关于全视差全息体视图成像系统光瞳尺寸的研究
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摘要
构建了一种全视差全息体视图的成像系统模型,成像系统因三维物体具有一定深度分布而存在波前像差,运用带像差衍射受限系统的相关理论对该模型进行了相关分析。采用矩形光瞳为成像系统的出瞳函数,计算得到在无像差、小像差和大像差三种像差下光学传递函数与空间频率、出瞳尺寸三者间的变化关系,并以光学传递函数与空间频率的积分值作为该成像系统的成像质量的评价指标,得到不同像差条件下积分值与出瞳尺寸的曲线,优化矩形光瞳的孔径尺寸,获得在全视差全息体视图的打印平台中孔径光阑的最佳尺寸,以提高全视差全息体视图的成像质量。
A model of the full-parallax holographic stereographic imaging system is built. The wavefront aberration exists because of the depth distribution of three-dimensional(3D) objects, and this aberration is analyzed by the related theory of diffraction-limited imaging system. Rectangular pupil is used as the exit pupil of the imaging system.The relationship among the optical transfer function(OTF), the spatial frequency, and the pupil size is obtained in such situations as non-aberration, small-aberration and large-aberration. In addition, the imaging quality can be evaluated by the integral values of OTF on spatial frequency, the variation relationship between the integral value of OTF and pupil size is obtained under different aberration conditions, so as to optimize the size of rectangular pupil and get the optimal aperture size on printing platform of full-parallax holographic stereogram to improve the imaging quality.
A model of the full-parallax holographic stereographic imaging system is built. The wavefront aberration exists because of the depth distribution of three-dimensional(3D) objects, and this aberration is analyzed by the related theory of diffraction-limited imaging system. Rectangular pupil is used as the exit pupil of the imaging system.The relationship among the optical transfer function(OTF), the spatial frequency, and the pupil size is obtained in such situations as non-aberration, small-aberration and large-aberration. In addition, the imaging quality can be evaluated by the integral values of OTF on spatial frequency, the variation relationship between the integral value of OTF and pupil size is obtained under different aberration conditions, so as to optimize the size of rectangular pupil and get the optimal aperture size on printing platform of full-parallax holographic stereogram to improve the imaging quality.
引文
1 John Peter Tapsell.Direct-Write Digital Holography Development and Research of a Hologram Printer[D].Sussex:University of Sussex,2008:19-112.
2 Guo Chunhua,Yu Jia,Wang Jincheng,et al..Laser direct writing of full-parallax synthetic hologram[J].Acta Photonica Sinica,2010,39(3):518-522.郭春华,于佳,王金城,等.全视差合成全息图的激光直写拍摄[J].光子学报,2010,39(3):518-512.
3 M W Halle.The Generalized Holographic Stereogram[D].Massachusetts:Massachusetts Institute of Technology,1993.
4 J Hahn,H Kim,Y Lim,et al..Wide viewing angle dynamic holographic stereogram with a curved array of spatial light modulators[J].Opt Express,2008,16(16):12372-12386.
5 Y S Cheng,R C Chang.Image-plane cylindrical holographic stereogram[J].Appl Opt,2000,39(23):4058-4069.
6 Y Takaki,K Ikeda.Simplified calculation method for computer-generated holographic stereograms from multi-view images[J].Opt Express,2013,21(8):9652-9663.
7 K Hong,S G Park,J Yeom,et al..Resolution enhancement of holographic printer using a Hogel overlapping method[J].Opt Express,2013,21(12):14047-14055.
8 J Jia,J.Liu,G.Jin,et al..Fast and effective occlusion culling for 3D holographic displays by inverse orthographic projection with low angular sampling[J].Appl Opt,2014,53(27):6287-6293.
9 G Xue,J Liu,X Li,et al..Multiplexing encoding method for full-color dynamic 3D holographic display[J].Opt Express,2014,22(15):18473-18482.
10 Z Zhang,J Liu,J Jia,et al..Tunable nonuniform sampling method for fast calculation and intensity modulation in 3D dynamic holographic display[J].Opt Lett,2013,38(15):2676-2679.
11 Han Jian,Liu Juan,Liu Dongmei,et al..Optimizing approach of wavefront aberration in the recording of holographic lens based on spatial light modulator[J].Chinese J Lasers,2014,41(2):0209023.韩剑,刘娟,刘冬梅,等.基于空间光调制器的全息透镜记录波前像差优化方法[J].中国激光,2014,41(2):0209023.
12 Sang Xinzhu,Yu Xunbo,Zhao Tianqi,et al..Three-dimensional display with smooth motion parallax[J].Chinese J Lasers,2014,41(2):0209011.桑新柱,于迅博,赵天奇,等.具有平滑运动视差的三维显示技术[J].中国激光,2014,41(2):0209011.
13 X Z Sang,F C Fan,S Choi,et al..Three-dimensional display based on the holographic functional screen[J].Opt Eng,2011,50(9):091303.
14 H Zhang,Y Zhao,L C Cao,et al..Three-dimensional display technologies in wave and ray optics:a review[J].Chin Opt Lett,2014,12(6):060002.
15 H Zhang,Y Zhao,L Cao,et al..Fully computed holographic stereogram based algorithm for computer-generated holograms with accurate depth cues[J].Opt Express,2015,23(4):3901-3913.
16 Xiaoyu Jiang,Chuang Pei,Xingpeng Yan,et al..Optimization of exit pupil function:improvement on the OTF of full parallax holographic stereograms[J].J Opt,2013,15(12):125402.
