Abstract

Ptychography is a scanning coherent diffractive imaging (CDI) technique that relies upon a high level of stability of the illumination during the course of an experiment. This is particularly an issue for coherent short wavelength sources, where the beam intensity is usually tightly focused on the sample in order to maximize the photon flux density on the illuminated region of the sample and thus a small change in the beam position results in a significant change in illumination of the sample. We present an improved ptychographic method that allows for limited stability of the illumination wavefront and thus significantly improve the reconstruction quality without additional prior knowledge. We have tested our reconstruction method in a proof of concept experiment, where the beam instability of a visible light source was emulated using a piezo driven mirror, and also in a short wavelength microscopy CDI setup using a high harmonic generation source in the extreme ultraviolet range. Our work shows a natural extension of the ptychography method that paves the way to use ptychographic imaging with any limited pointing stability coherent source such as free electron or soft X-ray lasers and improve reconstruction quality of long duration synchrotron experiments.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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  1. J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
    [Crossref]
  2. H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
    [Crossref] [PubMed]
  3. J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004).
    [Crossref]
  4. J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imag. Elect. Phys. 150, 87–184 (2008).
    [Crossref]
  5. P. Thibault and V. Elser, “X-ray diffraction microscopy,” Condens. Matt. Phys. 1, 237–255, (2010).
  6. J. N. Clark and A. G. Peele, “Simultaneous sample and spatial coherence characterisation using diffractive imaging,” Appl Phys, Lett. 99, 154103 (2011).
    [Crossref]
  7. G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, “Coherent diffractive imaging and partial coherence,” Phys. Rev. B 75, 104102 (2007).
    [Crossref]
  8. B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, and G. J. Williams, “Lensless imaging using broadband x-ray sources,” Nature Photonics 5, 420–424 (2011).
    [Crossref]
  9. P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
    [Crossref] [PubMed]
  10. L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
    [Crossref]
  11. D. H. Parks, X. Shi, and S. D. Kevan, “Partially coherent x-ray diffractive imaging of complex objects,” Phys. Rev. A 89, 063824 (2014).
    [Crossref]
  12. S. Marchesini, A. Schirotzek, C. Yang, H.-t. Wu, and F. Maia, “Augmented projections for ptychographic imaging,” Inverse Problems 29, 115009 (2013).
    [Crossref]
  13. D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
    [Crossref] [PubMed]
  14. A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
    [Crossref] [PubMed]
  15. N. Halko, P. G. Martinsson, Y. Shkolnisky, and M. Tygert, “An algorithm for the principal component analysis of large data sets,” SIAM J. Sci, Comput. 33, 2580–2594 (2011).
    [Crossref]
  16. J. N. Clark, C. T. Putkunz, E. K. Curwood, D. J. Vine, R. Scholten, I. McNulty, K. A. Nugent, and A. G. Peele, “Dynamic sample imaging in coherent diffractive imaging,” Opt. Lett. 36, 1954–1956 (2011).
    [Crossref] [PubMed]
  17. P. Baksh, M. Odstrčil, H. Kim, S. Boden, J.G. Frey, and W.S. Brocklesby, “Wide-field broadband EUV transmission ptychography using a high harmonic source,” Opt. Lett.41, (in press 2016).
  18. M. van Heel and M. Schatz, “Fourier shell correlation threshold criteria,” Journal of structural biology 151, 250–262 (2005).
    [Crossref] [PubMed]
  19. M. Odstrčil, P. Baksh, H. Kim, S. Boden, W. Brocklesby, and J. Frey, “Ultra-broadband ptychography with self-consistent coherence estimation from a high harmonic source,” Proc. SPIE 9589, 958912(2015).
    [Crossref]
  20. 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] [PubMed]
  21. R. A. Dilanian, B. O. Chen, S. Teichmann, L. V. Dao, H. M. Quiney, and K. A. Nugent, “High-harmonic-generation spectrum reconstruction from Young’s double-slits interference pattern using the maximum entropy method,” Opt. Lett. 33, 2341 (2008).
    [Crossref] [PubMed]

2015 (1)

M. Odstrčil, P. Baksh, H. Kim, S. Boden, W. Brocklesby, and J. Frey, “Ultra-broadband ptychography with self-consistent coherence estimation from a high harmonic source,” Proc. SPIE 9589, 958912(2015).
[Crossref]

