Abstract

Fourier transform holography (FTH) is a noise-resistant imaging technique which allows for nanometer spatial resolution x-ray imaging, where the inclusion of a small reference scattering object provides the otherwise missing phase information. With FTH, one normally requires a considerable distance between the sample and the reference to ensure spatial separation of the reconstruction and its autocorrelation. We demonstrate however that this requirement can be omitted at the small cost of iteratively separating the reconstruction and autocorrelation. In doing so, the photon efficiency of FTH can be increased due to a smaller illumination area, and we show how the presence of the reference prevents the non-uniqueness problems often encountered with plane-wave iterative phase retrieval. The method was tested on a cobalt/platinum multilayer exhibiting out of plane magnetized domains, where the magnetic circular dichroism effect was used to image the magnetic domains at the cobalt L3-edge at 780eV.

© 2012 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]

2012

E. Guehrs, A. M. Stadler, S. Flewett, S. Frommel, J. Geilhufe, B. Pfau, T. Rander, S. Schaffert, G. Buldt, and S. Eisebitt, “Soft x-ray tomoholography,” New J. Phys.14(1), 013022 (2012).
[CrossRef]

S. Flewett, S. Schaffert, J. Mohanty, E. Guehrs, J. Geilhufe, C. M. Gunther, B. Pfau, and S. Eisebitt, “Method for Single-Shot Coherent Diffractive Imaging of Magnetic Domains,” Phys. Rev. Lett.108(22), 223902 (2012).
[CrossRef]

2011

C. M. Gunther, B. Pfau, R. Mitzner, B. Siemer, S. Roling, H. Zacharias, O. Kutz, I. Rudolph, D. Schondelmaier, R. Treusch, and S. Eisebitt, “Sequential femtosecond X-ray imaging,” Nat. Photonics5(2), 99–102 (2011).
[CrossRef]

J. J. Turner, X. J. Huang, O. Krupin, K. A. Seu, D. Parks, S. Kevan, E. Lima, K. Kisslinger, I. McNulty, R. Gambino, S. Mangin, S. Roy, and P. Fischer, “X-ray Diffraction Microscopy of Magnetic Structures,” Phys. Rev. Lett.107(3), 033904 (2011).
[CrossRef] [PubMed]

2010

D. L. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tyliszczak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-Resolution X-ray Lensless Imaging by Differential Holographic Encoding,” Phys. Rev. Lett.105(4), 043901 (2010).
[CrossRef] [PubMed]

J. N. Clark, C. T. Putkunz, M. A. Pfeifer, A. G. Peele, G. J. Williams, B. Chen, K. A. Nugent, C. Hall, W. Fullagar, S. Kim, and I. McNulty, “Use of a complex constraint in coherent diffractive imaging,” Opt. Express18(3), 1981–1993 (2010).
[CrossRef] [PubMed]

B. Pfau, C. M. Günther, R. Könnecke, E. Guehrs, O. Hellwig, W. F. Schlotter, and S. Eisebitt, “Magnetic imaging at linearly polarized x-ray sources,” Opt. Express18(13), 13608–13615 (2010).
[CrossRef] [PubMed]

J. Steinbrener, J. Nelson, X. J. Huang, S. Marchesini, D. Shapiro, J. J. Turner, and C. Jacobsen, “Data preparation and evaluation techniques for x-ray diffraction microscopy,” Opt. Express18(18), 18598–18614 (2010).
[CrossRef] [PubMed]

B. Pfau, C. M. Gunther, S. Schaffert, R. Mitzner, B. Siemer, S. Roling, H. Zacharias, O. Kutz, I. Rudolph, R. Treusch, and S. Eisebitt, “Femtosecond pulse x-ray imaging with a large field of view,” New J. Phys.12(9), 095006 (2010).
[CrossRef]

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von Konig, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[CrossRef]

2009

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(24), 243902 (2009).
[CrossRef] [PubMed]

S. Flewett, H. M. Quiney, C. Q. Tran, and K. A. Nugent, “Extracting coherent modes from partially coherent wavefields,” Opt. Lett.34(14), 2198–2200 (2009).
[CrossRef] [PubMed]

2008

G. J. Williams, E. Hanssen, A. G. Peele, M. A. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. D. de Jonge, S. Vogt, L. Tilley, and K. A. Nugent, “High-resolution X-ray imaging of Plasmodium falciparum-infected red blood cells,” Cytometry A73A(10), 949–957 (2008).
[CrossRef] [PubMed]

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,” Nat. Photonics2(9), 560–563 (2008).
[CrossRef]

D. P. DePonte, U. Weierstall, K. Schmidt, J. Warner, D. Starodub, J. C. H. Spence, and R. B. Doak, “Gas dynamic virtual nozzle for generation of microscopic droplet streams,” J. Phys. D Appl. Phys.41(19), 195505 (2008).
[CrossRef]

