Abstract

Superresolution in lensless near-field ptychography is demonstrated via the application of a strongly curved illumination function. The reconstruction is performed using the Rayleigh–Sommerfeld diffraction integral, which is implemented via a pixel-size adjustable angular spectrum method. In this manner, the reconstructed object details, which are not only smaller than the pixel size of the sensor but even smaller than the smallest resolvable object detail defined by the effective NA of the 2D sensor, are enabled. The expected resolution, as predicted by the angles of scatter present in the optical configuration, is experimentally validated using a US air force resolution test target. The approach discussed here is not limited to ptychography; it can be extended to other coherent diffractive imaging modalities such as object scanning holography or optical diffraction tomography, so as to enable high-resolution near-field quantitative phase imaging.

© 2018 Optical Society of America

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References

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  1. P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
    [Crossref]
  2. O. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
    [Crossref]
  3. A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
    [Crossref]
  4. A. M. Maiden, M. J. Humphry, F. Zhang, and J. M. Rodenburg, “Super-resolution imaging via ptychography,” J. Opt. Soc. Am. A 28, 604–612 (2011).
    [Crossref]
  5. A. M. Maiden, M. J. Humphry, and J. M. Rodenburg, “Ptychographic transmission microscopy in three dimensions using a multi-slice approach,” J. Opt. Soc. Am. A 29, 1606–1614 (2012).
    [Crossref]
  6. M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express 16, 7264–7278 (2008).
    [Crossref]
  7. A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
    [Crossref]
  8. F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21, 13592–13606 (2013).
    [Crossref]
  9. M. J. Holler, A. Diaz, M. Guizar-Sicairos, P. Karven, E. Farm, E. Harkonen, M. Ritala, A. M. J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16  nm isotropic 3D resolution,” Sci. Rep. 4, 3857 (2014).
    [Crossref]
  10. M. J. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Muller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543, 402–406 (2017).
    [Crossref]
  11. Y. Jiang, Z. Chen, Y. Han, P. Deb, H. Gao, S. Xie, P. Purohit, M. W. Tate, J. Park, S. M. Gruner, V. Elser, and D. A. Muller, “Electron ptychography of 2D materials to deep sub-ångström resolution,” Nature 559, 343–349 (2018).
    [Crossref]
  12. D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, “Subwavelength coherent imaging of periodic samples using a 13.5  nm tabletop high-harmonic light source,” Nat. Photonics 11, 259–263 (2017).
    [Crossref]
  13. L. Valzania, T. Feurer, P. Zolliker, and E. Hack, “Terahertz ptychography,” Opt. Lett. 43, 543–546 (2018).
    [Crossref]
  14. J. Marrison, L. Räty, P. Marriott, and P. O’Toole, “Stain-free imaging of A549 cells using quantitative phase information,” in EMC Conference, Birmingham, UK (2011).
  15. D. Claus, A. M. Maiden, F. Zhang, F. G. R. Sweeney, M. J. Humphry, H. Schluesener, and J. M. Rodenburg, “Quantitative phase contrast optimised cancerous cell differentiation via ptychography,” Opt. Express 20, 9911–9918 (2012).
    [Crossref]
  16. A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. 35, 2585–2587 (2010).
    [Crossref]
  17. D. Claus, D. J. Robinson, D. G. Chetwynd, Y. Shuo, W. T. Pike, J. J. D. J. T. Garcia, and J. M. Rodenburg, “Dual wavelength optical metrology using ptychography,” J. Opt. 15, 035702 (2013).
    [Crossref]
  18. J. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imaging Electron Phys. 150, 87–184 (2008).
    [Crossref]
  19. M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3, 1927 (2013).
    [Crossref]
  20. J. W. Goodman, Introduction to Fourier Optics, 1st ed. (McGraw-Hill, 1968).
  21. E. Abbe, “Beitrag zur theorie des mikroskops und der mikroskopischen auflösung,” Arch. Mikrosk. Anat. 9, 413–418 (1873).
    [Crossref]
  22. D. Claus and J. M. Rodenburg, “Pixel size adjustment in coherent diffractive imaging within the Rayleigh-Sommerfeld regime,” Appl. Opt. 54, 1936–1944 (2015).
    [Crossref]
  23. W. Lukosz, “Optical systems with resolving powers exceeding the classical limit,” J. Opt. Soc. Am. 56, 1463–1472 (1966).
    [Crossref]
  24. W. Lukosz, “Optical systems with resolving powers exceeding the classical limit. II,” J. Opt. Soc. Am. 57, 932–941 (1967).
    [Crossref]
  25. G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, “Fresnel coherent diffractive imaging: treatment and analysis of data,” New J. Phys. 12, 035020 (2010).
    [Crossref]
  26. J. C. Wyant, Lecturenotes: Modern Optical Testing (2009).
  27. J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004).
    [Crossref]
  28. J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, “Transmission microscopy without lenses for objects of unlimited size,” Ultramicroscopy 107, 227–231 (2007).
    [Crossref]
  29. O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographic iterative engine,” Ultramicroscopy 108, 481–487 (2008).
    [Crossref]
  30. D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography.,” Ultramicroscopy 138, 13–21 (2014).
    [Crossref]
  31. J. R. Fienup, “Econstruction of object having a latent reference point,” J. Opt. Soc. Am. 73, 1421–1426 (1983).
    [Crossref]
  32. D. Claus and D. Iliescu, “Optical parameters and space-bandwidth product optimization in digital holographic microscopy,” Appl. Opt. 52, A410–A422 (2012).
    [Crossref]

