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首页> 外文期刊>Micron: The international research and review journal for microscopy >Quantitative comparison between real space and Bloch wave methods in image simulation
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Quantitative comparison between real space and Bloch wave methods in image simulation

机译：图像仿真中真实空间与光滑波动方法的定量比较

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Both Bloch wave (BW) and real space multislice (RS-MS) methods are based on the Schrodinger equation. The BW method is considered to be the most accurate and popular simulation method used in various simulations, and it has solved many crystallographic problems. In this paper, we verified that the aforementioned two methods are similar to each other with minor difference. First, the RS-MS method is implemented in the real space, while the BW method is carried out in the reciprocal space. Furthermore, by quantitatively calculating exit wavefunctions of four crystals, i.e., Cu, MgAl2O4, Mg44Rh7 and KNbO3, we found that the RS-MS method offers certain advantages over the BW method. Firstly, the RS-MS method takes all the structure factors into account to calculate crystal potentials, so accuracy loss caused from the crystal potential is effectively avoided. Secondly, the dimension of the scattering matrix for the RS-MS method is proportional to the area of the 2 dimensional (2D) unit cell which is perpendicular to the incident beam direction, whereas that for the BW method is proportional to the square of the area of the 2D unit cell. To reduce computation time, reduction of dimension of the scattering matrix for the BW method has to be performed, thus accuracy loss is inevitable even if compensated by the Bethe potential method. For crystals with a small 2D unit cell, both simulation methods work well. When the area of the 2D unit cell is larger than square of 2.0 nm, for example KNbO3, the size of the scattering matrix of the BW method is too large to be carried out by simulation and one should use the RS-MS method instead. This paper presents a tutorial comparison of the different methods.
机译：Bloch波（BW）和真实空间多层（RS-MS）方法都基于Schrodinger方程。 BW方法被认为是各种模拟中使用的最准确和流行的仿真方法，解决了许多晶体检查问题。在本文中，我们核实上述两种方法彼此相似，具有轻微的差异。首先，RS-MS方法在真实空间中实现，而BW方法在往复空间中执行。此外，通过定量计算四个晶体的出口波力，即Cu，MgAl2O4，Mg44RH7和KNBO3，我们发现RS-MS方法提供了通过BW方法的某些优点。首先，RS-MS方法考虑到所有结构因素以计算晶体电位，因此有效地避免了由晶体电位引起的精度损耗。其次，对于RS-MS方法的散射矩阵的尺寸与垂直于入射光束方向的2维（2D）单元电池的面积成比例，而对于BW方法的尺寸是与入射光束方向的面积成比例2D单元电池的区域。为了减少计算时间，必须执行用于BW方法的散射矩阵的尺寸的尺寸，因此即使通过贝特电位方法补偿，即使补偿也是不可避免的。对于具有小型2D单元电池的晶体，两个模拟方法都很好地工作。当2D单元电池的面积大于2.0nm的正方形时，例如KNBO3，BW方法的散射矩阵的尺寸太大而无法通过模拟进行，并且应该使用RS-MS方法。本文介绍了不同方法的教程比较。

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