Abstract

A noise-robust extension of iterative phase retrieval algorithms that does not need to assume a noise model is proposed. It works by adapting the intensity constraints using the reconstructed object. Using a proof-of-principle ptychographic experiment with visible light and a spatial light modulator to create an object, the proposed method is tested and it compares favorably to the Extended Ptychographic Iterative Engine (ePIE) with reduced step size. The method is general, so it can also be applied to other iterative reconstruction schemes such as phase retrieval using focus variation.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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    [Crossref]

2017 (5)

M. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543(7645), 402–406 (2017).
[Crossref] [PubMed]

P. Dwivedi, A. P. Konijnenberg, S. F. Pereira, and H. P. Urbach, “New method for probe position correction for ptychography,” Proc. SPIE 10329, 103292Y (2017).
[Crossref]

A.P. Konijnenberg, W.M.J. Coene, and H.P. Urbach, “Non-iterative phase retrieval by phase modulation through a single parameter,” Ultramicroscopy 174, 70–78 (2017).
[Crossref] [PubMed]

Y. Zhang, P. Song, and Q. Dai, “Fourier ptychographic microscopy using a generalized Anscombe transform approximation of the mixed Poisson-Gaussian likelihood,” Opt. Express 25(1), 168 (2017).
[Crossref] [PubMed]

C. Wang, Z. Xu, H. Liu, Y. Wang, J. Wang, and R. Tai, “Background noise removal in x-ray ptychography,” Appl. Opt. 56(8), 2099 (2017).
[Crossref] [PubMed]

2016 (6)

C. Zuo, J. Sun, and Q. Chen, “Adaptive step-size strategy for noise-robust Fourier ptychographic microscopy,” Opt. Express 24(18), 20724 (2016).
[Crossref] [PubMed]

A. P. Konijnenberg, W. M. J. Coene, S. F. Pereira, and H. P. Urbach, “Combining ptychographical algorithms with the Hybrid Input-Output (HIO) algorithm,” Ultramicroscopy 171, 43–54 (2016).
[Crossref] [PubMed]

J. Zhong, L. Tian, P. Varma, and L. Waller, “Nonlinear optimization algorithm for partially coherent phase retrieval and source recovery,” IEEE Trans. Comput. Imaging 2(3), 310–322 (2016).
[Crossref]

H. Yang, R. N. Rutte, L. Jones, M. Simson, R. Sagawa, H. Ryll, M. Huth, T. J. Pennycook, M.L.H. Green, H. Soltau, Y. Kondo, B. G. Davis, and P. D. Nellist, “Simultaneous atomic-resolution electron ptychography and z-contrast imaging of light and heavy elements in complex nanostructures,” Nat. Commun. 7, 12532 (2016).
[Crossref] [PubMed]

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6, 27384 (2016).
[Crossref] [PubMed]

S. Marchesini, H. Krishnan, B. J. Daurer, D. A. Shapiro, T. Perciano, J. A. Sethian, and F. R. N. C. Maia, “SHARP: a distributed GPU-based ptychographic solver,” J. Appl. Crystallogr. 49(4), 1245–1252 (2016).
[Crossref]

2015 (2)

B. Zhang, D. F. Gardner, M. D. Seaberg, E. R. Shanblatt, H. C. Kapteyn, M. M. Murnane, and D. E. Adams, “High contrast 3d imaging of surfaces near the wavelength limit using tabletop EUV ptychography,” Ultramicroscopy 158, 98–104 (2015).
[Crossref] [PubMed]

L. Yeh, J. Dong, J. Zhong, L. Tian, M. Chen, G. Tang, M. Soltanolkotabi, and L. Waller, “Experimental robustness of Fourier ptychography phase retrieval algorithms,” Opt. Express 23(26), 33214 (2015).
[Crossref]

2014 (2)

T. M. Godden, R. Suman, M. J. Humphry, J. M. Rodenburg, and A. M. Maiden, “Ptychographic microscope for three-dimensional imaging,” Opt. Express 22(10), 12513 (2014).
[Crossref] [PubMed]

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

2013 (2)

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref]

A.M. Maiden, G.R. Morrison, B. Kaulich, A. Gianoncelli, and J.M. Rodenburg, “Soft x-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

2012 (2)

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys. 14(6), 63004 (2012).
[Crossref]

P. Godard, M. Allain, V. Chamard, and J. Rodenburg, “Noise models for low counting rate coherent diffraction imaging,” Opt. Express 20(23), 25914 (2012).
[Crossref] [PubMed]

2010 (1)

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] [PubMed]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

2008 (1)

2004 (1)

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

1978 (1)

Adams, D. E.