2018 (2)

Y. Jiang, Z. Chen, Y. Han, P. Deb, H. Gao, S. Xie, P. Purohit, M. W. Tate, J. Park, S. M. Gruner, V. Elser, and D. A. Muller, “Electron ptychography of 2D materials to deep sub-ångström resolution,” Nature 559, 343–349 (2018).
[Crossref]

L. Valzania, T. Feurer, P. Zolliker, and E. Hack, “Terahertz ptychography,” Opt. Lett. 43, 543–546 (2018).
[Crossref]

2017 (2)

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, “Subwavelength coherent imaging of periodic samples using a 13.5  nm tabletop high-harmonic light source,” Nat. Photonics 11, 259–263 (2017).
[Crossref]

M. J. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Muller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543, 402–406 (2017).
[Crossref]

2015 (1)

2014 (2)

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography.,” Ultramicroscopy 138, 13–21 (2014).
[Crossref]

M. J. Holler, A. Diaz, M. Guizar-Sicairos, P. Karven, E. Farm, E. Harkonen, M. Ritala, A. M. J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16  nm isotropic 3D resolution,” Sci. Rep. 4, 3857 (2014).
[Crossref]

2013 (3)

D. Claus, D. J. Robinson, D. G. Chetwynd, Y. Shuo, W. T. Pike, J. J. D. J. T. Garcia, and J. M. Rodenburg, “Dual wavelength optical metrology using ptychography,” J. Opt. 15, 035702 (2013).
[Crossref]

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3, 1927 (2013).
[Crossref]

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21, 13592–13606 (2013).
[Crossref]

2012 (4)

2011 (1)

2010 (2)

A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. 35, 2585–2587 (2010).
[Crossref]

G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, “Fresnel coherent diffractive imaging: treatment and analysis of data,” New J. Phys. 12, 035020 (2010).
[Crossref]

2009 (2)

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
[Crossref]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref]

2008 (4)

O. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref]

J. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imaging Electron Phys. 150, 87–184 (2008).
[Crossref]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographic iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

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

2007 (1)

J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, “Transmission microscopy without lenses for objects of unlimited size,” Ultramicroscopy 107, 227–231 (2007).
[Crossref]

2004 (1)

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004).
[Crossref]

1983 (1)

1967 (1)

1966 (1)

1873 (1)

E. Abbe, “Beitrag zur theorie des mikroskops und der mikroskopischen auflösung,” Arch. Mikrosk. Anat. 9, 413–418 (1873).
[Crossref]

Abbe, E.

E. Abbe, “Beitrag zur theorie des mikroskops und der mikroskopischen auflösung,” Arch. Mikrosk. Anat. 9, 413–418 (1873).
[Crossref]

Adams, D. E.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, “Subwavelength coherent imaging of periodic samples using a 13.5  nm tabletop high-harmonic light source,” Nat. Photonics 11, 259–263 (2017).
[Crossref]

Aeppli, G.

M. J. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Muller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543, 402–406 (2017).
[Crossref]

Batey, D. J.