L. M. Stadler, C. Gutt, T. Autenrieth, O. Leupold, S. Rehbein, Y. Chushkin, and G. Grübel, “Hard x ray holographic diffraction imaging,” Phys. Rev. Lett.100(24), 245503 (2008).
[CrossRef] [PubMed]

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

W. F. Schlotter, R. Rick, K. Chen, A. Scherz, J. Stohr, J. Luning, S. Eisebitt, C. Gunther, W. Eberhardt, O. Hellwig, and I. McNulty, “Multiple reference Fourier transform holography with soft x rays,” Appl. Phys. Lett.89(16), 163112 (2006).
[CrossRef]

2004

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by X-ray spectro-holography,” Nature432(7019), 885–888 (2004).
[CrossRef] [PubMed]

2003

S. Eisebitt, M. Lorgen, W. Eberhardt, J. Luning, J. Stohr, C. T. Rettner, O. Hellwig, E. E. Fullerton, and G. Denbeaux, “Polarization effects in coherent scattering from magnetic specimen: Implications for x-ray holography, lensless imaging, and correlation spectroscopy,” Phys. Rev. B68(10), 104419 (2003).
[CrossRef]

J. Grabis, A. Nefedov, and H. Zabel, “Diffractometer for soft x-ray resonant magnetic scattering,” Rev. Sci. Instrum.74(9), 4048–4051 (2003).
[CrossRef]

2000

R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, “Potential for biomolecular imaging with femtosecond X-ray pulses,” Nature406(6797), 752–757 (2000).
[CrossRef] [PubMed]

1999

J. W. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature400(6742), 342–344 (1999).
[CrossRef]

1992

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High-resolution imaging by Fourier-Transform X-ray holography,” Science256(5059), 1009–1012 (1992).
[CrossRef] [PubMed]

1991

1982

1965

G. W. Stroke, “Lensless Fourier-Transform Method for Optical Holography,” Appl. Phys. Lett.6(10), 201–202 (1965).
[CrossRef]

Abbey, B.

G. J. Williams, E. Hanssen, A. G. Peele, M. A. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. D. de Jonge, S. Vogt, L. Tilley, and K. A. Nugent, “High-resolution X-ray imaging of Plasmodium falciparum-infected red blood cells,” Cytometry A73A(10), 949–957 (2008).
[CrossRef] [PubMed]

Acremann, Y.

D. L. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tyliszczak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-Resolution X-ray Lensless Imaging by Differential Holographic Encoding,” Phys. Rev. Lett.105(4), 043901 (2010).
[CrossRef] [PubMed]

Anderson, E. H.

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High-resolution imaging by Fourier-Transform X-ray holography,” Science256(5059), 1009–1012 (1992).
[CrossRef] [PubMed]

Autenrieth, T.

L. M. Stadler, C. Gutt, T. Autenrieth, O. Leupold, S. Rehbein, Y. Chushkin, and G. Grübel, “Hard x ray holographic diffraction imaging,” Phys. Rev. Lett.100(24), 245503 (2008).
[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,” Nat. Photonics2(9), 560–563 (2008).
[CrossRef]

Balaur, E.

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(24), 243902 (2009).
[CrossRef] [PubMed]

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,” Nat. Photonics2(9), 560–563 (2008).
[CrossRef]

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,” Nat. Photonics2(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,” Nat. Photonics2(9), 560–563 (2008).
[CrossRef]

Buldt, G.

E. Guehrs, A. M. Stadler, S. Flewett, S. Frommel, J. Geilhufe, B. Pfau, T. Rander, S. Schaffert, G. Buldt, and S. Eisebitt, “Soft x-ray tomoholography,” New J. Phys.14(1), 013022 (2012).
[CrossRef]

Bunk, O.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von Konig, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[CrossRef]

Cadenazzi, G.

G. J. Williams, E. Hanssen, A. G. Peele, M. A. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. D. de Jonge, S. Vogt, L. Tilley, and K. A. Nugent, “High-resolution X-ray imaging of Plasmodium falciparum-infected red blood cells,” Cytometry A73A(10), 949–957 (2008).
[CrossRef] [PubMed]

Chapman, H. N.

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,” Nat. Photonics2(9), 560–563 (2008).
[CrossRef]

Charalambous, P.

J. W. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature400(6742), 342–344 (1999).
[CrossRef]

Chen, B.

Chen, K.

W. F. Schlotter, R. Rick, K. Chen, A. Scherz, J. Stohr, J. Luning, S. Eisebitt, C. Gunther, W. Eberhardt, O. Hellwig, and I. McNulty, “Multiple reference Fourier transform holography with soft x rays,” Appl. Phys. Lett.89(16), 163112 (2006).
[CrossRef]

Chushkin, Y.

L. M. Stadler, C. Gutt, T. Autenrieth, O. Leupold, S. Rehbein, Y. Chushkin, and G. Grübel, “Hard x ray holographic diffraction imaging,” Phys. Rev. Lett.100(24), 245503 (2008).
[CrossRef] [PubMed]

Clark, J.