B. Zhang, D. F. Gardner, M. D. Seaberg, E. R. Shanblatt, H. C. Kapteyn, M. M. Murnane, and D. E. Adams, “High contrast 3d imaging of surfaces near the wavelength limit using tabletop EUV ptychography,” Ultramicroscopy 158, 98–104 (2015).
[Crossref] [PubMed]

Aeppli, G.

M. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543(7645), 402–406 (2017).
[Crossref] [PubMed]

Allain, M.

Bian, L.

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6, 27384 (2016).
[Crossref] [PubMed]

Bunk, O.

M. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543(7645), 402–406 (2017).
[Crossref] [PubMed]

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

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

Chamard, V.

Chang, H.

H. Chang and S. Marchesini, “A general framework for denoising phaseless diffraction measurements,” arXiv:1611.01417 (2016).

Chen, F.

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6, 27384 (2016).
[Crossref] [PubMed]

Chen, M.

Chen, Q.

Chung, J.

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6, 27384 (2016).
[Crossref] [PubMed]

Coene, W. M. J.

A. P. Konijnenberg, W. M. J. Coene, S. F. Pereira, and H. P. Urbach, “Combining ptychographical algorithms with the Hybrid Input-Output (HIO) algorithm,” Ultramicroscopy 171, 43–54 (2016).
[Crossref] [PubMed]

Coene, W.M.J.

A.P. Konijnenberg, W.M.J. Coene, and H.P. Urbach, “Non-iterative phase retrieval by phase modulation through a single parameter,” Ultramicroscopy 174, 70–78 (2017).
[Crossref] [PubMed]

Dai, Q.

Y. Zhang, P. Song, and Q. Dai, “Fourier ptychographic microscopy using a generalized Anscombe transform approximation of the mixed Poisson-Gaussian likelihood,” Opt. Express 25(1), 168 (2017).
[Crossref] [PubMed]

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6, 27384 (2016).
[Crossref] [PubMed]

Daurer, B. J.

S. Marchesini, H. Krishnan, B. J. Daurer, D. A. Shapiro, T. Perciano, J. A. Sethian, and F. R. N. C. Maia, “SHARP: a distributed GPU-based ptychographic solver,” J. Appl. Crystallogr. 49(4), 1245–1252 (2016).
[Crossref]

Davis, B. G.

H. Yang, R. N. Rutte, L. Jones, M. Simson, R. Sagawa, H. Ryll, M. Huth, T. J. Pennycook, M.L.H. Green, H. Soltau, Y. Kondo, B. G. Davis, and P. D. Nellist, “Simultaneous atomic-resolution electron ptychography and z-contrast imaging of light and heavy elements in complex nanostructures,” Nat. Commun. 7, 12532 (2016).
[Crossref] [PubMed]

Diaz, A.

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

Dierolf, M.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

Dinapoli, R.

M. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543(7645), 402–406 (2017).
[Crossref] [PubMed]

Dong, J.

Dwivedi, P.

P. Dwivedi, A. P. Konijnenberg, S. F. Pereira, and H. P. Urbach, “New method for probe position correction for ptychography,” Proc. SPIE 10329, 103292Y (2017).
[Crossref]

Färm, E.

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

Faulkner, H. M. L.

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

Fienup, J. R.

Gardner, D. F.

B. Zhang, D. F. Gardner, M. D. Seaberg, E. R. Shanblatt, H. C. Kapteyn, M. M. Murnane, and D. E. Adams, “High contrast 3d imaging of surfaces near the wavelength limit using tabletop EUV ptychography,” Ultramicroscopy 158, 98–104 (2015).
[Crossref] [PubMed]

Gianoncelli, A.