2014 (2)

D. H. Parks, X. Shi, and S. D. Kevan, “Partially coherent x-ray diffractive imaging of complex objects,” Phys. Rev. A 89, 063824 (2014).
[Crossref]

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

2013 (3)

S. Marchesini, A. Schirotzek, C. Yang, H.-t. Wu, and F. Maia, “Augmented projections for ptychographic imaging,” Inverse Problems 29, 115009 (2013).
[Crossref]

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
[Crossref] [PubMed]

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] [PubMed]

2011 (4)

J. N. Clark, C. T. Putkunz, E. K. Curwood, D. J. Vine, R. Scholten, I. McNulty, K. A. Nugent, and A. G. Peele, “Dynamic sample imaging in coherent diffractive imaging,” Opt. Lett. 36, 1954–1956 (2011).
[Crossref] [PubMed]

N. Halko, P. G. Martinsson, Y. Shkolnisky, and M. Tygert, “An algorithm for the principal component analysis of large data sets,” SIAM J. Sci, Comput. 33, 2580–2594 (2011).
[Crossref]

J. N. Clark and A. G. Peele, “Simultaneous sample and spatial coherence characterisation using diffractive imaging,” Appl Phys, Lett. 99, 154103 (2011).
[Crossref]

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, and G. J. Williams, “Lensless imaging using broadband x-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

2010 (1)

P. Thibault and V. Elser, “X-ray diffraction microscopy,” Condens. Matt. Phys. 1, 237–255, (2010).

2009 (2)

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

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

2008 (2)

2007 (1)

G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, “Coherent diffractive imaging and partial coherence,” Phys. Rev. B 75, 104102 (2007).
[Crossref]

2005 (1)

M. van Heel and M. Schatz, “Fourier shell correlation threshold criteria,” Journal of structural biology 151, 250–262 (2005).
[Crossref] [PubMed]

2004 (2)

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

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

1999 (1)

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[Crossref]

Abbey, B.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, and G. J. Williams, “Lensless imaging using broadband x-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

Baksh, P.

M. Odstrčil, P. Baksh, H. Kim, S. Boden, W. Brocklesby, and J. Frey, “Ultra-broadband ptychography with self-consistent coherence estimation from a high harmonic source,” Proc. SPIE 9589, 958912(2015).
[Crossref]

P. Baksh, M. Odstrčil, H. Kim, S. Boden, J.G. Frey, and W.S. Brocklesby, “Wide-field broadband EUV transmission ptychography using a high harmonic source,” Opt. Lett.41, (in press 2016).

Balaur, E.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, and G. J. Williams, “Lensless imaging using broadband x-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

Batey, D. J.

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

Bean, R.

Berenguer, F.

Boden, S.

M. Odstrčil, P. Baksh, H. Kim, S. Boden, W. Brocklesby, and J. Frey, “Ultra-broadband ptychography with self-consistent coherence estimation from a high harmonic source,” Proc. SPIE 9589, 958912(2015).
[Crossref]

P. Baksh, M. Odstrčil, H. Kim, S. Boden, J.G. Frey, and W.S. Brocklesby, “Wide-field broadband EUV transmission ptychography using a high harmonic source,” Opt. Lett.41, (in press 2016).

Brocklesby, W.

M. Odstrčil, P. Baksh, H. Kim, S. Boden, W. Brocklesby, and J. Frey, “Ultra-broadband ptychography with self-consistent coherence estimation from a high harmonic source,” Proc. SPIE 9589, 958912(2015).
[Crossref]

Brocklesby, W.S.

P. Baksh, M. Odstrčil, H. Kim, S. Boden, J.G. Frey, and W.S. Brocklesby, “Wide-field broadband EUV transmission ptychography using a high harmonic source,” Opt. Lett.41, (in press 2016).

Cadenazzi, G. A.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, and G. J. Williams, “Lensless imaging using broadband x-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

Charalambous, P.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[Crossref]

Chen, B.

Chen, B. O.

Clark, J. N.

