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“Indirect” High-Resolution Transmission Electron Microscopy: Aberration Measurement and Wavefunction Reconstruction

Published online by Cambridge University Press:  01 August 2004

Angus I. Kirkland  and
Rüdiger R. Meyer
Angus I. Kirkland
Affiliation:
University of Oxford, Department of Materials, Parks Road, Oxford OX1 3PH, UK
Rüdiger R. Meyer
Affiliation:
University of Oxford, Department of Materials, Parks Road, Oxford OX1 3PH, UK
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Abstract

Improvements in instrumentation and image processing techniques mean that methods involving reconstruction of focal or beam-tilt series of images are now realizing the promise they have long offered. This indirect approach recovers both the phase and the modulus of the specimen exit plane wave function and can extend the interpretable resolution. However, such reconstructions require the a posteriori determination of the objective lens aberrations, including the actual beam tilt, defocus, and twofold and threefold astigmatism. In this review, we outline the theory behind exit plane wavefunction reconstruction and describe methods for the accurate and automated determination of the required coefficients of the wave aberration function. Finally, recent applications of indirect reconstruction in the structural analysis of complex oxides are presented.

Keywords

high resolution electron microscopyimage reconstructionaberration measurement
Type
Review Paper
Information
Microscopy and Microanalysis , Volume 10 , Issue 4 , August 2004 , pp. 401 - 413
Copyright
© 2004 Microscopy Society of America

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References

REFERENCES

Abbe, E. (1873). Beiträge zur Theorie des Mikroskops und der Mikroskopischen Wahrnehmung. Schultze Archiv f mikrosk Anatomie 9, 413–468.Google Scholar
Bednorz, G. & Muller, Z. (1986). Possible high Tc superconductivity in the Ba-La-Cu-O system. Z Physik B64, 189–193.Google Scholar
Boothroyd, C. (1998). Why don't high resolution simulations and images match? J Microsc 190, 99–108.Google Scholar
Boothroyd, C. (2000). Quantification of high resolution electron microscope images of carbon. Ultramicroscopy 83, 159–168.Google Scholar
Chand, G., Saxton, W., & Kirkland, A. (1995). Aberration measurement and automated alignment of the TEM. In Institute of Physics Conference Series, EMAG 95, Cherns, D. (Ed.), vol. 147, pp. 297–300. London: Institute of Physics.
Coene, W., Janssen, G., Op de Beeck, M., & van Dyck, D. (1992). Phase retrieval through focus variation for ultra-resolution in field-emission transmission electron microscopy. Phys Rev Letts 69, 3743–3746.Google Scholar
Coene, W.M.J., Thust, A., Op de Beeck, M., & van Dyck, D. (1996). Maximum-likelihood method for focus-variation image reconstruction in high resolution transmission electron microscopy. Ultramicroscopy 64, 109–135.Google Scholar
Connolly, E., Sloan, J., & Tilley, R.J.D. (1996). Perovskite related phases in the Nd4Ti4O14-NdTiO3 system. Eur J Solid State Inorg Chem 33, 371–383.Google Scholar
Cowley, J.M. & Moodie, A.F. (1957). The scattering of electrons by atoms and crystals. I. A new theoretical approach. Acta Cryst 10, 609–619.Google Scholar
de Ruijter, W.J. (1995). Imaging properties and application of slow-scan charge-coupled-device cameras suitable for electron microscopy. Micron 26, 247–275.Google Scholar
Goodman, P. & Moodie, A.F. (1974). Numerical evaluation of n-beam wave functions in electron scattering by the multislice method. Acta Cryst A 30, 280–290.Google Scholar
Haider, M., Rose, H., Uhlemann, S., Schwan, E., Kabius, B., & Urban, K. (1998). A spherical-aberration-corrected 200 kV transmission electron microscope. Ultramicroscopy 75, 53–60.Google Scholar
