计算全息视角扩展和编码效率研究
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摘要
随着计算机技术,高分辨率数字图像传感器(CCD,CMOS)和高分辨率数字空间光调制器技术的进一步完善。计算全息技术在动态三维显示,光学微操纵等方面的应用越来越广泛。然而,将计算全息应用于三维动态实时再现在技术方面仍然存在着一些问题。在对三维物体进行计算全息编码再现的实验流程中,计算全息图的编码步骤至关重要。通常的计算全息编码是将物体近似看作是离散点的集合,所有物点的全息图样分别直接计算得到,最后相加来获得整个物体的全息图样。该方法需要将三维物体抽样出的每一个物点的全息图样一个一个计算出来,因此运算量非常大。而庞大的运算量使得实时产生三维图像的计算全息图样不太可能非常理想的实现。另外,由于程控液晶空间光调制器分辨率的限制,计算全息三维再现有效视角太小,导致三维物体计算全息再现观察范围非常有限。本论文重点研究的是计算全息在三维再现中存在问题及解决方法:
1.为扩大全息再现视角而提出的视角扩展编码方法。由于程控液晶空间光调制器像素分辨率的限制,其衍射特性决定物体的再现像超出了双眼同时直接观察的范围。我们可以通过视角变换来实现视角扩展。该论文中提出一种利用LC-SLM(液晶空间光调制器)的高级衍射光来增大再现视角的计算全息编码方法。与普通计算全息编码方法所不同的是,该方法首先对视角超出所用LC-SLM允许范围的物波信息进行预处理,使预处理后的物波视角满足Nyquist(奈奎斯特)抽样定理;然后再进行计算全息编码。将这种计算全息图用相应的程控LC-SLM再现时,被记录的实际物波信息可在空间光调制器的特定高衍射级上得到恢复,从而实现大视角物体的全息再现。
2.为解决计算全息编码运算量太大的问题所用的预存储表格法中,首先将三维物体根据其深度抽样成一系列离散平面片,并将平面片抽样成离散点。由于每一个平面片所对应的放大率是一致的,所以我们可以选择每一个平面上的中心点的干涉条纹图样作为主要的全息条纹。其余物点的全息图样可以由截取主要全息条纹图样然后平移获得。根据其余物点与中心物点的相对位置坐标,选择将主要条纹全息图样中的以某一坐标为中心的全息图样片段截取出来,然后再将用同样方法得到的其余物点的全息图样片段相加得到该平面的全息图样。最终通过累加一系列平面片的全息图样获得整个物体全息图样。
With the development of computer technology ,high resolving digital image sensor (CCD or CMOS) and high resolving digital spatial light modulator (SLM), Computer-generated holography (CGH) which is used in dynamic real-time three-dimensional (3D) display and optical micromanipulation is a powerful technology. However, the CGH used in the 3D dynamic real-time reconstruction has its disadvantage. In the generation and reconstruction process of computer-generated holograms pattern, the encoding is very important .Usually the 3D real objects can be approximated as a collection of self-luminous points of light, the fringe patterns for all object points are directly calculated respectively. Finally all the fringe patterns are added up to obtain the whole interference pattern of the object image. This approach shows a computation complexity, since it requires one by one calculation of the fringe pattern per image point per hologram sample. Thus, real-time generation of the CGH pattern for a 3-D image can not be achievable easily. In this paper we mainly research the problems and the solutions of CGH for 3D real object in the common method:
[1] In order to enlarge reconstraction viewing-angle, wo suggest a viewing-angle enlargement method. Because the pixel pitches of the SLM are not fine, its diffracted trait decide the reconstruction of 3D object exceed the viewing-zone .we can achieve viewing-angle enlargement by viewing-angle transforming, In this method, the pretreatment is done for object information whose angle exceeding sampling frequency of SLM. After this pretreatment the angle of this object’s wave satisfies the sampling theorem. Then the recorded object is encoded . This hologram can be reconstructed by SLM . The reconstructed image of the object can be reproduced in the high-order of the SLM , so we can reconstruct the object by large view angle . The encoding method and some expressions according to the analysis of theory are given . Finally the example of encoding in this way and the simulation result of prove that this method is right.
[2] In order to alleviate computation of the digital holograms of 3-D objects, this paper suggests a new LUT method. A 3-D object can be treated a set of image planes discretely sliced in the z-direction, in which each image plane having a fixed depth is approximated as some collection of self-luminous object points of light. In this method, only the fringe patterns of the center points on each image plane are pre-calculated, called principal fringe patterns and those be stored . Then, the fringe patterns for other object points on each image plane can be obtained by simply shifting this pre-calculated principal fringe patterns according to the displaced values from the center to those points and adding them together.