J. N. Clark, C. T. Putkunz, E. K. Curwood, D. J. Vine, R. Scholten, I. McNulty, K. A. Nugent, and A. G. Peele, “Dynamic sample imaging in coherent diffractive imaging,” Opt. Lett. 36, 1954–1956 (2011).
[Crossref] [PubMed]

J. N. Clark and A. G. Peele, “Simultaneous sample and spatial coherence characterisation using diffractive imaging,” Appl Phys, Lett. 99, 154103 (2011).
[Crossref]

Claus, D.

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

Curwood, E. K.

Dao, L. V.

Diaz, A.

Dilanian, R. A.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

R. A. Dilanian, B. O. Chen, S. Teichmann, L. V. Dao, H. M. Quiney, and K. A. Nugent, “High-harmonic-generation spectrum reconstruction from Young’s double-slits interference pattern using the maximum entropy method,” Opt. Lett. 33, 2341 (2008).
[Crossref] [PubMed]

Elser, V.

P. Thibault and V. Elser, “X-ray diffraction microscopy,” Condens. Matt. Phys. 1, 237–255, (2010).

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]

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

Flewett, S.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

Frey, J.

M. Odstrčil, P. Baksh, H. Kim, S. Boden, W. Brocklesby, and J. Frey, “Ultra-broadband ptychography with self-consistent coherence estimation from a high harmonic source,” Proc. SPIE 9589, 958912(2015).
[Crossref]

Frey, J.G.

P. Baksh, M. Odstrčil, H. Kim, S. Boden, J.G. Frey, and W.S. Brocklesby, “Wide-field broadband EUV transmission ptychography using a high harmonic source,” Opt. Lett.41, (in press 2016).

Halko, N.

N. Halko, P. G. Martinsson, Y. Shkolnisky, and M. Tygert, “An algorithm for the principal component analysis of large data sets,” SIAM J. Sci, Comput. 33, 2580–2594 (2011).
[Crossref]

Henderson, C. A.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, and G. J. Williams, “Lensless imaging using broadband x-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

Kevan, S. D.

D. H. Parks, X. Shi, and S. D. Kevan, “Partially coherent x-ray diffractive imaging of complex objects,” Phys. Rev. A 89, 063824 (2014).
[Crossref]

Kim, H.

M. Odstrčil, P. Baksh, H. Kim, S. Boden, W. Brocklesby, and J. Frey, “Ultra-broadband ptychography with self-consistent coherence estimation from a high harmonic source,” Proc. SPIE 9589, 958912(2015).
[Crossref]

P. Baksh, M. Odstrčil, H. Kim, S. Boden, J.G. Frey, and W.S. Brocklesby, “Wide-field broadband EUV transmission ptychography using a high harmonic source,” Opt. Lett.41, (in press 2016).

Kirz, J.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[Crossref]

Maia, F.

S. Marchesini, A. Schirotzek, C. Yang, H.-t. Wu, and F. Maia, “Augmented projections for ptychographic imaging,” Inverse Problems 29, 115009 (2013).
[Crossref]

Maiden, A. M.

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

Marchesini, S.

S. Marchesini, A. Schirotzek, C. Yang, H.-t. Wu, and F. Maia, “Augmented projections for ptychographic imaging,” Inverse Problems 29, 115009 (2013).
[Crossref]

Martinsson, P. G.

N. Halko, P. G. Martinsson, Y. Shkolnisky, and M. Tygert, “An algorithm for the principal component analysis of large data sets,” SIAM J. Sci, Comput. 33, 2580–2594 (2011).
[Crossref]

McNulty, I.

J. N. Clark, C. T. Putkunz, E. K. Curwood, D. J. Vine, R. Scholten, I. McNulty, K. A. Nugent, and A. G. Peele, “Dynamic sample imaging in coherent diffractive imaging,” Opt. Lett. 36, 1954–1956 (2011).
[Crossref] [PubMed]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

Menzel, A.

Miao, J.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[Crossref]

Nugent, K. A.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, and G. J. Williams, “Lensless imaging using broadband x-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

J. N. Clark, C. T. Putkunz, E. K. Curwood, D. J. Vine, R. Scholten, I. McNulty, K. A. Nugent, and A. G. Peele, “Dynamic sample imaging in coherent diffractive imaging,” Opt. Lett. 36, 1954–1956 (2011).
[Crossref] [PubMed]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

R. A. Dilanian, B. O. Chen, S. Teichmann, L. V. Dao, H. M. Quiney, and K. A. Nugent, “High-harmonic-generation spectrum reconstruction from Young’s double-slits interference pattern using the maximum entropy method,” Opt. Lett. 33, 2341 (2008).
[Crossref] [PubMed]

G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, “Coherent diffractive imaging and partial coherence,” Phys. Rev. B 75, 104102 (2007).
[Crossref]

Odstrcil, M.

