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X-ray ptychography


X-ray ptychographic microscopy combines the advantages of raster scanning X-ray microscopy with the more recently developed techniques of coherent diffraction imaging. It is limited neither by the fabricational challenges associated with X-ray optics nor by the requirements of isolated specimen preparation, and offers in principle wavelength-limited resolution, as well as stable access and solution to the phase problem. In this Review, we discuss the basic principles of X-ray ptychography and summarize the main milestones in the evolution of X-ray ptychographic microscopy and tomography over the past ten years, since its first demonstration with X-rays. We also highlight the potential for applications in the life and materials sciences, and discuss the latest advanced concepts and probable future developments.

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Fig. 1: X-ray ptychography as a combination of conventional STXM and CDI.
Fig. 2: Schematic representation of the most basic ptychography algorithm, and exemplary results from an advanced object and probe retrieval approach.
Fig. 3: Advanced X-ray ptychography concepts.
Fig. 4: Application examples (3D renderings) of results obtained by ptychographic X-ray computed tomography.
Fig. 5: Application examples of advanced X-ray ptychography concepts.


  1. 1.

    Abbe, E. Beiträge zur theorie des mikroskops und der mikroskopischen wahrnehmung. Arch. Mikrosk. Anat. 9, 413–418 (1873).

    Article  Google Scholar 

  2. 2.

    Hell, S. W., Schmidt, R. & Egner, A. Diffraction-unlimited three-dimensional optical nanoscopy with opposing lenses. Nat. Photon. 3, 381–387 (2009).

    ADS  Article  Google Scholar 

  3. 3.

    Kirz, J. & Jacobsen, C. The history and future of X-ray microscopy. J. Phys. Conf. Ser. 186, 012001 (2009).

    Article  Google Scholar 

  4. 4.

    Sakdinawat, A. & Attwood, D. Nanoscale X-ray imaging. Nat. Photon. 4, 840–848 (2010).

    ADS  Article  Google Scholar 

  5. 5.

    Bruck, Y. M. & Sodin, L. G. On the ambiguity of the image reconstruction problem. Opt. Commun. 30, 304–308 (1979).

    ADS  Article  Google Scholar 

  6. 6.

    Fienup, J. R. Reconstruction of an object from the modulus of its Fourier transform. Opt. Lett. 3, 27–29 (1978).

    ADS  Article  Google Scholar 

  7. 7.

    Miao, J., Charalambous, P., Kirz, J. & Sayre, D. Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens. Nature 400, 342–344 (1999).

    ADS  Article  Google Scholar 

  8. 8.

    Abbey, B. et al. Keyhole coherent diffractive imaging. Nat. Phys. 4, 394–398 (2008).

    Article  Google Scholar 

  9. 9.

    Chapman, H. N. & Nugent, K. A. Coherent lensless X-ray imaging. Nat. Photon. 4, 833–839 (2010).

    ADS  Article  Google Scholar 

  10. 10.

    Faulkner, H. M. L. & Rodenburg, J. M. Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm. Phys. Rev. Lett. 93, 023903 (2004).

    ADS  Article  Google Scholar 

  11. 11.

    Rodenburg, J. M. & Faulkner, H. M. L. A phase retrieval algorithm for shifting illumination. Appl. Phys. Lett. 85, 4795–4797 (2004).

    ADS  Article  Google Scholar 

  12. 12.

    Thibault, P., Dierolf, M., Menzel, A., Bunk, O. & David, C. High-resolution scanning X-ray diffraction microscopy. Science 321, 379–382 (2008).

    ADS  Article  Google Scholar 

  13. 13.

    Thibault, P., Dierolf, M., Bunk, O., Menzel, A. & Pfeiffer, F. Probe retrieval in ptychographic coherent diffractive imaging. Ultramicroscopy 109, 338–343 (2008).

    Article  Google Scholar 

  14. 14.

    Guizar-Sicairos, M. & Fienup, J. R. Phase retrieval with transverse translation diversity: a nonlinear optimization approach. Opt. Express 16, 7264–7278 (2008).

    ADS  Article  Google Scholar 

  15. 15.

    Maiden, A. M. & Rodenburg, J. M. An improved ptychographical phase retrieval algorithm for diffractive imaging. Ultramicroscopy 109, 1256–1262 (2009).

