Abstract

As a newly developed coherent diffraction-imaging (CDI) imaging method, the ptychographical iterative engine not only can bypass the difficulty of having high-quality optics in x-ray microscopy by a numerical reconstruction algorithm, but also has obvious advantages on traditional CDI methods in both converging speeds and view fields. However, like in the other CDI methods, the reconstruction of the image from the intensity data of a weakly diffracting specimen is still difficult because of the low signal to noise ratio. To improve this situation, a modification to the currently used algorithms is suggested to double the presence of high spatial frequencies in the diffraction pattern and accordingly to enhance the contrast and fine details of the reconstructions. The simulation and experimental results are presented, and the results can be extended to other CDI methods also.

© 2012 Optical Society of America

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    [CrossRef]
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2011

M. J. Humphrey, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, Nat. Comms. 3, 730 (2011).
[CrossRef]

2010

Z. Fucai and J. M. Rodenburg, Phys. Rev. B 82, 121104 (2010).
[CrossRef]

2008

J. M. Rodenburg, Adv. Imaging Electron Phys. 150, 87 (2008).
[CrossRef]

2007

J. M Rodenburg, A. Hurst, and A. Cullis, Ultramicroscopy 107, 227 (2007).
[CrossRef]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

2006

2005

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, Proc. Natl. Acad. Sci. USA 102, 15343 (2005).
[CrossRef]

2003

H. He, S. Marchesini, M. Howells, U. Weierstall, G. Hembree, and J. C. H. Spence, Acta Crystallogr. Sect. A 59, 143 (2003).
[CrossRef]

2002

J. Spence, U. Weierstall, and M. Howells, Philos. Trans. 360, 875 (2002).
[CrossRef]

U. Weierstall, Q. Chen, J. Spence, M. Howells, M. Isaacson, and R. Panepucci, Ultramicroscopy 90, 171 (2002).
[CrossRef]

1999

J. Miao, C. Charalambous, J. Kirz, and D. Sayre, Nature 400, 342 (1999).
[CrossRef]

1982

Barty, A.

Beetz, T.

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, J. Opt. Soc. Am. A 23, 1179 (2006).
[CrossRef]

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, Proc. Natl. Acad. Sci. USA 102, 15343 (2005).
[CrossRef]

Bunk, O.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Chapman, H. N.

Charalambous, C.

J. Miao, C. Charalambous, J. Kirz, and D. Sayre, Nature 400, 342 (1999).
[CrossRef]

Chen, Q.

U. Weierstall, Q. Chen, J. Spence, M. Howells, M. Isaacson, and R. Panepucci, Ultramicroscopy 90, 171 (2002).
[CrossRef]

Cui, C.

Cullis, A.

J. M Rodenburg, A. Hurst, and A. Cullis, Ultramicroscopy 107, 227 (2007).
[CrossRef]

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, Phys. Rev. Lett. 98, 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, Phys. Rev. Lett. 98, 034801 (2007).
[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, Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Elser, V.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, Proc. Natl. Acad. Sci. USA 102, 15343 (2005).
[CrossRef]

Fienup, J. R.

Fucai, Z.

Z. Fucai and J. M. Rodenburg, Phys. Rev. B 82, 121104 (2010).
[CrossRef]

Harder, R.

M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, Nature 442, 63 (2006).
[CrossRef]

Hau Riege, S. P.

He, H.

Hembree, G.

H. He, S. Marchesini, M. Howells, U. Weierstall, G. Hembree, and J. C. H. Spence, Acta Crystallogr. Sect. A 59, 143 (2003).
[CrossRef]

Howells, M.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, Proc. Natl. Acad. Sci. USA 102, 15343 (2005).
[CrossRef]

H. He, S. Marchesini, M. Howells, U. Weierstall, G. Hembree, and J. C. H. Spence, Acta Crystallogr. Sect. A 59, 143 (2003).
[CrossRef]

J. Spence, U. Weierstall, and M. Howells, Philos. Trans. 360, 875 (2002).
[CrossRef]

U. Weierstall, Q. Chen, J. Spence, M. Howells, M. Isaacson, and R. Panepucci, Ultramicroscopy 90, 171 (2002).
[CrossRef]

Howells, M. R.

Humphrey, M. J.

M. J. Humphrey, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, Nat. Comms. 3, 730 (2011).
[CrossRef]

Hurst, A.

J. M Rodenburg, A. Hurst, and A. Cullis, Ultramicroscopy 107, 227 (2007).
[CrossRef]

Hurst, A. C.

M. J. Humphrey, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, Nat. Comms. 3, 730 (2011).
[CrossRef]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Isaacson, M.

U. Weierstall, Q. Chen, J. Spence, M. Howells, M. Isaacson, and R. Panepucci, Ultramicroscopy 90, 171 (2002).
[CrossRef]

Jacobsen, C.

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, J. Opt. Soc. Am. A 23, 1179 (2006).
[CrossRef]

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, Proc. Natl. Acad. Sci. USA 102, 15343 (2005).
[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, Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Johnson, I.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Kirz, J.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, Proc. Natl. Acad. Sci. USA 102, 15343 (2005).
[CrossRef]

J. Miao, C. Charalambous, J. Kirz, and D. Sayre, Nature 400, 342 (1999).
[CrossRef]

Kraus, B.

M. J. Humphrey, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, Nat. Comms. 3, 730 (2011).
[CrossRef]

Lima, E.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, Proc. Natl. Acad. Sci. USA 102, 15343 (2005).
[CrossRef]

Maiden, A. M.

