Abstract

We propose a noniterative method for real-time measuring and imaging of a complex-valued object based on a specially designed sampling array, named as the convolution-solvable sampling array (CSSA). We demonstrate that the wavefront of an object wave can be directly filtered from the Fourier transform of the diffraction intensity pattern of the object wave through a CSSA. As this method requires only a single measurement of the diffraction intensity pattern and does not need any iterative algorithm and lens systems in principle, it provides a practically valuable approach for real-time imaging of a complex-valued object in a wide range of wavelengths.

© 2010 Optical Society of America

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M. Guizar-Sicairos and J. R. Fienup, Opt. Lett. 33, 2668 (2008).
[CrossRef] [PubMed]

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, Phys. Rev. Lett. 100, 155503 (2008).
[CrossRef] [PubMed]

2007

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] [PubMed]

N. Nakajima, Phys. Rev. Lett. 98, 223901 (2007).
[CrossRef] [PubMed]

M. Guizar-Sicairos and J. R. Fienup, Opt. Express 15, 17592 (2007).
[CrossRef] [PubMed]

2005

L. D. Turner, K. F. E. M. Domen, and R. E. Scholten, Phys. Rev. A 72, 031403(R) (2005).
[CrossRef]

2004

H. I. Campbell, S. Zhang, A. H. Greenaway, and S. Restaino, Opt. Lett. 29, 2707 (2004).
[CrossRef] [PubMed]

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

1998

1996

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef] [PubMed]

1982

Barnea, Z.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef] [PubMed]

Bunk, O.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, Phys. Rev. Lett. 100, 155503 (2008).
[CrossRef] [PubMed]

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] [PubMed]

Campbell, H. I.

Chapman, H. N.

Cookson, D. F.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef] [PubMed]

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] [PubMed]

David, C.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, Phys. Rev. Lett. 100, 155503 (2008).
[CrossRef] [PubMed]

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] [PubMed]

Dierolf, M.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, Phys. Rev. Lett. 100, 155503 (2008).
[CrossRef] [PubMed]

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] [PubMed]

Domen, K. F. E. M.

L. D. Turner, K. F. E. M. Domen, and R. E. Scholten, Phys. Rev. A 72, 031403(R) (2005).
[CrossRef]

Eberhardt, W.

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

Eisebitt, S.

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

Fienup, J. R.

Gray, J.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, Phys. Rev. Lett. 100, 155503 (2008).
[CrossRef] [PubMed]

Greenaway, A. H.

Guizar-Sicairos, M.

Guo, C. S.

Gureyev, T. E.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef] [PubMed]

Hellwig, O.

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

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

Jefimovs, K.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, Phys. Rev. Lett. 100, 155503 (2008).
[CrossRef] [PubMed]

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] [PubMed]

Johnson, I.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, Phys. Rev. Lett. 100, 155503 (2008).
[CrossRef] [PubMed]

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] [PubMed]

Kapteyn, H. C.

La-o-vorakiat, C.

Lörgen, M.

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

Lu, L. L.

Lüning, J.

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

Miao, J.

Murnane, M. M.

Nakajima, N.

N. Nakajima, Phys. Rev. Lett. 98, 223901 (2007).
[CrossRef] [PubMed]

Nugent, K. A.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef] [PubMed]

Paganin, D.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef] [PubMed]

Paul, A.

Pfeiffer, F.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, Phys. Rev. Lett. 100, 155503 (2008).
[CrossRef] [PubMed]

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] [PubMed]

Raines, K. S.

Raymondson, D. A.

Renker, D.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, Phys. Rev. Lett. 100, 155503 (2008).
[CrossRef] [PubMed]

Restaino, S.

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

Sandberg, R. L.

Sayre, D.

Schlotter, W. F.

Scholten, R. E.

L. D. Turner, K. F. E. M. Domen, and R. E. Scholten, Phys. Rev. A 72, 031403(R) (2005).
[CrossRef]

Stöohr, J.

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

Turner, L. D.

L. D. Turner, K. F. E. M. Domen, and R. E. Scholten, Phys. Rev. A 72, 031403(R) (2005).
[CrossRef]

Wang, H. T.

Wei, G. X.

Zhang, S.

Appl. Opt.

J. Opt. Soc. Am. A

Nature

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

Opt. Express

Opt. Lett.

Phys. Rev. A

L. D. Turner, K. F. E. M. Domen, and R. E. Scholten, Phys. Rev. A 72, 031403(R) (2005).
[CrossRef]

Phys. Rev. Lett.

N. Nakajima, Phys. Rev. Lett. 98, 223901 (2007).
[CrossRef] [PubMed]

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] [PubMed]

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, Phys. Rev. Lett. 100, 155503 (2008).
[CrossRef] [PubMed]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

(a) Example of the CSSA. (b) Corresponding spatial filter used for the CDI. (c) Schematic of the experimental setup.

Fig. 2
Fig. 2

(a) Object used in the experiment; it is a transparency of a Chinese character. (b) One example of the recorded Fraunhofer diffraction intensity patterns of the object wave through the CSSA. (c) Reconstructed image of the extracted wave after counterpropagating to the specimen plane in a computer.

Fig. 3
Fig. 3

(a) Pure phase object used in the experiment. (b) Recovered amplitude of the object wave on the CSSA plane. (c) Recovered phase distribution of the same object wave. (d) Phase distribution of the reconstructed image obtained by counterpropagating the measured object wave to the object plane.

Equations (2)

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g ( r ) = F 1 { I F ( ρ ) } = I 0 { s ( r ) [ P ( r ) + δ ( r ) ] } { s ( r ) [ P ( r ) + δ ( r ) ] } = C 0 A R 2 δ ( r ) + C 0 m = 1 M δ ( r r m ) A m A R   exp [ j ( φ m φ R ) ] + C 0 m = 1 M δ ( r + r m ) A m A R   exp [ j ( φ m φ R ) ] + C 0 m = 1 M n = 1 M δ ( r r m + r n ) A m A n   exp [ j ( φ m φ n ) ] ,
g ( r ) P ( r ) = C 0 m = 1 M δ ( r r m ) A R A m   exp [ j ( φ m φ R ) ] = s ( 0 ) s ( r ) P ( r ) ,

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