    Article  Google Scholar 

  16. 16.

    Thibault, P. & Guizar-Sicairos, M. Maximum-likelihood refinement for coherent diffractive imaging. New J. Phys. 14, 063004 (2012).

    ADS  Article  Google Scholar 

  17. 17.

    Rodenburg, J. M. in Advances in Imaging and Electron Physics (ed. Hawkes, P.) Vol. 150, 87–184 (Elsevier, 2008).

  18. 18.

    Hoppe, W. Beugung im inhomogenen primärstrahlwellenfeld. I. Prinzip einer phasenmessung von elektronenbeungungsinterferenzen. Acta Crystallogr. A 25, 495–501 (1969).

    ADS  Article  Google Scholar 

  19. 19.

    Hegerl, R. & Hoppe, W. Dynamische theorie der kristallstrukturanalyse durch elektronenbeugung im inhomogenen primärstrahlwellenfeld. Berich. Bunsen. Phys. Chem. 74, 1148–1154 (1970).

    Article  Google Scholar 

  20. 20.

    Hoppe, W. Trace structure analysis, ptychography, phase tomography. Ultramicroscopy 10, 187–198 (1982).

    Article  Google Scholar 

  21. 21.

    Bates, R. H. T. & Rodenburg, J. M. Sub-ångström transmission microscopy: a Fourier transform algorithm for microdiffraction plane intensity information. Ultramicroscopy 31, 303–307 (1989).

    Article  Google Scholar 

  22. 22.

    McCallum, B. C. & Rodenburg, J. M. Two-dimensional demonstration of Wigner phase-retrieval microscopy in the STEM configuration. Ultramicroscopy 45, 371–380 (1992).

    Article  Google Scholar 

  23. 23.

    Rodenburg, J. M., McCallum, B. C. & Nellist, P. D. Experimental tests on double-resolution coherent imaging via STEM. Ultramicroscopy 48, 304–314 (1993).

    Article  Google Scholar 

  24. 24.

    Chapman, H. N. Phase-retrieval X-ray microscopy by Wigner-distribution deconvolution. Ultramicroscopy 66, 153–172 (1996).

    Article  Google Scholar 

  25. 25.

    Rodenburg, J. M., Hurst, A. C. & Cullis, A. G. Transmission microscopy without lenses for objects of unlimited size. Ultramicroscopy 107, 227–231 (2007).

    Article  Google Scholar 

  26. 26.

    Bunk, O. et al. Influence of the overlap parameter on the convergence of the ptychographical iterative engine. Ultramicroscopy 108, 481–487 (2008).

    Article  Google Scholar 

  27. 27.

    Dierolf, M. et al. Ptychography and lensless X-ray imaging. Europhys. News 39, 22–24 (January–February, 2008).

    Article  Google Scholar 

  28. 28.

    Rodenburg, J. M. et al. Hard-X-ray lensless imaging of extended objects. Phys. Rev. Lett. 98, 034801 (2007).

    ADS  Article  Google Scholar 

  29. 29.

    Dierolf, M. et al. Ptychographic X-ray computed tomography at the nanoscale. Nature 467, 436–439 (2010).

    ADS  Article  Google Scholar 

  30. 30.

    Guizar-Sicairos, M. et al. Phase tomography from X-ray coherent diffractive imaging projections. Opt. Express 19, 21345–21357 (2011).

    ADS  Article  Google Scholar 

  31. 31.

    Diaz, A. et al. Quantitative X-ray phase nanotomography. Phys. Rev. B 85, 020104 (2012).

    ADS  Article  Google Scholar 

  32. 32.

    Menzel, A., Diaz, A. & Guizar-Sicairos, M. Ptychographic imaging at the Swiss Light Source. Synchrotron Rad. News 26, 26–31 (2013).

    Article  Google Scholar 

  33. 33.

    Holler, M. et al. X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution. Sci. Rep. 4, 3857 (2014).

    Article  Google Scholar 

  34. 34.

    Enders, B. & Thibault, P. PtyPy: ptychography reconstruction for python. Zenodo. (2014).

    Google Scholar 

  35. 35.

    Marchesini, S. et al. SHARP: a distributed GPU-based ptychographic solver. J. Appl. Cryst. 49, 1245–1252 (2016).

