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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 butterfly-shaped 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 and 0.83 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.
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Keywords:
- horizontal flat-topped white beams /
- diffraction mask /
- generalized Huygens-Fresnel diffraction integral /
- cylindrical lens
[1] Yoon K H, Kang M K, Lee H, Kim S K 2018 Appl. Opt. 57 A101
[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 2017 Acta 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, L B 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 2013 Acta 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, L B D 2008 Acta Phys. Sin. 57 2919 (in Chinese) [赵保银, 吕百达 2008 57 2919]
[14] Liu Z, Wang X, Zhao D 2015 Opt. Laser Technol. 69 154
[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. 61 244203 (in Chinese) [江浩, 张新廷, 国承山 2012 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 L 2004 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]
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[1] Yoon K H, Kang M K, Lee H, Kim S K 2018 Appl. Opt. 57 A101
[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 2017 Acta 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, L B 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 2013 Acta 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, L B D 2008 Acta Phys. Sin. 57 2919 (in Chinese) [赵保银, 吕百达 2008 57 2919]
[14] Liu Z, Wang X, Zhao D 2015 Opt. Laser Technol. 69 154
[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. 61 244203 (in Chinese) [江浩, 张新廷, 国承山 2012 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 L 2004 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]
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