Honda, T., Tomita, T., Kaneyama, T., & Ishida, Y. (1994). Field-emission ultrahigh-resolution analytical electron microscope. Ultramicroscopy 54, 132–144.Google Scholar
Hosokawa, F., Tomita, T., Naruse, M., Honda, T., Hartel, P., & Haider, M. (2003). A spherical aberration-corrected 200 kV TEM. J Electron Microsc 52, 3–10.Google Scholar
Hutchison, J.L., Doole, R.C., Dunin-Borkowski, R.E., Sloan, J., & Green, M.H. (1999). The development and assessment of a high performance field-emission-gun analytical HREM for materials science applications. JEOL News 34E, 10–15.Google Scholar
Jia, C., Lentzen, M., & Urban, K. (2003). Atomic-resolution imaging of oxygen in perovskite ceramics. Science 299, 870–873.Google Scholar
Jia, C. & Thust, A. (1999). Investigation of atomic displacements at a S3111 twin boundary in BaTiO3 by means of phase retrieval electron microscopy. Phys Rev Lett 82, 5052–5055.Google Scholar
Jin, S., Tiefel, T.H., McCormack, M., Fastnacht, R.A., Ramesh, R., & Chen, L.H. (1994). Thousandfold change in resistivity in magnetoresistive La-Ca-Mn-O films. Science 264, 413–415.Google Scholar
Kirkland, A., Meyer, R., Dunin-Borkowski, R., Hutchison, J., & Saxton, W. (1999). Comprehensive characterisation of a FEGTEM. In Institute of Physics Conference Series, EMAG 99, Kiely, C., (Ed.), vol. 161, pp. 259–262. London: Institute of Physics.
Kirkland, A.I. & Saxton, W.O. (2002). Cation segregation in Nb16Wi8O94 using high angle annular dark field STEM imaging and image processing. J Microsc 206, 1–6.Google Scholar
Kirkland, A.I., Saxton, W.O., & Chand, G. (1997). Multiple beam tilt microscopy for super resolved imaging. J Electron Microsc 1, 11–22.Google Scholar
Kirkland, A.I., Saxton, W.O., Chau, K.L., Tsuno, K., & Kawasaki, M. (1995). Super-resolution by aperture synthesis: Tilt series reconstruction in CTEM. Ultramicroscopy 57, 355–374.Google Scholar
Kirkland, E. (1984). Improved high resolution image processing of bright field electron micrographs I. Theory. Ultramicroscopy 15, 151–172.Google Scholar
Kirkland, E. (1988). High resolution processing of electron micrographs. In Image and Signal Processing in Electron Microscopy, Proceedings of the 6th Pfefferkorn Conference, Niagara, Hawkes, P.W., Ottensmeyer, F.P., Saxton, W.O. & Rosenfeld, A. (Eds.), pp. 139–147. Chicago: Scanning Microscopy International.
Kirkland, E., Siegel, B., Uyeda, N., & Fujiyoshi, Y. (1985). Improved high resolution image processing of bright field electron micrographs II. Experiment. Ultramicroscopy 17, 87–104.Google Scholar
Kisielowski, C., Hetherington, C., Wang, Y., Kilaas, R., O'Keefe, M., & Thust, A. (2001). Imaging columns of light elements carbon, nitrogen and oxygen with sub-angstrom resolution. Ultramicroscopy 89, 243–263.Google Scholar
Koster, A.J. (1989). Practical autotuning of a transmission electron microscope. Ultramicroscopy 31, 473–474.Google Scholar
Koster, A.J. & de Ruijter, W.J. (1992). Practical autoalignment of transmission electron microscopes. Ultramicroscopy 40, 89–107.Google Scholar
Koster, A.J., de Ruijter, W.J., van den Bos, A., & van der Mast, K.D. (1989). Autotuning of a TEM using minimum electron dose. Ultramicroscopy 27, 251–272.Google Scholar
Koster, A.J., van den Bos, A., & van der Mast, K.D. (1987). An autofocus method for a TEM. Ultramicroscopy 21, 209–222.Google Scholar
Krivanek, O.L. (1976). A method for determining the coefficient of spherical aberration from a single micrograph. Optik 45, 97–101.Google Scholar
Krivanek, O.L., Gubbens, A.J., Dellby, N., & Meyer, C.E. (1992). Design and first applications of a post-column imaging filter. Microsc Microanal Microstruct 3, 187–199.Google Scholar
Krivanek, O.L. & Leber, M.L. (1994). Autotuning for 1 Å resolution. In Proceedings of the 13th ICEM, vol. 1 of Electron Microscopy 1994, Jouffrey, B. & Coliex, C. (Eds.), pp. 157–158. Paris: les Editions de Physique.