A.M. Maiden, G.R. Morrison, B. Kaulich, A. Gianoncelli, and J.M. Rodenburg, “Soft x-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

Godard, P.

Godden, T. M.

Green, M.L.H.

H. Yang, R. N. Rutte, L. Jones, M. Simson, R. Sagawa, H. Ryll, M. Huth, T. J. Pennycook, M.L.H. Green, H. Soltau, Y. Kondo, B. G. Davis, and P. D. Nellist, “Simultaneous atomic-resolution electron ptychography and z-contrast imaging of light and heavy elements in complex nanostructures,” Nat. Commun. 7, 12532 (2016).
[Crossref] [PubMed]

Guizar-Sicairos, M.

M. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543(7645), 402–406 (2017).
[Crossref] [PubMed]

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

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys. 14(6), 63004 (2012).
[Crossref]

M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express 16(10), 7264 (2008).
[Crossref] [PubMed]

Härkönen, E.

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

Holler, M.

M. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543(7645), 402–406 (2017).
[Crossref] [PubMed]

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

Horstmeyer, R.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref]

Humphry, M. J.

Huth, M.

H. Yang, R. N. Rutte, L. Jones, M. Simson, R. Sagawa, H. Ryll, M. Huth, T. J. Pennycook, M.L.H. Green, H. Soltau, Y. Kondo, B. G. Davis, and P. D. Nellist, “Simultaneous atomic-resolution electron ptychography and z-contrast imaging of light and heavy elements in complex nanostructures,” Nat. Commun. 7, 12532 (2016).
[Crossref] [PubMed]

Jones, L.

H. Yang, R. N. Rutte, L. Jones, M. Simson, R. Sagawa, H. Ryll, M. Huth, T. J. Pennycook, M.L.H. Green, H. Soltau, Y. Kondo, B. G. Davis, and P. D. Nellist, “Simultaneous atomic-resolution electron ptychography and z-contrast imaging of light and heavy elements in complex nanostructures,” Nat. Commun. 7, 12532 (2016).
[Crossref] [PubMed]

Kapteyn, H. C.

B. Zhang, D. F. Gardner, M. D. Seaberg, E. R. Shanblatt, H. C. Kapteyn, M. M. Murnane, and D. E. Adams, “High contrast 3d imaging of surfaces near the wavelength limit using tabletop EUV ptychography,” Ultramicroscopy 158, 98–104 (2015).
[Crossref] [PubMed]

Karvinen, P.

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

Kaulich, B.

A.M. Maiden, G.R. Morrison, B. Kaulich, A. Gianoncelli, and J.M. Rodenburg, “Soft x-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

Kondo, Y.

H. Yang, R. N. Rutte, L. Jones, M. Simson, R. Sagawa, H. Ryll, M. Huth, T. J. Pennycook, M.L.H. Green, H. Soltau, Y. Kondo, B. G. Davis, and P. D. Nellist, “Simultaneous atomic-resolution electron ptychography and z-contrast imaging of light and heavy elements in complex nanostructures,” Nat. Commun. 7, 12532 (2016).
[Crossref] [PubMed]

Konijnenberg, A. P.

P. Dwivedi, A. P. Konijnenberg, S. F. Pereira, and H. P. Urbach, “New method for probe position correction for ptychography,” Proc. SPIE 10329, 103292Y (2017).
[Crossref]

A. P. Konijnenberg, W. M. J. Coene, S. F. Pereira, and H. P. Urbach, “Combining ptychographical algorithms with the Hybrid Input-Output (HIO) algorithm,” Ultramicroscopy 171, 43–54 (2016).
[Crossref] [PubMed]

Konijnenberg, A.P.

A.P. Konijnenberg, W.M.J. Coene, and H.P. Urbach, “Non-iterative phase retrieval by phase modulation through a single parameter,” Ultramicroscopy 174, 70–78 (2017).
[Crossref] [PubMed]

Krishnan, H.

