采用衍射掩模产生白光横向平顶光束
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摘要
白光横向平顶光束在定向背光式自由立体显示器中有重要应用.本文提出一种采用带蝶形小孔阵列的衍射掩模片获得白光横向平顶光束的方法.根据广义惠更斯-菲涅耳衍射积分和多波长叠加原理,推导出光强分布计算式.设计一套实验装置,数值模拟并实验验证出射光束在不同距离的横向光强分布以及小孔蝶形凹度(蝶形中心高度与边长的比值)对横向光强分布的影响.结果表明:当选择小孔蝶形凹度为0.50—0.66时,可以得到平顶因子F 0.89的白光横向平顶光束,横向平顶光束的宽度随着传输距离的增大而增大,而平顶因子基本不变.实验还发现柱面透镜的折射色散和衍射色散可以互相抵消,使白光横向平顶光束基本无色散.
The flat-topped beam is a special beam with wide applications in the directional backlight autostereoscopic display,and it is used as a directional backlight in the horizontal direction. However, it is still challenge to white light flat-topped beams with the traditional flat-topped beam shaper. In this paper, it is proposed that diffraction mask with butterflyshaped hole arrays and cylindrical lens be used to produce the horizontal flat-topped white beams. The surface of the LCD backlight mask is covered by a layer of diffraction mask, where the butterfly-shaped holes are arranged in line along the vertical direction. Simultaneously, the height and width, hole center height are kept identical, and the ratio between the center depth and the perimeter of butterfly-shape hole is defined as the concavity. A flat convex cylindrical lens is placed in front of diffraction mask gaplessly. The uniform light field from LCD backlight is transformed into the white light flat-topped beams and projected on the receiving screen by the diffraction mask and cylindrical lens. Based on the Huygens-Fresnel diffraction integral, the intensity distribution formula of diffraction of the single wavelength light source on the receiving screen is derived. Furthermore, the intensity distribution formula on the screen is derived by super positioning the multiple wavelengths. The proposed method is verified by both numerical simulation and experimental validation. Numerical simulations elucidate the effects of the different transmission distance and butterfly hole concavity on the white light flat-topped beam flat-topped factor. The stimulated results show that the propagation distance does not influence the white light beam transverse intensity distribution characteristics of flat top. With the beam propagation distance increasing, the horizontal width of flat-topped beam becomes larger. When the concavity of the butterfly hole decreases, light intensity distribution shifts from Gaussian to flat type. However, the flat-topped factor decreases when the butterfly concavity is too small. The optimal concavity varies from 0.4 to 0.6, where the flattened factor of the transverse flat-topped beams reaches 0.89. In the experiments, films are produced with the diffraction of butterfly hole array mask. The height and width of butterfly are both 48 μm, and the concavities of the butterfly are 1, 0.83, 0.66 and0.83 respectively. The cylindrical lens adopts PMMA cylindrical lens grating plate, with a thickness of 8 mm, a grating density for 18 line/inch, and the cylindrical lens curvature radius R is 2.67 mm. The experimental results show that the beam transmission is consistent with the result of numerical simulation. When concavity of the butterfly is 0.5, the flat factors of the white light horizontal of flat-topped beams are higher than 0.89 in a range from 500 mm to 2000 mm.Moreover, we also discuss the dispersion effects of shaft flat-topped beams and off-axis flat-topped beams, showing that the refraction and dispersion of the cylindrical lens can cancel out each other, so that the horizontal flat-toped white beams is basically dispersionless.
The flat-topped beam is a special beam with wide applications in the directional backlight autostereoscopic display,and it is used as a directional backlight in the horizontal direction. However, it is still challenge to white light flat-topped beams with the traditional flat-topped beam shaper. In this paper, it is proposed that diffraction mask with butterflyshaped hole arrays and cylindrical lens be used to produce the horizontal flat-topped white beams. The surface of the LCD backlight mask is covered by a layer of diffraction mask, where the butterfly-shaped holes are arranged in line along the vertical direction. Simultaneously, the height and width, hole center height are kept identical, and the ratio between the center depth and the perimeter of butterfly-shape hole is defined as the concavity. A flat convex cylindrical lens is placed in front of diffraction mask gaplessly. The uniform light field from LCD backlight is transformed into the white light flat-topped beams and projected on the receiving screen by the diffraction mask and cylindrical lens. Based on the Huygens-Fresnel diffraction integral, the intensity distribution formula of diffraction of the single wavelength light source on the receiving screen is derived. Furthermore, the intensity distribution formula on the screen is derived by super positioning the multiple wavelengths. The proposed method is verified by both numerical simulation and experimental validation. Numerical simulations elucidate the effects of the different transmission distance and butterfly hole concavity on the white light flat-topped beam flat-topped factor. The stimulated results show that the propagation distance does not influence the white light beam transverse intensity distribution characteristics of flat top. With the beam propagation distance increasing, the horizontal width of flat-topped beam becomes larger. When the concavity of the butterfly hole decreases, light intensity distribution shifts from Gaussian to flat type. However, the flat-topped factor decreases when the butterfly concavity is too small. The optimal concavity varies from 0.4 to 0.6, where the flattened factor of the transverse flat-topped beams reaches 0.89. In the experiments, films are produced with the diffraction of butterfly hole array mask. The height and width of butterfly are both 48 μm, and the concavities of the butterfly are 1, 0.83, 0.66 and0.83 respectively. The cylindrical lens adopts PMMA cylindrical lens grating plate, with a thickness of 8 mm, a grating density for 18 line/inch, and the cylindrical lens curvature radius R is 2.67 mm. The experimental results show that the beam transmission is consistent with the result of numerical simulation. When concavity of the butterfly is 0.5, the flat factors of the white light horizontal of flat-topped beams are higher than 0.89 in a range from 500 mm to 2000 mm.Moreover, we also discuss the dispersion effects of shaft flat-topped beams and off-axis flat-topped beams, showing that the refraction and dispersion of the cylindrical lens can cancel out each other, so that the horizontal flat-toped white beams is basically dispersionless.
