用于激光光束整形的连续自由曲面的设计
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摘要
设计一个有效的连续自由曲面,将给定的准直激光光束映射成任意模式的目标照明,仍然是一个具有挑战性的问题。提出一种基于光线映射来构造连续自由曲面的方法,通过计算光源与目标区域两者辐照度分布之间的光线映射关系,构造出光滑连续的自由曲面。对于准直输入光束,采用最优运输法计算光源与目标之间的光线映射;根据折反射定律和可积条件,推导出用于求解可积映射关系和连续自由曲面的一般条件;证明在小角度近似的情况下,基于最优运输法得到的光线映射关系可以满足可积条件;通过逐线积分法求解出满足一定边界条件的线性平流方程,从而完成连续自由曲面的构造。实验表明,利用逐线积分法求解标准积分方程构造出的连续自由曲面能实现任意模式的目标照明,能量利用率达98.95%。结果表明,基于最优运输法得到的光线映射关系在自由曲面和目标平面之间的距离较大时近似可积,提供了一种有效的构造连续自由曲面的方法。
Currently,designing an effective continuous freeform surface to map agiven light source to an arbitrary target illumination pattern is still a challenging problem for collimated input beams.A method is proposed for constructing continuous freeform surfaces based on ray-mapping.The method requires the calculation of a ray mapping between the source and the irradiance distribution on the target plane.The challenging aspect of this approach is to find an integrable mapping ensuring a continuous surface.A ray mapping between the source and the irradiance distribution on the target plane is calculated via optimal mass transport(OMT)for a collimated input beam;According to the law of reflection/refraction and an integrability condition,ageneral condition for the surface and ray mapping is derived.It is shown that in a small-angle approximation the mapping calculated via optimal mass transport can satisfy the integrability conditions and the surface can be constructed by solving a linear advection Eq.with appropriate boundary conditions.Experimental results indicate the continuous freeform surface constructed by the line-by-line integration method can realize an arbitrary target illumination pattern.The energy utilization is up to 98.95%.The results show that the optimal mass transport mapping is approximately integrable over a wide range of distances between the freeform and the target plane.An efficient way is proposed to construct the surface.
Currently,designing an effective continuous freeform surface to map agiven light source to an arbitrary target illumination pattern is still a challenging problem for collimated input beams.A method is proposed for constructing continuous freeform surfaces based on ray-mapping.The method requires the calculation of a ray mapping between the source and the irradiance distribution on the target plane.The challenging aspect of this approach is to find an integrable mapping ensuring a continuous surface.A ray mapping between the source and the irradiance distribution on the target plane is calculated via optimal mass transport(OMT)for a collimated input beam;According to the law of reflection/refraction and an integrability condition,ageneral condition for the surface and ray mapping is derived.It is shown that in a small-angle approximation the mapping calculated via optimal mass transport can satisfy the integrability conditions and the surface can be constructed by solving a linear advection Eq.with appropriate boundary conditions.Experimental results indicate the continuous freeform surface constructed by the line-by-line integration method can realize an arbitrary target illumination pattern.The energy utilization is up to 98.95%.The results show that the optimal mass transport mapping is approximately integrable over a wide range of distances between the freeform and the target plane.An efficient way is proposed to construct the surface.
引文
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[2]吴仍茂.自由曲面照明设计方法的研究[D].杭州:浙江大学,2013.Wu Rengmao.Research on the design method of freeform illumination[D].Hangzhou:Zhejiang University,2013.
[3]Schruben J S.Analysis of rotationally symmetric reflectors for illuminating systems[J].Journal of the Optical Society of America,1974,64(1):55-58.
[4]Tai W,Schwarte R.Design of an aspherical lens to generate a homogenous irradiance for three-dimensional sensors with a light-emitting diode source[J].Appl.Opt.,2000,39(31):5801-5805.