M. Odstrčil, P. Baksh, H. Kim, S. Boden, W. Brocklesby, and J. Frey, “Ultra-broadband ptychography with self-consistent coherence estimation from a high harmonic source,” Proc. SPIE 9589, 958912(2015).
[Crossref]

P. Baksh, M. Odstrčil, H. Kim, S. Boden, J.G. Frey, and W.S. Brocklesby, “Wide-field broadband EUV transmission ptychography using a high harmonic source,” Opt. Lett.41, (in press 2016).

Parks, D. H.

D. H. Parks, X. Shi, and S. D. Kevan, “Partially coherent x-ray diffractive imaging of complex objects,” Phys. Rev. A 89, 063824 (2014).
[Crossref]

Peele, A. G.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, and G. J. Williams, “Lensless imaging using broadband x-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

J. N. Clark and A. G. Peele, “Simultaneous sample and spatial coherence characterisation using diffractive imaging,” Appl Phys, Lett. 99, 154103 (2011).
[Crossref]

J. N. Clark, C. T. Putkunz, E. K. Curwood, D. J. Vine, R. Scholten, I. McNulty, K. A. Nugent, and A. G. Peele, “Dynamic sample imaging in coherent diffractive imaging,” Opt. Lett. 36, 1954–1956 (2011).
[Crossref] [PubMed]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, “Coherent diffractive imaging and partial coherence,” Phys. Rev. B 75, 104102 (2007).
[Crossref]

Peterson, I.

Putkunz, C. T.

J. N. Clark, C. T. Putkunz, E. K. Curwood, D. J. Vine, R. Scholten, I. McNulty, K. A. Nugent, and A. G. Peele, “Dynamic sample imaging in coherent diffractive imaging,” Opt. Lett. 36, 1954–1956 (2011).
[Crossref] [PubMed]

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, and G. J. Williams, “Lensless imaging using broadband x-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

Quiney, H. M.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, and G. J. Williams, “Lensless imaging using broadband x-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

R. A. Dilanian, B. O. Chen, S. Teichmann, L. V. Dao, H. M. Quiney, and K. A. Nugent, “High-harmonic-generation spectrum reconstruction from Young’s double-slits interference pattern using the maximum entropy method,” Opt. Lett. 33, 2341 (2008).
[Crossref] [PubMed]

G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, “Coherent diffractive imaging and partial coherence,” Phys. Rev. B 75, 104102 (2007).
[Crossref]

Robinson, I. K.

Rodenburg, J. M.

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

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] [PubMed]

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

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

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

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

Sayre, D.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[Crossref]

Schatz, M.

M. van Heel and M. Schatz, “Fourier shell correlation threshold criteria,” Journal of structural biology 151, 250–262 (2005).
[Crossref] [PubMed]

Schirotzek, A.

S. Marchesini, A. Schirotzek, C. Yang, H.-t. Wu, and F. Maia, “Augmented projections for ptychographic imaging,” Inverse Problems 29, 115009 (2013).
[Crossref]

Scholten, R.

Shi, X.

D. H. Parks, X. Shi, and S. D. Kevan, “Partially coherent x-ray diffractive imaging of complex objects,” Phys. Rev. A 89, 063824 (2014).
[Crossref]

Shkolnisky, Y.

N. Halko, P. G. Martinsson, Y. Shkolnisky, and M. Tygert, “An algorithm for the principal component analysis of large data sets,” SIAM J. Sci, Comput. 33, 2580–2594 (2011).
[Crossref]

Teichmann, S.

Thibault, P.

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
[Crossref] [PubMed]

P. Thibault and V. Elser, “X-ray diffraction microscopy,” Condens. Matt. Phys. 1, 237–255, (2010).

Tygert, M.

