Abstract

The formation of holograms is interpreted as the consequence of the bilinearity of the ambiguity function. Reconstruction can then be regarded as the manipulation of the ambiguity function. Specifically, we show that in the case of in-line holography, the reconstruction can be regarded as phase tomography. In this way we provide a unified picture for the formulation of both noninterferometric and interferometric phase-retrieval techniques.

© 2007 Optical Society of America

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G. Situ and J. Zhang, Proc. SPIE 5642, 108 (2005).
[CrossRef]

2004

2003

T. Alieva and M. J. Bastinaans, IEEE Trans. Signal Process. 51, 112 (2003).
[CrossRef]

2002

J. W. Miao, T. Ishikawa, B. Johnason, E. H. Anderson, B. Lai, and K. O. Hodgson, Phys. Rev. Lett. 89, 088303 (2002).
[CrossRef] [PubMed]

Y. Nishino, T. Ishikawa, K. Hayashi, Y. Takahashi, and E. Matsubara, Phys. Rev. B 66, 092105 (2002).
[CrossRef]

1998

1997

J. Tu and S. Tamura, Phys. Rev. E 55, 1946 (1997).
[CrossRef]

K. B. Wolf and A. L. Rivera, Opt. Commun. 144, 36 (1997).
[CrossRef]

1994

M. G. Raymer, M. Beck, and D. F. McAlster, Phys. Rev. Lett. 72, 1137 (1994).
[CrossRef] [PubMed]

1993

1992

F. Hlawatsch and G. F. Boudreaux-Bartels, IEEE Signal Process. Mag. 9, 21 (1992).
[CrossRef]

1983

1982

1974

1962

E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. A 52, 1123 (1962).
[CrossRef]

1951

W. L. Bragg and G. L. Rogers, Nature 167, 190 (1951).
[CrossRef] [PubMed]

Alieva, T.

T. Alieva and M. J. Bastinaans, IEEE Trans. Signal Process. 51, 112 (2003).
[CrossRef]

Anderson, E. H.

J. W. Miao, T. Ishikawa, B. Johnason, E. H. Anderson, B. Lai, and K. O. Hodgson, Phys. Rev. Lett. 89, 088303 (2002).
[CrossRef] [PubMed]

Barty, A.

Bastinaans, M. J.

T. Alieva and M. J. Bastinaans, IEEE Trans. Signal Process. 51, 112 (2003).
[CrossRef]

Beck, M.

M. G. Raymer, M. Beck, and D. F. McAlster, Phys. Rev. Lett. 72, 1137 (1994).
[CrossRef] [PubMed]

Boudreaux-Bartels, G. F.

F. Hlawatsch and G. F. Boudreaux-Bartels, IEEE Signal Process. Mag. 9, 21 (1992).
[CrossRef]

Bragg, W. L.

W. L. Bragg and G. L. Rogers, Nature 167, 190 (1951).
[CrossRef] [PubMed]

Fienup, J. R.

Gopinathan, U.

Hayashi, K.

Y. Nishino, T. Ishikawa, K. Hayashi, Y. Takahashi, and E. Matsubara, Phys. Rev. B 66, 092105 (2002).
[CrossRef]

Hlawatsch, F.

F. Hlawatsch and G. F. Boudreaux-Bartels, IEEE Signal Process. Mag. 9, 21 (1992).
[CrossRef]

Hodgson, K. O.

J. W. Miao, T. Ishikawa, B. Johnason, E. H. Anderson, B. Lai, and K. O. Hodgson, Phys. Rev. Lett. 89, 088303 (2002).
[CrossRef] [PubMed]

Ishikawa, T.

J. W. Miao, T. Ishikawa, B. Johnason, E. H. Anderson, B. Lai, and K. O. Hodgson, Phys. Rev. Lett. 89, 088303 (2002).
[CrossRef] [PubMed]

Y. Nishino, T. Ishikawa, K. Hayashi, Y. Takahashi, and E. Matsubara, Phys. Rev. B 66, 092105 (2002).
[CrossRef]

Johnason, B.

J. W. Miao, T. Ishikawa, B. Johnason, E. H. Anderson, B. Lai, and K. O. Hodgson, Phys. Rev. Lett. 89, 088303 (2002).
[CrossRef] [PubMed]

Jüeptner, W.

U. Schnars and W. Jüeptner, Digital Holography (Springer, 2004).

Lai, B.

J. W. Miao, T. Ishikawa, B. Johnason, E. H. Anderson, B. Lai, and K. O. Hodgson, Phys. Rev. Lett. 89, 088303 (2002).
[CrossRef] [PubMed]

Leith, E. N.

E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. A 52, 1123 (1962).
[CrossRef]

Lohmann, A. W.

Matsubara, E.

Y. Nishino, T. Ishikawa, K. Hayashi, Y. Takahashi, and E. Matsubara, Phys. Rev. B 66, 092105 (2002).
[CrossRef]

McAlster, D. F.

M. G. Raymer, M. Beck, and D. F. McAlster, Phys. Rev. Lett. 72, 1137 (1994).
[CrossRef] [PubMed]

Miao, J. W.

J. W. Miao, T. Ishikawa, B. Johnason, E. H. Anderson, B. Lai, and K. O. Hodgson, Phys. Rev. Lett. 89, 088303 (2002).
[CrossRef] [PubMed]

Monaghan, D. S.

Nishino, Y.

Y. Nishino, T. Ishikawa, K. Hayashi, Y. Takahashi, and E. Matsubara, Phys. Rev. B 66, 092105 (2002).
[CrossRef]

Nugent, K. A.

