Abstract

We propose a tri-arm (or Y-shaped) multipinhole (MP) interferometer for wavefront measurement based on a specially designed tri-arm MP plate. We demonstrate that the complex amplitude of a wavefront sampled by the tri-arm MP plate inserted between the object and the detector plane can be extracted directly from the Fourier transform of a far-field diffraction intensity pattern without the need for any iterative algorithm. A form of coherent diffractive imaging based on a rotatable tri-arm MP plate is also demonstrated, which provides a feasible approach for lensless diffractive imaging in real time

© 2009 Optical Society of America

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2009

2008

F. Ghebremichael, G. P. Andersen, and K. S. Gurley, “Holography-based wavefront sensing,” Appl. Opt. 47, A62-A69 (2008).
[CrossRef]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379-382 (2008).
[CrossRef]

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[CrossRef]

2007

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

M. Ares, S. Royo, and J. Caum, “Shack-Hartmann sensor based on a cylindrical microlens array,” Opt. Lett. 32, 769-771(2007).
[CrossRef]

2005

A. V. Goncharov, J. C. Dainty, and S. Esposito, “Compact multireference wavefront sensor design,” Opt. Lett. 30, 2721-2723(2005).
[CrossRef]

L. Seifert, H. J. Tiziani, and W. Osten, “Wavefront reconstruction with the adaptive Shack-Hartmann sensor,” Opt. Commun. 245, 255-269 (2005).
[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, 15343-15346(2005).

2004

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]

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,” Nature 432, 885-888 (2004).

H. I. Campbell, S. Zhang, A. H. Greenaway, and S. Restaino, “Generalized phase diversity for wave-front sensing,” Opt. Lett. 29, 2707-2709 (2004).
[CrossRef]

2003

V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am. A 20, 40-55 (2003).
[CrossRef]

G. J. Williams, M. A. Pfeifer, I. A. Vartanyants, and I. K. Robinson, “Three-dimensional imaging of microstructure in Au nanocrystals,” Phys. Rev. Lett. 90, 175501 (2003).
[CrossRef]

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a Carbon nanotube from diffraction intensities,” Science 300, 1419-1421(2003).
[CrossRef]

2002

2000

1999

1998

1997

1996

1994

1992

1982

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758-2769 (1982).
[CrossRef]

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829-832 (1982).

1972

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

Acton, D. S.

Andersen, G. P.

Anderson, E. H.

J. Miao, T. Ishikawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Hodgson, “High resolution 3D X-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088303 (2002).
[CrossRef]

Ares, M.

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, 15343-15346(2005).

Bunk, O.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379-382 (2008).
[CrossRef]

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (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, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Burton, D. R.

Campbell, H. I.

Caum, J.

Chapman, H. N.

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).

Chen, C. W.

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, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Dainty, J. C.

David, C.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[CrossRef]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379-382 (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, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Dierolf, M.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[CrossRef]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379-382 (2008).
[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, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Duncan, A. L.

Eberhardt, W.

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,” Nature 432, 885-888 (2004).

Eisebitt, S.

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,” Nature 432, 885-888 (2004).

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, 15343-15346(2005).

V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am. A 20, 40-55 (2003).
[CrossRef]

Esposito, S.

Faulkner, H. M. L.

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]

Fienup, J. R.

Franceschetti, G.

Gao, M.

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a Carbon nanotube from diffraction intensities,” Science 300, 1419-1421(2003).
[CrossRef]

Gdeisat, M. A.

Gerchberg, R. W.

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

Ghebremichael, F.

Ghiglia, D. C.

Goncharov, A. V.

Gonsalves, R. A.

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829-832 (1982).

Gray, J.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[CrossRef]

Greenaway, A. H.

Guo, C. S.

Gurley, K. S.

Gutmann, B.

He, J. L.

Hellwig, O.

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,” Nature 432, 885-888 (2004).

Herráez, M. A.

Hodgson, K. O.

J. Miao, T. Ishikawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Hodgson, “High resolution 3D X-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088303 (2002).
[CrossRef]

J. Miao, T. Ohsuna, O. Terasaki, K. O. Hodgson, and M. A. O'Keefe, “Atomic resolution three-dimensional electron diffraction microscopy,” Phys. Rev. Lett. 89, 155502 (2002).
[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, 15343-15346(2005).

Hurst, A. C.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Ishikawa, T.

J. Miao, T. Ishikawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Hodgson, “High resolution 3D X-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088303 (2002).
[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, 15343-15346(2005).

Jefimovs, K.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (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, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Jitsuno, T.

Johnson, B.