    Google Scholar 

  36. 36.

    Nashed, Y. S. G. et al. Parallel ptychographic reconstruction. Opt. Express 22, 32082–32097 (2014).

    ADS  Article  Google Scholar 

  37. 37.

    Pelz, P. M. et al. On-the-fly scans for X-ray ptychography. Appl. Phys. Lett. 105, 251101 (2014).

    ADS  Article  Google Scholar 

  38. 38.

    Deng, J. et al. Continuous motion scan ptychography: characterization for increased speed in coherent X-ray imaging. Opt. Express 23, 5438–5451 (2015).

    ADS  Article  Google Scholar 

  39. 39.

    Dierolf, M. et al. Ptychographic coherent diffractive imaging of weakly scattering specimens. New J. Phys. 12, 035017 (2010).

    ADS  Article  Google Scholar 

  40. 40.

    Maiden, A. M., Humphry, M. J., Sarahan, M. C., Kraus, B. & Rodenburg, J. M. An annealing algorithm to correct positioning errors in ptychography. Ultramicroscopy 120, 64–72 (2012).

    Article  Google Scholar 

  41. 41.

    Beckers, M. et al. Drift correction in ptychographic diffractive imaging. Ultramicroscopy 126, 44–47 (2013).

    Article  Google Scholar 

  42. 42.

    Zhang, F. et al. Translation position determination in ptychographic coherent diffraction imaging. Opt. Express 21, 13592–13606 (2013).

    ADS  Article  Google Scholar 

  43. 43.

    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).

    ADS  Article  Google Scholar 

  44. 44.

    Suzuki, A. et al. High-resolution multislice X-ray ptychography of extended thick objects. Phys. Rev. Lett. 112, 053903 (2014).

    ADS  Article  Google Scholar 

  45. 45.

    Guizar-Sicairos, M. et al. Role of the illumination spatial-frequency spectrum for ptychography. Phys. Rev. B 86, 100103 (2012).

    ADS  Article  Google Scholar 

  46. 46.

    Giewekemeyer, K. et al. Quantitative biological imaging by ptychographic X-ray diffraction microscopy. Proc. Natl Acad. Sci. USA 107, 529–534 (2010).

    ADS  Article  Google Scholar 

  47. 47.

    Thibault, P. & Menzel, A. Reconstructing state mixtures from diffraction measurements. Nature 494, 68–71 (2013).

    ADS  Article  Google Scholar 

  48. 48.

    Enders, B. et al. Ptychography with broad-bandwidth radiation. Appl. Phys. Lett. 104, 171104 (2014).

    ADS  Article  Google Scholar 

  49. 49.

    Godard, P. et al. Three-dimensional high-resolution quantitative microscopy of extended crystals. Nat. Commun. 2, 568 (2011).

    Article  Google Scholar 

  50. 50.

    Godard, P., Allain, M. & Chamard, V. Imaging of highly inhomogeneous strain field in nanocrystals using X-ray Bragg ptychography: a numerical study. Phys. Rev. B 84, 144109 (2011).

    ADS  Article  Google Scholar 

  51. 51.

    Hruszkewycz, S. O. et al. Quantitative nanoscale imaging of lattice distortions in epitaxial semiconductor heterostructures using nanofocused X-ray Bragg projection ptychography. Nano Lett. 12, 5148–5154 (2012).

    ADS  Article  Google Scholar 

  52. 52.

    Takahashi, Y. et al. Bragg X-ray ptychography of a silicon crystal: visualization of the dislocation strain field and the production of a vortex beam. Phys. Rev. B 87, 121201 (2013).

    ADS  Article  Google Scholar 

  53. 53.

    Holt, M. V. et al. Strain imaging of nanoscale semiconductor heterostructures with X-ray Bragg projection ptychography. Phys. Rev. Lett. 112, 165502 (2014).

    ADS  Article  Google Scholar 

  54. 54.

    Chamard, V. et al. Strain in a silicon-on-insulator nanostructure revealed by 3D X-ray Bragg ptychography. Sci. Rep. 5, 9827 (2015).

    Article  Google Scholar 

  55. 55.

