多级衍射全息光栅与神经网络的光学互连
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摘要
光学系统由于其巨大的互连和内在的并行处理能力，特别适应于超
大容量数据处理和计算。神经网络是包括有很多简单处理元素的大型信
息处理系统。这些处理元素以并行方式互连，从而具有一定的总体计算
功能。神经网络中的高密度的互连最适于用光学方法实现。因此用光学
方法实现神经网络成为目前比较热门的研究课题。
在神经网络半个世纪的发展过程中，人们提出了数以百计的模型，
其中以Hopfield数理模型最具代表性。Hopfield模型实际上是一个自联
想记忆或联想记忆模型。由于其记忆是以外积矩阵的方式被存储的，也
称为“外积模型”。因而可以用矢量－矩阵积来实现。目前提出实现矢量-
矩阵积的光学方法很多，本论文提出了一种实现矢量-矩阵积的光学方法。
由于神经网络中的巨大的神经元之间的互连可以借用光学手段实
现，从而使光学互连成为实现神经网络最具有吸引力的潜在技术。光学
互连技术在数字光计算、光通信、光计算机及神经网络等领域具有广阔
的应用前景。其中自由空间光互连是一种最基本的互连形式。典型的完
善混洗互连网络(PS和FPS)以能构造任意形式的互连网络来实现任意
互连而倍受关注。
光栅作为一种分光元件，在光谱测量、光计算及光学信息处理中发
挥着重要作用。已提出用简单的成像系统和全息光栅来实现PS和FPS的
方案，且得到较满意的结果。全息光栅由其制作方便、成本低等优点，
己有很多的应用。目前已提出用许多方法包括计算机技术和微电子加工
技术制作具有多种性质和特点的各种光栅，如计算全息光栅、二元光栅
等，本论文基于传统的光学全息法，制作了一种新的光栅──多级衍射
全息光栅。将该光栅用于二透镜成像系统，作为滤波器，实现了矢量-矩
阵积的光学互连。为用光学方法实现神经网络的光学互连提供一种切实
可行的实验方案，并为光学神经网络从基础研究走向实际应用提供了一
定的实验基础。
本论文所做的工作主要有三个部分：本文的第一部分首先详尽地综
述了光互连意义、分类及光互连网络中的完善混洗网络的原理和目前所
提出的实现方法。其次详细地论述了神经系统的基本原理，介绍了神经
网络的基本概念和实现它的光学方案。主要介绍Hopfield数理模型及有
关的光学系统、光学神经网络实现所面临的主要困难。
本文的第二部分对透镜成像系统引入了物空间调制的概念，即在物
空间的任意位置对光场进行调制，并从理论上对透镜成像系统物空间调
制的输出效应进行了研究，从相干成像系统和非相干成像系统两种情况
进行讨论，并给出了其数学表达式。研究分析了当在输入面放置2-D数
据阵列，在物空间任一点适当引入光栅、棱镜、光楔等具有分光光学元
件，可以对输入数据阵列实现PS和FPS互连。因此证明了PS和FPS光
互连可作为特定物空间调制的一个应用实例。
本论文的第三部分首先提出了用MachZehnder干涉仪分两步记录制
作具有多缓衍射的全息光栅的方法。第一步先用两相干光束A；＊）和
A。（X）同时照明全息干版 H；，将 H；曝光制成的吸收型光栅经化学漂白
转化为位相光栅。再将这个位相光栅H；作母版，复位到光路中原来的位
置。再用丙梧干光束民（X）和B。（X）同时照明H1，调节两反射镜，改
变照明 H1的角度。当满足一定条件时，使 B；（X）照明 H；所得的衍射点
恰好落在由民（X）照明H；所得的各相邻衍射点之中点。在紧靠干版H；
之后放置干版民作为第二次记录，处理后得到所需的全息光栅。观察并
记录了这种全息光栅的夫琅和费衍射谱，利用这种多级衍射全息光栅实
现了图象多重。
其次在双透镜组成光学系统里，将输入信息作为物函数放在第一个
透镜的前焦平面上，多级衍射全息光栅作为滤波器放在其后焦平面上即
频谱平面上。利用多级衍射全息光栅的衍射效应实现了一点到多点的光
学互连，从而实现了 卜 的神经网络的光学互连。然后再把两个l0光
栅正交密接组合实现了2－D神经网络的光学互连。
实验结果表明：用本文制作的多级衍射光栅实现神经网络的互连是
－可行的，且具有结构简单、操作容易等特点。光栅制作时引入的综合噪
音对输出质量的影响及各衍射级能量的不均衡问题尚待进一步改进。
The optical system, with its massive interconnection and parallel processing capabilities, is particularly suitable for megalo-capacity data processing and computation. The neural network is a large-scale information processing system which consists of a great many simple processing units and those processing units are connected parallelly to perform a computation function collectively. The high density interconnections in the neural networks are more suitable for the optical implementation. So, in recent years attention has been paid to problems concerning the optical implementation.of neural networks