J. Miao, T. Ishikawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Hodgson, “High resolution 3D X-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088303 (2002).
[CrossRef]

Johnson, I.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (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, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Juptner, W.

Jüptner, W.

Kendrick, R. L.

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, 15343-15346(2005).

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).

Lai, B.

J. Miao, T. Ishikawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Hodgson, “High resolution 3D X-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088303 (2002).
[CrossRef]

Lalor, M. J.

Lane, R. G.

Liao, J.

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, 15343-15346(2005).

Lörgen, M.

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,” Nature 432, 885-888 (2004).

Lu, L. L.

Lüning, J.

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,” Nature 432, 885-888 (2004).

Marano, S.

Menzel, A.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379-382 (2008).
[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, 15343-15346(2005).

Miao, J.

J. Miao, T. Ohsuna, O. Terasaki, K. O. Hodgson, and M. A. O'Keefe, “Atomic resolution three-dimensional electron diffraction microscopy,” Phys. Rev. Lett. 89, 155502 (2002).
[CrossRef]

J. Miao, T. Ishikawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Hodgson, “High resolution 3D X-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088303 (2002).
[CrossRef]

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).

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, 1662-1669 (1998).
[CrossRef]

Nagahara, L. A.

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a Carbon nanotube from diffraction intensities,” Science 300, 1419-1421(2003).
[CrossRef]

Nakai, S.

Nakatsuka, M.

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, 15343-15346(2005).

Ohsuna, T.

J. Miao, T. Ohsuna, O. Terasaki, K. O. Hodgson, and M. A. O'Keefe, “Atomic resolution three-dimensional electron diffraction microscopy,” Phys. Rev. Lett. 89, 155502 (2002).
[CrossRef]

O'Keefe, M. A.

J. Miao, T. Ohsuna, O. Terasaki, K. O. Hodgson, and M. A. O'Keefe, “Atomic resolution three-dimensional electron diffraction microscopy,” Phys. Rev. Lett. 89, 155502 (2002).
[CrossRef]

Osten, W.

L. Seifert, H. J. Tiziani, and W. Osten, “Wavefront reconstruction with the adaptive Shack-Hartmann sensor,” Opt. Commun. 245, 255-269 (2005).
[CrossRef]

C. Wagner, S. Seebacher, W. Osten, and W. Jüptner, “Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology,” Appl. Opt. 38, 4812-4820(1999).
[CrossRef]

Palmieri, F.

Pfeifer, M. A.

G. J. Williams, M. A. Pfeifer, I. A. Vartanyants, and I. K. Robinson, “Three-dimensional imaging of microstructure in Au nanocrystals,” Phys. Rev. Lett. 90, 175501 (2003).
[CrossRef]

Pfeiffer, F.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379-382 (2008).
[CrossRef]

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (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, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping Theory, Algorithms and Software (Wiley, 1998).

Renker, D.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[CrossRef]

Restaino, S.

Robinson, I. K.

G. J. Williams, M. A. Pfeifer, I. A. Vartanyants, and I. K. Robinson, “Three-dimensional imaging of microstructure in Au nanocrystals,” Phys. Rev. Lett. 90, 175501 (2003).
[CrossRef]

Rodenburg, J. M.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[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]

Romero, L. A.

Royo, S.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 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, 15343-15346(2005).

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).

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, 1662-1669 (1998).
[CrossRef]

Schlotter, W. F.

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,” Nature 432, 885-888 (2004).

Schnars, U.

Seebacher, S.

Seifert, L.

L. Seifert, H. J. Tiziani, and W. Osten, “Wavefront reconstruction with the adaptive Shack-Hartmann sensor,” Opt. Commun. 245, 255-269 (2005).
[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, 15343-15346(2005).

Stöhr, J.

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,” Nature 432, 885-888 (2004).

Tallon, M.

Terasaki, O.

J. Miao, T. Ohsuna, O. Terasaki, K. O. Hodgson, and M. A. O'Keefe, “Atomic resolution three-dimensional electron diffraction microscopy,” Phys. Rev. Lett. 89, 155502 (2002).
[CrossRef]

Thibault, P.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379-382 (2008).
[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, 15343-15346(2005).

Tiziani, H. J.

L. Seifert, H. J. Tiziani, and W. Osten, “Wavefront reconstruction with the adaptive Shack-Hartmann sensor,” Opt. Commun. 245, 255-269 (2005).
[CrossRef]

Tong, D. M.

Vartanyants, I.

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a Carbon nanotube from diffraction intensities,” Science 300, 1419-1421(2003).
[CrossRef]

Vartanyants, I. A.

