Abstract

Coherent diffraction imaging (CDI) for visualizing objects at atomic resolution has been realized as a promising tool for imaging single molecules. Drawbacks of CDI are associated with the difficulty of the numerical phase retrieval from experimental diffraction patterns; a fact which stimulated search for better numerical methods and alternative experimental techniques. Common phase retrieval methods are based on iterative procedures which propagate the complex-valued wave between object and detector plane. Constraints in both, the object and the detector plane are applied. While the constraint in the detector plane employed in most phase retrieval methods requires the amplitude of the complex wave to be equal to the squared root of the measured intensity, we propose a novel Fourier-domain constraint, based on an analogy to holography. Our method allows achieving a low-resolution reconstruction already in the first step followed by a high-resolution reconstruction after further steps. In comparison to conventional schemes this Fourier-domain constraint results in a fast and reliable convergence of the iterative reconstruction process.

© 2011 OSA

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    [CrossRef]
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2011

E. Steinwand, J.-N. Longchamp, and H.-W. Fink, “Coherent low-energy electron diffraction on individual nanometer sized objects,” Ultramicroscopy 111(4), 282–284 (2011).
[CrossRef] [PubMed]

2010

O. Kamimura, T. Dobashi, K. Kawahara, T. Abe, and K. Gohara, “10-kV diffractive imaging using newly developed electron diffraction microscope,” Ultramicroscopy 110(2), 130–133 (2010).
[CrossRef] [PubMed]

B. W. J. McNeil and N. R. Thompson, “X-ray free-electron lasers,” Nature Photon. 4(12), 814–821 (2010).
[CrossRef]

H. N. Chapman and K. A. Nugent, “Coherent lensless X-ray imaging,” Nature Photon. 4(12), 833–839 (2010).
[CrossRef]

R. A. Dilanian, G. J. Williams, L. W. Whitehead, D. J. Vine, A. G. Peele, E. Balaur, I. McNulty, H. M. Quiney, and K. A. Nugent, “Coherent diffractive imaging: a new statistically regularized amplitude constraint,” New J. Phys. 12(9), 093042 (2010).
[CrossRef]

F. C. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82(12), 121104 (2010).
[CrossRef]

2009

D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. de Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A 80(6), 063823 (2009).
[CrossRef]

W. J. Huang, J. M. Zuo, B. Jiang, K. W. Kwon, and M. Shim, “Sub-angstrom-resolution diffractive imaging of single nanocrystals,” Nature Phys. 5(2), 129–133 (2009).
[CrossRef]

2008

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. W. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nature Photon. 2(9), 560–563 (2008).
[CrossRef]

2007

P. Thibault and I. C. Rankenburg, “Optical diffraction microscopy in a teaching laboratory,” Am. J. Phys. 75(9), 827–832 (2007).
[CrossRef]

2006

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97(2), 025506 (2006).
[CrossRef] [PubMed]

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, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef] [PubMed]

2004

G. Oszlányi and A. Süto, “Ab initio structure solution by charge flipping,” Acta Crystallogr. A 60(2), 134–141 (2004).
[CrossRef] [PubMed]

2003

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68(14), 140101 (2003).
[CrossRef]

M. Valle, A. Zavialov, W. Li, S. M. Stagg, J. Sengupta, R. C. Nielsen, P. Nissen, S. C. Harvey, M. Ehrenberg, and J. Frank, “Incorporation of aminoacyl-tRNA into the ribosome as seen by cryo-electron microscopy,” Nat. Struct. Mol. Biol. 10(11), 899–906 (2003).
[CrossRef] [PubMed]

1998

1987

1982

1972

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

1952

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. 5(6), 843–843 (1952).
[CrossRef]

Abbey, B.

D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. de Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A 80(6), 063823 (2009).
[CrossRef]

Abe, T.

O. Kamimura, T. Dobashi, K. Kawahara, T. Abe, and K. Gohara, “10-kV diffractive imaging using newly developed electron diffraction microscope,” Ultramicroscopy 110(2), 130–133 (2010).
[CrossRef] [PubMed]

Bajt, S.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. W. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nature Photon. 2(9), 560–563 (2008).
[CrossRef]

Balaur, E.