Paganin, D.

Papoulis, A.

Raymer, M. G.

M. G. Raymer, M. Beck, and D. F. McAlster, Phys. Rev. Lett. 72, 1137 (1994).
[CrossRef] [PubMed]

Rivera, A. L.

K. B. Wolf and A. L. Rivera, Opt. Commun. 144, 36 (1997).
[CrossRef]

Roberts, A.

Rogers, G. L.

W. L. Bragg and G. L. Rogers, Nature 167, 190 (1951).
[CrossRef] [PubMed]

Schnars, U.

U. Schnars and W. Jüeptner, Digital Holography (Springer, 2004).

Semichaevsky, A.

Sheridan, J. T.

Situ, G.

Takahashi, Y.

Y. Nishino, T. Ishikawa, K. Hayashi, Y. Takahashi, and E. Matsubara, Phys. Rev. B 66, 092105 (2002).
[CrossRef]

Tamura, S.

J. Tu and S. Tamura, Phys. Rev. E 55, 1946 (1997).
[CrossRef]

Teague, M. R.

Testorf, M.

Tu, J.

J. Tu and S. Tamura, Phys. Rev. E 55, 1946 (1997).
[CrossRef]

Upatnieks, J.

E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. A 52, 1123 (1962).
[CrossRef]

Wolf, K. B.

K. B. Wolf and A. L. Rivera, Opt. Commun. 144, 36 (1997).
[CrossRef]

Zhang, J.

G. Situ and J. Zhang, Proc. SPIE 5642, 108 (2005).
[CrossRef]

Appl. Opt.

IEEE Signal Process. Mag.

F. Hlawatsch and G. F. Boudreaux-Bartels, IEEE Signal Process. Mag. 9, 21 (1992).
[CrossRef]

IEEE Trans. Signal Process.

T. Alieva and M. J. Bastinaans, IEEE Trans. Signal Process. 51, 112 (2003).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nature

W. L. Bragg and G. L. Rogers, Nature 167, 190 (1951).
[CrossRef] [PubMed]

Opt. Commun.

K. B. Wolf and A. L. Rivera, Opt. Commun. 144, 36 (1997).
[CrossRef]

Opt. Lett.

Phys. Rev. B

Y. Nishino, T. Ishikawa, K. Hayashi, Y. Takahashi, and E. Matsubara, Phys. Rev. B 66, 092105 (2002).
[CrossRef]

Phys. Rev. E

J. Tu and S. Tamura, Phys. Rev. E 55, 1946 (1997).
[CrossRef]

Phys. Rev. Lett.

M. G. Raymer, M. Beck, and D. F. McAlster, Phys. Rev. Lett. 72, 1137 (1994).
[CrossRef] [PubMed]

J. W. Miao, T. Ishikawa, B. Johnason, E. H. Anderson, B. Lai, and K. O. Hodgson, Phys. Rev. Lett. 89, 088303 (2002).
[CrossRef] [PubMed]

Proc. SPIE

G. Situ and J. Zhang, Proc. SPIE 5642, 108 (2005).
[CrossRef]

Other

U. Schnars and W. Jüeptner, Digital Holography (Springer, 2004).

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Figures (2)

Fig. 1
Fig. 1

Schematic geometry of the WDF of the superposition of a band-limited signal s ( x ) and an incline plane wave.

Fig. 2
Fig. 2

Schematic geometry of the AF of the superposition of a band-limited signal s ( x ) and an incline plane wave r ( x ) . The lower box shows the Fourier spectrum of the hologram.

Tables (1)

Tables Icon

Table 1 Comparison of Interferometric and Noninterferometric Phase-Retrieval Techniques Based on the AF

Equations (9)

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

W s ( x , ν ) = s ( x + x ¯ 2 ) s * ( x x ¯ 2 ) exp [ j 2 π ν x ¯ ] d x ¯ .
W y ( x , ν ) = W s ( x , ν ) + W r ( x , ν ) + W s r ( x , ν ) + W r s ( x , ν ) ,
W s r ( x , ν ) = s ( x + x ¯ 2 ) r * ( x x ¯ 2 ) exp [ j 2 π ν x ¯ ] d x ¯ ,
A s ( ν ¯ , x ¯ ) = s ( x + x ¯ 2 ) s * ( x x ¯ 2 ) exp [ j 2 π ν ¯ x ] d x ,
A y ( ν ¯ , x ¯ ) = A s ( ν ¯ , x ¯ ) + A r ( ν ¯ , x ¯ ) + A s r ( ν ¯ , x ¯ ) + A r s ( ν ¯ , x ¯ ) ,
A y ( ν ¯ , 0 ) = A s ( ν ¯ , 0 ) + A r ( ν ¯ , 0 ) + A s r ( ν ¯ , 0 ) + A r s ( ν ¯ , 0 )
= A s ( ν ¯ , 0 ) + δ ( ν ¯ ) + S ( ν ¯ + ν 0 ) + S * ( ν ¯ ν 0 ) .
A y ( ν ¯ , x ¯ ) = A s ( ν ¯ , x ¯ ) + δ ( ν ¯ ) + exp [ j π ν ¯ x ¯ ] S ( ν ¯ ) + exp [ j π ν ¯ x ¯ ] S * ( ν ¯ ) ,
A y ( ν ¯ , z i ν ¯ ) = A s ( ν ¯ , z i ν ¯ ) + δ ( ν ¯ ) + exp [ j π z i ν ¯ 2 ] S ( ν ¯ ) + exp [ j π z i ν ¯ 2 ] S * ( ν ¯ ) .

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