17 Pei Chuang,Jiang Xiaoyu,Yan Xingpeng,et al..A novel perspective slice method to improve resolution of reconstruction parallax image in holographic stereogram[J].Laser&Optoelectronics Progress,2015,52(9):090901.裴闯,蒋晓瑜,闫兴鹏,等.采用视角切片法提高全息体视图再现视差图像分辨率[J].激光与光电子学进展,2015,52(9):090901.
18 M W Halle,S A Benton,M A Klug,et al..Ultragram:a generalized holographic stereogram[C].SPIE,1991,1461:142-155.
19 Muyo G,Harvey A R.Decomposition of the optical transfer function:wavefront coding imaging systems[J].Opt Lett,2005,30(20):2715-2717.
20 Hilaire P S.Modulation transfer function and optimum sampling of holographic stereograms[J].Appl Opt,1994,33(5):768-774.
21 LüNaiguang.Fourier Optics[M].Beijing:China Machine Press,2006:144-169.吕乃光.傅里叶光学[M].北京:机械工业出版社,2006:144-169.
22 Goodman J W.Introduction to Fourier Optics[M].New York:Mcgraw-Hill,1996.
2 Guo Chunhua,Yu Jia,Wang Jincheng,et al..Laser direct writing of full-parallax synthetic hologram[J].Acta Photonica Sinica,2010,39(3):518-522.郭春华,于佳,王金城,等.全视差合成全息图的激光直写拍摄[J].光子学报,2010,39(3):518-512.
3 M W Halle.The Generalized Holographic Stereogram[D].Massachusetts:Massachusetts Institute of Technology,1993.
4 J Hahn,H Kim,Y Lim,et al..Wide viewing angle dynamic holographic stereogram with a curved array of spatial light modulators[J].Opt Express,2008,16(16):12372-12386.
5 Y S Cheng,R C Chang.Image-plane cylindrical holographic stereogram[J].Appl Opt,2000,39(23):4058-4069.
6 Y Takaki,K Ikeda.Simplified calculation method for computer-generated holographic stereograms from multi-view images[J].Opt Express,2013,21(8):9652-9663.
7 K Hong,S G Park,J Yeom,et al..Resolution enhancement of holographic printer using a Hogel overlapping method[J].Opt Express,2013,21(12):14047-14055.
8 J Jia,J.Liu,G.Jin,et al..Fast and effective occlusion culling for 3D holographic displays by inverse orthographic projection with low angular sampling[J].Appl Opt,2014,53(27):6287-6293.
9 G Xue,J Liu,X Li,et al..Multiplexing encoding method for full-color dynamic 3D holographic display[J].Opt Express,2014,22(15):18473-18482.
10 Z Zhang,J Liu,J Jia,et al..Tunable nonuniform sampling method for fast calculation and intensity modulation in 3D dynamic holographic display[J].Opt Lett,2013,38(15):2676-2679.
11 Han Jian,Liu Juan,Liu Dongmei,et al..Optimizing approach of wavefront aberration in the recording of holographic lens based on spatial light modulator[J].Chinese J Lasers,2014,41(2):0209023.韩剑,刘娟,刘冬梅,等.基于空间光调制器的全息透镜记录波前像差优化方法[J].中国激光,2014,41(2):0209023.
12 Sang Xinzhu,Yu Xunbo,Zhao Tianqi,et al..Three-dimensional display with smooth motion parallax[J].Chinese J Lasers,2014,41(2):0209011.桑新柱,于迅博,赵天奇,等.具有平滑运动视差的三维显示技术[J].中国激光,2014,41(2):0209011.
13 X Z Sang,F C Fan,S Choi,et al..Three-dimensional display based on the holographic functional screen[J].Opt Eng,2011,50(9):091303.
14 H Zhang,Y Zhao,L C Cao,et al..Three-dimensional display technologies in wave and ray optics:a review[J].Chin Opt Lett,2014,12(6):060002.
15 H Zhang,Y Zhao,L Cao,et al..Fully computed holographic stereogram based algorithm for computer-generated holograms with accurate depth cues[J].Opt Express,2015,23(4):3901-3913.
16 Xiaoyu Jiang,Chuang Pei,Xingpeng Yan,et al..Optimization of exit pupil function:improvement on the OTF of full parallax holographic stereograms[J].J Opt,2013,15(12):125402.
17 Pei Chuang,Jiang Xiaoyu,Yan Xingpeng,et al..A novel perspective slice method to improve resolution of reconstruction parallax image in holographic stereogram[J].Laser&Optoelectronics Progress,2015,52(9):090901.裴闯,蒋晓瑜,闫兴鹏,等.采用视角切片法提高全息体视图再现视差图像分辨率[J].激光与光电子学进展,2015,52(9):090901.
18 M W Halle,S A Benton,M A Klug,et al..Ultragram:a generalized holographic stereogram[C].SPIE,1991,1461:142-155.
19 Muyo G,Harvey A R.Decomposition of the optical transfer function:wavefront coding imaging systems[J].Opt Lett,2005,30(20):2715-2717.
20 Hilaire P S.Modulation transfer function and optimum sampling of holographic stereograms[J].Appl Opt,1994,33(5):768-774.
21 LüNaiguang.Fourier Optics[M].Beijing:China Machine Press,2006:144-169.吕乃光.傅里叶光学[M].北京:机械工业出版社,2006:144-169.
22 Goodman J W.Introduction to Fourier Optics[M].New York:Mcgraw-Hill,1996.
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