Phase retrieval from image intensities: why does exit wave restoration using IWFR work so well?

Area of Science:

• Electron microscopy
• Holography
• Image processing

Background:

• In-line holography reconstructs wave functions from intensity images.
• Iterative wave function reconstruction (IWFR) is an advanced technique for this purpose.

Purpose of the Study:

• To verify the efficacy of IWFR for atomic-resolution exit wave function (EWF) estimation.
• To assess the convergence speed and robustness of IWFR.

Main Methods:

• Utilized a set of through-focus images to reconstruct the complex wave function.
• Employed Fourier transforms of observed intensities as input for IWFR.
• Investigated the impact of defocus step variations and spherical aberration errors.

Main Results:

• IWFR provided highly accurate atomic-resolution EWF estimates with rapid convergence.
• The method demonstrated robustness across a wide range of defocus steps.
• Reconstructed EWFs showed minimal aberrations even with initial estimation errors.

Conclusions:

• IWFR is an effective and efficient method for reconstructing high-quality EWFs from electron microscopy data.
• The technique is suitable for routine use with stable microscopes capable of acquiring multiple high-quality images.
• IWFR is valuable for analyzing phase objects, particularly with Cs-corrected microscopes, by enabling post-processing aberration correction.