Zhang Hongye, Liu Zhanwei, Wen Huihui, Xie Huimin, Liu Chao
School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, People's Republic of China.
School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, People's Republic of China.
Ultramicroscopy. 2016 Dec;171:34-42. doi: 10.1016/j.ultramic.2016.08.019. Epub 2016 Aug 31.
Geometrical phase analysis (GPA) is typically a powerful tool to investigate the deformation in high resolution transmission electron microscopy images and has been used in various fields. The traditional GPA method using the fast Fourier transform, referred to as global-GPA (G-GPA) here, is based on the relationship between the displacement and the phase difference. In this paper, a subset-GPA (S-GPA) is introduced for further improvement. The S-GPA performs the windowed Fourier transform block by block in the image. The maximum strain measurement scale of the GPA method is theoretically analyzed on the basic of the phase spectrum extraction process. The upper limit is one third of the atomic spacing. The results of various numerical simulations verified that the S-GPA method performs better than the traditional G-GPA method in both the homogeneous and inhomogeneous deformation conditions, with the evaluation parameter of calculation reliability of S-GPA 10% higher than G-GPA. Specifically, the measurement accuracy of S-GPA is about three times higher than the G-GPA when calculating small strain (less than 2000με). For the large strain (greater than 150000με), the measurement accuracy of S-GPA is about 50% higher than that of the G-GPA. Besides, the S-GPA method can significantly eliminate the phase filling effect, while the G-GPA cannot. The S-GPA method has been successfully applied to analyze the strain field distribution in an lnGaAs/InAlAs supperlattice heterostructure.
几何相位分析（GPA）通常是研究高分辨率透射电子显微镜图像中变形的有力工具，并且已在各个领域中得到应用。这里将使用快速傅里叶变换的传统GPA方法称为全局GPA（G-GPA），它基于位移与相位差之间的关系。本文引入了一种子区域GPA（S-GPA）以进一步改进。S-GPA在图像中逐块执行加窗傅里叶变换。基于相位谱提取过程从理论上分析了GPA方法的最大应变测量尺度。上限是原子间距的三分之一。各种数值模拟结果表明，在均匀和非均匀变形条件下，S-GPA方法均比传统的G-GPA方法表现更好，S-GPA的计算可靠性评估参数比G-GPA高10%。具体而言，在计算小应变（小于2000με）时，S-GPA的测量精度比G-GPA高约三倍。对于大应变（大于150000με），S-GPA的测量精度比G-GPA高约50%。此外，S-GPA方法可以显著消除相位填充效应，而G-GPA则不能。S-GPA方法已成功应用于分析lnGaAs/InAlAs超晶格异质结构中的应变场分布。