The simple model for neural network proposed by Hopfield has attracted much attention in the field of optical information processing. A lot of researches have been done with regard to the optical implementation of the neural networks. In all optical neural networks developed, the optical interconnection is a fundamental problem to be solved. Several methods have been proposed for the sake of yielding the matrix-vector product of an interconnection weigh matrix(IWM) and an input state.
On the other hand, as a splitter beam instrument , grating still plays an important role in spectrum measure, optical computation, and optical information processing. In this paper, the author makes a new grating──holographic grating with multiorder diffraction, based on the traditional optical holographic method, used to implement matrix vector optical interconnection.
The work is divided into three parts. In the first part, optical interconnection and the principle of perfect shuffle in optical interconnection networks are presented in detail as a first step. Then the principle of the neural network and optical implementation, Hopfield model and its optical systems and the main difficulty of implementation of the optical neural networks are also presented.
In the second part, a new concept of object spatial modulation
is introduced to lenses imaging system, into which is then theoretically researched, and its mathematical formula is given. It is thus proved that PS (perfect shuffle) and FPS (Folded PS) is an application example of the specific object spatial modulation.
In the third part, the method of holographic grating with multiorder diffraction made by using Mach-Zehnder inter ferometer in two stepped is presented, the principle of this method is interpreted in detail. The Fourier spectrum of this grating sample and the experiment result of image multiplication by using multiorder diffraction grating are also given.
Then, in the two-lens optical system, input information as object function is placed in the front focal plane, Holographic grating with multiorder diffraction as filter is placed in the back focal plane, and its multiorder diffraction effect can be used for optical interconnection form one to many points, so 1-D optical inter connects is implemented, then, 2-D optical interconnect of neural network is implemented through the normal contract of two 1-D grating.
The experiment results show that the method used in this projetct is feasible, simple in structure and easily operational. What remain to be improved are the effect of the general noise in grating-making on the output quality and the imbalance of diffraction order intensity.