1.为扩大全息再现视角而提出的视角扩展编码方法。由于程控液晶空间光调制器像素分辨率的限制,其衍射特性决定物体的再现像超出了双眼同时直接观察的范围。我们可以通过视角变换来实现视角扩展。该论文中提出一种利用LC-SLM(液晶空间光调制器)的高级衍射光来增大再现视角的计算全息编码方法。与普通计算全息编码方法所不同的是,该方法首先对视角超出所用LC-SLM允许范围的物波信息进行预处理,使预处理后的物波视角满足Nyquist(奈奎斯特)抽样定理;然后再进行计算全息编码。将这种计算全息图用相应的程控LC-SLM再现时,被记录的实际物波信息可在空间光调制器的特定高衍射级上得到恢复,从而实现大视角物体的全息再现。
2.为解决计算全息编码运算量太大的问题所用的预存储表格法中,首先将三维物体根据其深度抽样成一系列离散平面片,并将平面片抽样成离散点。由于每一个平面片所对应的放大率是一致的,所以我们可以选择每一个平面上的中心点的干涉条纹图样作为主要的全息条纹。其余物点的全息图样可以由截取主要全息条纹图样然后平移获得。根据其余物点与中心物点的相对位置坐标,选择将主要条纹全息图样中的以某一坐标为中心的全息图样片段截取出来,然后再将用同样方法得到的其余物点的全息图样片段相加得到该平面的全息图样。最终通过累加一系列平面片的全息图样获得整个物体全息图样。
With the development of computer technology ,high resolving digital image sensor (CCD or CMOS) and high resolving digital spatial light modulator (SLM), Computer-generated holography (CGH) which is used in dynamic real-time three-dimensional (3D) display and optical micromanipulation is a powerful technology. However, the CGH used in the 3D dynamic real-time reconstruction has its disadvantage. In the generation and reconstruction process of computer-generated holograms pattern, the encoding is very important .Usually the 3D real objects can be approximated as a collection of self-luminous points of light, the fringe patterns for all object points are directly calculated respectively. Finally all the fringe patterns are added up to obtain the whole interference pattern of the object image. This approach shows a computation complexity, since it requires one by one calculation of the fringe pattern per image point per hologram sample. Thus, real-time generation of the CGH pattern for a 3-D image can not be achievable easily. In this paper we mainly research the problems and the solutions of CGH for 3D real object in the common method:
[1] In order to enlarge reconstraction viewing-angle, wo suggest a viewing-angle enlargement method. Because the pixel pitches of the SLM are not fine, its diffracted trait decide the reconstruction of 3D object exceed the viewing-zone .we can achieve viewing-angle enlargement by viewing-angle transforming, In this method, the pretreatment is done for object information whose angle exceeding sampling frequency of SLM. After this pretreatment the angle of this object’s wave satisfies the sampling theorem. Then the recorded object is encoded . This hologram can be reconstructed by SLM . The reconstructed image of the object can be reproduced in the high-order of the SLM , so we can reconstruct the object by large view angle . The encoding method and some expressions according to the analysis of theory are given . Finally the example of encoding in this way and the simulation result of prove that this method is right.
[2] In order to alleviate computation of the digital holograms of 3-D objects, this paper suggests a new LUT method. A 3-D object can be treated a set of image planes discretely sliced in the z-direction, in which each image plane having a fixed depth is approximated as some collection of self-luminous object points of light. In this method, only the fringe patterns of the center points on each image plane are pre-calculated, called principal fringe patterns and those be stored . Then, the fringe patterns for other object points on each image plane can be obtained by simply shifting this pre-calculated principal fringe patterns according to the displaced values from the center to those points and adding them together.
引文
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[2]F.Zernike, Phase contrast, new method for the microscopic observation of transparent object, Physica9,686.
[3]D.Gabor, A new microscopic principle , Nature, vol.161, No.4098,777-778 (1948).
[4]D.Gabor, Microscopy by reconstructedwave-fronts, Proc.R.Soc.London A, Vol.197, No.1051,454-487(1949).
[5] Leith E N,Upamieks J.Reconstructed wavefronts and communication theory.J Opt Soc Am,1962,52:1123-1130.
[6]于美文,光全息学及其应用,北京理工大学出版社,1996,8。
[7]郁道银,谈恒英.工程光学.北京:机械工业出版社,2001:313-319。
[8]谈苏庆 顾兵。用三基色傅立叶计算全息再现彩色像。南京师大学报,2001年03期。
[9] 周革,张以谟。多焦距多通道全息光学元件。光学学报,Vol.11(7). 636-639.