R. A. Dilanian, G. J. Williams, L. W. Whitehead, D. J. Vine, A. G. Peele, E. Balaur, I. McNulty, H. M. Quiney, and K. A. Nugent, “Coherent diffractive imaging: a new statistically regularized amplitude constraint,” New J. Phys. 12(9), 093042 (2010).
[CrossRef]

Barty, A.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. W. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nature Photon. 2(9), 560–563 (2008).
[CrossRef]

Beetz, T.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef] [PubMed]

Bogan, M. J.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. W. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nature Photon. 2(9), 560–563 (2008).
[CrossRef]

Boutet, S.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. W. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nature Photon. 2(9), 560–563 (2008).
[CrossRef]

Chapman, H. N.

H. N. Chapman and K. A. Nugent, “Coherent lensless X-ray imaging,” Nature Photon. 4(12), 833–839 (2010).
[CrossRef]

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. W. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nature Photon. 2(9), 560–563 (2008).
[CrossRef]

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68(14), 140101 (2003).
[CrossRef]

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15(6), 1662–1669 (1998).
[CrossRef]

Clark, J. N.

D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. de Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A 80(6), 063823 (2009).
[CrossRef]

Cui, C. W.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. W. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nature Photon. 2(9), 560–563 (2008).
[CrossRef]

de Jonge, M. D.

D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. de Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A 80(6), 063823 (2009).
[CrossRef]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97(2), 025506 (2006).
[CrossRef] [PubMed]

Dhal, B. B.

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97(2), 025506 (2006).
[CrossRef] [PubMed]

Dilanian, R. A.

R. A. Dilanian, G. J. Williams, L. W. Whitehead, D. J. Vine, A. G. Peele, E. Balaur, I. McNulty, H. M. Quiney, and K. A. Nugent, “Coherent diffractive imaging: a new statistically regularized amplitude constraint,” New J. Phys. 12(9), 093042 (2010).
[CrossRef]

Dobashi, T.

O. Kamimura, T. Dobashi, K. Kawahara, T. Abe, and K. Gohara, “10-kV diffractive imaging using newly developed electron diffraction microscope,” Ultramicroscopy 110(2), 130–133 (2010).
[CrossRef] [PubMed]

Ehrenberg, M.

M. Valle, A. Zavialov, W. Li, S. M. Stagg, J. Sengupta, R. C. Nielsen, P. Nissen, S. C. Harvey, M. Ehrenberg, and J. Frank, “Incorporation of aminoacyl-tRNA into the ribosome as seen by cryo-electron microscopy,” Nat. Struct. Mol. Biol. 10(11), 899–906 (2003).
[CrossRef] [PubMed]

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, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef] [PubMed]

Fienup, J. R.

Fink, H.-W.

E. Steinwand, J.-N. Longchamp, and H.-W. Fink, “Coherent low-energy electron diffraction on individual nanometer sized objects,” Ultramicroscopy 111(4), 282–284 (2011).
[CrossRef] [PubMed]

Frank, J.

M. Valle, A. Zavialov, W. Li, S. M. Stagg, J. Sengupta, R. C. Nielsen, P. Nissen, S. C. Harvey, M. Ehrenberg, and J. Frank, “Incorporation of aminoacyl-tRNA into the ribosome as seen by cryo-electron microscopy,” Nat. Struct. Mol. Biol. 10(11), 899–906 (2003).
[CrossRef] [PubMed]

Frank, M.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. W. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nature Photon. 2(9), 560–563 (2008).
[CrossRef]

Gerchberg, R. W.

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

Gohara, K.

O. Kamimura, T. Dobashi, K. Kawahara, T. Abe, and K. Gohara, “10-kV diffractive imaging using newly developed electron diffraction microscope,” Ultramicroscopy 110(2), 130–133 (2010).
[CrossRef] [PubMed]

Hajdu, J.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. W. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nature Photon. 2(9), 560–563 (2008).
[CrossRef]

Harvey, S. C.

