Electron ptychography of 2D materials to deep sub-ångström resolution (original) (raw)

• Meyer, J. C., Girit, C. O., Crommie, M. F. & Zettl, A. Imaging and dynamics of light atoms and molecules on graphene. Nature 454, 319–322 (2008).
  Article ADS PubMed CAS Google Scholar
• Krivanek, O. L. et al. Atom-by-atom structural and chemical analysis by annular dark-field electron microscopy. Nature 464, 571–574 (2010).
  Article ADS PubMed CAS Google Scholar
• Huang, P. Y. et al. Grains and grain boundaries in single-layer graphene atomic patchwork quilts. Nature 469, 389–392 (2011).
  Article ADS PubMed CAS Google Scholar
• Sparrow, C. M. On spectroscopic resolving power. Astrophys. J. 44, 76–86 (1916).
  Article ADS Google Scholar
• Black, G. & Linfoot, E. H. Spherical aberration and the information content of optical images. Proc. R. Soc. Lond. A 239, 522–540 (1957).
  Article ADS MATH CAS Google Scholar
• Haider, M. et al. Electron microscopy image enhanced. Nature 392, 768–769 (1998).
  Article ADS CAS Google Scholar
• Batson, P. E., Dellby, N. & Krivanek, O. L. Sub-ångström resolution using aberration corrected electron optics. Nature 418, 617–620 (2002).
  Article ADS PubMed CAS Google Scholar
• Erni, R., Rossell, M. D., Kisielowski, C. & Dahmen, U. Atomic-resolution imaging with a sub-50-pm electron probe. Phys. Rev. Lett. 102, 096101 (2009).
  Article ADS PubMed CAS Google Scholar
• Sawada, H. et al. STEM imaging of 47-pm-separated atomic columns by a spherical aberration-corrected electron microscope with a 300-kV cold field emission gun. J. Electron Microsc. 58, 357–361 (2009).
  Article CAS Google Scholar
• Kaiser, U. et al. Transmission electron microscopy at 20kV for imaging and spectroscopy. Ultramicroscopy 111, 1239–1246 (2011).
  Article PubMed CAS Google Scholar
• Meyer, J. C. et al. Accurate measurement of electron beam induced displacement cross sections for single-layer graphene. Phys. Rev. Lett. 108, 196102 (2012).
  Article ADS PubMed CAS Google Scholar
• Sawada, H., Sasaki, T., Hosokawa, F. & Suenaga, K. Atomic-resolution STEM imaging of graphene at low voltage of 30 kV with resolution enhancement by using large convergence angle. Phys. Rev. Lett. 114, 166102 (2015).
  Article ADS PubMed CAS Google Scholar
• Linck, M. et al. Chromatic aberration correction for atomic resolution TEM imaging from 20 to 80 kV. Phys. Rev. Lett. 117, 076101 (2016).
  Article ADS PubMed CAS Google Scholar
• Henderson, R. The potential and limitations of neutrons, electrons and X-rays for atomic resolution microscopy of unstained biological molecules. Q. Rev. Biophys. 28, 171–193 (1995).
  Article PubMed CAS Google Scholar
• Gabor, D. A new microscopic principle. Nature 161, 777–778 (1948).
  Article ADS PubMed CAS Google Scholar
• Hoppe, W. Beugung im inhomogenen Primärstrahlwellenfeld. I. Prinzip einer Phasenmessung von Elektronenbeungungsinterferenzen. Acta Crystallogr. A 25, 495–501 (1969).
  Article ADS Google Scholar
• Nellist, P. D., McCallum, B. C. & Rodenburg, J. M. Resolution beyond the ‘information limit’ in transmission electron microscopy. Nature 374, 630–632 (1995).
  Article ADS CAS Google Scholar
• Nellist, P. D. & Rodenburg, J. M. Electron ptychography. I. Experimental demonstration beyond the conventional resolution limits. Acta Crystallogr. A 54, 49–60 (1998).
