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A reflection on partial coherence in electron microscopy

J Fertig, H Rose

    Ultramicroscopy
    |April 1, 1977
    PubMed
    Summary
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    Partial coherence in dark-field electron microscopy is explored, revealing atom size impacts coherence. Analytical expressions for coherence degree are derived for scanning transmission electron microscopy (STEM) and conventional transmission electron microscopy (CTEM).

    Area of Science:

    • Physics
    • Materials Science
    • Microscopy

    Background:

    • Partial coherence, a concept from light optics, is extended to electron microscopy.
    • Understanding coherence is crucial for high-resolution imaging in electron microscopy.

    Purpose of the Study:

    • To investigate partial coherence in dark-field electron microscopy.
    • To analyze the influence of lens aberrations and finite atom size on coherence.
    • To derive analytical expressions for the degree of coherence in STEM and CTEM.

    Main Methods:

    • Theoretical investigation of secondary wave sources from two atoms.
    • Calculation of the real degree of coherence (gamma r) considering lens aberrations.
    • Analysis of coherence as a function of image coordinates at atomic resolution.

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  • Derivation of analytical expressions for gamma r applicable to current STEM and CTEM resolutions.

    • Main Results:

    • The finite size of atoms significantly affects the degree of coherence at atomic resolution.
    • The degree of coherence becomes dependent on the image coordinate.
    • Analytical expressions for gamma r were obtained for both STEM and CTEM.
    • Dark-field intensity distributions were calculated for two-atom objects in STEM.

    Conclusions:

    • The study provides a theoretical framework for partial coherence in dark-field electron microscopy.
    • The derived expressions are valuable for interpreting high-resolution images in STEM and CTEM.
    • Finite atom size is a critical factor influencing coherence and image formation at the atomic scale.