G. J. Williams, M. A. Pfeifer, I. A. Vartanyants, and I. K. Robinson, “Three-dimensional imaging of microstructure in Au nanocrystals,” Phys. Rev. Lett. 90, 175501 (2003).
[CrossRef]

Wagner, C.

Wang, H. T.

Wei, G. X.

Williams, G. J.

G. J. Williams, M. A. Pfeifer, I. A. Vartanyants, and I. K. Robinson, “Three-dimensional imaging of microstructure in Au nanocrystals,” Phys. Rev. Lett. 90, 175501 (2003).
[CrossRef]

Yamaguchi, I.

Yoon, G. Y.

Zebker, H. A.

Zhang, L.

Zhang, R.

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a Carbon nanotube from diffraction intensities,” Science 300, 1419-1421(2003).
[CrossRef]

Zhang, S.

Zhang, T.

Zhu, Y. Y.

Zuo, J. M.

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a Carbon nanotube from diffraction intensities,” Science 300, 1419-1421(2003).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

Nature

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).

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,” Nature 432, 885-888 (2004).

Opt. Commun.

L. Seifert, H. J. Tiziani, and W. Osten, “Wavefront reconstruction with the adaptive Shack-Hartmann sensor,” Opt. Commun. 245, 255-269 (2005).
[CrossRef]

Opt. Eng.

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829-832 (1982).

Opt. Lett.

Optik (Jena)

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

Phys. Rev. Lett.

J. Miao, T. Ishikawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Hodgson, “High resolution 3D X-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088303 (2002).
[CrossRef]

J. Miao, T. Ohsuna, O. Terasaki, K. O. Hodgson, and M. A. O'Keefe, “Atomic resolution three-dimensional electron diffraction microscopy,” Phys. Rev. Lett. 89, 155502 (2002).
[CrossRef]

G. J. Williams, M. A. Pfeifer, I. A. Vartanyants, and I. K. Robinson, “Three-dimensional imaging of microstructure in Au nanocrystals,” Phys. Rev. Lett. 90, 175501 (2003).
[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]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[CrossRef]

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, 15343-15346(2005).

Science

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a Carbon nanotube from diffraction intensities,” Science 300, 1419-1421(2003).
[CrossRef]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379-382 (2008).
[CrossRef]

Other

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping Theory, Algorithms and Software (Wiley, 1998).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the experimental setup of the tri-arm MPI.

Fig. 2
Fig. 2

Example of the specially designed MP plate used in the tri-arm MPI.

Fig. 3
Fig. 3

Illustration of phase retrieval based on the tri-arm MP plate. (a) Phase of the complex amplitudes sampled by the MP plate shown in Fig. 2. (b) Far-field diffraction intensity pattern recorded at the detector plane. (c) Phase distribution of the Fourier transform of the far-field intensity pattern in (b). (d) Amplitude distribution of the Fourier transform of the same far-field intensity pattern.

Fig. 4
Fig. 4

Experimental results. (a) One example of the far-field diffraction patterns recorded in the experiments. (b) Measured amplitude distribution of the object wave on the MP plate. (c) Measured phase distribution of the object wave on the MP plate. (d) Image reconstructed by the measured complex amplitude after backpropagation to the specimen plane.

Equations (7)

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I P ( ρ ) = I 0 | m = 0 M A m exp ( j φ m ) F { circ [ ( r r m ) / R ] } | 2 ,
g ( r ) = F 1 { I P ( ρ ) } = m = 0 M n = 0 M P m n ( r ) A m A n exp [ j ( φ m φ n ) ] ,
P m n ( r ) = circ [ ( α r m ) / R ] circ * [ ( α r n r ) / R ] d α .
P m n ( r ) = P 0 δ [ ( α r m ) ] δ [ ( α r n r ) ] d α = P 0 δ ( r r m + r n ) ,
g ( r ) = P 0 m = 0 M n = 0 M δ ( r r m + r n ) A m A n exp [ j ( φ m φ n ) ] = P 0 A 0 2 δ ( r ) + P 0 m = 1 M δ ( r r m ) A m A 0 exp [ j ( φ m φ 0 ) ] + P 0 n = 1 M δ ( r + r n ) A n A 0 exp [ j ( φ n φ 0 ) ] + P 0 p = 1 M q = 1 M δ ( r r p + r q ) A p A q exp [ j ( φ p φ q ) ] .
r p r q r m , r m r n , ( m , n , p , q = 1 , 2 , , M ) ,
g ( r m ) = P 0 A 0 A m exp [ i ( φ m φ 0 ) ] , ( m = 1 , 2 , 3 M ) .

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