Domain-Resolved STC Analysis for Full Displacement-Gradient and Strain–Rotation Mapping in a Magnesium Twin-Boundary HRTEM Image

Fourier-based analysis of strain and rotation in differently oriented crystal domains in high-resolution electron microscopy lattice images requires consideration of the lattice signals and reciprocal bases associated with each domain. Here, the strain tensor using the computational Fourier transform moiré (STC) method was applied to a high-resolution transmission electron microscopy (HRTEM) image of a magnesium twin boundary by combining domain-specific reciprocal bases, amplitude-based pixel selection, far-field referencing, and real-space stitching. Uniform synthetic deformations verified the recovery of all four displacement-gradient components and their strain–rotation decomposition. Spatially varying deformations with added noise were used to evaluate sensitivity to filter radius and signal-amplitude threshold. With identical filtering and common evaluation pixels, STC and geometric phase analysis yielded similar results, including filter-induced attenuation of deformation peaks. In a two-domain synthetic image with a 36.87° orientation difference, applying the filter, carrier, and reconstruction basis of one domain to the other produced componentwise root-mean-square errors of approximately 23–50 percentage points. Basis mixing alone cannot explain these errors; carrier mismatch, changes in the transmitted signal, and low signal amplitudes also contribute. The experimental maps show relative projected strain and residual rotation referenced to the far field of each domain, with the boundary core excluded. Bragg-signal amplitudes support domain-specific signal assignment but do not independently validate strain accuracy, and quantitative interpretation remains limited in regions with weak signals.