N. Halko, P. G. Martinsson, Y. Shkolnisky, and M. Tygert, “An algorithm for the principal component analysis of large data sets,” SIAM J. Sci, Comput. 33, 2580–2594 (2011).
[Crossref]

van Heel, M.

M. van Heel and M. Schatz, “Fourier shell correlation threshold criteria,” Journal of structural biology 151, 250–262 (2005).
[Crossref] [PubMed]

Vila-Comamala, J.

Vine, D. J.

J. N. Clark, C. T. Putkunz, E. K. Curwood, D. J. Vine, R. Scholten, I. McNulty, K. A. Nugent, and A. G. Peele, “Dynamic sample imaging in coherent diffractive imaging,” Opt. Lett. 36, 1954–1956 (2011).
[Crossref] [PubMed]

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, and G. J. Williams, “Lensless imaging using broadband x-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

Whitehead, L. W.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, and G. J. Williams, “Lensless imaging using broadband x-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

Williams, G. J.

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, and G. J. Williams, “Lensless imaging using broadband x-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, “Coherent diffractive imaging and partial coherence,” Phys. Rev. B 75, 104102 (2007).
[Crossref]

Wu, H.-t.

S. Marchesini, A. Schirotzek, C. Yang, H.-t. Wu, and F. Maia, “Augmented projections for ptychographic imaging,” Inverse Problems 29, 115009 (2013).
[Crossref]

Yang, C.

S. Marchesini, A. Schirotzek, C. Yang, H.-t. Wu, and F. Maia, “Augmented projections for ptychographic imaging,” Inverse Problems 29, 115009 (2013).
[Crossref]

Zhang, F.

Adv. Imag. Elect. Phys. (1)

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

Appl Phys, Lett. (1)

J. N. Clark and A. G. Peele, “Simultaneous sample and spatial coherence characterisation using diffractive imaging,” Appl Phys, Lett. 99, 154103 (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, 4795–4797 (2004).
[Crossref]

Condens. Matt. Phys. (1)

P. Thibault and V. Elser, “X-ray diffraction microscopy,” Condens. Matt. Phys. 1, 237–255, (2010).

Inverse Problems (1)

S. Marchesini, A. Schirotzek, C. Yang, H.-t. Wu, and F. Maia, “Augmented projections for ptychographic imaging,” Inverse Problems 29, 115009 (2013).
[Crossref]

Journal of structural biology (1)

M. van Heel and M. Schatz, “Fourier shell correlation threshold criteria,” Journal of structural biology 151, 250–262 (2005).
[Crossref] [PubMed]

Nature (2)

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
[Crossref] [PubMed]

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[Crossref]

Nature Photonics (1)

B. Abbey, L. W. Whitehead, H. M. Quiney, D. J. Vine, G. A. Cadenazzi, C. A. Henderson, K. A. Nugent, E. Balaur, C. T. Putkunz, A. G. Peele, and G. J. Williams, “Lensless imaging using broadband x-ray sources,” Nature Photonics 5, 420–424 (2011).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (1)

D. H. Parks, X. Shi, and S. D. Kevan, “Partially coherent x-ray diffractive imaging of complex objects,” Phys. Rev. A 89, 063824 (2014).
[Crossref]

Phys. Rev. B (1)

G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, “Coherent diffractive imaging and partial coherence,” Phys. Rev. B 75, 104102 (2007).
[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, 023903 (2004).
[Crossref] [PubMed]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

Proc. SPIE (1)

M. Odstrčil, P. Baksh, H. Kim, S. Boden, W. Brocklesby, and J. Frey, “Ultra-broadband ptychography with self-consistent coherence estimation from a high harmonic source,” Proc. SPIE 9589, 958912(2015).
[Crossref]

SIAM J. Sci, Comput. (1)

N. Halko, P. G. Martinsson, Y. Shkolnisky, and M. Tygert, “An algorithm for the principal component analysis of large data sets,” SIAM J. Sci, Comput. 33, 2580–2594 (2011).
[Crossref]

Ultramicroscopy (2)

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

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

Other (1)

P. Baksh, M. Odstrčil, H. Kim, S. Boden, J.G. Frey, and W.S. Brocklesby, “Wide-field broadband EUV transmission ptychography using a high harmonic source,” Opt. Lett.41, (in press 2016).