引文
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[2]Su Y F,Cai Z J,Liu Q,Lu Y F,Guo P L,Shi L Y,Wu J H 2018 Opt.Rev.25 254
[3]Yao S J,Wang L H,Lin C L,Zhang M 2018 J.Real-Time Image PR.14 481
[4]Fan Z C,Chen G W,Wang J C,Liao H G 2018 IEEE T.Bio-Med.Eng.65 378
[5]Su J B,Liang H W,Chen H Y,Zhou Y G,Fan H,Lin D K,Zhou J Y,Wang J H 2015 J.Disp.Technol.30 887(in Chinese)[苏剑邦,梁浩文,陈海域,周延桂,范杭,林岱坤,周建英,王嘉辉2015液晶与显示30 887]
[6]Ma H Q,Wang X L,Fan H,Wang J H,Zhou J Y,Zhou Y G 2017 Las.Optoelect.Prog.54 118(in Chinese)[马鸿钦,王晓露,范杭,王嘉辉,周建英,周延桂2017激光与光电子学进展54 118]
[7]Chen F P,Zhang X T,Liu C J,Qi Y,Zhuang Q R 2017Acta Phot.Sin.46 95(in Chinese)[陈芳萍,张晓婷,刘楚嘉,漆宇,庄其仁2017光子学报46 95]
[8]Liang H W,An S Z,Wang J H,Zhou Y G,Fan H,Peter Krebs,Zhou J Y 2014 J.Disp.Technol.10 695
[9]Luo S R,LüB D 2000 Laser Technol.24 256(in Chinese)[罗时荣,吕百达2000激光技术24 256]
[10]Liu L H 2013 Ph.D.Dissertation(Changchun:University of Chinese Academy of Sciences)(in Chinese)[刘丽红2013博士学位论文(长春:中国科学院大学)]
[11]Nie S Z,Yu J,Fan Z W,Ge W Q,Liu Y,Zhang X 2013Acta Opt.Sin.33 25(in Chinese)[聂树真,余锦,樊仲维,葛文琦,刘洋,张雪2013光学学报33 25]
[12]Li S,Wang Y L,Lu Z W,Ding L,Cui C,Chen Y,Yuan D P,Ba D X,Zheng Z X,Yuan H,Shi L,Bai Z X,Liu Z H,Zhu C Y,Dong Y K,Zhou L X 2016 Opt.Commun.367 181
[13]Zhao B Y,LüB D 2008 Acta Phys.Sin.57 2919(in Chinese)[赵保银,吕百达2008物理学报57 2919]
[14]Liu Z,Wang X,Zhao D 2015 Opt.Laser Technol.69154
[15]Liu J,Yang Y F,He Y,Liu G W,Zheng X 2014 Acta Opt.Sin.34 235(in Chinese)[刘键,杨艳芳,何英,刘国威,郑晓2014光学学报34 235]
[16]Wu P,Zhuang J,Lu B D 2004 Chin.J.Lasers 31 48(in Chinese)[吴平,庄建,吕百达2004中国激光31 48]
[17]Jiang H,Zhang X T,Guo C S 2012 Acta Phys.Sin.61244203(in Chinese)[江浩,张新廷,国承山2012物理学报61 244203]
[18]Zhang M J,Gao W Y,Niu Q Y,Yuan X Q 2015 Infrar.Laser Eng.44 2411(in Chinese)[张明军,高文英,牛泉云,袁兴起2015红外与激光工程44 2411]
[19]He X,Wu F T,Li P,Chen Z Y 2014 Sci.Sin-Phys.Mech.Astron.7 705(in Chinese)[何西,吴逢铁,李攀,陈姿言2014中国科学:物理学力学天文学7 705]
[20]Li H X,Lou Q H,Ye Z H,Dong J X,Wei Y R,Ling L2004 High Power Laser Particle Beams 16 729(in Chinese)[李红霞,楼祺洪,叶震寰,董景星,魏运荣,凌磊2004强激光与粒子束16 729]
[21]Born M,Wolf E(translated by Yang J Q)2009 Principles of Optics(Beijing:Electronic Industry Press)pp478–479(in Chinese)[马科斯·玻恩,埃米尔·沃耳夫著(杨葭荪译)2009光学原理(北京:电子工业出版社)第478—479页]