S. Marchesini, H. Krishnan, B. J. Daurer, D. A. Shapiro, T. Perciano, J. A. Sethian, and F. R. N. C. Maia, “SHARP: a distributed GPU-based ptychographic solver,” J. Appl. Crystallogr. 49(4), 1245–1252 (2016).
[Crossref]

Liu, H.

Maia, F. R. N. C.

S. Marchesini, H. Krishnan, B. J. Daurer, D. A. Shapiro, T. Perciano, J. A. Sethian, and F. R. N. C. Maia, “SHARP: a distributed GPU-based ptychographic solver,” J. Appl. Crystallogr. 49(4), 1245–1252 (2016).
[Crossref]

Maiden, A. M.

Maiden, A.M.

A.M. Maiden, G.R. Morrison, B. Kaulich, A. Gianoncelli, and J.M. Rodenburg, “Soft x-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

Marchesini, S.

S. Marchesini, H. Krishnan, B. J. Daurer, D. A. Shapiro, T. Perciano, J. A. Sethian, and F. R. N. C. Maia, “SHARP: a distributed GPU-based ptychographic solver,” J. Appl. Crystallogr. 49(4), 1245–1252 (2016).
[Crossref]

H. Chang and S. Marchesini, “A general framework for denoising phaseless diffraction measurements,” arXiv:1611.01417 (2016).

Menzel, A.

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

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

Morrison, G.R.

A.M. Maiden, G.R. Morrison, B. Kaulich, A. Gianoncelli, and J.M. Rodenburg, “Soft x-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

Müller, E.

M. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543(7645), 402–406 (2017).
[Crossref] [PubMed]

Murnane, M. M.

B. Zhang, D. F. Gardner, M. D. Seaberg, E. R. Shanblatt, H. C. Kapteyn, M. M. Murnane, and D. E. Adams, “High contrast 3d imaging of surfaces near the wavelength limit using tabletop EUV ptychography,” Ultramicroscopy 158, 98–104 (2015).
[Crossref] [PubMed]

Nellist, P. D.

H. Yang, R. N. Rutte, L. Jones, M. Simson, R. Sagawa, H. Ryll, M. Huth, T. J. Pennycook, M.L.H. Green, H. Soltau, Y. Kondo, B. G. Davis, and P. D. Nellist, “Simultaneous atomic-resolution electron ptychography and z-contrast imaging of light and heavy elements in complex nanostructures,” Nat. Commun. 7, 12532 (2016).
[Crossref] [PubMed]

Ou, X.

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6, 27384 (2016).
[Crossref] [PubMed]

Pennycook, T. J.

H. Yang, R. N. Rutte, L. Jones, M. Simson, R. Sagawa, H. Ryll, M. Huth, T. J. Pennycook, M.L.H. Green, H. Soltau, Y. Kondo, B. G. Davis, and P. D. Nellist, “Simultaneous atomic-resolution electron ptychography and z-contrast imaging of light and heavy elements in complex nanostructures,” Nat. Commun. 7, 12532 (2016).
[Crossref] [PubMed]

Perciano, T.

S. Marchesini, H. Krishnan, B. J. Daurer, D. A. Shapiro, T. Perciano, J. A. Sethian, and F. R. N. C. Maia, “SHARP: a distributed GPU-based ptychographic solver,” J. Appl. Crystallogr. 49(4), 1245–1252 (2016).
[Crossref]

Pereira, S. F.

P. Dwivedi, A. P. Konijnenberg, S. F. Pereira, and H. P. Urbach, “New method for probe position correction for ptychography,” Proc. SPIE 10329, 103292Y (2017).
[Crossref]

A. P. Konijnenberg, W. M. J. Coene, S. F. Pereira, and H. P. Urbach, “Combining ptychographical algorithms with the Hybrid Input-Output (HIO) algorithm,” Ultramicroscopy 171, 43–54 (2016).
[Crossref] [PubMed]

Pfeiffer, F.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

Raabe, J.

M. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543(7645), 402–406 (2017).
[Crossref] [PubMed]

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

Ritala, M.