Supplementary Material (1)

NameDescription
» Visualization 1: MP4 (2555 KB)      An animation of the reconstructed probe

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Figures (8)

Fig. 1
Fig. 1 The schema a) shows our visible light ptychography setup. The HeNe laser beam is deflected by a motorized mirror M, cropped by a pinhole P and projected on a sample S using lens L. The scattered light is collected by a microscope lens L′ (NA=0.4) and demagnified on to a camera C that is placed near to the Fourier plane. The schema b) shows the HHG setup. The lens L focuses the IR beam on a gas cell G. The generated EUV light is separated from the fundamental beam by an aluminum filter F. The EUV light is partly spectrally filtered by multilayer mirror M, focused on a pinhole P and propagated on the sample S. The diffracted light is collected by an EUV sensitive camera C. More details can be found in Ref. [17].
Fig. 2
Fig. 2 a) Double spiral probe position scanning path used for the HeNe experiment showing all 463 scanning positions. Figure b) shows desired angular beam deflections used to simulate low pointing stability in the HeNe experiment simulating roughly Lorentz distribution of the beam deflections.
Fig. 3
Fig. 3 Reconstructions of graphite particles shown in hue-saturation-value (HSV) complex colorscale. Image a) shows a reconstruction of the dataset with stable illumination using the standard ePIE method. Image (b) shows a reconstruction of the same sample illuminated with an actively disturbed probe, and reconstructed using the OPRP method. Image (c) shows reconstruction after illumination with an actively disturbed probe performed using the standard ePIE algorithm. The reconstruction quality of (b) is comparable to reconstruction (a) even though in image (b) the probe is actively disturbed, while in (a) the probe is stable. Reconstruction (b) shows significant improvement compared to (c), where the standard ePIE method was used on an actively disturbed probe. The last image (d) shows Fourier ring correlation (FRC) between images (a) and (b) compared to two reconstructions of independent datasets with steady illumination (red).
Fig. 4
Fig. 4 The first row shows the reconstructed eigenprobes Ui in HSV complex colorscale and their relative singular values intensity |Si|/∑|Si| in percents. The second row shows complex evolution Vi of each eigenmode Ui during the scan [Fig. 2(a)] in complex HSV scale. This representation was used to demonstrate that the modes distribution is dominated by the illumination modulation [Fig. 2(b)]. Diameter of the illumination probe is roughly 140 μm. Diameter of the illumination probe is roughly 140 µm. (See Fig. 8 in the Appendix).
Fig. 5
Fig. 5 Examples of the illumination probe reconstructions for several different positions. See Visualization 1 for an animation of the reconstructed probe.
Fig. 6
Fig. 6 Ptychography reconstruction of a biological sample. (a) standard ePIE method (b) improved OPRP based on ePIE method. Images (c) and (d) show expanded and contrast enhanced regions of (a) and (b) with details of the neurons and its dendrites. The numbered areas indicate some of the regions where the OPRP method is seen to improve the reconstruction. Details are given in the text.
Fig. 7
Fig. 7 The first row shows the reconstructed eigenprobes Ui of the HHG illumination and their relative amplitudes |Si|/∑|Si| in percents. The second row shows a complex evolution Vi of each eigenmode Ui during the spiral ptychography scan. The diameter of the illumination probe is roughly 11 μm.
Fig. 8
Fig. 8 Reconstruction of all the modes that OPRP method was able to recover for the steady dataset (1th and 2nd row) and the actively disturbed dataset (3rd and 4th rows). The OPRP method was able to recover beam movements and subpixel shifts even for the steady dataset. The beam movements were mostly caused by thermal drifts during the ptychography experiment. If the modes are too weak (e.g. eigenprobes 6 and 7 in the first row), then their relative intensity S i /S is effectively zero.

Equations (6)

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ψ j ( r ) = P ( r ) O ( r + R j ) .
I j ( q ) = | Ψ ( q ) | 2 = | 𝔉 ( P ( r ) O ( r + R j ) ) | 2 ,
Ψ ^ j ( q ) = I j ( q ) | Ψ j ( q ) | Ψ j ( q )
[ U , S , V ] = tsvd ( P , n )
P ^ = U S V * .
P ( j + 1 ) = α P ( j ) + ( 1 α ) U S V * ,

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