Abstract

We have demonstrated that the extended ptychographic iterative engine (ePIE) algorithm can be applied to retrieve the phase information of the vectorial scattered field of a subwavelength object with the amplitude of the scattered field as input. We applied this technique combined with coherent Fourier scatterometry to determine the phase of the scattered field of a subwavelength grating, illuminated by a focused laser beam.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. O. El Gawhary, N. Kumar, S. F. Pereira, W. M. J. Coene, and H. P. Urbach, “Performance analysis of coherent fourier scatterometry,” Appl. Phys. B 105(4), 775–781 (2011).
    [Crossref]
  2. N. Kumar, P. Petrik, G. K. P. Ramanandan, O. El Gwhary, S. F. Pereira, W. M. J. Coene, and H. P. Urbaach, “Reconstruction of sub-wavelength features and nano-positioning of gratings using coherent fourier scatterometry,” Opt. Express 22(20), 24678–24688 (2014).
    [Crossref]
  3. S. Roy, N. Kumar, S. F. Pereira, and H. P. Urbach, “Interferometric coherent fourier scatterometry: a method for obtaining high sensitivity in the optical inverse-grating problem,” J. Opt. 15(7), 075707 (2013).
    [Crossref]
  4. R. W. Gerchberg, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  5. J. R. Fienup, “Reconstruction of an object from the modulus of its fourier transform,” Opt. Lett. 3(1), 27–29 (1978).
    [Crossref]
  6. H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
    [Crossref]
  7. A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. 35(15), 2585–2587 (2010).
    [Crossref]
  8. G. R. Brady, M. Guizar-Sicairos, and J. R. Fienup, “Optical wavefront measurement using phase retrieval with transverse translation diversity,” Opt. Express 17(2), 624–639 (2009).
    [Crossref]
  9. J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
    [Crossref]
  10. M. Dierolf, A. T. P. Menzel, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
    [Crossref]
  11. F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82(12), 121415 (2010).
    [Crossref]
  12. P. Wang, F. Zhang, S. Gao, M. Zhang, and A. I. Kirkland, “Electron ptychographic diffractive imaging of boron atoms in LaB6 crystals,” Sci. Rep. 7(1), 2857 (2017).
    [Crossref]
  13. J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
    [Crossref]
  14. W. Hoppe, “Beugung im inhomogenen primärstrahlwellenfeld. i. prinzip einer phasenmessung von elektronenbeungungsinterferenzen,” Acta Crystallogr., Sect. A 25(4), 495–501 (1969).
    [Crossref]
  15. R. Hegerl and W. Hoppe, “Dynamische theorie der kristallstrukturanalyse durch elektronenbeugung im inhomogenen primärstrahlwellenfeld,” Berichte der Bunsengesellschaft für Physikalische Chemie 74(11), 1148–1154 (1970).
    [Crossref]
  16. O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108(5), 481–487 (2008).
    [Crossref]
  17. A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
    [Crossref]
  18. X. Xu, A. P. Konijnenberg, S. F. Pereira, and H. P. Urbach, “Phase retrieval of the full vectorial field applied to coherent fourier scatterometry,” Opt. Express 25(24), 29574–29586 (2017).
    [Crossref]
  19. N. Kumar, L. Cisotto, S. Roy, G. K. P. Ramanandan, S. F. Pereira, and H. P. Urbaach, “Determination of the full scattering matrix using coherent fourier scatterometry,” Appl. Opt. 55(16), 4408–4413 (2016).
    [Crossref]

2017 (2)

P. Wang, F. Zhang, S. Gao, M. Zhang, and A. I. Kirkland, “Electron ptychographic diffractive imaging of boron atoms in LaB6 crystals,” Sci. Rep. 7(1), 2857 (2017).
[Crossref]

X. Xu, A. P. Konijnenberg, S. F. Pereira, and H. P. Urbach, “Phase retrieval of the full vectorial field applied to coherent fourier scatterometry,” Opt. Express 25(24), 29574–29586 (2017).
[Crossref]

2016 (1)

2014 (1)

2013 (1)

S. Roy, N. Kumar, S. F. Pereira, and H. P. Urbach, “Interferometric coherent fourier scatterometry: a method for obtaining high sensitivity in the optical inverse-grating problem,” J. Opt. 15(7), 075707 (2013).
[Crossref]

2011 (1)

