A flux-preserving non-linear inline holography reconstruction algorithm for partially coherent electrons

Area of Science:

• Physics
• Materials Science
• Microscopy

Background:

• Phase retrieval in Transmission Electron Microscopy (TEM) typically requires large defocus ranges.
• Aberrations and spatial coherence effects complicate phase reconstruction.

Purpose of the Study:

• To develop a computationally efficient, flux-preserving algorithm for reconstructing the phase of the exit-face wave function from focal series in TEM.
• To enable phase reconstruction over large focal ranges and with arbitrary spatial coherence.

Main Methods:

• An iterative computer algorithm was designed, neglecting aberration effects under specific conditions.
• The algorithm is flux-preserving and handles focal series with large defocus and partial spatial coherence.
• Reconstruction was performed using an experimental data set.

Main Results:

• Successful reconstruction of focal series data was achieved.
• The algorithm demonstrates computational efficiency and flux preservation.
• Implications for the Transport of Intensity Equation (TIE) under partial spatial coherence were discussed.

Conclusions:

• The developed iterative algorithm provides an efficient method for phase retrieval in TEM.
• The flux-preserving approach has implications for TIE applications in partially coherent imaging.
• The method shows promise for advanced TEM applications, with a comparison to off-axis holography.