  Article Google Scholar
• Thibault, P. et al. High-resolution scanning X-ray diffraction microscopy. Science 321, 379–382 (2008).
  Article ADS PubMed CAS Google Scholar
• Maiden, A. M. & Rodenburg, J. M. An improved ptychographical phase retrieval algorithm for diffractive imaging. Ultramicroscopy 109, 1256–1262 (2009).
  Article PubMed CAS Google Scholar
• Thibault, P. & Menzel, A. Reconstructing state mixtures from diffraction measurements. Nature 494, 68–71 (2013).
  Article ADS PubMed CAS Google Scholar
• Li, P., Edo, T. B. & Rodenburg, J. M. Ptychographic inversion via Wigner distribution deconvolution: noise suppression and probe design. Ultramicroscopy 147, 106–113 (2014).
  Article PubMed CAS Google Scholar
• Yang, H. et al. Simultaneous atomic-resolution electron ptychography and Z-contrast imaging of light and heavy elements in complex nanostructures. Nat. Commun. 7, 12532 (2016).
  Article ADS PubMed PubMed Central CAS Google Scholar
• Pelz, P. M., Qiu, W. X., Bücker, R., Kassier, G. & Miller, R. J. D. Low-dose cryo electron ptychography via non-convex Bayesian optimization. Sci. Rep. 7, 9883 (2017).
  Article ADS PubMed PubMed Central Google Scholar
• Maiden, A. M., Humphry, M. J. & Rodenburg, J. M. Ptychographic transmission microscopy in three dimensions using a multi-slice approach. J. Opt. Soc. Am. A 29, 1606–1614 (2012).
  Article ADS CAS Google Scholar
• Gao, S. et al. Electron ptychographic microscopy for three-dimensional imaging. Nat. Commun. 8, 163 (2017).
  Article ADS PubMed PubMed Central CAS Google Scholar
• Rodenburg, J. M., Hurst, A. C. & Cullis, A. G. Transmission microscopy without lenses for objects of unlimited size. Ultramicroscopy 107, 227–231 (2007).
  Article PubMed CAS Google Scholar
• Rodenburg, J. M. et al. Hard-X-ray lensless imaging of extended objects. Phys. Rev. Lett. 98, 034801 (2007).
  Article ADS PubMed CAS Google Scholar
• Hüe, F., Rodenburg, J. M., Maiden, A. M., Sweeney, F. & Midgley, P. A. Wave-front phase retrieval in transmission electron microscopy via ptychography. Phys. Rev. B 82, 121415 (2010).
  Article ADS CAS Google Scholar
• Hüe, F., Rodenburg, J. M., Maiden, A. M. & Midgley, P. A. Extended ptychography in the transmission electron microscope: possibilities and limitations. Ultramicroscopy 111, 1117–1123 (2011).
  Article PubMed CAS Google Scholar
• Putkunz, C. T. et al. Atom-scale ptychographic electron diffractive imaging of boron nitride cones. Phys. Rev. Lett. 108, 073901 (2012).
  Article ADS PubMed CAS Google Scholar
• D’Alfonso, A. J. et al. Deterministic electron ptychography at atomic resolution. Phys. Rev. B 89, 064101 (2014).
  Article ADS CAS Google Scholar
• Pennycook, T. J. et al. Efficient phase contrast imaging in STEM using a pixelated detector. Part 1: experimental demonstration at atomic resolution. Ultramicroscopy 151, 160–167 (2015).
  Article PubMed CAS Google Scholar
• Yang, H. et al. Electron ptychographic phase imaging of light elements in crystalline materials using Wigner distribution deconvolution. Ultramicroscopy 180, 173–179 (2017).
  Article PubMed CAS Google Scholar
• Wang, P., Zhang, F., Gao, S., Zhang, M. & Kirkland, A. I. Electron ptychographic diffractive imaging of boron atoms in LaB6 crystals. Sci. Rep. 7, 2857 (2017).
  Article ADS PubMed PubMed Central CAS Google Scholar
• Humphry, M. J., Kraus, B., Hurst, A. C., Maiden, A. M. & Rodenburg, J. M. Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging. Nat. Commun. 3, 730 (2012).
