Probability calculus for quantitative HREM. Part II: entropy and likelihood concepts.

Area of Science:

• Materials Science
• Crystallography
• Electron Microscopy

Background:

• Extracting atomic coordinates from high-resolution electron microscopy (HREM) images is crucial for materials characterization.
• Existing methods for parameter estimation in HREM image analysis have limitations regarding noise assumptions and error handling.

Purpose of the Study:

• To describe a novel R-factor refinement technique for atomic coordinate extraction from HREM images.
• To compare the suitability of maximum likelihood and maximum entropy techniques for HREM applications.
• To present a robust solution for parameter estimation in HREM, addressing practical challenges.

Main Methods:

• Iterative simulation and global optimization for R-factor refinement.
• Probability density estimation for unknown parameters.
• Comparison of maximum likelihood and maximum entropy methods.
• Synthesis of two point-cloud techniques.

Main Results:

• R-factor refinement with independent Monte-Carlo error calibration is presented as a versatile HREM analysis method.
• The proposed technique does not require assumptions about noise being additive, uncorrelated, or Gaussian.
• The method allows for the incorporation of systematic errors.

Conclusions:

• The R-factor refinement technique offers a flexible and robust approach to atomic coordinate extraction from HREM data.
• This method overcomes limitations of conventional estimation techniques, particularly concerning noise properties.
• The synthesis of point-cloud techniques provides a practical solution for HREM image analysis.