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography.,” Ultramicroscopy 138, 13–21 (2014).
[Crossref]

Bean, R.

Berenguer, F.

Bevis, C.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, “Subwavelength coherent imaging of periodic samples using a 13.5  nm tabletop high-harmonic light source,” Nat. Photonics 11, 259–263 (2017).
[Crossref]

Bunk, O.

M. J. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Muller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543, 402–406 (2017).
[Crossref]

M. J. Holler, A. Diaz, M. Guizar-Sicairos, P. Karven, E. Farm, E. Harkonen, M. Ritala, A. M. J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16  nm isotropic 3D resolution,” Sci. Rep. 4, 3857 (2014).
[Crossref]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref]

O. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographic iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

Chen, B.

Chen, Z.

Y. Jiang, Z. Chen, Y. Han, P. Deb, H. Gao, S. Xie, P. Purohit, M. W. Tate, J. Park, S. M. Gruner, V. Elser, and D. A. Muller, “Electron ptychography of 2D materials to deep sub-ångström resolution,” Nature 559, 343–349 (2018).
[Crossref]

Chetwynd, D. G.

D. Claus, D. J. Robinson, D. G. Chetwynd, Y. Shuo, W. T. Pike, J. J. D. J. T. Garcia, and J. M. Rodenburg, “Dual wavelength optical metrology using ptychography,” J. Opt. 15, 035702 (2013).
[Crossref]

Claus, D.

Cloetens, P.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3, 1927 (2013).
[Crossref]

Cullis, A. G.

J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, “Transmission microscopy without lenses for objects of unlimited size,” Ultramicroscopy 107, 227–231 (2007).
[Crossref]

David, C.

O. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref]

Deb, P.

Y. Jiang, Z. Chen, Y. Han, P. Deb, H. Gao, S. Xie, P. Purohit, M. W. Tate, J. Park, S. M. Gruner, V. Elser, and D. A. Muller, “Electron ptychography of 2D materials to deep sub-ångström resolution,” Nature 559, 343–349 (2018).
[Crossref]

Diaz, A.

M. J. Holler, A. Diaz, M. Guizar-Sicairos, P. Karven, E. Farm, E. Harkonen, M. Ritala, A. M. J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16  nm isotropic 3D resolution,” Sci. Rep. 4, 3857 (2014).
[Crossref]

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21, 13592–13606 (2013).
[Crossref]

Dierolf, M.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3, 1927 (2013).
[Crossref]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref]

O. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographic iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

Dinapoli, R.

M. J. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Muller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543, 402–406 (2017).
[Crossref]

Elser, V.

Y. Jiang, Z. Chen, Y. Han, P. Deb, H. Gao, S. Xie, P. Purohit, M. W. Tate, J. Park, S. M. Gruner, V. Elser, and D. A. Muller, “Electron ptychography of 2D materials to deep sub-ångström resolution,” Nature 559, 343–349 (2018).
[Crossref]

Enders, B.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3, 1927 (2013).
[Crossref]

Farm, E.

M. J. Holler, A. Diaz, M. Guizar-Sicairos, P. Karven, E. Farm, E. Harkonen, M. Ritala, A. M. J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16  nm isotropic 3D resolution,” Sci. Rep. 4, 3857 (2014).
[Crossref]

Faulkner, H. M. L.

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004).
[Crossref]

Feurer, T.

Fienup, J. R.

Galloway, B. R.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, “Subwavelength coherent imaging of periodic samples using a 13.5  nm tabletop high-harmonic light source,” Nat. Photonics 11, 259–263 (2017).
[Crossref]

Gao, H.

Y. Jiang, Z. Chen, Y. Han, P. Deb, H. Gao, S. Xie, P. Purohit, M. W. Tate, J. Park, S. M. Gruner, V. Elser, and D. A. Muller, “Electron ptychography of 2D materials to deep sub-ångström resolution,” Nature 559, 343–349 (2018).
[Crossref]

Garcia, J. J. D. J. T.

D. Claus, D. J. Robinson, D. G. Chetwynd, Y. Shuo, W. T. Pike, J. J. D. J. T. Garcia, and J. M. Rodenburg, “Dual wavelength optical metrology using ptychography,” J. Opt. 15, 035702 (2013).
[Crossref]

Gardner, D. F.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, “Subwavelength coherent imaging of periodic samples using a 13.5  nm tabletop high-harmonic light source,” Nat. Photonics 11, 259–263 (2017).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 1st ed. (McGraw-Hill, 1968).

