
Mathematical modeling analysis of freeform reflector for rectangular uniform illumination with surface source |
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| Affiliation: | 1.Jiangsu Provoncial Research Center of Light Industrial Optoelectronic Engineering and Technology,School of Science,Jiangnan University, Wuxi 214000,China |
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| Abstract: | Since the general reflectors cannot control the surface source effectively and there is unavoidable chromatic dispersion in lens, we proposed a freeform reflector design method. In our scheme, the surface source was located at the top of the reflector, whose luminous surface back faced the target plane. The surface source was divided to micro surfaces by finite element method, which were treated as point sources. According to the rectangular illumination distribution, the energy relationship between surface source and target plane was established. Meanwhile, the mathematical model of the reflector could be directly computed based on the theory of the differential geometry and Snell's law, then the numerical solution of freeform reflector could be calculated by Matlab software without feedback optimizing. By example,the numerical solution of the reflector of the table lamp was obtained by using associated software and the performance of the reflector was simulated by optical software. It is revealed that the illumination uniformity on target plane is above 0.8, while the energy efficiency can reach about 0.9. |
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