M. Valle, A. Zavialov, W. Li, S. M. Stagg, J. Sengupta, R. C. Nielsen, P. Nissen, S. C. Harvey, M. Ehrenberg, and J. Frank, “Incorporation of aminoacyl-tRNA into the ribosome as seen by cryo-electron microscopy,” Nat. Struct. Mol. Biol. 10(11), 899–906 (2003).
[CrossRef] [PubMed]

Hau-Riege, S. P.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. W. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nature Photon. 2(9), 560–563 (2008).
[CrossRef]

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68(14), 140101 (2003).
[CrossRef]

He, H.

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68(14), 140101 (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, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef] [PubMed]

Howells, M. R.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. W. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nature Photon. 2(9), 560–563 (2008).
[CrossRef]

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68(14), 140101 (2003).
[CrossRef]

Huang, W. J.

W. J. Huang, J. M. Zuo, B. Jiang, K. W. Kwon, and M. Shim, “Sub-angstrom-resolution diffractive imaging of single nanocrystals,” Nature Phys. 5(2), 129–133 (2009).
[CrossRef]

Jacobsen, C.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef] [PubMed]

Jiang, B.

W. J. Huang, J. M. Zuo, B. Jiang, K. W. Kwon, and M. Shim, “Sub-angstrom-resolution diffractive imaging of single nanocrystals,” Nature Phys. 5(2), 129–133 (2009).
[CrossRef]

Kamimura, O.

O. Kamimura, T. Dobashi, K. Kawahara, T. Abe, and K. Gohara, “10-kV diffractive imaging using newly developed electron diffraction microscope,” Ultramicroscopy 110(2), 130–133 (2010).
[CrossRef] [PubMed]

Kawahara, K.

O. Kamimura, T. Dobashi, K. Kawahara, T. Abe, and K. Gohara, “10-kV diffractive imaging using newly developed electron diffraction microscope,” Ultramicroscopy 110(2), 130–133 (2010).
[CrossRef] [PubMed]

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, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef] [PubMed]

Kwon, K. W.

W. J. Huang, J. M. Zuo, B. Jiang, K. W. Kwon, and M. Shim, “Sub-angstrom-resolution diffractive imaging of single nanocrystals,” Nature Phys. 5(2), 129–133 (2009).
[CrossRef]

Lee, J. Y.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. W. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nature Photon. 2(9), 560–563 (2008).
[CrossRef]

Li, W.

M. Valle, A. Zavialov, W. Li, S. M. Stagg, J. Sengupta, R. C. Nielsen, P. Nissen, S. C. Harvey, M. Ehrenberg, and J. Frank, “Incorporation of aminoacyl-tRNA into the ribosome as seen by cryo-electron microscopy,” Nat. Struct. Mol. Biol. 10(11), 899–906 (2003).
[CrossRef] [PubMed]

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, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef] [PubMed]

Longchamp, J.-N.

E. Steinwand, J.-N. Longchamp, and H.-W. Fink, “Coherent low-energy electron diffraction on individual nanometer sized objects,” Ultramicroscopy 111(4), 282–284 (2011).
[CrossRef] [PubMed]

Marchesini, S.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. W. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nature Photon. 2(9), 560–563 (2008).
[CrossRef]

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68(14), 140101 (2003).
[CrossRef]

McNeil, B. W. J.

B. W. J. McNeil and N. R. Thompson, “X-ray free-electron lasers,” Nature Photon. 4(12), 814–821 (2010).
[CrossRef]

McNulty, I.

R. A. Dilanian, G. J. Williams, L. W. Whitehead, D. J. Vine, A. G. Peele, E. Balaur, I. McNulty, H. M. Quiney, and K. A. Nugent, “Coherent diffractive imaging: a new statistically regularized amplitude constraint,” New J. Phys. 12(9), 093042 (2010).
[CrossRef]

D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. de Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A 80(6), 063823 (2009).
[CrossRef]

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, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef] [PubMed]

Miao, J.