    Hruszkewycz, S. O. et al. High-resolution three-dimensional structural microscopy by single-angle Bragg ptychography. Nat. Mater. 16, 244–251 (2016).

    ADS  Article  Google Scholar 

  56. 56.

    Hruszkewycz, S. O. et al. Structural sensitivity of X-ray Bragg projection ptychography to domain patterns in epitaxial thin films. Phys. Rev. A 94, 043803 (2016).

    ADS  Article  Google Scholar 

  57. 57.

    Stockmar, M. et al. Near-field ptychography: phase retrieval for inline holography using a structured illumination. Sci. Rep. 3, 1927 (2013).

    Article  Google Scholar 

  58. 58.

    Stockmar, M. et al. X-ray near-field ptychography for optically thick specimens. Phys. Rev. Appl. 3, 014005 (2015).

    ADS  Article  Google Scholar 

  59. 59.

    Robisch, A. L. & Salditt, T. Phase retrieval for object and probe using a series of defocus near-field images. Opt. Express 21, 23345–23357 (2013).

    ADS  Article  Google Scholar 

  60. 60.

    Stockmar, M. et al. X-ray nanotomography using near-field ptychography. Opt. Express 23, 12720–12731 (2015).

    ADS  Article  Google Scholar 

  61. 61.

    Beckers, M. et al. Chemical contrast in soft X-ray ptychography. Phys. Rev. Lett. 107, 208101 (2011).

    ADS  Article  Google Scholar 

  62. 62.

    Maiden, A. M., Morrison, G. R., Kaulich, B., Gianoncelli, A. & Rodenburg, J. M. Soft X-ray spectromicroscopy using ptychography with randomly phased illumination. Nat. Commun. 4, 1669 (2013).

    ADS  Article  Google Scholar 

  63. 63.

    Shapiro, D. A. et al. Chemical composition mapping with nanometre resolution by soft X-ray microscopy. Nat. Photon. 8, 765–769 (2014).

    ADS  Article  Google Scholar 

  64. 64.

    Zhu, X. et al. Measuring spectroscopy and magnetism of extracted and intracellular magnetosomes using soft X-ray ptychography. Proc. Natl Acad. Sci. USA 113, E8219–E8227 (2016).

    Article  Google Scholar 

  65. 65.

    Deng, J. et al. Simultaneous cryo X-ray ptychographic and fluorescence microscopy of green algae. Proc. Natl Acad. Sci. USA 112, 2314–2319 (2015).

    ADS  Article  Google Scholar 

  66. 66.

    Kewish, C. M. et al. The potential for two-dimensional crystallography of membrane proteins at future X-ray free-electron laser sources. New J. Phys. 12, 035005 (2010).

    ADS  Article  Google Scholar 

  67. 67.

    Schropp, A. et al. Full spatial characterization of a nanofocused X-ray free-electron laser beam by ptychographic imaging. Sci. Rep. 3, 1633 (2013).

    Article  Google Scholar 

  68. 68.

    Seiboth, F. et al. Perfect X-ray focusing via fitting corrective glasses to aberrated optics. Nat. Commun. 8, 14623 (2017).

    ADS  Article  Google Scholar 

  69. 69.

    Trtik, P., Diaz, A., Guizar-Sicairos, M., Menzel, A. & Bunk, O. Density mapping of hardened cement paste using ptychographic X-ray computed tomography. Cem. Conr. Compos. 36, 71–77 (2013).

    Article  Google Scholar 

  70. 70.

    Esmaeili, M. et al. Ptychographic X-ray tomography of silk fiber hydration. Macromolecules 46, 434–439 (2013).

    ADS  Article  Google Scholar 

  71. 71.

    Esmaeili, M. et al. Monitoring moisture distribution in textile materials using grating interferometry and ptychographic X-ray imaging. Text. Res. J. 85, 80–90 (2014).

    Article  Google Scholar 

  72. 72.

    Høydalsvik, K. et al. In situ X-ray ptychography imaging of high-temperature CO2 acceptor particle agglomerates. Appl. Phys. Lett. 104, 241909 (2014).

    ADS  Article  Google Scholar 

  73. 73.

    Diaz, A., Guizar-Sicairos, M., Poeppel, A., Menzel, A. & Bunk, O. Characterization of carbon fibers using X-ray phase nanotomography. Carbon 67, 98–103 (2014).

