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数字全息研究领域目前存在两种不同的数字全息图取样模型.按照这两种模型进行研究时, 不但涉及较复杂的数学运算, 在许多情况下还会导致不同的研究结果, 不便于理论分析及实际应用.基于对数字全息图记录的物理过程分析及电荷藕合器件(charge coupled device, CCD)几何结构的研究, 本文将这两种取样模型简化为相同的数学表达式. 利用数字全息图的余弦级数展开及取样定理对简化模型的研究表明, 简化模型不但具有清晰的物理意义, 而且可以方便地为应用研究服务. 基于简化模型对物光波通过光学系统到达CCD的数字全息记录系统进行了研究, 导出得到实验证实的波前重建表达式.There are two sampling models of digital hologram in digital holographic research. The complex mathematical operation is involved in these two models, thereby leading to different results frequently and inconvenient theoretical analysis and practical application. Based on the analysis of physical processes in recording digital hologram and the study on geometry structure of CCD detector, the two sampling models are simplified into the same mathematical expression in this paper. Through studying the simplified model with cosine series expansion of digital hologram and sampling theorem, it is shown that the model has clear physical meanings and can be used for application study conveniently. Using the simplified model, we study digital holographic recording system with optical system and exact wavefront reconstruction expression verified in experiment.
[1] Goodman J W, Lawrence R W 1967 Appl. Phys. Lett. 11 77
[2] Huang T 1971 Proc. IEEE 159 1335
[3] Zhang T, Yamaguchi I 1998 Opt. Lett. 23 1221
[4] Seebacher S, Osten W, Baumbach T, Juptner W 2001 Opt. Lasers Eng. 36 103
[5] Thomas K 2002 Opt. Eng. 41 771
[6] Thomas K 2002 Opt. Eng. 41 1829
[7] Guo C S, Zhang L, Rong Z Y, Wang H T 2003 Opt. Eng. 42 2768
[8] Thomas K 2003 Opt. Eng. 42 2772
[9] Thomas K 2004 Handbook of Holographic Interferometry Optical and Digital Methods (Weinheim: Wiley-VCH) p141
[10] Qian X F, Zhang L, Dong K P 2006 Acta Photon. Sin. 35 1565 (in Chinese) [钱晓凡, 张磊, 董可平2006 光子学报 35 1565]
[11] Picart P, Leval J 2008 J. Opt. Soc. Am. A 25 1744
[12] Li J C, Zhang Y P, Xu W 2009 Acta Phys. Sin. 58 5385 (in Chinese) [李俊昌, 张亚萍, 许尉 2009 58 5385]
[13] L Q N, Chen Y L, Yuan R, Ge B Z, Gao Y, Zhang Y M 2009 Appl. Opt. 48 7000
[14] Zhou W J, Hu W T, Guo L, Xu Q S, Yu Y J 2010 Acta Phys. Sin. 59 8499 (in Chinese) [周文静, 胡文涛, 郭路, 徐强胜, 于瀛洁 2010 , 59 8499]
[15] Hu H F, Wang X L, Guo W G, Zhai H C, Wang P 2011 Acta Phys. Sin. 60 017901 (in Chinese) [胡浩丰, 王晓雷, 郭文刚, 翟宏琛, 王攀 2011 60 017901]
[16] Gao P, Yao B L, Min J W, Guo R L, Ma B H, Zheng J J, Lei M, Yan S H, Dan D, Ye T 2012 Opt. Lett. 37 3630
[17] Goodman J W 2006 An Introduction to Fourier Optics (3nd Ed.) (Beijing: Publishing House of Electronics Industry) pp12, 99, 141 (in Chinese) [Goodman J W 2006 傅里叶光学导论(第三版)(中译本) (北京: 电子工业出版社) 第12, 99, 141页]
[18] Gonzalez R C, Richard E W, Steven L E 2005 Digital Image Processing Using MATLAB (Beijing: Publishing House of Electronics Industry) pp239-246 (in Chinese) [冈萨雷斯, 数字图像处理(MATLAB版) (中译本) (北京: 电子工业出版社, 第239–246页]
[19] Picart P, Moisson E, Mounier D 2003 Appl. Opt. 42 1947
[20] Collins S A 1970 J. Opt. Soc. Am. 60 1168
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[1] Goodman J W, Lawrence R W 1967 Appl. Phys. Lett. 11 77
[2] Huang T 1971 Proc. IEEE 159 1335
[3] Zhang T, Yamaguchi I 1998 Opt. Lett. 23 1221
[4] Seebacher S, Osten W, Baumbach T, Juptner W 2001 Opt. Lasers Eng. 36 103
[5] Thomas K 2002 Opt. Eng. 41 771
[6] Thomas K 2002 Opt. Eng. 41 1829
[7] Guo C S, Zhang L, Rong Z Y, Wang H T 2003 Opt. Eng. 42 2768
[8] Thomas K 2003 Opt. Eng. 42 2772
[9] Thomas K 2004 Handbook of Holographic Interferometry Optical and Digital Methods (Weinheim: Wiley-VCH) p141
[10] Qian X F, Zhang L, Dong K P 2006 Acta Photon. Sin. 35 1565 (in Chinese) [钱晓凡, 张磊, 董可平2006 光子学报 35 1565]
[11] Picart P, Leval J 2008 J. Opt. Soc. Am. A 25 1744
[12] Li J C, Zhang Y P, Xu W 2009 Acta Phys. Sin. 58 5385 (in Chinese) [李俊昌, 张亚萍, 许尉 2009 58 5385]
[13] L Q N, Chen Y L, Yuan R, Ge B Z, Gao Y, Zhang Y M 2009 Appl. Opt. 48 7000
[14] Zhou W J, Hu W T, Guo L, Xu Q S, Yu Y J 2010 Acta Phys. Sin. 59 8499 (in Chinese) [周文静, 胡文涛, 郭路, 徐强胜, 于瀛洁 2010 , 59 8499]
[15] Hu H F, Wang X L, Guo W G, Zhai H C, Wang P 2011 Acta Phys. Sin. 60 017901 (in Chinese) [胡浩丰, 王晓雷, 郭文刚, 翟宏琛, 王攀 2011 60 017901]
[16] Gao P, Yao B L, Min J W, Guo R L, Ma B H, Zheng J J, Lei M, Yan S H, Dan D, Ye T 2012 Opt. Lett. 37 3630
[17] Goodman J W 2006 An Introduction to Fourier Optics (3nd Ed.) (Beijing: Publishing House of Electronics Industry) pp12, 99, 141 (in Chinese) [Goodman J W 2006 傅里叶光学导论(第三版)(中译本) (北京: 电子工业出版社) 第12, 99, 141页]
[18] Gonzalez R C, Richard E W, Steven L E 2005 Digital Image Processing Using MATLAB (Beijing: Publishing House of Electronics Industry) pp239-246 (in Chinese) [冈萨雷斯, 数字图像处理(MATLAB版) (中译本) (北京: 电子工业出版社, 第239–246页]
[19] Picart P, Moisson E, Mounier D 2003 Appl. Opt. 42 1947
[20] Collins S A 1970 J. Opt. Soc. Am. 60 1168
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