Maximum likelihood estimation of structure parameters from high resolution electron microscopy images. Part I: a...

Area of Science:

• Electron Microscopy
• Materials Science
• Statistical Analysis

Background:

• Electron microscopy offers high-precision structure determination beyond its resolution limits.
• Quantitative, model-based methods are crucial for achieving this precision.
• Maximum Likelihood (ML) estimation is statistically optimal for parameter estimation.

Purpose of the Study:

• To equip microscopists with tools for precise structure parameter estimation using ML.
• To review the theoretical framework of ML estimation in electron microscopy.
• To detail model assessment, estimator derivation, precision limits, and confidence intervals.

Main Methods:

• Review of the theoretical framework for Maximum Likelihood (ML) estimation.
• Derivation of the ML estimator for structure parameters.
• Analysis of precision limits and construction of confidence regions/intervals.

Main Results:

• Provides a comprehensive theoretical foundation for ML estimation in electron microscopy.
• Outlines methods for assessing models and deriving ML estimators.
• Defines the limits of precision and methods for confidence interval construction.

Conclusions:

• Maximum Likelihood estimation is the most appropriate method for precise structure determination in electron microscopy.
• This paper serves as a foundational guide for applying ML methods.
• A companion paper will demonstrate a practical application of these methods.