Phase retrieval in TEM using Fresnel images.

Area of Science:

• Electron microscopy
• Optical physics
• Computational imaging

Background:

• Sideband holography is a common method for phase recovery in electron microscopy.
• In-line holography offers a potential alternative, but phase recovery from Fresnel images of aperiodic objects presents challenges.

Purpose of the Study:

• To investigate and validate methods for phase recovery using in-line holography with Fresnel images.
• To assess the reliability and accuracy of these methods for aperiodic objects in electron microscopy.

Main Methods:

• Utilized computed simulations and experimental data to test phase recovery algorithms.
• Employed an error functional minimization approach, comparing experimental and calculated image intensities.
• Implemented a conjugate gradient algorithm and explored strategies to avoid local minima, such as increasing parameter ratios and incremental relaxation of phase bandwidth.

Main Results:

• The conjugate gradient algorithm demonstrated reliable phase recovery, even for objects with large phase variations.
• Minimizing the error functional by increasing known/unknown parameters improved convergence probability.
• Analytic expressions for error gradients were crucial for practical implementation.
• Accurate phase shifts were measured, indicating the method's sensitivity.

Conclusions:

• In-line holography with Fresnel images provides a viable alternative for phase recovery in electron microscopy.
• The conjugate gradient algorithm offers robust and accurate phase reconstruction.
• Understanding factors limiting accuracy is essential for reliable application of Fresnel image-based phase recovery.