Phase retrieval of electron rocking curves using total variation and total squared variation regularizations

Area of Science:

• Materials Science
• Crystallography
• Electron Microscopy

Background:

• Convergent-beam electron diffraction (CBED) is crucial for analyzing crystal structures.
• Phase retrieval from electron rocking curves is challenging due to noise and dynamical diffraction effects.
• Accurate determination of lattice displacement fields is essential for understanding material defects.

Purpose of the Study:

• To propose a new phase retrieval method for electron rocking curves.
• To enable the determination of three-dimensional lattice displacement fields.
• To address noise and sparsity in displacement field reconstruction.

Main Methods:

• Developed a phase retrieval algorithm incorporating total variation and total squared variation regularizations.
• Applied the method to electron rocking curves affected by dynamical diffraction.
• Utilized sparse characteristics of displacement fields for improved accuracy.

Main Results:

• The proposed algorithm effectively suppresses noise and background signals.
• Demonstrated accurate reconstruction of sparse displacement fields, particularly near lattice defects.
• Validated the method's efficacy on experimental rocking curves from a stainless steel stacking fault.

Conclusions:

• The novel phase retrieval technique is effective for analyzing electron diffraction data.
• The method enhances the determination of 3D lattice displacements along the beam direction.
• Accurate phase reconstruction is achievable even with complex dynamical diffraction effects.