Abstract

Recently, we have proposed a coherent diffractive imaging using a noniterative phase retrieval method with the filter of an aperture array. The first (to our knowledge) experimental demonstration of this coherent imaging is presented here, in which a complex-valued object illuminated by a diode laser is reconstructed from the isolated diffraction intensities of the object’s wave field, transmitted through an array filter of square apertures by using the phase retrieval method. This imaging method requires only a single measurement of the diffraction intensity and does not need a tight object’s support constraint utilized in iterative phase retrieval algorithms or a reference wave used in holographic techniques.

© 2011 Optical Society of America

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2010 (2)

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J.Sto¨hr, Phys. Rev. Lett. 105, 043901 (2010).
[Crossref] [PubMed]

C. S. Guo, K. Liang, X. T. Zhang, and H. T. Wang, Opt. Lett. 35, 850 (2010).
[Crossref] [PubMed]

2008 (4)

A. Rosenhahn, R. Barth, F. Staier, T. Simpson, S. Mittler, S. Eisebitt, and M. Grunze, J. Opt. Soc. Am. A 25, 416 (2008).
[Crossref]

N. Nakajima, J. Opt. Soc. Am. A 25, 742 (2008).
[Crossref]

A. V. Martin and L. J. Allen, Opt. Commun. 281, 5114 (2008).
[Crossref]

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge and I. McNulty, Nat. Phys. 4, 394 (2008).
[Crossref]

2007 (1)

2006 (2)

2004 (1)

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, Nature 432, 885 (2004).
[Crossref] [PubMed]

1982 (1)

Abbey, B.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge and I. McNulty, Nat. Phys. 4, 394 (2008).
[Crossref]

Acremann, Y.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J.Sto¨hr, Phys. Rev. Lett. 105, 043901 (2010).
[Crossref] [PubMed]

Allen, L. J.

A. V. Martin and L. J. Allen, Opt. Commun. 281, 5114 (2008).
[Crossref]

Barth, R.

Barty, A.

Beetz, T.

Cassou, K.

Caumes, J.

Chapman, H. N.

Clark, J. N.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge and I. McNulty, Nat. Phys. 4, 394 (2008).
[Crossref]

Cui, C.

De Jonge, M.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge and I. McNulty, Nat. Phys. 4, 394 (2008).
[Crossref]

Eberhardt, W.

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, Nature 432, 885 (2004).
[Crossref] [PubMed]

Eisebitt, S.

A. Rosenhahn, R. Barth, F. Staier, T. Simpson, S. Mittler, S. Eisebitt, and M. Grunze, J. Opt. Soc. Am. A 25, 416 (2008).
[Crossref]

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, Nature 432, 885 (2004).
[Crossref] [PubMed]

Fajardo, M.

Farle, M.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J.Sto¨hr, Phys. Rev. Lett. 105, 043901 (2010).
[Crossref] [PubMed]

Fienup, J. R.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J.Sto¨hr, Phys. Rev. Lett. 105, 043901 (2010).
[Crossref] [PubMed]

J. R. Fienup, Appl. Opt. 21, 2758 (1982).
[Crossref] [PubMed]

Fischer, P.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J.Sto¨hr, Phys. Rev. Lett. 105, 043901 (2010).
[Crossref] [PubMed]

Friedenberger, N.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J.Sto¨hr, Phys. Rev. Lett. 105, 043901 (2010).
[Crossref] [PubMed]

Gautier, M. J.

Grunze, M.

Guizar-Sicairos, M.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J.Sto¨hr, Phys. Rev. Lett. 105, 043901 (2010).
[Crossref] [PubMed]

Guo, C. S.

Hau-Riege, S. P.

He, H.

Hellwig, O.

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, Nature 432, 885 (2004).
[Crossref] [PubMed]

Howells, M. R.

Jacobsen, C.

Kazamias, S.

Kos-Rosset, M.

Liang, K.

Lörgen, M.

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, Nature 432, 885 (2004).
[Crossref] [PubMed]

Lüning, J.

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, Nature 432, 885 (2004).
[Crossref] [PubMed]

Marchesini, S.

Martin, A. V.

A. V. Martin and L. J. Allen, Opt. Commun. 281, 5114 (2008).
[Crossref]

McNulty, I.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge and I. McNulty, Nat. Phys. 4, 394 (2008).
[Crossref]

Merdji, H.

Mittler, S.

Nakajima, N.

Noy, A.

Nugent, K. A.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge and I. McNulty, Nat. Phys. 4, 394 (2008).
[Crossref]

Ollefs, K.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J.Sto¨hr, Phys. Rev. Lett. 105, 043901 (2010).
[Crossref] [PubMed]

Paganin, D. M.

Pavlov, K. M.

Peele, A. G.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge and I. McNulty, Nat. Phys. 4, 394 (2008).
[Crossref]

Pfeifer, M. A.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge and I. McNulty, Nat. Phys. 4, 394 (2008).
[Crossref]

Podorov, S. G.

Rey, G.

Rosen, R.

Rosenhahn, A.

Scherz, A.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J.Sto¨hr, Phys. Rev. Lett. 105, 043901 (2010).
[Crossref] [PubMed]

Schlotter, W. F.

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, Nature 432, 885 (2004).
[Crossref] [PubMed]

Shapiro, D.

Simpson, T.

Spence, J. C. H.

Staier, F.

Sto¨hr, J.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J.Sto¨hr, Phys. Rev. Lett. 105, 043901 (2010).
[Crossref] [PubMed]

Stöhr, J.

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, Nature 432, 885 (2004).
[Crossref] [PubMed]

Tylisztzak, T.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J.Sto¨hr, Phys. Rev. Lett. 105, 043901 (2010).
[Crossref] [PubMed]

Wang, H. T.

Weierstall, U.

Williams, G. J.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge and I. McNulty, Nat. Phys. 4, 394 (2008).
[Crossref]

Wu, B.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J.Sto¨hr, Phys. Rev. Lett. 105, 043901 (2010).
[Crossref] [PubMed]

Zeitoun, P.

Zhang, X. T.

Zhu, D.

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J.Sto¨hr, Phys. Rev. Lett. 105, 043901 (2010).
[Crossref] [PubMed]

Appl. Opt. (1)

J. Opt. Soc. Am. A (3)

Nat. Phys. (1)

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge and I. McNulty, Nat. Phys. 4, 394 (2008).
[Crossref]

Nature (1)

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, Nature 432, 885 (2004).
[Crossref] [PubMed]

Opt. Commun. (1)

A. V. Martin and L. J. Allen, Opt. Commun. 281, 5114 (2008).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

D. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tylisztzak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J.Sto¨hr, Phys. Rev. Lett. 105, 043901 (2010).
[Crossref] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Schematic arrangement of the experiment. The isolated diffraction intensity of each aperture from those of the adjoining apertures is measured in the detector.

Fig. 2
Fig. 2

(a) Modulus of the object image by a convex lens. (b) Measured intensity pattern. (c) Modulus and (d) phase of the reconstructed object. The solid curves in (e) and (f), and the dotted curve in (e) show the cross-sectional profiles of (c) and (d), and (a), respectively, along the horizontal lines through the positions indicated by the arrows.

Fig. 3
Fig. 3

Same as Fig. 2, except for the object with phase variation. The three lines of the object were covered with the film of a half-wave retarder.

Equations (2)

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| K ( a x n , a y m ) | 2 | F ( x , y ) R ( x x n , y y m ) d x d y | 2 ,
ϕ ( x n , y m ) I 1 [ I [ D ( x n , y m ) ] 2 i sinh ( 2 π c α ) ] ,

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