O. El Gawhary, N. Kumar, S. F. Pereira, W. M. J. Coene, and H. P. Urbach, “Performance analysis of coherent fourier scatterometry,” Appl. Phys. B 105(4), 775–781 (2011).
[Crossref]

2010 (3)

A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. 35(15), 2585–2587 (2010).
[Crossref]

M. Dierolf, A. T. P. Menzel, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[Crossref]

F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82(12), 121415 (2010).
[Crossref]

2009 (2)

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref]

G. R. Brady, M. Guizar-Sicairos, and J. R. Fienup, “Optical wavefront measurement using phase retrieval with transverse translation diversity,” Opt. Express 17(2), 624–639 (2009).
[Crossref]

2008 (1)

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108(5), 481–487 (2008).
[Crossref]

2007 (1)

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref]

2004 (2)

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[Crossref]

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref]

1978 (1)

1972 (1)

R. W. Gerchberg, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

1970 (1)

R. Hegerl and W. Hoppe, “Dynamische theorie der kristallstrukturanalyse durch elektronenbeugung im inhomogenen primärstrahlwellenfeld,” Berichte der Bunsengesellschaft für Physikalische Chemie 74(11), 1148–1154 (1970).
[Crossref]

1969 (1)

W. Hoppe, “Beugung im inhomogenen primärstrahlwellenfeld. i. prinzip einer phasenmessung von elektronenbeungungsinterferenzen,” Acta Crystallogr., Sect. A 25(4), 495–501 (1969).
[Crossref]

Brady, G. R.

Bunk, O.

M. Dierolf, A. T. P. Menzel, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[Crossref]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108(5), 481–487 (2008).
[Crossref]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref]

Cisotto, L.

Coene, W. M. J.

Cullis, A. G.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref]

David, C.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref]

Dierolf, M.

M. Dierolf, A. T. P. Menzel, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[Crossref]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108(5), 481–487 (2008).
[Crossref]

Dobson, B. R.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref]

El Gawhary, O.

O. El Gawhary, N. Kumar, S. F. Pereira, W. M. J. Coene, and H. P. Urbach, “Performance analysis of coherent fourier scatterometry,” Appl. Phys. B 105(4), 775–781 (2011).
[Crossref]

El Gwhary, O.

Faulkner, H. M. L.

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref]

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[Crossref]

Fienup, J. R.

Gao, S.

P. Wang, F. Zhang, S. Gao, M. Zhang, and A. I. Kirkland, “Electron ptychographic diffractive imaging of boron atoms in LaB6 crystals,” Sci. Rep. 7(1), 2857 (2017).
[Crossref]

Gerchberg, R. W.

R. W. Gerchberg, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Guizar-Sicairos, M.

Hegerl, R.

R. Hegerl and W. Hoppe, “Dynamische theorie der kristallstrukturanalyse durch elektronenbeugung im inhomogenen primärstrahlwellenfeld,” Berichte der Bunsengesellschaft für Physikalische Chemie 74(11), 1148–1154 (1970).
[Crossref]

Hoppe, W.

R. Hegerl and W. Hoppe, “Dynamische theorie der kristallstrukturanalyse durch elektronenbeugung im inhomogenen primärstrahlwellenfeld,” Berichte der Bunsengesellschaft für Physikalische Chemie 74(11), 1148–1154 (1970).
[Crossref]

W. Hoppe, “Beugung im inhomogenen primärstrahlwellenfeld. i. prinzip einer phasenmessung von elektronenbeungungsinterferenzen,” Acta Crystallogr., Sect. A 25(4), 495–501 (1969).
[Crossref]

Hüe, F.

F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82(12), 121415 (2010).
[Crossref]

Humphry, M. J.

Hurst, A. C.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref]

Jefimovs, K.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[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 ptychographical iterative engine,” Ultramicroscopy 108(5), 481–487 (2008).
[Crossref]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref]

Kewish, C. M.

M. Dierolf, A. T. P. Menzel, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[Crossref]

Kirkland, A. I.

P. Wang, F. Zhang, S. Gao, M. Zhang, and A. I. Kirkland, “Electron ptychographic diffractive imaging of boron atoms in LaB6 crystals,” Sci. Rep. 7(1), 2857 (2017).
[Crossref]

Konijnenberg, A. P.

Kumar, N.

