Why Do We Need to Use Three-Dimensional (3D) Fourier Transform (FT) Analysis to Evaluate a High-Performance...

Area of Science:

• Materials Science
• Physics
• Microscopy

Background:

• Sub-angstrom resolution in transmission electron microscopes (TEM) is limited by partial temporal coherence after spherical aberration (Cs) correction.
• Traditional Young's fringe tests are insufficient for evaluating ultra-high-resolution electron microscopes.
• Existing tilted-beam diffractogram methods fail with significant nonlinear contributions.

Purpose of the Study:

• To propose and generalize a novel method for evaluating temporal coherence in Cs-corrected TEMs.
• To overcome limitations of existing techniques for determining the true information limit of advanced electron microscopes.

Main Methods:

• Developed a method based on the three-dimensional (3D) Fourier transform (FT) of through-focus TEM images.
• Generalized the 3D FT analysis and derived the 3D transmission cross-coefficient.
• Evaluated the performance of Cs-corrected TEMs at lower voltages using this method.

Main Results:

• The 3D FT analysis can extract linear image information from image intensity.
• It enables separate evaluation of two linear image contributions on Ewald sphere envelopes.
• This method successfully works with strong scattering objects, unlike diffractogram analysis.

Conclusions:

• The generalized 3D FT analysis provides a robust method for evaluating temporal coherence in ultra-high-resolution TEM.
• This technique allows direct observation of linear image transfer down to tens of picometers.
• It is essential for accurately characterizing the performance of advanced electron microscopes.