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, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef] [PubMed]

Nielsen, R. C.

M. Valle, A. Zavialov, W. Li, S. M. Stagg, J. Sengupta, R. C. Nielsen, P. Nissen, S. C. Harvey, M. Ehrenberg, and J. Frank, “Incorporation of aminoacyl-tRNA into the ribosome as seen by cryo-electron microscopy,” Nat. Struct. Mol. Biol. 10(11), 899–906 (2003).
[CrossRef] [PubMed]

Nissen, P.

M. Valle, A. Zavialov, W. Li, S. M. Stagg, J. Sengupta, R. C. Nielsen, P. Nissen, S. C. Harvey, M. Ehrenberg, and J. Frank, “Incorporation of aminoacyl-tRNA into the ribosome as seen by cryo-electron microscopy,” Nat. Struct. Mol. Biol. 10(11), 899–906 (2003).
[CrossRef] [PubMed]

Noy, A.

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68(14), 140101 (2003).
[CrossRef]

Nugent, K. A.

R. A. Dilanian, G. J. Williams, L. W. Whitehead, D. J. Vine, A. G. Peele, E. Balaur, I. McNulty, H. M. Quiney, and K. A. Nugent, “Coherent diffractive imaging: a new statistically regularized amplitude constraint,” New J. Phys. 12(9), 093042 (2010).
[CrossRef]

H. N. Chapman and K. A. Nugent, “Coherent lensless X-ray imaging,” Nature Photon. 4(12), 833–839 (2010).
[CrossRef]

D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. de Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A 80(6), 063823 (2009).
[CrossRef]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97(2), 025506 (2006).
[CrossRef] [PubMed]

Oszlányi, G.

G. Oszlányi and A. Süto, “Ab initio structure solution by charge flipping,” Acta Crystallogr. A 60(2), 134–141 (2004).
[CrossRef] [PubMed]

Paterson, D.

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97(2), 025506 (2006).
[CrossRef] [PubMed]

Peele, A. G.

R. A. Dilanian, G. J. Williams, L. W. Whitehead, D. J. Vine, A. G. Peele, E. Balaur, I. McNulty, H. M. Quiney, and K. A. Nugent, “Coherent diffractive imaging: a new statistically regularized amplitude constraint,” New J. Phys. 12(9), 093042 (2010).
[CrossRef]

D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. de Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A 80(6), 063823 (2009).
[CrossRef]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97(2), 025506 (2006).
[CrossRef] [PubMed]

Pfeifer, M. A.

D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. de Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A 80(6), 063823 (2009).
[CrossRef]

Quiney, H. M.

R. A. Dilanian, G. J. Williams, L. W. Whitehead, D. J. Vine, A. G. Peele, E. Balaur, I. McNulty, H. M. Quiney, and K. A. Nugent, “Coherent diffractive imaging: a new statistically regularized amplitude constraint,” New J. Phys. 12(9), 093042 (2010).
[CrossRef]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97(2), 025506 (2006).
[CrossRef] [PubMed]

Rankenburg, I. C.

P. Thibault and I. C. Rankenburg, “Optical diffraction microscopy in a teaching laboratory,” Am. J. Phys. 75(9), 827–832 (2007).
[CrossRef]

Rodenburg, J. M.

F. C. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82(12), 121104 (2010).
[CrossRef]

Sakdinawat, A. E.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. W. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nature Photon. 2(9), 560–563 (2008).
[CrossRef]

Saxton, W. O.

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

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, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef] [PubMed]

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15(6), 1662–1669 (1998).
[CrossRef]

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. 5(6), 843–843 (1952).
[CrossRef]

Seibert, M. M.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. W. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nature Photon. 2(9), 560–563 (2008).
[CrossRef]

Sengupta, J.