Kuglin, C.D. & Hines, D.C. (1975). The phase correlation image alignment method. In Proceedings of the IEEE International Conference on Cybernetics and Society, pp. 163–165. New York: IEEE.
Lehmann, M., Geiger, D., Büscher, I., Zandbergen, H.W., van Dyck, D., & Lichte, H. (2002). Quantitative analysis of focal series of off axis holograms. In Proceedings of the 15th ICEM, vol. 3 of Electron Microscopy 2002, Engelbrecht, J., Sewell, T., Witcomb, M., Cross, R. & Richards, P. (Eds.), pp. 279–280. Durban, South Africa: Microscopy Society of Southern Africa.
Lehmann, M. & Lichte, H. (2002). Tutorial on off axis electron holography. Microsc Microanal 8, 447–466.Google Scholar
Lehmann, M., Lichte, H., Geiger, D., Lang, G., & Schweda, E. (1999). Electron holography at atomic dimensions—Present state. Mater Charact 42, 249–263.Google Scholar
Lentzen, M., Jahnen, B., Jia, C.L., Thust, A., Tillmann, K., & Urban, K. (2002). High-resolution imaging with an aberration-corrected transmission electron microscope. Ultramicroscopy 92, 233–242.Google Scholar
Levin, I., Bendersky, L., Vanderah, T., Roth, R., & Stafsudd, O. (1998). A series of incommensurately modulated AnBnO3n+2 phases in the SrTiO3-Sr2Nb2O7 quasibinary system. Mater Res Bull 33, 501–517.Google Scholar
Lichte, H. (1991). Electron image plane off-axis holography of atomic structures. In Advances in Optical and Electron Microscopy, vol. 12, pp. 25–91. London: Academic Press.
Lichtenberg, P., Herrnberger, A., Wiedenmann, K., & Mannhart, J. (2001). Synthesis of perovskite-related layered AnBnO3n+2 = ABOx type niobates and titanates and a study of their structural, electric and magnetic properties. Prog Solid State Chem 29, 1–70.Google Scholar
Meyer, R. (2002). Ph.D. thesis. Quantitative Automated Object-Wave Restoration in High Resolution Electron Microscopy. Dresden, Germany: Dresden Technical University.