G. J. Williams, E. Hanssen, A. G. Peele, M. A. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. D. de Jonge, S. Vogt, L. Tilley, and K. A. Nugent, “High-resolution X-ray imaging of Plasmodium falciparum-infected red blood cells,” Cytometry A73A(10), 949–957 (2008).
[CrossRef] [PubMed]

Clark, J. N.

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,” Nat. Photonics2(9), 560–563 (2008).
[CrossRef]

de Jonge, M. D.

G. J. Williams, E. Hanssen, A. G. Peele, M. A. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. D. de Jonge, S. Vogt, L. Tilley, and K. A. Nugent, “High-resolution X-ray imaging of Plasmodium falciparum-infected red blood cells,” Cytometry A73A(10), 949–957 (2008).
[CrossRef] [PubMed]

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]

Denbeaux, G.

S. Eisebitt, M. Lorgen, W. Eberhardt, J. Luning, J. Stohr, C. T. Rettner, O. Hellwig, E. E. Fullerton, and G. Denbeaux, “Polarization effects in coherent scattering from magnetic specimen: Implications for x-ray holography, lensless imaging, and correlation spectroscopy,” Phys. Rev. B68(10), 104419 (2003).
[CrossRef]

DePonte, D. P.

D. P. DePonte, U. Weierstall, K. Schmidt, J. Warner, D. Starodub, J. C. H. Spence, and R. B. Doak, “Gas dynamic virtual nozzle for generation of microscopic droplet streams,” J. Phys. D Appl. Phys.41(19), 195505 (2008).
[CrossRef]

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]

Dierolf, M.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von Konig, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[CrossRef]

Dilanian, R. A.

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B. Pfau, C. M. Gunther, S. Schaffert, R. Mitzner, B. Siemer, S. Roling, H. Zacharias, O. Kutz, I. Rudolph, R. Treusch, and S. Eisebitt, “Femtosecond pulse x-ray imaging with a large field of view,” New J. Phys.12(9), 095006 (2010).
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D. L. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tyliszczak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-Resolution X-ray Lensless Imaging by Differential Holographic Encoding,” Phys. Rev. Lett.105(4), 043901 (2010).
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C. M. Gunther, B. Pfau, R. Mitzner, B. Siemer, S. Roling, H. Zacharias, O. Kutz, I. Rudolph, D. Schondelmaier, R. Treusch, and S. Eisebitt, “Sequential femtosecond X-ray imaging,” Nat. Photonics5(2), 99–102 (2011).
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J. J. Turner, X. J. Huang, O. Krupin, K. A. Seu, D. Parks, S. Kevan, E. Lima, K. Kisslinger, I. McNulty, R. Gambino, S. Mangin, S. Roy, and P. Fischer, “X-ray Diffraction Microscopy of Magnetic Structures,” Phys. Rev. Lett.107(3), 033904 (2011).
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G. J. Williams, E. Hanssen, A. G. Peele, M. A. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. D. de Jonge, S. Vogt, L. Tilley, and K. A. Nugent, “High-resolution X-ray imaging of Plasmodium falciparum-infected red blood cells,” Cytometry A73A(10), 949–957 (2008).
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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(24), 243902 (2009).
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J. N. Clark, C. T. Putkunz, M. A. Pfeifer, A. G. Peele, G. J. Williams, B. Chen, K. A. Nugent, C. Hall, W. Fullagar, S. Kim, and I. McNulty, “Use of a complex constraint in coherent diffractive imaging,” Opt. Express18(3), 1981–1993 (2010).
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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,” Nat. Photonics2(9), 560–563 (2008).
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Nature

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Figures (2)

Fig. 1
Fig. 1

(a) SEM image of the object aperture and reference aperture. The bright region on the right hand side of the object aperture is a closed reference aperture from a previous measurement. (b) the aperture array used for measuring the coherence. (c) The diffraction pattern from the sample with the small (80nm) reference, and (d) is the diffraction pattern from the sample with the larger (200nm) reference aperture.

Fig. 2
Fig. 2

(a) FTH reconstruction of the object, (b) Fourier transform of the measured diffraction after the distant reference objects have been closed, (c) the iterative reconstruction obtained using the smaller 80nm reference object, (d) the iterative reconstruction of a similar magnetic domain sample but with a larger 200nm reference object.. The object aperture has a diameter of 2µm, and the pixel sizes in panels (a), (c) and (d) is 23 nm.

Equations (3)

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

| FT( O+ΔO ) | 2 =I+ΔI.
ΔI= | FT( ΔO ) | 2 +2{ FT( O )FT( ΔO ) }.
ΔI= | FT( ΔO ) | 2 +2{ FT( O )FT( ΔO ) }+2{ FT( R )FT( ΔO ) }.

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