M. Valle, A. Zavialov, W. Li, S. M. Stagg, J. Sengupta, R. C. Nielsen, P. Nissen, S. C. Harvey, M. Ehrenberg, and J. Frank, “Incorporation of aminoacyl-tRNA into the ribosome as seen by cryo-electron microscopy,” Nat. Struct. Mol. Biol. 10(11), 899–906 (2003).
[CrossRef] [PubMed]

Shaevitz, J. W.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. W. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nature Photon. 2(9), 560–563 (2008).
[CrossRef]

Shapiro, 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, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef] [PubMed]

Shapiro, D. A.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. W. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nature Photon. 2(9), 560–563 (2008).
[CrossRef]

Shim, M.

W. J. Huang, J. M. Zuo, B. Jiang, K. W. Kwon, and M. Shim, “Sub-angstrom-resolution diffractive imaging of single nanocrystals,” Nature Phys. 5(2), 129–133 (2009).
[CrossRef]

Spence, J. C. H.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. W. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nature Photon. 2(9), 560–563 (2008).
[CrossRef]

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68(14), 140101 (2003).
[CrossRef]

Stagg, S. M.

M. Valle, A. Zavialov, W. Li, S. M. Stagg, J. Sengupta, R. C. Nielsen, P. Nissen, S. C. Harvey, M. Ehrenberg, and J. Frank, “Incorporation of aminoacyl-tRNA into the ribosome as seen by cryo-electron microscopy,” Nat. Struct. Mol. Biol. 10(11), 899–906 (2003).
[CrossRef] [PubMed]

Steinwand, E.

E. Steinwand, J.-N. Longchamp, and H.-W. Fink, “Coherent low-energy electron diffraction on individual nanometer sized objects,” Ultramicroscopy 111(4), 282–284 (2011).
[CrossRef] [PubMed]

Süto, A.

G. Oszlányi and A. Süto, “Ab initio structure solution by charge flipping,” Acta Crystallogr. A 60(2), 134–141 (2004).
[CrossRef] [PubMed]

Szoke, A.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. W. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nature Photon. 2(9), 560–563 (2008).
[CrossRef]

Thibault, P.

P. Thibault and I. C. Rankenburg, “Optical diffraction microscopy in a teaching laboratory,” Am. J. Phys. 75(9), 827–832 (2007).
[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, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef] [PubMed]

Thompson, N. R.

B. W. J. McNeil and N. R. Thompson, “X-ray free-electron lasers,” Nature Photon. 4(12), 814–821 (2010).
[CrossRef]

Tran, C. Q.

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97(2), 025506 (2006).
[CrossRef] [PubMed]

Valle, M.

M. Valle, A. Zavialov, W. Li, S. M. Stagg, J. Sengupta, R. C. Nielsen, P. Nissen, S. C. Harvey, M. Ehrenberg, and J. Frank, “Incorporation of aminoacyl-tRNA into the ribosome as seen by cryo-electron microscopy,” Nat. Struct. Mol. Biol. 10(11), 899–906 (2003).
[CrossRef] [PubMed]

Vine, D. J.

R. A. Dilanian, G. J. Williams, L. W. Whitehead, D. J. Vine, A. G. Peele, E. Balaur, I. McNulty, H. M. Quiney, and K. A. Nugent, “Coherent diffractive imaging: a new statistically regularized amplitude constraint,” New J. Phys. 12(9), 093042 (2010).
[CrossRef]

D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. de Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A 80(6), 063823 (2009).
[CrossRef]

Weierstall, U.

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68(14), 140101 (2003).
[CrossRef]

Whitehead, L. W.

R. A. Dilanian, G. J. Williams, L. W. Whitehead, D. J. Vine, A. G. Peele, E. Balaur, I. McNulty, H. M. Quiney, and K. A. Nugent, “Coherent diffractive imaging: a new statistically regularized amplitude constraint,” New J. Phys. 12(9), 093042 (2010).
[CrossRef]

Williams, G. J.