Gruner, S. M.

Y. Jiang, Z. Chen, Y. Han, P. Deb, H. Gao, S. Xie, P. Purohit, M. W. Tate, J. Park, S. M. Gruner, V. Elser, and D. A. Muller, “Electron ptychography of 2D materials to deep sub-ångström resolution,” Nature 559, 343–349 (2018).
[Crossref]

Guizar-Sicairos, M.

M. J. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Muller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543, 402–406 (2017).
[Crossref]

M. J. Holler, A. Diaz, M. Guizar-Sicairos, P. Karven, E. Farm, E. Harkonen, M. Ritala, A. M. J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16  nm isotropic 3D resolution,” Sci. Rep. 4, 3857 (2014).
[Crossref]

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

Hack, E.

Han, Y.

Y. Jiang, Z. Chen, Y. Han, P. Deb, H. Gao, S. Xie, P. Purohit, M. W. Tate, J. Park, S. M. Gruner, V. Elser, and D. A. Muller, “Electron ptychography of 2D materials to deep sub-ångström resolution,” Nature 559, 343–349 (2018).
[Crossref]

Harkonen, E.

M. J. Holler, A. Diaz, M. Guizar-Sicairos, P. Karven, E. Farm, E. Harkonen, M. Ritala, A. M. J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16  nm isotropic 3D resolution,” Sci. Rep. 4, 3857 (2014).
[Crossref]

Holler, M. J.

M. J. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Muller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543, 402–406 (2017).
[Crossref]

M. J. Holler, A. Diaz, M. Guizar-Sicairos, P. Karven, E. Farm, E. Harkonen, M. Ritala, A. M. J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16  nm isotropic 3D resolution,” Sci. Rep. 4, 3857 (2014).
[Crossref]

Humphry, M. J.

Hurst, A. C.

J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, “Transmission microscopy without lenses for objects of unlimited size,” Ultramicroscopy 107, 227–231 (2007).
[Crossref]

Iliescu, D.

Jiang, Y.

Y. Jiang, Z. Chen, Y. Han, P. Deb, H. Gao, S. Xie, P. Purohit, M. W. Tate, J. Park, S. M. Gruner, V. Elser, and D. A. Muller, “Electron ptychography of 2D materials to deep sub-ångström resolution,” Nature 559, 343–349 (2018).
[Crossref]

Johnson, I.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographic iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

Kapteyn, H. C.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, “Subwavelength coherent imaging of periodic samples using a 13.5  nm tabletop high-harmonic light source,” Nat. Photonics 11, 259–263 (2017).
[Crossref]

Karl, R.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, “Subwavelength coherent imaging of periodic samples using a 13.5  nm tabletop high-harmonic light source,” Nat. Photonics 11, 259–263 (2017).
[Crossref]

Karven, P.

M. J. Holler, A. Diaz, M. Guizar-Sicairos, P. Karven, E. Farm, E. Harkonen, M. Ritala, A. M. J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16  nm isotropic 3D resolution,” Sci. Rep. 4, 3857 (2014).
[Crossref]

Kraus, B.

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

Kynde, S.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographic iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

Lukosz, W.

Maiden, A. M.

Mancini, G. F.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, “Subwavelength coherent imaging of periodic samples using a 13.5  nm tabletop high-harmonic light source,” Nat. Photonics 11, 259–263 (2017).
[Crossref]

Marriott, P.

J. Marrison, L. Räty, P. Marriott, and P. O’Toole, “Stain-free imaging of A549 cells using quantitative phase information,” in EMC Conference, Birmingham, UK (2011).

Marrison, J.

J. Marrison, L. Räty, P. Marriott, and P. O’Toole, “Stain-free imaging of A549 cells using quantitative phase information,” in EMC Conference, Birmingham, UK (2011).

Marti, O.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographic iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

Menzel, A.

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21, 13592–13606 (2013).
[Crossref]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref]

O. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref]

Muller, D. A.

Y. Jiang, Z. Chen, Y. Han, P. Deb, H. Gao, S. Xie, P. Purohit, M. W. Tate, J. Park, S. M. Gruner, V. Elser, and D. A. Muller, “Electron ptychography of 2D materials to deep sub-ångström resolution,” Nature 559, 343–349 (2018).
[Crossref]

Muller, E.