N. Kumar, L. Cisotto, S. Roy, G. K. P. Ramanandan, S. F. Pereira, and H. P. Urbaach, “Determination of the full scattering matrix using coherent fourier scatterometry,” Appl. Opt. 55(16), 4408–4413 (2016).
[Crossref]

N. Kumar, P. Petrik, G. K. P. Ramanandan, O. El Gwhary, S. F. Pereira, W. M. J. Coene, and H. P. Urbaach, “Reconstruction of sub-wavelength features and nano-positioning of gratings using coherent fourier scatterometry,” Opt. Express 22(20), 24678–24688 (2014).
[Crossref]

S. Roy, N. Kumar, S. F. Pereira, and H. P. Urbach, “Interferometric coherent fourier scatterometry: a method for obtaining high sensitivity in the optical inverse-grating problem,” J. Opt. 15(7), 075707 (2013).
[Crossref]

O. El Gawhary, N. Kumar, S. F. Pereira, W. M. J. Coene, and H. P. Urbach, “Performance analysis of coherent fourier scatterometry,” Appl. Phys. B 105(4), 775–781 (2011).
[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 ptychographical iterative engine,” Ultramicroscopy 108(5), 481–487 (2008).
[Crossref]

Maiden, A. M.

F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82(12), 121415 (2010).
[Crossref]

A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. 35(15), 2585–2587 (2010).
[Crossref]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref]

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 ptychographical iterative engine,” Ultramicroscopy 108(5), 481–487 (2008).
[Crossref]

Menzel, A. T. P.

M. Dierolf, A. T. P. Menzel, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[Crossref]

Midgley, P. A.

F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82(12), 121415 (2010).
[Crossref]

Pereira, S. F.

Petrik, P.

Pfeiffer, F.

M. Dierolf, A. T. P. Menzel, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[Crossref]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108(5), 481–487 (2008).
[Crossref]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref]

Ramanandan, G. K. P.

Rodenburg, J. M.

A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. 35(15), 2585–2587 (2010).
[Crossref]

F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82(12), 121415 (2010).
[Crossref]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref]

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[Crossref]

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref]

Roy, S.

N. Kumar, L. Cisotto, S. Roy, G. K. P. Ramanandan, S. F. Pereira, and H. P. Urbaach, “Determination of the full scattering matrix using coherent fourier scatterometry,” Appl. Opt. 55(16), 4408–4413 (2016).
[Crossref]

S. Roy, N. Kumar, S. F. Pereira, and H. P. Urbach, “Interferometric coherent fourier scatterometry: a method for obtaining high sensitivity in the optical inverse-grating problem,” J. Opt. 15(7), 075707 (2013).
[Crossref]

Schneider, P.

M. Dierolf, A. T. P. Menzel, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[Crossref]

Sweeney, F.

F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82(12), 121415 (2010).
[Crossref]

Urbaach, H. P.

Urbach, H. P.

X. Xu, A. P. Konijnenberg, S. F. Pereira, and H. P. Urbach, “Phase retrieval of the full vectorial field applied to coherent fourier scatterometry,” Opt. Express 25(24), 29574–29586 (2017).
[Crossref]

S. Roy, N. Kumar, S. F. Pereira, and H. P. Urbach, “Interferometric coherent fourier scatterometry: a method for obtaining high sensitivity in the optical inverse-grating problem,” J. Opt. 15(7), 075707 (2013).
[Crossref]

O. El Gawhary, N. Kumar, S. F. Pereira, W. M. J. Coene, and H. P. Urbach, “Performance analysis of coherent fourier scatterometry,” Appl. Phys. B 105(4), 775–781 (2011).
[Crossref]

Wang, P.

P. Wang, F. Zhang, S. Gao, M. Zhang, and A. I. Kirkland, “Electron ptychographic diffractive imaging of boron atoms in LaB6 crystals,” Sci. Rep. 7(1), 2857 (2017).
[Crossref]

Wepf, R.

M. Dierolf, A. T. P. Menzel, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[Crossref]

Xu, X.

Zhang, F.

P. Wang, F. Zhang, S. Gao, M. Zhang, and A. I. Kirkland, “Electron ptychographic diffractive imaging of boron atoms in LaB6 crystals,” Sci. Rep. 7(1), 2857 (2017).
[Crossref]

Zhang, M.