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

Rodenburg, J.

Rodenburg, J. M.

T. M. Godden, R. Suman, M. J. Humphry, J. M. Rodenburg, and A. M. Maiden, “Ptychographic microscope for three-dimensional imaging,” Opt. Express 22(10), 12513 (2014).
[Crossref] [PubMed]

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

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

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

Rodenburg, J.M.

A.M. Maiden, G.R. Morrison, B. Kaulich, A. Gianoncelli, and J.M. Rodenburg, “Soft x-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

Rutte, R. N.

H. Yang, R. N. Rutte, L. Jones, M. Simson, R. Sagawa, H. Ryll, M. Huth, T. J. Pennycook, M.L.H. Green, H. Soltau, Y. Kondo, B. G. Davis, and P. D. Nellist, “Simultaneous atomic-resolution electron ptychography and z-contrast imaging of light and heavy elements in complex nanostructures,” Nat. Commun. 7, 12532 (2016).
[Crossref] [PubMed]

Ryll, H.

H. Yang, R. N. Rutte, L. Jones, M. Simson, R. Sagawa, H. Ryll, M. Huth, T. J. Pennycook, M.L.H. Green, H. Soltau, Y. Kondo, B. G. Davis, and P. D. Nellist, “Simultaneous atomic-resolution electron ptychography and z-contrast imaging of light and heavy elements in complex nanostructures,” Nat. Commun. 7, 12532 (2016).
[Crossref] [PubMed]

Sagawa, R.

H. Yang, R. N. Rutte, L. Jones, M. Simson, R. Sagawa, H. Ryll, M. Huth, T. J. Pennycook, M.L.H. Green, H. Soltau, Y. Kondo, B. G. Davis, and P. D. Nellist, “Simultaneous atomic-resolution electron ptychography and z-contrast imaging of light and heavy elements in complex nanostructures,” Nat. Commun. 7, 12532 (2016).
[Crossref] [PubMed]

Seaberg, M. D.

B. Zhang, D. F. Gardner, M. D. Seaberg, E. R. Shanblatt, H. C. Kapteyn, M. M. Murnane, and D. E. Adams, “High contrast 3d imaging of surfaces near the wavelength limit using tabletop EUV ptychography,” Ultramicroscopy 158, 98–104 (2015).
[Crossref] [PubMed]

Sethian, J. A.

S. Marchesini, H. Krishnan, B. J. Daurer, D. A. Shapiro, T. Perciano, J. A. Sethian, and F. R. N. C. Maia, “SHARP: a distributed GPU-based ptychographic solver,” J. Appl. Crystallogr. 49(4), 1245–1252 (2016).
[Crossref]

Shanblatt, E. R.

B. Zhang, D. F. Gardner, M. D. Seaberg, E. R. Shanblatt, H. C. Kapteyn, M. M. Murnane, and D. E. Adams, “High contrast 3d imaging of surfaces near the wavelength limit using tabletop EUV ptychography,” Ultramicroscopy 158, 98–104 (2015).
[Crossref] [PubMed]

Shapiro, D. A.

S. Marchesini, H. Krishnan, B. J. Daurer, D. A. Shapiro, T. Perciano, J. A. Sethian, and F. R. N. C. Maia, “SHARP: a distributed GPU-based ptychographic solver,” J. Appl. Crystallogr. 49(4), 1245–1252 (2016).
[Crossref]

Simson, M.

H. Yang, R. N. Rutte, L. Jones, M. Simson, R. Sagawa, H. Ryll, M. Huth, T. J. Pennycook, M.L.H. Green, H. Soltau, Y. Kondo, B. G. Davis, and P. D. Nellist, “Simultaneous atomic-resolution electron ptychography and z-contrast imaging of light and heavy elements in complex nanostructures,” Nat. Commun. 7, 12532 (2016).
[Crossref] [PubMed]

Soltanolkotabi, M.

Soltau, H.