[10] 刘玉照 。激光全息存储技术。情报科学,2000年05期。
[11]R.Brown, A.W.Lohmann. Appl.Opt,1966(5):96
[12]A.Kozma, D.L.Kelly. Appl.Opt,1965(4):387
[13]任秀云,程欣,刘轩, 等. 基于空间光调制器的计算全息成像特性. 光子学报, 2005, 34(1):110-113.
[14] 陈炳初,雷宏香,蔡志岗。用MATLAB制作迂回相位编码的傅立叶变换计算全息图。中山大学研究生学刊,2006。
[15] Hwi Kim, Joonku Hahn, Howon Lee, and Byoungho Lee。Computer-generated holograms of triangle mesh-modeled three-dimensional objects。Optical Society of America,2007。
[16] Detlef Leseberg。Computer-generated three-dimensional image Holograms。Applied optics,1992。
[17] C. S. Guo, Weitian Wang ,L. Z. Cai.Dot-array rainbow hologram .Optics letters , 1996.
[18] Alf Ritter, Joachim Bottger, Oliver Deussen, Matthias Konig, Thomas Strothotte. Hardware-based rendering of full-parallax syntheticholograms .Applied optics,1999.
[19] Detlef Leseberg . Computer-generated three-dimensional image holograms. Applied optics,1992.
[20] David Abookasis and Joseph Rosen. Three types of computer-generated hologram synthesized from multiple angular viewpoints of a three-dimensional scene. Applied optics,2006.
[21] Detlef Leseberg and Christian Frere. Computer-generated holograms of 3-D objects composed of tilted planar segments. Appl.Opt, 1988.
[22] Kyoji Matsushima and Masahiro Takai. Recurrence formulas for fast creation of synthetic three-dimensional holograms. Appl.Opt, 2000.
[23] 苏显渝,李继陶。信息光学。科学出版社,199.159页。
[24] Peter John Rodrigo, Ivan R. Perch-Nielsen, Carlo Amadeo Alonzo and Jesper Glückstad。GPC-based optical micromanipulation in 3D real-time using a single spatial light modulator。Optics express,2006。
[25]H. Melville, G.F. Milne, G.C. Spalding, W.Sibbett, K. Dholakia and D. McGloin. Optical trapping of three-dimensional structures using dynamic holograms,2003。
[26] Ethan Schonbrun, Rafael Piestun, Pamela Jordan, Jon Cooper, Kurt D Wulff , Johannes Courtial, Miles Padgett . 3D interferometric optical tweezers using a single spatial light modulator. Optics express,2005.
[27] Kodikullam V. Avudainayagam and Chitralekha S. Avudainayagam。Holographic multivergence target for subjective measurement of the astigmatic error of the human eye。Optics letters,2007.
[28] Hua Liu, Zhenwu Lu, Fengyou Li, Qiang Sun . Design of a novel hologram for full measurement of large and deep convex aspheric surfaces .Optics express ,2007.
[29] Jian Sheng, Edwin Malkiel, and Joseph Katz. Digital holographic microscope for measuring three-dimensional particle distributions and motions. Applied optics,2006.
[30] Kuniharu takizawa, Takanori Fujii, Toshihiro Sunaga, Kiyoshi Kishi.Three-dimensional large-screen display with reflection-mode spatial light modulators and a single-projection optical system: analysis of a retardation-modulation method. Applied optics,1998.
[31] 大越孝敬。三维成像技术。机械工业出版社,1982。
[32] 陈海云。LC - SLM 的光学调制特性及其在全息中的应用。激光杂志,2007。
[33] A. V. Kudryashov, J. Gonglewski, S. Browne and R. Highland。Liquid crystal phase modulator for adaptive optics. Temporal performance characterization。 Opt. Commun,1997。
[34] G. D. Love。 Wave-front correction and production of Zernike modes with a liquid-crystal spatial light modulator。 Appl. Opt,1997。
[35] O.Natoba, T.J.Naughton,Y.Frauel, et al。 Real-time three-dimensional object reconstruction by use of a phase-encoded digital hologram。 Appl. Opt,2002。
[36]陈怀新,魏宏刚,陈祯培,等。采用液晶空间光调制器的可控性阵列菲涅耳波带片。 光子学报, 2001。
[37] D. G. Grier。A revolution in optical manipulation。 Nature,2003 。
[38] K. Ladavac and D. G. Grier。Microoptomechanical pumps assembled and driven by holographic optical vortex arrays。 Opt. Express,2004。
[39] D. McGloin, G. C. Spalding, H. Melville。Application of spatial light modulators in atom optics。 Opt. Expres,2003。
[40]GUO Cheng-shan, LIU Xuan, HE Jing-liang, et al. Optimal Annular Structure of Optical Vortices. Opt. Express, 2004。
[41] 荣振宇, 国承山, 张莉, 等.液晶光调制计算全息相移器, 中国激光, 2004, 30(6): 693-697.
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