Subset geometric phase analysis method for deformation evaluation of HRTEM images.

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.