Meyer, R., Kirkland, A., & Saxton, W. (2002). A new method for the determination of the wave aberration function for high resolution TEM. 1. Measurement of the symmetric abberations. Ultramicroscopy 92, 89–109.Google Scholar
Meyer, R., Kirkland, A., & Saxton, W. (2004). A new method for the determination of the wave aberration function for high resolution TEM. 2. Measurement of the antisymmetric abberations. Ultramicroscopy, in press.Google Scholar
Meyer, R., Sloan, J., Dunin-Borkowski, R., Kirkland, A., Novotny, M., Bailey, S., Hutchison, J., & Green, M. (2000a). Discrete atom imaging of one-dimensional crystals formed within single walled carbon nanotubes. Science 289, 1324–1326.Google Scholar
Meyer, R.R. & Kirkland, A.I. (1998). The effects of electron and photon scattering on signal and noise transfer properties of scintillators in CCD cameras used for electron detection. Ultramicroscopy 75, 23–33.Google Scholar
Meyer, R.R. & Kirkland, A.I. (2000). Characterisation of the signal and noise transfer of CCD cameras for electron detection. Microsc Res Tech 49, 269–280.Google Scholar
Meyer, R.R., Kirkland, A.I., Dunin-Borkowski, R.E., & Hutchison, J.L. (2000b). Experimental characterisation of CCD cameras for HREM at 300 kV. Ultramicroscopy 85, 9–13.Google Scholar
Nellist, P. & Pennycook, S. (1998). Subangstrom resolution by underfocused incoherent transmission electron microscopy. Phys Rev Lett 81, 4156–4159.Google Scholar
Nellist, P.D., McCallum, B.C., & Rodenburg, J.M. (1995). Resolution beyond the information limit in transmission electron microscopy. Nature 374, 630–632.Google Scholar
O'Keefe, M. (1992). Resolution in high-resolution electron microscopy. Ultramicroscopy 47, 282–297.Google Scholar
O'Keefe, M., Hetherington, C., Wang, Y., Nelson, E., Turner, J., Kisielowski, C., Malm, J.O., Mueller, R., Ringnalda, J., Pan, M., & Thust, A. (2001a). Sub-angstrom high-resolution transmission electron microscopy at 300 keV. Ultramicroscopy 89, 215–241.Google Scholar
O'Keefe, M., Nelson, E., Wang, Y., & Thust, A. (2001b). Sub-angstrom resolution of atomistic structures below 0.8Å. Phil Mag B 81, 1861–1878.Google Scholar
Op de Beeck, M., van Dyck, D., & Coene, W. (1996). Wave function reconstruction in HRTEM: The parabola method. Ultramicroscopy 64, 167–183.Google Scholar
Orchowski, A., Rau, W.D., & Lichte, H. (1995). Electron holography surmounts the resolution limit of electron microscopy. Phys Rev Lett 74, 399–402.Google Scholar
Otten, M.T. & Coene, W.M.J. (1993). High-resolution imaging on a field-emission TEM. Ultramicroscopy 48, 77–91.Google Scholar
Pan, M. (1998). TEM autotuning with slow-scan CCD cameras. In Proceedings of the 14th ICEM, vol. 1 of Electron Microscopy 1998, Benavidez, H.A.C. & Yacaman, M.J. (Eds.), pp. 263–264. Cancun: Institute of Physics.
Pennycook, S. & Jesson, D. (1995). Incoherent imaging of crystals using thermally scattered electrons. Proc Roy Soc A 449, 273–293.Google Scholar
Rodenburg, J.M. & Bates, R.H.T. (1992). The theory of superresolution electron-microscopy via Wigner-distribution deconvolution. Phil Trans R Soc Lond A 339, 521–553.Google Scholar
Rose, H. (1981). Correction of aperture aberrations in magnetic systems with threefold symmetry. Nucl Instrum Methods 187, 187–194.Google Scholar
Rose, H. (1990). Outline of a spherically corrected semiplanatic medium voltage transmission electron microscope. Optik 85, 19–24.Google Scholar
Saxton, W. (1994a). Accurate alignment of sets of images. J Microsc 174, 61–68.Google Scholar
Saxton, W. (1994b). What is the focus variation method, is it new, is it direct? Ultramicroscopy 55, 171–181.Google Scholar
Saxton, W.O. (1988). Accurate atom positions from focal and tilted beam series of high resolution electron micrographs. In Image and Signal Processing in Electron Microscopy, Proceedings of the 6th Pfefferkorn Conference, Niagara, Hawkes, P.W., Ottens-meyer, P.P., Saxton, W.O. & Rosenfeld, A. (Eds.), pp. 213–224. Chicago: Scanning Microscopy International.
