Abstract

We describe a method where phase and amplitude of a wavefront are obtained by processing a sequence of pattern produced by the interference between the light transmitted by a scanning pinhole (which is sequentially shifted) and a reference pinhole. Simulations and experimental results are presented.

© 2011 Optical Society of America

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References

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2011

2010

2009

2008

2007

F. Zhang, G. Pedrini, and W. Osten, Phys. Rev. A 75, 043805 (2007).
[CrossRef]

2006

2005

2004

H. M. L. Faulkner and J. M. Rodenburg, Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef] [PubMed]

2003

Y. Zhang, G. Pedrini, W. Osten, and H. Tiziani, Opt. Express 11, 3234 (2003).
[CrossRef] [PubMed]

E. Allaria, S. Brugioni, S. De Nicola, P. Ferraro, S. Grilli, and R. Meucci, Opt. Commun. 215, 257 (2003).
[CrossRef]

2002

1997

1994

1985

1982

1972

R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972).

1948

D. Gabor, Nature 161, 777 (1948).
[CrossRef] [PubMed]

Allaria, E.

E. Allaria, S. Brugioni, S. De Nicola, P. Ferraro, S. Grilli, and R. Meucci, Opt. Commun. 215, 257 (2003).
[CrossRef]

Almoro, P.

Bao, P.

Brugioni, S.

E. Allaria, S. Brugioni, S. De Nicola, P. Ferraro, S. Grilli, and R. Meucci, Opt. Commun. 215, 257 (2003).
[CrossRef]

Candès, E.

E. Candès, M. Wakin, IEEE Signal Process. Mag. 25, 21 (2008).
[CrossRef]

Colomb, T.

Cuche, E.

De Charrière, F.

De Nicola, S.

E. Allaria, S. Brugioni, S. De Nicola, P. Ferraro, S. Grilli, and R. Meucci, Opt. Commun. 215, 257 (2003).
[CrossRef]

Den, T.

Depeursinge, C.

Dong, B. Z.

Ersoy, O. K.

Faulkner, H. M. L.

H. M. L. Faulkner and J. M. Rodenburg, Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef] [PubMed]

Ferraro, P.

E. Allaria, S. Brugioni, S. De Nicola, P. Ferraro, S. Grilli, and R. Meucci, Opt. Commun. 215, 257 (2003).
[CrossRef]

Fienup, J. R.

Fink, H.-W.

Gabor, D.

D. Gabor, Nature 161, 777 (1948).
[CrossRef] [PubMed]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972).

Gopinathan, U.

Grilli, S.

E. Allaria, S. Brugioni, S. De Nicola, P. Ferraro, S. Grilli, and R. Meucci, Opt. Commun. 215, 257 (2003).
[CrossRef]

Gu, B. Y.

Itoh, H.

Javidi, B.

Kondoh, T.

Kuehn, J.

Latychevskaia, T.

Marian, A.

Marquet, P.

Meucci, R.

E. Allaria, S. Brugioni, S. De Nicola, P. Ferraro, S. Grilli, and R. Meucci, Opt. Commun. 215, 257 (2003).
[CrossRef]

Montfort, F.

Nagai, K.

Nakajima, N.

Nakamura, T.

Osten, W.

Ouchi, C.

Pedrini, G.

Rodenburg, J. M.

H. M. L. Faulkner and J. M. Rodenburg, Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef] [PubMed]

Sato, G.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972).

Schnars, U.

Setomoto, Y.

Sheppard, C. J. R.

Teague, M. R.

Teshima, T.

Tiziani, H.

Wakin, M.

E. Candès, M. Wakin, IEEE Signal Process. Mag. 25, 21 (2008).
[CrossRef]

Yamaguchi, I.

Yamaguchi, K.

Yang, G. Z.

Yaroslavsky, L.

L. Yaroslavsky, Digital Holography and Digital Image Processing: Principles, Methods, Algorithms (Kluwer, 2004).

Zhang, F.

P. Bao, F. Zhang, G. Pedrini, and W. Osten, Opt. Lett. 33, 309 (2008).
[CrossRef] [PubMed]

F. Zhang, G. Pedrini, and W. Osten, Phys. Rev. A 75, 043805 (2007).
[CrossRef]

Zhang, T.

Zhang, Y.

Zhuang, J.

Appl. Opt.

IEEE Signal Process. Mag.

E. Candès, M. Wakin, IEEE Signal Process. Mag. 25, 21 (2008).
[CrossRef]

J. Display Technol.

J. Opt. Soc. Am. A

Nature

D. Gabor, Nature 161, 777 (1948).
[CrossRef] [PubMed]

Opt. Commun.

E. Allaria, S. Brugioni, S. De Nicola, P. Ferraro, S. Grilli, and R. Meucci, Opt. Commun. 215, 257 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Optik

R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972).

Phys. Rev. A

F. Zhang, G. Pedrini, and W. Osten, Phys. Rev. A 75, 043805 (2007).
[CrossRef]

Phys. Rev. Lett.

H. M. L. Faulkner and J. M. Rodenburg, Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef] [PubMed]

Other

L. Yaroslavsky, Digital Holography and Digital Image Processing: Principles, Methods, Algorithms (Kluwer, 2004).

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Figures (2)

Fig. 1
Fig. 1

(a) Recording arrangement, (b) FT of the recorded intensity, (c) filtering, (d) iFT, (e) complex amplitude on a grid, (f) reconstruction of the object.

Fig. 2
Fig. 2

(a) Original mask used for the experiment ( 2.5 mm × 2.5 mm ). (b) Retrieved phase of the wavefront at the scanning pinhole plane ( 128 × 128 points). (c) Reconstructions of the object from the complex amplitude.

Equations (6)

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U ( x A , y A ) = | U ( x A , y A ) | exp { i ϕ ( x A , y A ) } ,
U ( x B , y B ) = | U ( x B , y B ) | exp { i ϕ ( x B , y B ) } .
V A ( ξ , η ) = 1 i λ | U ( x A , y A ) | exp { i ϕ ( x A , y A ) } exp { i 2 π r A / λ } r A cos ( θ ) ,
V B ( ξ , η ) = 1 i λ | U ( x B , y B ) | exp { i ϕ ( x B , y B ) } exp { i 2 π r B / λ } r B cos ( θ ) ,
I ( ξ , η ) = | V A ( ξ , η ) | 2 + | V B ( ξ , η ) | 2 + V A ( ξ , η ) V B * ( ξ , η ) + V A * ( ξ , η ) V B ( ξ , η ) = [ cos ( θ ) λ ] 2 { | U ( x A , y A ) r A | 2 + | U ( x B , y B ) r B | 2 } + [ cos ( θ ) λ ] 2 { 2 | γ A B | | U ( x A , y A ) | | U ( x B , y B ) | cos { 2 π ( r A r B ) / λ + ϕ ( x A , y A ) ϕ ( x B , y B ) } r A r B } ,
V A ( ξ , η ) V B * ( ξ , η ) = [ cos ( θ ) λ ] 2 | γ A B | | U ( x A , y A ) | | U ( x B , y B ) | exp { i [ 2 π ( r A r B ) / λ + ϕ ( x A , y A ) ϕ ( x B , y B ) ] } r A r B

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