微觀定出奈米晶體的結構可以促使了解其性質並被廣泛地運用。很多研究已顯示利用高分辨電子顯微鏡可以達到細微尺度的訊息。然而仍未有發表重構三維結構達原子分辨率級的研究。
電子與原子的作用力很強，經過晶體內可同時產生數百束的繞射線而有相當程度的多次干射現象，使得在出口平面的波函數不能直接對應出結構的訊息。動力散射(dynamical scattering)的現象可由多層法(multislice theory)以及通道理論(channelling theory)來解釋。多層法主要是從光學物理的角度將電子通過樣品看作穿透一疊N個等距二維的相位及振幅物體。通道理論則是在實空間計算電子穿過原子通道的運動模式，而此模式可用其最低能量狀態亦即最受束縛的狀態來表示。本論文主要在探討由出口波利用逆多層法以及逆通道理論回復結構的可行性以及正確性。逆多層法是要定出電子束穿過晶體的原子層數。逆通道理論則是回復原子通道的厚度以及其最低狀態的能量。這兩種方法最主要目的皆是在於定性定量的決定原子通道中的原子顆數及種類。兩種方法皆測試在一模擬的鎳化矽(NiSi2)楔型結構與一實驗的鈦酸鍶(SrTiO3)在[110]方向的出口波。初步的研究結果顯示這兩種方法皆能有效的定出原子顆數及種類。
本論文最後介紹利用離散概念重構三維結構達原子分辨率級。材料在原子分辨率級可視為離散的原子分佈。將投影的結構訊息用矩陣描述則可以數學方法回復矩陣以達到重建三維原子分辨率的結構。

Finding the structure of nanocrystals to atomic scale can provide a greater understanding of the properties of nano-materials which may realize in many different applications. It has been widely studied that high resolution transmission electron microscope (HRTEM) can provide the information to a finer scale. However, atomic resolution tomography has not yet proposed.
Electrons interact with atoms strongly which cause hundreds of diffractions simultaneously resulting in multiple scattering. Therefore, the exit wave function does not reveal the structure information exactly. Dynamical scattering in the crystal can be described from the multislice theory and the channelling theory. The multislice theory presents the electrons are transmitted through a set of N two dimensional phase- and amplitude-objects in equal separation distances. The channelling theory derives the motion of electrons passing through an atom column in real space. This motion can be fairly expressed only by the most bound state of the electrons. This thesis discusses the potential of structure reversion from exit wave based on the two methods: reverse multislice method and reverse channelling method. From the reverse multislice method, it is intended to find the number of slices of atomic planes perpendicular to the incident electron beam direction. The reverse channelling method is mainly retrieving the thickness and the bound eigenenergy of the atom column. These two methods apply to analyze the number of atoms in every atom column and to distinguish chemically the different elements. Both methods are tested with a simulated wedge-shaped crystal NiSi2 and an experimental SrTiO3 [110] exit wave. The results show that these two methods can effectively determine the number and the type of the atoms.
A primary concept of discrete tomography is introduced. At the atomic level materials are made out of a discrete set of atoms. By representing the structure projection information as matrices, atomic resolution tomography can be obtained.

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