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Towards a quantitative theory for transmission X-ray microscopy.

James G McNally1, Christoph Pratsch1, Stephan Werner1

  • 1Helmholtz-Zentrum Berlin für Materialien und Energie, Elektronenspeicherring BESSY II, Albert-Einstein-Straße 15, 12489 Berlin, Germany.

Beilstein Journal of Nanotechnology
|July 22, 2025
PubMed
Summary

This study introduces a new framework for evaluating Transmission X-ray Microscopes (TXMs) using Mie theory. The research reveals that TXMs currently underestimate sample absorption, indicating a need for improved quantitative accuracy in materials analysis.

Keywords:
3D imagingMie theorymathematical modelnanoparticletransmission X-ray microscope

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Area of Science:

  • Materials Science
  • Advanced Microscopy Techniques
  • Nanotechnology

Background:

  • Transmission X-ray Microscopes (TXMs) are increasingly vital for quantitative materials analysis, particularly spectral analysis.
  • Existing TXM models lack rigorous quantitative validation, hindering reliable experimental measurements.
  • Accurate TXM modeling is crucial for validating quantitative spectral analysis in materials science.

Purpose of the Study:

  • To develop and validate an experimental and theoretical framework for quantitative evaluation of Transmission X-ray Microscopes (TXMs).
  • To assess the influence of specimen optical properties (absorption and phase) on TXM imaging.
  • To identify and quantify discrepancies between TXM measurements and theoretical predictions.

Main Methods:

  • Developed a TXM model using Mie theory to compute electric fields from nanospheres.
  • Approximated TXM condenser illumination as plane waves and the zone plate as a thin lens.
  • Conducted 3D measurements of 60 nm gold nanospheres and compared them with model predictions, including variations in illumination angle.

Main Results:

  • The developed model showed good qualitative agreement with 3D TXM measurements of gold nanospheres when both absorption (β) and phase (δ) properties were included.
  • Incorporating a slight tilt in condenser illumination improved model-experiment agreement, suggesting minor microscope misalignment.
  • Quantitative analysis revealed that TXMs underestimate gold nanosphere absorption by 10-20% compared to Beer's Law predictions.

Conclusions:

  • Both absorption and phase properties of a specimen significantly influence TXM image formation.
  • The developed Mie theory-based model provides a framework for quantitatively evaluating TXMs.
  • A significant quantitative discrepancy exists, with TXMs underestimating absorption, necessitating further investigation into microscope performance.