M. J. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Muller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543, 402–406 (2017).
[Crossref]

Murnane, M. M.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, “Subwavelength coherent imaging of periodic samples using a 13.5  nm tabletop high-harmonic light source,” Nat. Photonics 11, 259–263 (2017).
[Crossref]

Nugent, K. A.

G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, “Fresnel coherent diffractive imaging: treatment and analysis of data,” New J. Phys. 12, 035020 (2010).
[Crossref]

O’Toole, P.

J. Marrison, L. Räty, P. Marriott, and P. O’Toole, “Stain-free imaging of A549 cells using quantitative phase information,” in EMC Conference, Birmingham, UK (2011).

Park, J.

Y. Jiang, Z. Chen, Y. Han, P. Deb, H. Gao, S. Xie, P. Purohit, M. W. Tate, J. Park, S. M. Gruner, V. Elser, and D. A. Muller, “Electron ptychography of 2D materials to deep sub-ångström resolution,” Nature 559, 343–349 (2018).
[Crossref]

Peele, A. G.

G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, “Fresnel coherent diffractive imaging: treatment and analysis of data,” New J. Phys. 12, 035020 (2010).
[Crossref]

Peterson, I.

Pfeiffer, F.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3, 1927 (2013).
[Crossref]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref]

O. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographic iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

Pike, W. T.

D. Claus, D. J. Robinson, D. G. Chetwynd, Y. Shuo, W. T. Pike, J. J. D. J. T. Garcia, and J. M. Rodenburg, “Dual wavelength optical metrology using ptychography,” J. Opt. 15, 035702 (2013).
[Crossref]

Porter, C. L.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, “Subwavelength coherent imaging of periodic samples using a 13.5  nm tabletop high-harmonic light source,” Nat. Photonics 11, 259–263 (2017).
[Crossref]

Purohit, P.

Y. Jiang, Z. Chen, Y. Han, P. Deb, H. Gao, S. Xie, P. Purohit, M. W. Tate, J. Park, S. M. Gruner, V. Elser, and D. A. Muller, “Electron ptychography of 2D materials to deep sub-ångström resolution,” Nature 559, 343–349 (2018).
[Crossref]

Quiney, H. M.

G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, “Fresnel coherent diffractive imaging: treatment and analysis of data,” New J. Phys. 12, 035020 (2010).
[Crossref]

Raabe, A. M. J.

M. J. Holler, A. Diaz, M. Guizar-Sicairos, P. Karven, E. Farm, E. Harkonen, M. Ritala, A. M. J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16  nm isotropic 3D resolution,” Sci. Rep. 4, 3857 (2014).
[Crossref]

Raabe, J.

M. J. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Muller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543, 402–406 (2017).
[Crossref]

Räty, L.

J. Marrison, L. Räty, P. Marriott, and P. O’Toole, “Stain-free imaging of A549 cells using quantitative phase information,” in EMC Conference, Birmingham, UK (2011).

Ritala, M.

M. J. Holler, A. Diaz, M. Guizar-Sicairos, P. Karven, E. Farm, E. Harkonen, M. Ritala, A. M. J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16  nm isotropic 3D resolution,” Sci. Rep. 4, 3857 (2014).
[Crossref]

Robinson, D. J.

D. Claus, D. J. Robinson, D. G. Chetwynd, Y. Shuo, W. T. Pike, J. J. D. J. T. Garcia, and J. M. Rodenburg, “Dual wavelength optical metrology using ptychography,” J. Opt. 15, 035702 (2013).
[Crossref]

Robinson, I. K.

Rodenburg, J.

J. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imaging Electron Phys. 150, 87–184 (2008).
[Crossref]

Rodenburg, J. M.

