On the phase problem in electron microscopy: the relationship between structure factors, exit waves, and HREM images

Area of Science:

• Materials Science
• Crystallography
• Electron Microscopy

Background:

• Electron microscopy terminology, specifically 'phase', is ambiguous, causing confusion regarding phase information in recorded images.
• Distinguishing between crystallographic structure-factor phases and electron wave phases is crucial for accurate interpretation.
• This ambiguity impacts the understanding of phase information retrieval in imaging processes.

Purpose of the Study:

• To resolve the phase confusion in electron microscopy by clarifying the relationships between structure factors, exit waves, and high-resolution electron microscopy (HREM) images.
• To investigate the presence and loss of phase information during image recording.
• To compare different methods for phase determination from HREM data.

Main Methods:

• Analytical comparison of phases at different imaging stages for a weak phase object (WPO) model.
• Numerical calculation and comparison of phases using the multi-slice method based on dynamical diffraction theory.
• Experimental validation using high-resolution electron microscopy (HREM) data from a real crystal (Ti2S).

Main Results:

• Demonstrated that accurate structure factor-phases can be directly obtained from HREM images using crystallographic image processing.
• Showed that exit wave reconstruction and crystallographic image processing utilize similar information and yield comparable results.
• Confirmed the theoretical description of phase relationships through experimental data.

Conclusions:

• The study successfully clarifies the 'phase confusion' in electron microscopy.
• Direct retrieval of structure factor-phases from HREM images is feasible.
• The findings validate the use of crystallographic image processing and exit wave reconstruction for accurate structure determination.