离轴电子全息的数值模拟研究

【作者】 陈静；

【导师】 孙琦；

【作者基本信息】 复旦大学 ， 物理电子学， 2012， 硕士

【摘要】 本论文对离轴电子全息进行了数值模拟研究,主要内容包括四部分：第一部分讨论了离轴菲涅尔全息的记录和滤波重现；第二部分研究了离轴像面电子全息的计算机模拟和滤波重现；第三和第四部分分别应用神经网络法和遗传算法重现离轴电子全息图。一、离轴菲涅尔全息的记录和滤波重现菲涅尔全息直接记录物波本身,该过程不需要变换透镜或成像透镜,只要求全息记录平面处于物波的菲涅尔衍射距离之内。本文在介绍离轴菲涅尔全息的记录原理之后,选用两幅图片作为样品,利用计算机模拟生成离轴菲涅尔全息图,并采用滤波法进行重现。对全息图进行傅里叶变换后,得到0级和±1级谱；滤出±1级谱中的任一个,并将其移至频谱中心；经过逆傅里叶变换即可得到全息面上的物波分布；最后做逆向或正向菲涅尔衍射,即可得到无零级、无共轭像斑的物场分布。模拟结果显示,滤波法可以较好地重现出原物像,但重现精度随图片复杂度的增加而降低。二、离轴像面电子全息的计算机模拟和滤波重现在离轴像面电子全息图的记录过程中,样品被放置在一半视场内,入射电子束被分成两个部分：穿过样品的物波和在真空中传播的参考波。这两束波经过物镜后,在一个加有正电压的电子双棱镜的作用下发生偏转,在交叠区域形成全息图。本文选取两幅图分别作为振幅和相位构造样品的复像波,为了便于比较,设定这两幅图互补。利用该复像波模拟生成离轴像面电子全息图,然后采用滤波法进行重现。重现结果表明,虽然原像波的振幅和相位的基本信息均被重现出来,但由于滤波过程损失了部分信息,因此重现效果不佳。三、应用神经网络法重现离轴电子全息图本文采用误差反向传递神经网络对离轴电子全息图进行重现。神经网络的输入层包含49个神经元,其输入信号即为超级像素49个像素点的强度值；第一和第二隐层分别包含10个和5个神经元；输出层包含2个神经元,其输出值即为超级像素中心点像波的实部和虚部。本文利用随机产生的7×7训练图样对网络进行训练,训练完成后,将网络用于重现离轴电子全息图。从重现结果来看,原像波的振幅和相位均得到了较为清晰的重现。相对于滤波法,神经网络法重现的振幅和相位误差分别下降了60%和7%。本文随后对神经网络训练中采用的像波函数的展开阶数、参考波波矢以及超级像素的尺寸进行了讨论。结果表明,相对于一阶和零阶展开来说,像波函数的二阶展开具有更好的重现效果。对参考波波矢的研究显示,为得到较好的重现效果,一个超级像素中应包含一到两个周期的参考波,而参考波波矢的取向对于重现效果没有太大影响。基于参考波的特殊形式,文中采用竖直方向压缩的超级像素重现全息图。结果表明,重现误差随着超级像素竖直方向尺寸的压缩而减小。相对于尺寸为7×7的超级像素,尺寸为1×7的超级像素重现的振幅和相位误差分别下降了51%和36%。在上述讨论的基础上,本文提出了压缩超级像素神经网络法(Neural Network method with Compressed Superpixel, NN-CSP),应用该方法可以提高全息图的重现精度。四、应用遗传算法重现离轴电子全息图遗传算法利用全息图的全部信息搜索全局最优解,因此其重现效果较好而且抗噪声能力强。相对于滤波法,遗传算法重现的振幅和相位误差分别减小了69%和66%；相对于神经网络法,遗传算法则具有更好的灵活性。本文对参考波波矢以及超级像素的尺寸也进行了讨论。对参考波波矢的研究表明,要获得较好的重现效果,超级像素中应包含一到两个周期的参考波,而波矢的方向对重现结果无显著影响。根据所选取参考波的特殊形式,本文采用了压缩超级像素的方法来重现全息图。重现结果显示,随着超级像素尺寸的减小,重现误差也随之减小。相对于超级像素7×7,超级像素3×7重现的振幅和相位误差分别下降了15%和7%。在此讨论基础之上,本文提出了压缩超级像素遗传算法(Genetic Algorithm method with Compressed Superpixel, GA-CSP),该方法可用于重现任意取向参考波的全息图,并得到较好的重现效果。更多还原

