Analytic derivation of optimal imaging conditions for incoherent imaging in aberration-corrected electron microscopes.

The optimal lens parameters for incoherent imaging using third and fifth-order aberration-corrected electron microscopes are derived analytically. We propose simple models for the point spread function (PSF) and transfer function that give analytic formulae for the lateral resolution and depth resolution. We also derive an analytic formula for the contrast transfer function (CTF) in three dimensions and show that depth sectioning has an information limit equivalent to tomography with a missing cone of 90 degrees minus the aperture angle.

[1]  P D Nellist,et al.  Direct Sub-Angstrom Imaging of a Crystal Lattice , 2004, Science.

[2]  D. Muller,et al.  The electronic structure at the atomic scale of ultrathin gate oxides , 1999, Nature.

[3]  P. Nellist,et al.  Towards sub-0.5 A electron beams. , 2003, Ultramicroscopy.

[4]  P. H. Citrin,et al.  Atomic-scale imaging of individual dopant atoms and clusters in highly n-type bulk Si , 2002, Nature.

[5]  O. Krivanek,et al.  An electron microscope for the aberration-corrected era. , 2008, Ultramicroscopy.

[6]  O. L. Krivanek,et al.  Sub-ångstrom resolution using aberration corrected electron optics , 2002, Nature.

[7]  L. Allen,et al.  Three-dimensional ADF imaging of individual atoms by through-focal series scanning transmission electron microscopy. , 2006, Ultramicroscopy.

[8]  Andrew G. Glen,et al.  APPL , 2001 .

[9]  Zach,et al.  Upper limits for the residual aberrations of a high-resolution aberration-corrected STEM , 2000, Ultramicroscopy.

[10]  P. Voyles,et al.  Prospects for 3D, nanometer-resolution imaging by confocal STEM. , 2006, Ultramicroscopy.

[11]  Earl J. Kirkland,et al.  Advanced Computing in Electron Microscopy , 1998 .

[12]  P. Midgley,et al.  3D electron microscopy in the physical sciences: the development of Z-contrast and EFTEM tomography. , 2003, Ultramicroscopy.

[13]  O. Scherzer.  The Theoretical Resolution Limit of the Electron Microscope , 1949 .

[14]  E. H. Linfoot,et al.  Spherical aberration and the information content of optical images , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[15]  Russell F. Loane,et al.  Thermal vibrations in convergent‐beam electron diffraction , 1991 .

[16]  Peter Hartel,et al.  Advancing the Hexapole Cs-Corrector for the Scanning Transmission Electron Microscope , 2006, Microscopy and Microanalysis.

[17]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[18]  D. Muller,et al.  Depth Sectioning of Individual Dopant Atoms with Aberration-Corrected Scanning Transmission Electron Microscopy , 2007, Microscopy and Microanalysis.

[19]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[20]  Russell F. Loane,et al.  Incoherent imaging of zone axis crystals with ADF STEM , 1992 .

[21]  P. Batson,et al.  Simultaneous STEM imaging and electron energy-loss spectroscopy with atomic-column sensitivity , 1993, Nature.

[22]  L. Fitting Kourkoutis,et al.  Atomic-Scale Chemical Imaging of Composition and Bonding by Aberration-Corrected Microscopy , 2008, Science.