D. Claus and J. M. Rodenburg, “Pixel size adjustment in coherent diffractive imaging within the Rayleigh-Sommerfeld regime,” Appl. Opt. 54, 1936–1944 (2015).
[Crossref]

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography.,” Ultramicroscopy 138, 13–21 (2014).
[Crossref]

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21, 13592–13606 (2013).
[Crossref]

D. Claus, D. J. Robinson, D. G. Chetwynd, Y. Shuo, W. T. Pike, J. J. D. J. T. Garcia, and J. M. Rodenburg, “Dual wavelength optical metrology using ptychography,” J. Opt. 15, 035702 (2013).
[Crossref]

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

D. Claus, A. M. Maiden, F. Zhang, F. G. R. Sweeney, M. J. Humphry, H. Schluesener, and J. M. Rodenburg, “Quantitative phase contrast optimised cancerous cell differentiation via ptychography,” Opt. Express 20, 9911–9918 (2012).
[Crossref]

A. M. Maiden, M. J. Humphry, and J. M. Rodenburg, “Ptychographic transmission microscopy in three dimensions using a multi-slice approach,” J. Opt. Soc. Am. A 29, 1606–1614 (2012).
[Crossref]

A. M. Maiden, M. J. Humphry, F. Zhang, and J. M. Rodenburg, “Super-resolution imaging via ptychography,” J. Opt. Soc. Am. A 28, 604–612 (2011).
[Crossref]

A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. 35, 2585–2587 (2010).
[Crossref]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
[Crossref]

J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, “Transmission microscopy without lenses for objects of unlimited size,” Ultramicroscopy 107, 227–231 (2007).
[Crossref]

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004).
[Crossref]

Sarahan, M. C.

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

Schluesener, H.

Shanblatt, E. R.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, “Subwavelength coherent imaging of periodic samples using a 13.5  nm tabletop high-harmonic light source,” Nat. Photonics 11, 259–263 (2017).
[Crossref]

Shuo, Y.

D. Claus, D. J. Robinson, D. G. Chetwynd, Y. Shuo, W. T. Pike, J. J. D. J. T. Garcia, and J. M. Rodenburg, “Dual wavelength optical metrology using ptychography,” J. Opt. 15, 035702 (2013).
[Crossref]

Stockmar, M.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3, 1927 (2013).
[Crossref]

Sweeney, F. G. R.

Tanksalvala, M.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, “Subwavelength coherent imaging of periodic samples using a 13.5  nm tabletop high-harmonic light source,” Nat. Photonics 11, 259–263 (2017).
[Crossref]

Tate, M. W.

Y. Jiang, Z. Chen, Y. Han, P. Deb, H. Gao, S. Xie, P. Purohit, M. W. Tate, J. Park, S. M. Gruner, V. Elser, and D. A. Muller, “Electron ptychography of 2D materials to deep sub-ångström resolution,” Nature 559, 343–349 (2018).
[Crossref]

Thibault, O.

O. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref]

Thibault, P.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3, 1927 (2013).
[Crossref]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref]

Tsai, E. H. R.

M. J. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Muller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543, 402–406 (2017).
[Crossref]

Valzania, L.

Vila-Comamala, J.

Williams, G. J.

G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, “Fresnel coherent diffractive imaging: treatment and analysis of data,” New J. Phys. 12, 035020 (2010).
[Crossref]

Wyant, J. C.

J. C. Wyant, Lecturenotes: Modern Optical Testing (2009).

Xie, S.

Y. Jiang, Z. Chen, Y. Han, P. Deb, H. Gao, S. Xie, P. Purohit, M. W. Tate, J. Park, S. M. Gruner, V. Elser, and D. A. Muller, “Electron ptychography of 2D materials to deep sub-ångström resolution,” Nature 559, 343–349 (2018).
[Crossref]

Zanette, I.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3, 1927 (2013).
[Crossref]

Zhang, F.

Zhang, X.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, “Subwavelength coherent imaging of periodic samples using a 13.5  nm tabletop high-harmonic light source,” Nat. Photonics 11, 259–263 (2017).
[Crossref]

Zolliker, P.

Adv. Imaging Electron Phys. (1)

J. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imaging Electron Phys. 150, 87–184 (2008).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004).
[Crossref]

Arch. Mikrosk. Anat. (1)

E. Abbe, “Beitrag zur theorie des mikroskops und der mikroskopischen auflösung,” Arch. Mikrosk. Anat. 9, 413–418 (1873).
[Crossref]

J. Opt. (1)

D. Claus, D. J. Robinson, D. G. Chetwynd, Y. Shuo, W. T. Pike, J. J. D. J. T. Garcia, and J. M. Rodenburg, “Dual wavelength optical metrology using ptychography,” J. Opt. 15, 035702 (2013).
[Crossref]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (2)