【Abstract】 This thesis includes four parts:the first part is the simulation and filtering reconstruction of off-axis Fresnel hologram; the second part is the simulation and filtering reconstruction of image plane off-axis hologram; the last two parts are concentrated on the reconstruction of off-axis electron holograms using neural network method and genetic algorithm respectively.1. Recording and filtering reconstruction of the off-axis Fresnel hologramThe off-axis Fresnel hologram is recorded within the Fresnel diffraction distance. Two pictures are selected to construct off-axis Fresnel holograms in this thesis, and the filtering reconstruction method is chosen to reconstruct the holograms afterwards. Firstly, the hologram is Fourier transformed, yielding one centerband and two sidebands; secondly, one of the sidebands is isolated and centered to the origin of the Fourier space; thirdly, the object wave in the hologram plane is obtained after an inverse Fourier transform; finally, the obtained wave is Fresnel diffracted backwards or forwards, yielding the objective distribution which is free from the disturbance of the autocorrelation and the twin image. The filtering reconstruction method yields the original object image, but the reconstruction accuracy decreases with the increase in the complexity of the object image.2. Simulation and filtering reconstruction of the off-axis image plane hologramIn the recording of off-axis image plane holograms, the object under investigation covers only half of the object plane, whereas the other half serves as a reference area. The reference wave and the object wave are imaged by the objective lens and deflected towards each other by the biprism, yielding the hologram in the overlapping region. For better evaluation of the reconstruction results, two pictures which are complementary to each other are selected as the amplitude and phase of the complex image wave. This complex image wave is used to construct the off-axis image plane hologram, which is afterwards reconstructed by the filtering method. The reconstruction results show that although the basic information of the original image wave is acquired, the reconstruction accuracy is not good enough because of the information loss in the filtering process.3. Reconstruction of off-axis electron holograms by neural network methodThe back-propagation neural network is selected in this thesis to reconstruct the off-axis electron hologram. In this paper, the input layer of the back-propagation neural network contains49neurons to which the intensity values of the49pixels in one superpixel are applied. Two hidden layers are adopted here, in which the former contains10neurons and the latter contains5neurons. The output layer contains2neurons which output the real part and imaginary part of the image wave at the central pixel of the superpixel. The neural network is trained with patterns generated by calculating simulation holograms from known image wave function. The reconstruction results show that the amplitude and phase of the image wave are well reconstructed. Compared with the filtering method, reconstruction errors of the amplitude and phase of the neural network method are reduced by about60%and7%, respectively.Several influencing factors are systematically discussed, including expansion order of the image wave function, the reference wave and the size of the superpixel. The reconstruction errors show that the second-order expansion yields batter reconstruction results than the first and zero order expansions, because it approximates the image wave in real situation more accurately. The discussion of the reference wave vector shows that in order to obtain good reconstruction results, the superpixel should contain at least one cycle and no more than two cycles of the reference wave. The orientation of the reference wave vector is found to have little influence on the reconstruction results. Based on the special form of the reference wave (vertical fringes), superpixel with its vertical size compressed is used as the basic calculating unit to reconstruct the image wave. It is found that the reconstruction results are improved with compressing the vertical size of the superpixel. Compared with superpixel of7×7, the reconstruction errors of amplitude and phase reconstructed by superpixel of1x7are reduced by51%and36%, respectively.Based on the discussions above, the Neural Network method with Compressed Superpixel (NN-CSP) is proposed in this thesis. When applied to reconstruct holograms formed by arbitrarily oriented reference wave, this method can increase the reconstruction accuracy.4. Reconstruction of off-axis electron holograms by genetic algorithmGenetic algorithm uses the complete information of the hologram to search the optimal solution, which yields good reconstruction results and has strong power to resist noise. Compared with the filtering method, reconstruction errors of the amplitude and phase of the genetic algorithm are reduced by about69%and66%, respectively. Compared with the neural network method, genetic algorithm shows better flexibility.The effects of the reference wave vector and the size of the superpixel are discussed in this thesis. The discussion of the reference wave vector shows that in order to obtain good reconstruction results, the superpixel should contain one to two cycles of the reference wave, which is consistent with the results obtained in the neural network method. The orientation of the reference wave vector is found to have little influence on the reconstruction results. Based on the special form of the reference wave (vertical fringes), superpixel with its vertical size compressed is used as the basic calculating unit to reconstruct the image wave. It is found that the reconstruction results are improved with compressing the vertical size of the superpixel. Compared with superpixel of7×7, the reconstruction errors of amplitude and phase reconstructed by superpixel of3×7are reduced by15%and7%, respectively.On the basis of the previous discussions, Genetic Algorithm method with Compressed Superpixel (GA-CSP) is proposed in this thesis. This method can be used to reconstruct holograms with arbitrarily oriented reference wave and yields good reconstruction results.更多还原