The Numerical Simulation Of The Off-axis Digital Hologram Is Studied

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.