R. A. Dilanian, G. J. Williams, L. W. Whitehead, D. J. Vine, A. G. Peele, E. Balaur, I. McNulty, H. M. Quiney, and K. A. Nugent, “Coherent diffractive imaging: a new statistically regularized amplitude constraint,” New J. Phys. 12(9), 093042 (2010).
[CrossRef]

D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. de Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A 80(6), 063823 (2009).
[CrossRef]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97(2), 025506 (2006).
[CrossRef] [PubMed]

Zavialov, A.

M. Valle, A. Zavialov, W. Li, S. M. Stagg, J. Sengupta, R. C. Nielsen, P. Nissen, S. C. Harvey, M. Ehrenberg, and J. Frank, “Incorporation of aminoacyl-tRNA into the ribosome as seen by cryo-electron microscopy,” Nat. Struct. Mol. Biol. 10(11), 899–906 (2003).
[CrossRef] [PubMed]

Zhang, F. C.

F. C. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82(12), 121104 (2010).
[CrossRef]

Zuo, J. M.

W. J. Huang, J. M. Zuo, B. Jiang, K. W. Kwon, and M. Shim, “Sub-angstrom-resolution diffractive imaging of single nanocrystals,” Nature Phys. 5(2), 129–133 (2009).
[CrossRef]

Acta Crystallogr.

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. 5(6), 843–843 (1952).
[CrossRef]

Acta Crystallogr. A

G. Oszlányi and A. Süto, “Ab initio structure solution by charge flipping,” Acta Crystallogr. A 60(2), 134–141 (2004).
[CrossRef] [PubMed]

Am. J. Phys.

P. Thibault and I. C. Rankenburg, “Optical diffraction microscopy in a teaching laboratory,” Am. J. Phys. 75(9), 827–832 (2007).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

Nat. Struct. Mol. Biol.

M. Valle, A. Zavialov, W. Li, S. M. Stagg, J. Sengupta, R. C. Nielsen, P. Nissen, S. C. Harvey, M. Ehrenberg, and J. Frank, “Incorporation of aminoacyl-tRNA into the ribosome as seen by cryo-electron microscopy,” Nat. Struct. Mol. Biol. 10(11), 899–906 (2003).
[CrossRef] [PubMed]

Nature Photon.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. W. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nature Photon. 2(9), 560–563 (2008).
[CrossRef]

B. W. J. McNeil and N. R. Thompson, “X-ray free-electron lasers,” Nature Photon. 4(12), 814–821 (2010).
[CrossRef]

H. N. Chapman and K. A. Nugent, “Coherent lensless X-ray imaging,” Nature Photon. 4(12), 833–839 (2010).
[CrossRef]

Nature Phys.

W. J. Huang, J. M. Zuo, B. Jiang, K. W. Kwon, and M. Shim, “Sub-angstrom-resolution diffractive imaging of single nanocrystals,” Nature Phys. 5(2), 129–133 (2009).
[CrossRef]

New J. Phys.

R. A. Dilanian, G. J. Williams, L. W. Whitehead, D. J. Vine, A. G. Peele, E. Balaur, I. McNulty, H. M. Quiney, and K. A. Nugent, “Coherent diffractive imaging: a new statistically regularized amplitude constraint,” New J. Phys. 12(9), 093042 (2010).
[CrossRef]

Optik (Stuttg.)

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

Phys. Rev. A

D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. de Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A 80(6), 063823 (2009).
[CrossRef]

Phys. Rev. B

F. C. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82(12), 121104 (2010).
[CrossRef]

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68(14), 140101 (2003).
[CrossRef]

Phys. Rev. Lett.