大容量数据处理和计算。神经网络是包括有很多简单处理元素的大型信
息处理系统。这些处理元素以并行方式互连，从而具有一定的总体计算
功能。神经网络中的高密度的互连最适于用光学方法实现。因此用光学
方法实现神经网络成为目前比较热门的研究课题。
在神经网络半个世纪的发展过程中，人们提出了数以百计的模型，
其中以Hopfield数理模型最具代表性。Hopfield模型实际上是一个自联
想记忆或联想记忆模型。由于其记忆是以外积矩阵的方式被存储的，也
称为“外积模型”。因而可以用矢量－矩阵积来实现。目前提出实现矢量-
矩阵积的光学方法很多，本论文提出了一种实现矢量-矩阵积的光学方法。
由于神经网络中的巨大的神经元之间的互连可以借用光学手段实
现，从而使光学互连成为实现神经网络最具有吸引力的潜在技术。光学
互连技术在数字光计算、光通信、光计算机及神经网络等领域具有广阔
的应用前景。其中自由空间光互连是一种最基本的互连形式。典型的完
善混洗互连网络(PS和FPS)以能构造任意形式的互连网络来实现任意
互连而倍受关注。
光栅作为一种分光元件，在光谱测量、光计算及光学信息处理中发
挥着重要作用。已提出用简单的成像系统和全息光栅来实现PS和FPS的
方案，且得到较满意的结果。全息光栅由其制作方便、成本低等优点，
己有很多的应用。目前已提出用许多方法包括计算机技术和微电子加工
技术制作具有多种性质和特点的各种光栅，如计算全息光栅、二元光栅
等，本论文基于传统的光学全息法，制作了一种新的光栅──多级衍射
全息光栅。将该光栅用于二透镜成像系统，作为滤波器，实现了矢量-矩
阵积的光学互连。为用光学方法实现神经网络的光学互连提供一种切实
可行的实验方案，并为光学神经网络从基础研究走向实际应用提供了一
定的实验基础。
本论文所做的工作主要有三个部分：本文的第一部分首先详尽地综
述了光互连意义、分类及光互连网络中的完善混洗网络的原理和目前所
提出的实现方法。其次详细地论述了神经系统的基本原理，介绍了神经
网络的基本概念和实现它的光学方案。主要介绍Hopfield数理模型及有
关的光学系统、光学神经网络实现所面临的主要困难。
本文的第二部分对透镜成像系统引入了物空间调制的概念，即在物
空间的任意位置对光场进行调制，并从理论上对透镜成像系统物空间调
制的输出效应进行了研究，从相干成像系统和非相干成像系统两种情况
进行讨论，并给出了其数学表达式。研究分析了当在输入面放置2-D数
据阵列，在物空间任一点适当引入光栅、棱镜、光楔等具有分光光学元
件，可以对输入数据阵列实现PS和FPS互连。因此证明了PS和FPS光
互连可作为特定物空间调制的一个应用实例。
本论文的第三部分首先提出了用MachZehnder干涉仪分两步记录制
作具有多缓衍射的全息光栅的方法。第一步先用两相干光束A；＊）和
A。（X）同时照明全息干版 H；，将 H；曝光制成的吸收型光栅经化学漂白
转化为位相光栅。再将这个位相光栅H；作母版，复位到光路中原来的位
置。再用丙梧干光束民（X）和B。（X）同时照明H1，调节两反射镜，改
变照明 H1的角度。当满足一定条件时，使 B；（X）照明 H；所得的衍射点
恰好落在由民（X）照明H；所得的各相邻衍射点之中点。在紧靠干版H；
之后放置干版民作为第二次记录，处理后得到所需的全息光栅。观察并
记录了这种全息光栅的夫琅和费衍射谱，利用这种多级衍射全息光栅实
现了图象多重。
其次在双透镜组成光学系统里，将输入信息作为物函数放在第一个
透镜的前焦平面上，多级衍射全息光栅作为滤波器放在其后焦平面上即
频谱平面上。利用多级衍射全息光栅的衍射效应实现了一点到多点的光
学互连，从而实现了 卜 的神经网络的光学互连。然后再把两个l0光
栅正交密接组合实现了2－D神经网络的光学互连。
实验结果表明：用本文制作的多级衍射光栅实现神经网络的互连是
－可行的，且具有结构简单、操作容易等特点。光栅制作时引入的综合噪
音对输出质量的影响及各衍射级能量的不均衡问题尚待进一步改进。
The optical system, with its massive interconnection and parallel processing capabilities, is particularly suitable for megalo-capacity data processing and computation. The neural network is a large-scale information processing system which consists of a great many simple processing units and those processing units are connected parallelly to perform a computation function collectively. The high density interconnections in the neural networks are more suitable for the optical implementation. So, in recent years attention has been paid to problems concerning the optical implementation.of neural networks
The simple model for neural network proposed by Hopfield has attracted much attention in the field of optical information processing. A lot of researches have been done with regard to the optical implementation of the neural networks. In all optical neural networks developed, the optical interconnection is a fundamental problem to be solved. Several methods have been proposed for the sake of yielding the matrix-vector product of an interconnection weigh matrix(IWM) and an input state.