P. Wang, F. Zhang, S. Gao, M. Zhang, and A. I. Kirkland, “Electron ptychographic diffractive imaging of boron atoms in LaB6 crystals,” Sci. Rep. 7(1), 2857 (2017).
[Crossref]

Acta Crystallogr., Sect. A (1)

W. Hoppe, “Beugung im inhomogenen primärstrahlwellenfeld. i. prinzip einer phasenmessung von elektronenbeungungsinterferenzen,” Acta Crystallogr., Sect. A 25(4), 495–501 (1969).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (1)

O. El Gawhary, N. Kumar, S. F. Pereira, W. M. J. Coene, and H. P. Urbach, “Performance analysis of coherent fourier scatterometry,” Appl. Phys. B 105(4), 775–781 (2011).
[Crossref]

Appl. Phys. Lett. (1)

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[Crossref]

Berichte der Bunsengesellschaft für Physikalische Chemie (1)

R. Hegerl and W. Hoppe, “Dynamische theorie der kristallstrukturanalyse durch elektronenbeugung im inhomogenen primärstrahlwellenfeld,” Berichte der Bunsengesellschaft für Physikalische Chemie 74(11), 1148–1154 (1970).
[Crossref]

J. Opt. (1)

S. Roy, N. Kumar, S. F. Pereira, and H. P. Urbach, “Interferometric coherent fourier scatterometry: a method for obtaining high sensitivity in the optical inverse-grating problem,” J. Opt. 15(7), 075707 (2013).
[Crossref]

Nature (1)

M. Dierolf, A. T. P. Menzel, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Optik (1)

R. W. Gerchberg, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Phys. Rev. B (1)

F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82(12), 121415 (2010).
[Crossref]

Phys. Rev. Lett. (2)

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref]

Sci. Rep. (1)

P. Wang, F. Zhang, S. Gao, M. Zhang, and A. I. Kirkland, “Electron ptychographic diffractive imaging of boron atoms in LaB6 crystals,” Sci. Rep. 7(1), 2857 (2017).
[Crossref]

Ultramicroscopy (2)

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108(5), 481–487 (2008).
[Crossref]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. Experimental setup to retrieve the amplitude and phase of the scattered field (as shown in Fig. 2) of a diffraction grating.
Fig. 2.
Fig. 2. Intensity distribution of the experimental scattered field of the grating at the pupil plane. The red square indicates the region that is scanned by the check-board mask.
Fig. 3.
Fig. 3. (a) The cross-sections of the same intensity pattern is shown for different exposure times of $t=300 \mu s$ and $t=2000 \mu s$ where the former is not overexposed unlike the latter one. It can be seen here that the central peak of the modified intensity is several times higher than the measured intensity. (b) A zoom of the central peaks shows a clear saturation of the brightest peak.
Fig. 4.
Fig. 4. (a) Direct imaging of the 5 tiles mask that was used for the experiment. (b) The reconstructed mask by using the ePIE algorithm with 30 iterations and 79\% overlap.
Fig. 5.
Fig. 5. Retrieved amplitude and phase of the scattered field of a grating at the pupil illuminated by a focused laser beam. The input polarization is TM (perpendicular to the grating grooves)
Fig. 6.
Fig. 6. Mean square error of the retrieved scattered field as a function of the number of interactions.

Equations (11)

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ψ j ( r ) = O ( r ) P ( r R j ) .
I j ( r ) = | F { ψ j ( r ) } | 2 .
ψ k , j ( r ) = O k ( r ) P ( r R j ) .
Ψ k , j ( r ) = F { ψ k , j ( r ) } ( r ) .
Ψ k , j u p d ( r ) = I j ( r ) Ψ k , j ( r ) | Ψ k , j ( r ) | .
ψ k , j u p d ( r ) = F 1 { Ψ k , j u p d ( r ) } .
O k + 1 ( r ) = O k ( r ) + P ( r R j ) | P ( r R j ) | max 2 × [ ψ k , j u p d ( r ) ψ k , j ( r ) ] .
I j ( r ) = | F { O ( r + R j ) P ( r ) } | 2 .
P k + 1 ( r ) = P k ( r ) + O k ( r + R j ) | O k ( r + R j ) | max 2 × [ ψ k , j u p d ( r ) ψ k , j ( r ) ] .
Δ x o = λ f 1 N Δ x d .
Δ m = Δ m × Δ x d Δ x o .

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