Saxton, W.O. (1995). Observation of lens aberrations for very high-resolution electron microscopy. I. Theory. J Microsc 179, 201–214.Google Scholar
Saxton, W.O. (2000). A new way of measuring microscope aberrations. Ultramicroscopy 81, 41–45.Google Scholar
Scherzer, O. (1949). The theoretical resolution limit of the electron microscope. J Appl Phys 20, 20–29.Google Scholar
Schiske, P. (1973). Image processing using additional statistical information about the object. In Image Processing and Computer-Aided Design in Electron Optics, Hawkes, P. (Ed.), pp. 82–90. London: Academic Press.
Sleight, A.W. (1966). The crystal structure of Nb16W18O94, a member of a (MeO)xMeO3 family of compounds. Acta Chem Scand 20, 1102–1112.Google Scholar
Sloan, J. & Tilley, R. (1994). Layered perovskite phases in the Nd2Ti2O7-SrTiO3 system. Eur J Solid State Inorg Chem 31, 673–682.Google Scholar
Smith, D.J. (1997). The realization of atomic resolution with the electron microscope. Rep Prog Phys 60, 1513–1580.Google Scholar
Tanada, M., Tsuda, K., Terauchi, M., Tsuno, K., Kaneyama, T., Honda, T., & Ishida, M. (1999). A new 200 kV omega-filter electron microscope. J Microsc 194, 219–227.Google Scholar
Thomas, N.W. (1996). The compositional dependence of octahedral tilting in orthorhombic and tetragonal perovskites. Acta Crystall B 52, 16–31.Google Scholar
Thust, A., Coene, W., Op de Beeck, M., & van Dyck, D. (1996a). Focal-series reconstruction in HRTEM: Simulation studies on non-periodic objects. Ultramicroscopy 64, 211–230.Google Scholar
Thust, A., Jia, C., & Urban, K. (2002). Extraction of imaging parameters from the object wave function in phase-retrieval electron microscopy. In Proceedings of the 15th ICEM, vol. 3 of Electron Microscopy 2002, Engelbrecht, J., Sewell, T., Witcomb, M., Cross, R. & Richards, P. (Eds.), pp. 167–168. Durban, South Africa: Microscopy Society of South Africa.
Thust, A., Overwijk, M., Coene, W., & Lentzen, M. (1996b). Numerical correction of lens aberrations in phase retrieval HRTEM. Ultramicroscopy 64, 249–264.Google Scholar
Tilley, R. (1980). Chemical Physics of Solids and Their Surfaces. London: Royal Society of Chemistry.
Tsuno, K., Kaneyama, T., Honda, T., & Ishida, Y. (1999). Design of omega mode imaging energy filters. Nucl Instrum Methods A 427, 187–196.Google Scholar
Typke, D. & Dierksen, K. (1995). Determination of image aberrations in high resolution electron microscopy using diffractogram and cross-correlation methods. Optik 99, 155–166.Google Scholar
Urban, K., Kabius, B., Haider, M., & Rose, H. (1999). A way to higher resolution: Spherical-aberration correction in a 200 kV transmission electron microscope. J Electron Microsc 48, 821–826.Google Scholar
van Dyck, D., Op de Beeck, M., & Coene, W. (1993). A new approach to object wave-function reconstruction in electron-microscopy. Optik 93, 103–107.Google Scholar
Williams, T., Schmalle, H., Reller, A., Lichtenberg, F., Widmer, D., & Bednorz, G. (1991). The crystal structures of La2Ti2O7 and La5Ti5O17: High-resolution electron microscopy. J Solid State Chem 93, 534–548.Google Scholar
Zandbergen, H.W. & van Dyck, D. (2000). Exit wave reconstructions using through focus series of HREM images. Microsc Res and Tech 49, 301–323.Google Scholar
Zemlin, F. (1979). A practical procedure for alignment of a high resolution electron microscope. Ultramicroscopy 4, 241–245.Google Scholar
Zemlin, F., Weiss, K., Schiske, P., Kunath, W., & Herrmann, K.H. (1978). Coma-free alignment of high resolution electron microscopes with the aid of optical diffractograms. Ultramicroscopy 3, 49–60.Google Scholar