On the other hand, as a splitter beam instrument , grating still plays an important role in spectrum measure, optical computation, and optical information processing. In this paper, the author makes a new grating──holographic grating with multiorder diffraction, based on the traditional optical holographic method, used to implement matrix vector optical interconnection.
The work is divided into three parts. In the first part, optical interconnection and the principle of perfect shuffle in optical interconnection networks are presented in detail as a first step. Then the principle of the neural network and optical implementation, Hopfield model and its optical systems and the main difficulty of implementation of the optical neural networks are also presented.
In the second part, a new concept of object spatial modulation
is introduced to lenses imaging system, into which is then theoretically researched, and its mathematical formula is given. It is thus proved that PS (perfect shuffle) and FPS (Folded PS) is an application example of the specific object spatial modulation.
In the third part, the method of holographic grating with multiorder diffraction made by using Mach-Zehnder inter ferometer in two stepped is presented, the principle of this method is interpreted in detail. The Fourier spectrum of this grating sample and the experiment result of image multiplication by using multiorder diffraction grating are also given.
Then, in the two-lens optical system, input information as object function is placed in the front focal plane, Holographic grating with multiorder diffraction as filter is placed in the back focal plane, and its multiorder diffraction effect can be used for optical interconnection form one to many points, so 1-D optical inter connects is implemented, then, 2-D optical interconnect of neural network is implemented through the normal contract of two 1-D grating.
The experiment results show that the method used in this projetct is feasible, simple in structure and easily operational. What remain to be improved are the effect of the general noise in grating-making on the output quality and the imbalance of diffraction order intensity.
引文
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54 T-H. Chao and W. W., stoner, Optical implementation of a f eaturebased neural network with application to automatic target recognition, Appl. Opt., 1993, 32(8) : 1359
55 D. Psaltis, C. H. Park and J. Hong, Higher order asssociative memories and their optical implementations neural networks, 1988, 1(2) :149
56 J. Hong, S.Campbell and P. Yeh, Optical pattern classifier with perceptron learing, Appl. Opt., 1990, 29(20) :3019
57 Sh-q. Zhang and M. A. Karim, Optical implementation of cellular neural networks based on bias and join correlation, Appl. Opt., 1999, 38(5) :847
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59 R. A. Athale, H. H. Szu and C. B. Friedlander, Optical controlled nonlinearity in the correlation domain, Opt. Lett., 1986,11(7) :482
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61 A. D. Fisher, W. L. Lippincott and J. N. Lee, Optical implementations of associative networks with versatile adaptive learning capabilities, Appl. Opt., 1987, 26(23) :5039
62 E. G. Paek and D. Psaltis, Optical associative memory using Fourier transform holograms, Appl. Opt. ,1987, 26(5) : 428
