Crystal image analysis using $2D$ synchrosqueezed transforms
This work provides a new computational tool for materials scientists to analyze crystal defects and deformations from atomic-resolution images.
The authors propose algorithms using band-limited 2D synchrosqueezed transforms to extract mesoscopic and microscopic information from atomic crystal images, demonstrating efficiency and robustness on synthetic and real images.
We propose efficient algorithms based on a band-limited version of 2D synchrosqueezed transforms to extract mesoscopic and microscopic information from atomic crystal images. The methods analyze atomic crystal images as an assemblage of non-overlapping segments of 2D general intrinsic mode type functions, which are superpositions of non-linear wave-like components. In particular, crystal defects are interpreted as the irregularity of local energy; crystal rotations are described as the angle deviation of local wave vectors from their references; the gradient of a crystal elastic deformation can be obtained by a linear system generated by local wave vectors. Several numerical examples of synthetic and real crystal images are provided to illustrate the efficiency, robustness, and reliability of our methods.