Atomic contrast transfer in annular darkfield images


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We examine some of the assumptions underlying the standard optical equation as used for modelling high‐resolution annular darkfield (Z‐contrast) images of thin specimens. The validity of the approximations (i) that scattering occurs as spherical waves (atoms are point potentials) and (ii) that the depth of focus is infinite is found to be resolution‐dependent. The correction to the optical equation for non‐spherical wave scattering is found to be important when the probe size is of the order of 0·1 nm or smaller, and does not vanish in the ideal case of a large annular detector with no hole. Depth of focus becomes an important consideration at 100 kV for probes smaller than about 0·2 nm when the specimen thickness exceeds 10 nm. Both corrections can significantly degrade the effective point‐to‐point resolution of high‐resolution Z‐contrast images relative to that predicted by the standard optical equation. 1995 Blackwell Science Ltd

Original languageEnglish (US)
Pages (from-to)2-11
Number of pages10
JournalJournal of Microscopy
Issue number1
StatePublished - Oct 1995
Externally publishedYes


  • Annular darkfield
  • hollow‐cone darkfield
  • optical equation

ASJC Scopus subject areas

  • Pathology and Forensic Medicine
  • Histology

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