[5]Ries H,Muschaweck J.Tailored freeform optical surfaces[J].Opt.Soc.Am.A,2002,19(3),590-595.
[6]Situ W C,Han Y J,Li H T,et al.Combined feedback method for designing a free-form optical system with complicated illumination patterns for an extended LED source[J].Optics Express,2011,19(S5):A1022-A1030.
[7]Luo Y,Feng Z X,Han Y J,et al.Design of compact and smooth free-form optical system with uniform illumination for LED source[J].Optics Express,2010,18(9):9055-9063.
[8]Feng Z X,Luo Y,Han Y J.Design of LED free-form optical system for road lighting with high luminance/illuminance ratio[J].Optics Express,2010,18(21):22020-22031.
[9]Li H T,Chen S C,Han Y J,et al.A fast feedback method to design easy-molding freeform optical system with uniform illuminance and high light control efficiency[J].Optics Express,2013,21(1):1258-1269.
[10]Awamoto A,Ito Y,Ishizaki H,et al.Resolution improvement for HgCdTe IRCCD[J].SPIE,2013,1685:213-220.
[11]Oliker V.Optical design of freeform two-mirror beam-shaping system[J].Opt.Soc.Am.A,2007,24(12),3741-3752.
[12]李敏.基于LED扩展光源的自由曲面透镜设计研究[D].杭州:中国计量学院,2015.Li Min.Study on freeform lens design for LED extended sources[D].Hangzhou:China Jiliang University,2015.
[13]Kim H S,Kim C W.Compact mid-wavelength infrared zoom camera with 20:1zoom range and automatic athermalization[J].Optical Engineering,2015,41(7):1661-1667.
[14]Wang L,Qian K Y,Luo Y.Discontinuous free-form lens design for prescribed irradiance[J].Applied Optics,2007,46(18):3716-3723.
[15]Ding Y,Liu X,Zheng Z R,et al.Free-form LED lens for uniform illumination[J].Optics Express,2008,16(17):12958-12966.
[16]Wang K,Chen F,Liu Z Y,et al.Design of compact free-form lens for application specific light-emitting diode packaging[J].Optics Express,2010,18(2):413-425.
[17]Luo Y,Feng Z X,Han Y J,et al.Design of compact and smooth free-form optical system with uniform illuminance for LED source[J].Optics Express,2010,18(9):9055-9063.
[18]李姜欣,邢海英,何云堂,等.新型LED汽车前照灯光学系统设计[J].光学技术,2016,42(2):176-179.Li Jiangxin,Xing Haiying,He Yuntang,et al.A design of new LED headlight optical system[J].Optical Technique,2016,42(2):176-179.
[19]Bauerle A,Bruneton A,Loosen P,et al.Algorithm for irradiance tailoring using multiple free-form optical surfaces[J].Opt.Express,2012,20(13):14477-14485.
[20]Bruneton A,Bauerle A,Loosen P,et al.High resolution irradiance tailoring using multiple free-form surfaces[J].Opt.Express,2013,21(9):10563-10571.
[21]Feng Z,Huang L,Jin G,et al.Beam shaping system design using double free-form optical surfaces[J].Opt.Express,2013,21(12):14728-14735.
[22]Feng Z,Huang L,Jin G,et al.Designing double free-form optical surfaces for controlling both irradiance and wavefront[J].Opt.Express,2013,21(23):28693-28701.
[23]Gleyzes J P,Meygret A,Fratter C,et al.System overview and image ground segment[J].Institute of Electrical and Electronics Engineers Inc,2011,12:300-302.
[24]Glimm T,Oliker V I.Optical design of single reflector systems and the Monge-Kantorovich mass transfer problem[J].Math.Sci.,2003,117(3):4096-4108.
[25]Knott M,Smith C.On the optimal mapping of distributions[J].Optim.Theory,1984,43(5):39-49.
[26]Kaijser T.Computing the Kantorovich distance for images[J].Math.Imag,1998,9:173-191.