  Article ADS PubMed PubMed Central CAS Google Scholar
• Frojdh, E. et al. Count rate linearity and spectral response of the Medipix3RX chip coupled to a 300μm silicon sensor under high flux conditions. J. Instrum. 9, C04028 (2014).
  Article Google Scholar
• Rose, A. Vision Human and Electronic Ch. 1 (Plenum Press, New York, 1949).
  Google Scholar
• Tate, M. W. et al. High dynamic range pixel array detector for scanning transmission electron microscopy. Microsc. Microanal. 22, 237–249 (2016).
  Article ADS PubMed CAS Google Scholar
• Close, R., Chen, Z., Shibata, N. & Findlay, S. D. Towards quantitative, atomic-resolution reconstruction of the electrostatic potential via differential phase contrast using electrons. Ultramicroscopy 159, 124–137 (2015).
  Article PubMed CAS Google Scholar
• Lazić, I., Bosch, E. G. T. & Lazar, S. Phase contrast STEM for thin samples: integrated differential phase contrast. Ultramicroscopy 160, 265–280 (2016).
  Article PubMed CAS Google Scholar
• Maiden, A. M., Humphry, M. J., Zhang, F. & Rodenburg, J. M. Superresolution imaging via ptychography. J. Opt. Soc. Am. A 28, 604–612 (2011).
  Article ADS Google Scholar
• Rodenburg, J. M. & Bates, R. H. T. The theory of super-resolution electron microscopy via Wigner-distribution deconvolution. Philos. Trans. R. Soc. Lond. A 339, 521–553 (1992).
  Article ADS Google Scholar
• Lee, J. & Barbastathis, G. Denoised Wigner distribution deconvolution via low-rank matrix completion. Opt. Express 24, 20069–20079 (2016).
  Article ADS PubMed Google Scholar
• Abbe, E. The relation of aperture and power in the microscope. J. R. Microsc. Soc. 2, 300–309 (1882).
  Article Google Scholar
• van der Zande, A. M. et al. Tailoring the electronic structure in bilayer molybdenum disulfide via interlayer twist. Nano Lett. 14, 3869–3875 (2014).
  Article ADS PubMed CAS Google Scholar
• Hovden, R. & Muller, D. A. Efficient elastic imaging of single atoms on ultrathin supports in a scanning transmission electron microscope. Ultramicroscopy 123, 59–65 (2012).
  Article PubMed CAS Google Scholar
• Zuo, C., Sun, J. & Chen, Q. Adaptive step-size strategy for noise-robust Fourier ptychographic microscopy. Opt. Express 24, 20724–20744 (2016).
  Article ADS PubMed Google Scholar
• Maiden, A., Johnson, D. & Li, P. Further improvements to the ptychographical iterative engine. Optica 4, 736–745 (2017).
  Article Google Scholar
• Suzuki, A. et al. High-resolution multislice X-ray ptychography of extended thick objects. Phys. Rev. Lett. 112, 053903 (2014).
  Article ADS PubMed CAS Google Scholar
• Hovden, R., Jiang, Y., Xin, H. L. & Kourkoutis, L. F. Periodic artifact reduction in Fourier transforms of full field atomic resolution images. Microsc. Microanal. 21, 436–441 (2015).
  Article ADS PubMed CAS Google Scholar
• Allen, L. J., D’Alfonso, A. J. & Findlay, S. D. Modelling the inelastic scattering of fast electrons. Ultramicroscopy 151, 11–22 (2015).
  Article PubMed CAS Google Scholar
• Waasmaier, D. & Kirfel, A. New analytical scattering-factor functions for free atoms and ions. Acta Crystallogr. A 51, 416–431 (1995).
  Article Google Scholar
• Nellist, P. D. & Rodenburg, J. M. Beyond the conventional information limit: the relevant coherence function. Ultramicroscopy 54, 61–74 (1994).
  Article Google Scholar