    Article  Google Scholar 

  74. 74.

    Chen, B. et al. Three-dimensional structure analysis and percolation properties of a barrier marine coating. Sci. Rep. 3, 1177 (2013).

    Article  Google Scholar 

  75. 75.

    da Silva, J. C. et al. Assessment of the 3D pore structure and individual components of preshaped catalyst bodies by X-ray imaging. ChemCatChem 7, 413–416 (2015).

    Article  Google Scholar 

  76. 76.

    Holler, M. et al. High-resolution non-destructive three-dimensional imaging of integrated circuits. Nature 543, 402–406 (2017).

    ADS  Article  Google Scholar 

  77. 77.

    Piazza, V. et al. Revealing the structure of stereociliary actin by X-ray nanoimaging. ACS Nano 8, 12228–12237 (2014).

    Article  Google Scholar 

  78. 78.

    Kewish, C. M. et al. Ptychographic characterization of the wavefield in the focus of reflective hard X-ray optics. Ultramicroscopy 110, 325–329 (2010).

    Article  Google Scholar 

  79. 79.

    Schropp, A. et al. Hard X-ray nanobeam characterization by coherent diffraction microscopy. Appl. Phys. Lett. 96, 091102 (2010).

    ADS  Article  Google Scholar 

  80. 80.

    Schropp, A. et al. Hard X-ray scanning microscopy with coherent radiation: beyond the resolution of conventional X-ray microscopes. Appl. Phys. Lett. 100, 253112 (2012).

    ADS  Article  Google Scholar 

  81. 81.

    Vila-Comamala, J. et al. Characterization of high-resolution diffractive X-ray optics by ptychographic coherent diffractive imaging. Opt. Express 19, 21333–21344 (2011).

    ADS  Article  Google Scholar 

  82. 82.

    Vila-Comamala, J., Sakdinawat, A. & Guizar-Sicairos, M. Characterization of X-ray phase vortices by ptychographic coherent diffractive imaging. Opt. Lett. 39, 5281–5284 (2014).

    ADS  Article  Google Scholar 

  83. 83.

    Takahashi, Y. et al. Towards high-resolution ptychographic X-ray diffraction microscopy. Phys. Rev. B 83, 214109 (2011).

    Google Scholar 

  84. 84.

    Hönig, S. et al. Full optical characterization of coherent X-ray nanobeams by ptychographic imaging. Opt. Express 19, 16324–16329 (2011).

    ADS  Article  Google Scholar 

  85. 85.

    Zheng, G., Horstmeyer, R. & Yang, C. Wide-field, high-resolution Fourier ptychographic microscopy. Nat. Photon. 7, 739–745 (2013).

    ADS  Article  Google Scholar 

  86. 86.

    Sun, J., Chen, Q., Zhang, Y. & Zuo, C. Sampling criteria for Fourier ptychographic microscopy in object space and frequency space. Opt. Express 24, 15765–15781 (2016).

    ADS  Article  Google Scholar 

  87. 87.

    Bian, L. et al. Fourier ptychographic reconstruction using Wirtinger flow optimization. Opt. Express 23, 4856–4866 (2015).

    ADS  Article  Google Scholar 

  88. 88.

    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).

    ADS  Article  Google Scholar 

  89. 89.

    Cao, S., Kok, P., Li, P., Maiden, A. M. & Rodenburg, J. M. Modal decomposition of a propagating matter wave via electron ptychography. Phys. Rev. A 94, 063621 (2016).

    ADS  Article  Google Scholar 

  90. 90.

    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).

    ADS  Article  Google Scholar 

  91. 91.

    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).

    ADS  Article  Google Scholar 

  92. 92.

    Gao, S. et al. Electron ptychographic microscopy for three-dimensional imaging. Nat. Commun. 8, 163 (2017).

    ADS  Article  Google Scholar 

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We acknowledge financial support from the German Science Foundation (DFG) Gottfried Wilhelm Leibniz programme, and M. Dierolf for fruitful discussions and supplying material for Fig. 2a.

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Correspondence to Franz Pfeiffer.

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Pfeiffer, F. X-ray ptychography. Nature Photon 12, 9–17 (2018).

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