M. J. Humphrey, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, Nat. Comms. 3, 730 (2011).
[CrossRef]

Marchesini, S.

Miao, H.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, Proc. Natl. Acad. Sci. USA 102, 15343 (2005).
[CrossRef]

Miao, J.

J. Miao, C. Charalambous, J. Kirz, and D. Sayre, Nature 400, 342 (1999).
[CrossRef]

Neiman, A. M.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, Proc. Natl. Acad. Sci. USA 102, 15343 (2005).
[CrossRef]

Noy, A.

Panepucci, R.

U. Weierstall, Q. Chen, J. Spence, M. Howells, M. Isaacson, and R. Panepucci, Ultramicroscopy 90, 171 (2002).
[CrossRef]

Pfeifer, M. A.

M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, Nature 442, 63 (2006).
[CrossRef]

Pfeiffer, F.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Robinson, I. K.

M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, Nature 442, 63 (2006).
[CrossRef]

Rodenburg, J. M

J. M Rodenburg, A. Hurst, and A. Cullis, Ultramicroscopy 107, 227 (2007).
[CrossRef]

Rodenburg, J. M.

M. J. Humphrey, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, Nat. Comms. 3, 730 (2011).
[CrossRef]

Z. Fucai and J. M. Rodenburg, Phys. Rev. B 82, 121104 (2010).
[CrossRef]

J. M. Rodenburg, Adv. Imaging Electron Phys. 150, 87 (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, Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Rosen, R.

Sayre, D.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, Proc. Natl. Acad. Sci. USA 102, 15343 (2005).
[CrossRef]

J. Miao, C. Charalambous, J. Kirz, and D. Sayre, Nature 400, 342 (1999).
[CrossRef]

Shapiro, D.

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, J. Opt. Soc. Am. A 23, 1179 (2006).
[CrossRef]

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, Proc. Natl. Acad. Sci. USA 102, 15343 (2005).
[CrossRef]

Spence, J.

J. Spence, U. Weierstall, and M. Howells, Philos. Trans. 360, 875 (2002).
[CrossRef]

U. Weierstall, Q. Chen, J. Spence, M. Howells, M. Isaacson, and R. Panepucci, Ultramicroscopy 90, 171 (2002).
[CrossRef]

Spence, J. C. H.

Thibault, P.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, Proc. Natl. Acad. Sci. USA 102, 15343 (2005).
[CrossRef]

Vartanyants, I. A.

M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, Nature 442, 63 (2006).
[CrossRef]

Weierstall, U.

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, J. Opt. Soc. Am. A 23, 1179 (2006).
[CrossRef]

H. He, S. Marchesini, M. Howells, U. Weierstall, G. Hembree, and J. C. H. Spence, Acta Crystallogr. Sect. A 59, 143 (2003).
[CrossRef]

J. Spence, U. Weierstall, and M. Howells, Philos. Trans. 360, 875 (2002).
[CrossRef]

U. Weierstall, Q. Chen, J. Spence, M. Howells, M. Isaacson, and R. Panepucci, Ultramicroscopy 90, 171 (2002).
[CrossRef]

Williams, G. J.

M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, Nature 442, 63 (2006).
[CrossRef]

Acta Crystallogr. Sect. A

H. He, S. Marchesini, M. Howells, U. Weierstall, G. Hembree, and J. C. H. Spence, Acta Crystallogr. Sect. A 59, 143 (2003).
[CrossRef]

Adv. Imaging Electron Phys.

J. M. Rodenburg, Adv. Imaging Electron Phys. 150, 87 (2008).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

Nat. Comms.

M. J. Humphrey, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, Nat. Comms. 3, 730 (2011).
[CrossRef]

Nature

M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, Nature 442, 63 (2006).
[CrossRef]

J. Miao, C. Charalambous, J. Kirz, and D. Sayre, Nature 400, 342 (1999).
[CrossRef]

Philos. Trans.

J. Spence, U. Weierstall, and M. Howells, Philos. Trans. 360, 875 (2002).
[CrossRef]

Phys. Rev. B

Z. Fucai and J. M. Rodenburg, Phys. Rev. B 82, 121104 (2010).
[CrossRef]

Phys. Rev. Lett.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Proc. Natl. Acad. Sci. USA

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, Proc. Natl. Acad. Sci. USA 102, 15343 (2005).
[CrossRef]

Ultramicroscopy

J. M Rodenburg, A. Hurst, and A. Cullis, Ultramicroscopy 107, 227 (2007).
[CrossRef]

U. Weierstall, Q. Chen, J. Spence, M. Howells, M. Isaacson, and R. Panepucci, Ultramicroscopy 90, 171 (2002).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Schematic diagram of the optical setup.

Fig. 2.
Fig. 2.

Vectors A0(k)+Ad(k) and A0(k)+2Ad(k) in the complex plane.

Fig. 3.
Fig. 3.

Numerical simulation results. (a) The phase transmission of the object; (b) the diffraction pattern; (c) the reconstructed image with common PIE method; (d) the reconstructed image with our suggested method.

Fig. 4.
Fig. 4.

Experimental results. (a)–(c) Phase and (d)–(f) corresponding intensity imagereconstructions with, I(k), I(k) and (I(k))3, respectively.

Equations (2)

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

I(k)=|A0(k)+Ad(k)|2=|A0(k)|2+2|A0(k)||Ad(k)|cos(φ(k))+|Ad(k)|2.
I2(k)=|A0(k)|2|A0(k)+2Ad(k)|2.

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