H. Yang, R. N. Rutte, L. Jones, M. Simson, R. Sagawa, H. Ryll, M. Huth, T. J. Pennycook, M.L.H. Green, H. Soltau, Y. Kondo, B. G. Davis, and P. D. Nellist, “Simultaneous atomic-resolution electron ptychography and z-contrast imaging of light and heavy elements in complex nanostructures,” Nat. Commun. 7, 12532 (2016).
[Crossref] [PubMed]

Song, P.

Suman, R.

Sun, J.

Suo, J.

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6, 27384 (2016).
[Crossref] [PubMed]

Tai, R.

Tang, G.

Thibault, P.

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys. 14(6), 63004 (2012).
[Crossref]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

Tian, L.

J. Zhong, L. Tian, P. Varma, and L. Waller, “Nonlinear optimization algorithm for partially coherent phase retrieval and source recovery,” IEEE Trans. Comput. Imaging 2(3), 310–322 (2016).
[Crossref]

L. Yeh, J. Dong, J. Zhong, L. Tian, M. Chen, G. Tang, M. Soltanolkotabi, and L. Waller, “Experimental robustness of Fourier ptychography phase retrieval algorithms,” Opt. Express 23(26), 33214 (2015).
[Crossref]

Tsai, E. H. R.

M. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543(7645), 402–406 (2017).
[Crossref] [PubMed]

Urbach, H. P.

P. Dwivedi, A. P. Konijnenberg, S. F. Pereira, and H. P. Urbach, “New method for probe position correction for ptychography,” Proc. SPIE 10329, 103292Y (2017).
[Crossref]

A. P. Konijnenberg, W. M. J. Coene, S. F. Pereira, and H. P. Urbach, “Combining ptychographical algorithms with the Hybrid Input-Output (HIO) algorithm,” Ultramicroscopy 171, 43–54 (2016).
[Crossref] [PubMed]

Urbach, H.P.

A.P. Konijnenberg, W.M.J. Coene, and H.P. Urbach, “Non-iterative phase retrieval by phase modulation through a single parameter,” Ultramicroscopy 174, 70–78 (2017).
[Crossref] [PubMed]

Varma, P.

J. Zhong, L. Tian, P. Varma, and L. Waller, “Nonlinear optimization algorithm for partially coherent phase retrieval and source recovery,” IEEE Trans. Comput. Imaging 2(3), 310–322 (2016).
[Crossref]

Waller, L.

J. Zhong, L. Tian, P. Varma, and L. Waller, “Nonlinear optimization algorithm for partially coherent phase retrieval and source recovery,” IEEE Trans. Comput. Imaging 2(3), 310–322 (2016).
[Crossref]

L. Yeh, J. Dong, J. Zhong, L. Tian, M. Chen, G. Tang, M. Soltanolkotabi, and L. Waller, “Experimental robustness of Fourier ptychography phase retrieval algorithms,” Opt. Express 23(26), 33214 (2015).
[Crossref]

Wang, C.

Wang, J.

Wang, Y.

Xu, Z.

Yang, C.

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6, 27384 (2016).
[Crossref] [PubMed]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref]

Yang, H.

H. Yang, R. N. Rutte, L. Jones, M. Simson, R. Sagawa, H. Ryll, M. Huth, T. J. Pennycook, M.L.H. Green, H. Soltau, Y. Kondo, B. G. Davis, and P. D. Nellist, “Simultaneous atomic-resolution electron ptychography and z-contrast imaging of light and heavy elements in complex nanostructures,” Nat. Commun. 7, 12532 (2016).
[Crossref] [PubMed]

Yeh, L.

Zhang, B.

B. Zhang, D. F. Gardner, M. D. Seaberg, E. R. Shanblatt, H. C. Kapteyn, M. M. Murnane, and D. E. Adams, “High contrast 3d imaging of surfaces near the wavelength limit using tabletop EUV ptychography,” Ultramicroscopy 158, 98–104 (2015).
[Crossref] [PubMed]

Zhang, Y.

Zheng, G.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref]

Zhong, J.