63 H. J. white and W. A. Wright, Holographic implementation of a Hopfield model with discrete weights, Appl. Opt., 1988,27(2) :331
64 H. Kang , Ch-X. Yang, G-G. Mu and Zh-K. Wu, Real-time holographic associative memory using doped LiNb0_3 in a phase-conjugating resonator, Opt. Lett., 1990, 15(1) :637
65 F. Ito and K. Kitayama, Optical implementation of the Hopfield neural network using multiple fiber nets, Appl. Opt., 1989, 28(20) :4176
66 A. P. Goutzoulis, Comparison of laser diode and electronic residue position-coded Look-up tables , Opt. Eng., 1989, 28(4) :373
67 华建文,刘立人,李国强等,比例自变换实现神经网络光学互连,中国激光,1998,25(7) :643
68 J. J. Hopfield ,Neural network and physical system with emergent collective computational abilities, Proc, Natl. Acad. Sci. U.S.A. 1982,79(25) :2554
69 D. Psaltis and N. Farhat, Optical information processing based on an associative-memory model of neural nets with thresholding and feedback , Opt. Lett., 1985, 10 (2) : 98
70 S. Jutamulia, G. M. Storti , J. Lindmayer et al , Use of electron trapping materials in optical signal processing. 3: Modifiable Hopfiled type neural network s, Appl. Opt., 1991, 30(14) :1786
71 A.J. David and B.E.A. Saleh, optical implementation of the Hopfield algorithm using correlations, Appl. Opt., 1990,29(8):1063
72 P. Lalanne, P. Chavel and J. Taboury, Optical inner-prduct implementation of neural networks models, Appl. Opt.,1989,28(2):377
73 I. Shariv, O. Gila and A.A. Friesm, All-optical bipolar neural network with polarization-modulating neurons, Opt. Lett., 1991,16(21):1692
74 S.H. Song,S.S. Lee, Properties of holographic associative memory prepared by the polarization encoding process, Appl. Opt., 1988,27(15):3149
75 G.R. Gindi, A.F. Gmitro, K. parthasarathy, Hopfield model associative memory with nonzevo-diagonal termes in memory matrix, Appl. Opt.,1988,27(1):129
76 S.-H. Oh, T.-H. Yoon, J,C. Kim, Associative-memory model Based on neural networks:modification of Hopfield model, Opt. Lett.,1988,13(1):74
77 申金媛，张延，王许明等，全双极WTA神经网络模型的光学实现，电子学报，1992，20(10)：70
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79 丁铁英，徐军，申金嫒，张延，光电混合实现全双极WTA模型的新方法，光学学报，1995，15(10)：1414
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88 王应宗，非线性全息图多重再现象的理论，陕西师范大学学报，1985，13(1)34
89 聂守平，刘明，陈伯荣等，衍射强度分布的二元位相光栅，中国激光，1999，26(1)：44
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54 T-H. Chao and W. W., stoner, Optical implementation of a f eaturebased neural network with application to automatic target recognition, Appl. Opt., 1993, 32(8) : 1359
55 D. Psaltis, C. H. Park and J. Hong, Higher order asssociative memories and their optical implementations neural networks, 1988, 1(2) :149
56 J. Hong, S.Campbell and P. Yeh, Optical pattern classifier with perceptron learing, Appl. Opt., 1990, 29(20) :3019
57 Sh-q. Zhang and M. A. Karim, Optical implementation of cellular neural networks based on bias and join correlation, Appl. Opt., 1999, 38(5) :847
58 Y. Owechko, G. J. Dunning, E. Marom et al .Holographic associative memory with nonlinearities in the correlation domain, Appl. Opt., 1987, 26(10) :1900
59 R. A. Athale, H. H. Szu and C. B. Friedlander, Optical controlled nonlinearity in the correlation domain, Opt. Lett., 1986,11(7) :482
60 A. Yariv, S. K. Kwong and K. Kyuma, Demonstration of an all-optical associative holographic memory, Appl. Phys. Lett., 1986, 48(17) :1114