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97(2), 025506 (2006).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef] [PubMed]

Ultramicroscopy

O. Kamimura, T. Dobashi, K. Kawahara, T. Abe, and K. Gohara, “10-kV diffractive imaging using newly developed electron diffraction microscope,” Ultramicroscopy 110(2), 130–133 (2010).
[CrossRef] [PubMed]

E. Steinwand, J.-N. Longchamp, and H.-W. Fink, “Coherent low-energy electron diffraction on individual nanometer sized objects,” Ultramicroscopy 111(4), 282–284 (2011).
[CrossRef] [PubMed]

Supplementary Material (3)

» Media 1: AVI (51727 KB)     
» Media 2: AVI (84101 KB)     
» Media 3: AVI (36470 KB)     

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Figures (7)

Fig. 1
Fig. 1

Schematic representation of the iterative recovery of an object from its coherent diffraction pattern. The violet color highlights the Fourier domain while the blue color highlights the object domain. The red lines emphasize the filter components. The forward Fourier transform of the updated object distribution results in the complex-valued U i' which is used to build the Fourier-domain filter L i. The product of L i and the measured intensity I 0 provides U i + 1, the input for the next iteration.

Fig. 2
Fig. 2

Two-step recovery of the letter β from its simulated diffraction pattern (Media 1). (a) Inverted amplitude of the transmission function of the test object. (b) Simulated diffraction pattern shown in logarithmic intensity scale. (c) Inverted amplitude of the low-resolution reconstruction of the object obtained after the first step consisting of 90 iterations with μ1 = 0.001 and ε1 = 1. (d) Inverted amplitude of the object after the second step using additional 30 iterations with μ2 = 1 and ε2 = 1. (e) Error as a function of iteration number.

Fig. 3
Fig. 3

Amplitude distributions of the L-filter for different values of the parameter μ. (a) Amplitude of the simulated diffraction pattern of “β” and its intensity profile along the middle horizontal line (the maximum of the intensity is cropped). (b)-(f) Left column: amplitude distributions of the L-filter. Right column: intensity profiles of the L-filter along the middle horizontal line.

Fig. 4
Fig. 4

Two-step recovery of ribosome from its simulated diffraction pattern (Media 2). (a) Electron density of 70S ribosome. (b) Simulated diffraction pattern shown in logarithmic intensity scale. (c) Amplitude of the low-resolution reconstruction of the object obtained after the first step consisting of 105 iterations with μ1 = 0.0001 and ε1 = 10. (d) Amplitude of the object after the second step using additional 101 iterations with μ2 = 1 and ε2 = 1000. (e) Error as a function of iteration number.

Fig. 5
Fig. 5

Two-step recovery of the positions of a set of individual scatterers from its simulated diffraction pattern (Media 3). (a) Distribution of the scatterers. (b) Simulated diffraction pattern displayed in a logarithmic intensity scale. (c) Amplitude of the low-resolution reconstruction of the objects obtained after the 1st reconstruction step consisting of 60 iterations with μ1 = 0.01 and ε1 = 1. (d) Amplitude distribution of the objects after the second step using additional 10 iterations with μ2 = 1 and ε2 = 1. (e) Error as a function of iteration number.

Fig. 6
Fig. 6

Recovery of a set of round phase-shifting objects from its simulated diffraction pattern. (a) - (f) Left column: amplitude of the transmission function. Right column: phase of the transmission function. (a) - (b) Original distributions. (c) - (d) Distributions reconstructed by employing our L-filter. (e) - (f) Distributions reconstructed by the shrinkwrap method. (g) Error as a function of iteration number in the reconstruction by the L-filter method. (h) Error as a function of iteration number in the reconstruction by the shrinkwrap method.

Fig. 7
Fig. 7

Recovery of the letter “η” from its experimental diffraction pattern. (a) Scanning electron microscope image of the object. (b) Recorded diffraction pattern displayed in logarithmic intensity scale. (c) Recovered low-resolution image of the object after 200 iterations. (d) Recovered amplitude of the object after 560 iterations, (e) after 600 iterations. (f) Recovered amplitude of the object after 4000 iterations using a different routine that employs a tight mask.

Equations (5)

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U i + 1 = U i ' | U i ' | I 0
U i + 1 = U i ' | U i ' | 2 + ε U 0 U 0 * = L i U 0 U 0 * .
U i + 1 = U i ' | U i ' | 2 + ε μ U 0 U 0 * .
L i ( 1 ) μ 1 U 0 μ 1 | U 0 | 2 + ε ,
Error = | | U 0 | | U i ' | | | U 0 | ,

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