J. Zhong, L. Tian, P. Varma, and L. Waller, “Nonlinear optimization algorithm for partially coherent phase retrieval and source recovery,” IEEE Trans. Comput. Imaging 2(3), 310–322 (2016).
[Crossref]

L. Yeh, J. Dong, J. Zhong, L. Tian, M. Chen, G. Tang, M. Soltanolkotabi, and L. Waller, “Experimental robustness of Fourier ptychography phase retrieval algorithms,” Opt. Express 23(26), 33214 (2015).
[Crossref]

Zuo, C.

Appl. Opt. (1)

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 (2004).
[Crossref]

IEEE Trans. Comput. Imaging (1)

J. Zhong, L. Tian, P. Varma, and L. Waller, “Nonlinear optimization algorithm for partially coherent phase retrieval and source recovery,” IEEE Trans. Comput. Imaging 2(3), 310–322 (2016).
[Crossref]

J. Appl. Crystallogr. (1)

S. Marchesini, H. Krishnan, B. J. Daurer, D. A. Shapiro, T. Perciano, J. A. Sethian, and F. R. N. C. Maia, “SHARP: a distributed GPU-based ptychographic solver,” J. Appl. Crystallogr. 49(4), 1245–1252 (2016).
[Crossref]

Nat. Commun. (2)

A.M. Maiden, G.R. Morrison, B. Kaulich, A. Gianoncelli, and J.M. Rodenburg, “Soft x-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

H. Yang, R. N. Rutte, L. Jones, M. Simson, R. Sagawa, H. Ryll, M. Huth, T. J. Pennycook, M.L.H. Green, H. Soltau, Y. Kondo, B. G. Davis, and P. D. Nellist, “Simultaneous atomic-resolution electron ptychography and z-contrast imaging of light and heavy elements in complex nanostructures,” Nat. Commun. 7, 12532 (2016).
[Crossref] [PubMed]

Nat. Photonics (1)

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref]

Nature (1)

M. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543(7645), 402–406 (2017).
[Crossref] [PubMed]

New J. Phys. (1)

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys. 14(6), 63004 (2012).
[Crossref]

Opt. Express (6)

Opt. Lett. (2)

Proc. SPIE (1)

P. Dwivedi, A. P. Konijnenberg, S. F. Pereira, and H. P. Urbach, “New method for probe position correction for ptychography,” Proc. SPIE 10329, 103292Y (2017).
[Crossref]

Sci. Rep. (2)

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

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang, F. Chen, and Q. Dai, “Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient,” Sci. Rep. 6, 27384 (2016).
[Crossref] [PubMed]

Ultramicroscopy (5)

B. Zhang, D. F. Gardner, M. D. Seaberg, E. R. Shanblatt, H. C. Kapteyn, M. M. Murnane, and D. E. Adams, “High contrast 3d imaging of surfaces near the wavelength limit using tabletop EUV ptychography,” Ultramicroscopy 158, 98–104 (2015).
[Crossref] [PubMed]

A.P. Konijnenberg, W.M.J. Coene, and H.P. Urbach, “Non-iterative phase retrieval by phase modulation through a single parameter,” Ultramicroscopy 174, 70–78 (2017).
[Crossref] [PubMed]

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

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

A. P. Konijnenberg, W. M. J. Coene, S. F. Pereira, and H. P. Urbach, “Combining ptychographical algorithms with the Hybrid Input-Output (HIO) algorithm,” Ultramicroscopy 171, 43–54 (2016).
[Crossref] [PubMed]

Other (1)

H. Chang and S. Marchesini, “A general framework for denoising phaseless diffraction measurements,” arXiv:1611.01417 (2016).