61 A. D. Fisher, W. L. Lippincott and J. N. Lee, Optical implementations of associative networks with versatile adaptive learning capabilities, Appl. Opt., 1987, 26(23) :5039
62 E. G. Paek and D. Psaltis, Optical associative memory using Fourier transform holograms, Appl. Opt. ,1987, 26(5) : 428
63 H. J. white and W. A. Wright, Holographic implementation of a Hopfield model with discrete weights, Appl. Opt., 1988,27(2) :331
64 H. Kang , Ch-X. Yang, G-G. Mu and Zh-K. Wu, Real-time holographic associative memory using doped LiNb0_3 in a phase-conjugating resonator, Opt. Lett., 1990, 15(1) :637
65 F. Ito and K. Kitayama, Optical implementation of the Hopfield neural network using multiple fiber nets, Appl. Opt., 1989, 28(20) :4176
66 A. P. Goutzoulis, Comparison of laser diode and electronic residue position-coded Look-up tables , Opt. Eng., 1989, 28(4) :373
67 华建文,刘立人,李国强等,比例自变换实现神经网络光学互连,中国激光,1998,25(7) :643
68 J. J. Hopfield ,Neural network and physical system with emergent collective computational abilities, Proc, Natl. Acad. Sci. U.S.A. 1982,79(25) :2554
69 D. Psaltis and N. Farhat, Optical information processing based on an associative-memory model of neural nets with thresholding and feedback , Opt. Lett., 1985, 10 (2) : 98
70 S. Jutamulia, G. M. Storti , J. Lindmayer et al , Use of electron trapping materials in optical signal processing. 3: Modifiable Hopfiled type neural network s, Appl. Opt., 1991, 30(14) :1786
71 A.J. David and B.E.A. Saleh, optical implementation of the Hopfield algorithm using correlations, Appl. Opt., 1990,29(8):1063
72 P. Lalanne, P. Chavel and J. Taboury, Optical inner-prduct implementation of neural networks models, Appl. Opt.,1989,28(2):377
73 I. Shariv, O. Gila and A.A. Friesm, All-optical bipolar neural network with polarization-modulating neurons, Opt. Lett., 1991,16(21):1692
74 S.H. Song,S.S. Lee, Properties of holographic associative memory prepared by the polarization encoding process, Appl. Opt., 1988,27(15):3149
75 G.R. Gindi, A.F. Gmitro, K. parthasarathy, Hopfield model associative memory with nonzevo-diagonal termes in memory matrix, Appl. Opt.,1988,27(1):129
76 S.-H. Oh, T.-H. Yoon, J,C. Kim, Associative-memory model Based on neural networks:modification of Hopfield model, Opt. Lett.,1988,13(1):74
77 申金媛，张延，王许明等，全双极WTA神经网络模型的光学实现，电子学报，1992，20(10)：70
78 王许明，王健水，母国光，双极双向联想存储器的单通道光学实现，光学学报，1993，13(4)：336
79 丁铁英，徐军，申金嫒，张延，光电混合实现全双极WTA模型的新方法，光学学报，1995，15(10)：1414
80 X.-M.Wang,G.-G.Mu,Optical neural network with bipolar neural states,Appl.0pt.,1992,31(23)
81 朱伟利，陈岩松，多值神经网络改进模型及其光学实现，光学学报，1992，12(5)：458
82 朱伟利，陈岩松，李德华，正补态光学神经网络模型性能评估，光学学报，1993，13(1)：57
83 G.L. Rogers, Noncoherent optical processing, John, Wiley &, Sons, Inc.,1977,137
84 H. J. Caulfield, Handbook of optical holography, Acdemic Press, Inc, New York, !979, P191
85 V. Arrizon, E.L. Olazagasti, A.S. aeredia Talbot array illuminators with optimum compression ratio, Opt. Lett.,1996,21(4):233
86 S.J. Walker and J. Jahns, Array generation with multilevel phase gratings, J. Opt.Soc. Am.A.,1990,7(8):1509
87 R. L. Morrison, Symmetries that simplify the design of spot array phase gratings, T. Opt. Soc. Am. A., 1992,9(3):464
88 王应宗，非线性全息图多重再现象的理论，陕西师范大学学报，1985，13(1)34
89 聂守平，刘明，陈伯荣等，衍射强度分布的二元位相光栅，中国激光，1999，26(1)：44
90 J.W.Goodman,Introduction to Faurier optics,MC Grave-Hil,New York,1968.P 69
91 王永昭，光学全息，机械工业出版社，1981，P 12
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