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Bayesian Tomography for Projections with an Arbitrary Transmission Function with an Application in Electron

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Summary

Tomography reconstructions improve when using a physical transmission function instead of Beer's Law, especially for limited-angle electron microscopy data. This method is essential for accurate imaging of thicker samples.

Keywords:
Bayesian tomographyBeer’s Lawmaximum likelihoodmultiple scatteringphotonic band gapphysical transmission functiontransmission electron microscopetransmission-thickness relation

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Area of Science:

  • * Physics
  • * Materials Science
  • * Computational Imaging

Background:

  • * Tomography typically assumes probe transmission follows Beer's Law (exponential attenuation).
  • * Beer's Law is inaccurate for thicker samples in transmission electron microscopy (TEM).
  • * Previous simulations showed improved full-angle reconstructions with a physical transmission function.

Purpose of the Study:

  • * To generalize Bayesian tomography formalism for arbitrary transmission functions.
  • * To investigate the impact of a physical transmission function on limited-angle reconstructions.
  • * To establish the necessity of accurate transmission functions for limited-angle tomography.

Main Methods:

  • * Generalized the Bouman and Sauer Bayesian formalism to incorporate arbitrary transmission functions.
  • * Applied the generalized formalism to limited-angle (140°) tomographic reconstruction scenarios.
  • * Compared reconstructions using a physical transmission function versus Beer's Law.

Main Results:

  • * The generalized formalism reduces to the original when Beer's Law is used.
  • * Using a physical transmission function significantly improves tomographic reconstructions.
  • * Accurate transmission functions are crucial for limited-angle reconstructions.

Conclusions:

  • * The physical transmission function is a requirement for accurate limited-angle tomography.
  • * This generalized Bayesian approach enhances imaging capabilities for thicker TEM samples.
  • * The study highlights the limitations of Beer's Law in advanced imaging techniques.