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Figures (15)

Fig. 1
Fig. 1 The phase objects and the illuminating probe used for the ptychography experiment.
Fig. 2
Fig. 2 Experimental setup to generate ptychographic data sets to test the proposed algorithm on.
Fig. 3
Fig. 3 A measured intensity pattern (log scale) where a region is selected (red rectangle in the top left corner) to calculate the mean and the standard deviation of the noise.
Fig. 4
Fig. 4 Reconstructions of object 1.
Fig. 5
Fig. 5 A comparison of the estimated diffraction patterns (log scale) of object 1 using standard ePIE and the proposed algorithm. One can observe that in the proposed algorithm the higher spatial frequencies have a stronger presence, thus causing the reconstructed object to have a higher resolution.
Fig. 6
Fig. 6 Plot of the amplitude-based cost function L as a function of the number of iterations. For the regular ePIE algorithm, the estimated amplitudes are compared with the measured amplitudes yX(u), while for the proposed algorithm the estimated amplitudes are compared with the adapted amplitude constraints mX,est(u).
Fig. 7
Fig. 7 Reconstructions of object 2. For each probe position, 50 measurements were averaged. Position correction was used.
Fig. 8
Fig. 8 Reconstructions of object 2. For each probe position, a single measurement was taken. Correct probe positions were used in the reconstruction and no position correction was used.
Fig. 9
Fig. 9 Reconstructions of object 2. For each probe position, a single measurement was taken. Position correction was used.
Fig. 10
Fig. 10 Error plots of simulated ptychographic reconstructions of object 1. Left: the reconstruction errors as a function of the number iterations for different photon counts which are indicated on the horizontal axis of the plot on the right. The dotted blue curves correspond to the standard PIE algorithm, and the solid red curves correspond to the proposed algorithm. Right: the reconstruction errors after 1000 iterations for different photon counts.
Fig. 11
Fig. 11 Plots showing the reconstruction errors for the proposed method for different levels of Poisson noise when different numbers of PIE iterations are applied after the intensity constraint is updated.
Fig. 12
Fig. 12 Simulation results for ptychography with Gaussian noise.
Fig. 13
Fig. 13 Figures showing the amplitude and phase of the object, as well as the probe positions that were used to simulate the Fourier ptychography dataset.
Fig. 14
Fig. 14 Simulation results for Fourier ptychography.
Fig. 15
Fig. 15 Error plots of simulated through-focus reconstructions of object 1. Left: the reconstruction errors as a function of the number iterations for different photon counts which are indicated on the horizontal axis of the plot on the right. The dotted blue curves correspond to the standard sequential Gerchberg-Saxton algorithm, and the solid red curves correspond to the proposed algorithm. Right: the reconstruction errors after 500 iterations for different photon counts.

Equations (19)

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

m X ( u ) = | { O ( x ) P ( x X ) } ( u ) | 2 ,
z X ( u ) = | { O est ( x ) P ( x X ) } ( u ) | 2 .
P ( y | m ) = m y e m y ! .
P tot [ m X ( u ) ] = X , u P ( y X ( u ) | m X ( u ) ) ,
L [ O est ( x ) ] = log P tot [ z X ( u ) ] = X , u z X ( u ) y X ( u ) log z X ( u ) + log y X ( u ) ! .
O est ( x ) : = O est ( x ) μ d L d O est ( x ) * .
z y log z y y log y + 2 ( z y ) 2 .
L [ O est ( x ) ] = X , u ( z X ( u ) y X ( u ) ) 2 .
L [ O est ( x ) ] = X , u ( z X ( u ) y X ( u ) ) 2 .
P ( m | y ) = P ( y | m ) P ( m ) P ( y ) .
P ( m | y ) = e T y ( m 2 ) / 2 2 π .
L [ O est ( x ) ] = X , u T y ( z X ( u ) ) 2 .
T y ( m ) 2 = 2 ( log 2 π + log P ( m | y ) ) = 2 ( log 2 π + log P ( y | m ) + log ( P ( m ) log P ( y ) ) .
L [ O est ( x ) ] = X , u log P ( y X ( u ) | z X ( u ) ) ,
L X [ O est ( x ) ] = u ( z X ( u ) m X ( u ) ) 2 .
m X , est , k + 1 ( u ) = μ z X , k ( u ) + ( 1 μ ) m X , est , k ( u ) .
E [ O est ( x ) ] = x | c O est ( x ) O ( x ) | 2 x | O ( x ) | 2 ,
c * = x O ( x ) * O est ( x ) x | O est ( x ) | 2 .
L A [ O est ( x ) ] = u ( z A ( u ) m A ( u ) ) 2 ,

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