Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging

Diffractive imaging, in which image-forming optics are replaced by an inverse computation using scattered intensity data, could, in principle, realize wavelength-scale resolution in a transmission electron microscope. However, to date all implementations of this approach have suffered from various experimental restrictions. Here we demonstrate a form of diffractive imaging that unshackles the image formation process from the constraints of electron optics, improving resolution over that of the lens used by a factor of five and showing for the first time that it is possible to recover the complex exit wave (in modulus and phase) at atomic resolution, over an unlimited field of view, using low-energy (30 keV) electrons. Our method, called electron ptychography, has no fundamental experimental boundaries: further development of this proof-of-principle could revolutionize sub-atomic scale transmission imaging.

[1]  O. Scherzer,et al.  Über einige Fehler von Elektronenlinsen , 1936 .

[2]  O. Scherzer Spharische und chromatische Korrektur von Elektronen-Linsen , 1947 .

[3]  D. Gabor A New Microscopic Principle , 1948, Nature.

[4]  W. Hoppe,et al.  Beugung in inhomogenen Primärstrahlenwellenfeld. II. Lichtoptische Analogieversuche zur Phasenmessung von Gitterinterferenzen , 1969 .

[5]  W. Hoppe,et al.  Beugung im inhomogenen Primärstrahlwellenfeld. III. Amplituden- und Phasenbestimmung bei unperiodischen Objekten , 1969 .

[6]  W. Hoppe Beugung im inhomogenen Primärstrahlwellenfeld. I. Prinzip einer Phasenmessung von Elektronenbeungungsinterferenzen , 1969 .

[7]  W. Hoppe,et al.  Dynamische Theorie der Kristallstrukturanalyse durch Elektronenbeugung im inhomogenen Primärstrahlwellenfeld , 1970 .

[8]  Walter Hoppe,et al.  Trace structure analysis, ptychography, phase tomography , 1982 .

[9]  Hans-Werner Fink,et al.  Low-energy electron and ion projection microscopy , 1989 .

[10]  Fink,et al.  Holography with low-energy electrons. , 1990, Physical review letters.

[11]  J. Rodenburg,et al.  Double resolution imaging with infinite depth of focus in single lens scanning microscopy , 1994 .

[12]  B. C. McCallum,et al.  Resolution beyond the 'information limit' in transmission electron microscopy , 1995, Nature.

[13]  J. Miao,et al.  Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens , 1999, Nature.

[14]  U Weierstall,et al.  Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation. , 2002, Ultramicroscopy.

[15]  Peter Hawkes,et al.  Advances in Imaging and Electron Physics , 2002 .

[16]  J. Rodenburg,et al.  Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm. , 2004, Physical review letters.

[17]  M. Malac,et al.  Radiation damage in the TEM and SEM. , 2004, Micron.

[18]  J. Rodenburg,et al.  A phase retrieval algorithm for shifting illumination , 2004 .

[19]  S. Marchesini,et al.  Invited article: a [corrected] unified evaluation of iterative projection algorithms for phase retrieval. , 2006, The Review of scientific instruments.

[20]  A. G. Cullis,et al.  Transmission microscopy without lenses for objects of unlimited size. , 2007, Ultramicroscopy.

[21]  A. G. Cullis,et al.  Hard-x-ray lensless imaging of extended objects. , 2007, Physical review letters.

[22]  S. Marchesini Publisher's Note: “Invited Article: A unified evaluation of iterative projection algorithms for phase retrieval” [Rev. Sci. Instrum. 78, 011301 (2007)] , 2007 .

[23]  Garth J. Williams,et al.  Coherent diffractive imaging and partial coherence , 2007 .

[24]  J. Rodenburg Ptychography and Related Diffractive Imaging Methods , 2008 .

[25]  Garth J. Williams,et al.  Keyhole coherent diffractive imaging , 2008 .

[26]  O. Bunk,et al.  High-Resolution Scanning X-ray Diffraction Microscopy , 2008, Science.

[27]  J. Fienup,et al.  Phase retrieval with transverse translation diversity: a nonlinear optimization approach. , 2008, Optics express.

[28]  J. Rodenburg,et al.  An improved ptychographical phase retrieval algorithm for diffractive imaging. , 2009, Ultramicroscopy.

[29]  Peter Hawkes Aberration correction past and present , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[30]  J. Rodenburg,et al.  Wave-front phase retrieval in transmission electron microscopy via ptychography , 2010 .

[31]  Tim Salditt,et al.  Hard x-ray nanobeam characterization by coherent diffraction microscopy , 2010 .

[32]  O. Bunk,et al.  Ptychographic X-ray computed tomography at the nanoscale , 2010, Nature.

[33]  K. Gohara,et al.  10-kV diffractive imaging using newly developed electron diffraction microscope. , 2010, Ultramicroscopy.

[34]  K. Nugent Coherent methods in the X-ray sciences , 2009, 0908.3064.

[35]  A. Gölzhäuser,et al.  Low energy electron point source microscopy: beyond imaging , 2010, Journal of physics. Condensed matter : an Institute of Physics journal.

[36]  Elvio Carlino,et al.  Electron diffractive imaging of oxygen atoms in nanocrystals at sub-ångström resolution. , 2010, Nature nanotechnology.

[37]  Keita Kobayashi,et al.  Low voltage electron diffractive imaging of atomic structure in single-wall carbon nanotubes , 2011 .

[38]  T Salditt,et al.  Ptychographic coherent x-ray diffractive imaging in the water window. , 2011, Optics express.

[39]  Aberration correction in the STEM , 2022, Electron Microscopy and Analysis 1997.