Nat. Photonics (1)

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, “Subwavelength coherent imaging of periodic samples using a 13.5  nm tabletop high-harmonic light source,” Nat. Photonics 11, 259–263 (2017).
[Crossref]

Nature (2)

M. J. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Muller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543, 402–406 (2017).
[Crossref]

Y. Jiang, Z. Chen, Y. Han, P. Deb, H. Gao, S. Xie, P. Purohit, M. W. Tate, J. Park, S. M. Gruner, V. Elser, and D. A. Muller, “Electron ptychography of 2D materials to deep sub-ångström resolution,” Nature 559, 343–349 (2018).
[Crossref]

New J. Phys. (1)

G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, “Fresnel coherent diffractive imaging: treatment and analysis of data,” New J. Phys. 12, 035020 (2010).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Sci. Rep. (2)

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3, 1927 (2013).
[Crossref]

M. J. Holler, A. Diaz, M. Guizar-Sicairos, P. Karven, E. Farm, E. Harkonen, M. Ritala, A. M. J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16  nm isotropic 3D resolution,” Sci. Rep. 4, 3857 (2014).
[Crossref]

Science (1)

O. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref]

Ultramicroscopy (6)

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
[Crossref]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref]

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

J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, “Transmission microscopy without lenses for objects of unlimited size,” Ultramicroscopy 107, 227–231 (2007).
[Crossref]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographic iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography.,” Ultramicroscopy 138, 13–21 (2014).
[Crossref]

Other (3)

J. W. Goodman, Introduction to Fourier Optics, 1st ed. (McGraw-Hill, 1968).

J. C. Wyant, Lecturenotes: Modern Optical Testing (2009).

J. Marrison, L. Räty, P. Marriott, and P. O’Toole, “Stain-free imaging of A549 cells using quantitative phase information,” in EMC Conference, Birmingham, UK (2011).

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Figures (6)

Fig. 1.
Fig. 1. (a) Center of illumination function and center of aperture coincide; (b) displacement δ x results in de-centered illumination function and the recording of higher diffraction angles; (c) smallest lateral shift δ x in order to sample the object’s high spatial frequencies arising from the illumination function of semi-angle α with the angular overlap Ø angle (half-angle Δ α and corresponding lateral shift δ x account for possible opposite direction of incident plane-wave component, which results in doubling the angular range to 2 α , as to record plus and minus first maximum diffraction order).
Fig. 2.
Fig. 2. Schematic sketch of setup geometry.
Fig. 3.
Fig. 3. Illumination function (a) intensity, (b) phase, (c) intensity of axial beam profile in the vertical direction, (d) intensity of axial beam profile in the horizontal direction.
Fig. 4.
Fig. 4. Reconstructions obtained with different degrees of overlap: (a) 70%, (b) 80%, (c) 90%, and (d) 95%.
Fig. 5.
Fig. 5. (a) Angular spectrum ePIE intensity reconstruction for 10 times magnification ( 512 × 512 cropped diffraction patterns), (b) ePIE intensity reconstruction obtained from 512 × 512 pixels cropped diffraction pattern, (c) ePIE intensity reconstruction obtained from 1024 × 1024 pixels cropped diffraction pattern.
Fig. 6.
Fig. 6. Error metric for ePIE at 512 × 512 pixels , ASePIE at 512 × 512 pixels , and ePIE at 1024 × 1024 pixels .

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

NA Comb = sin [ asin ( NA Ill ) + asin ( NA Setup ) ] NA Ill + NA Setup .
P = λ NA Comb ,
NA Sensor = sin [ atan ( 2 d N Δ x ) ] 2 d N Δ x ,
P = λ d N Δ x ,
Δ x = λ d N Δ x
Δ α = α 1 α 2 = 1 f s β ,
Ø angle 1 1 f s β β + α = 1 1 f s asin ( NA Setup ) asin ( NA Ill ) + asin ( NA Setup ) ,
Δ α = α ( 1 Ø angle ) .
δ x = D tan α tan ( Δ α 2 ) D 2 ( 1 Ø angle ) .
Ø x = D δ x D 1 2 ( 1 + Ø angle ) .
f = d · β 1 β ,
β = 4 Δ x P = 4 Δ x ( NA ill + NA Setup ) λ ,

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