Abstract

An iterative phase retrieval method is proposed, which uses a sequence of diffraction intensity patterns recorded at different wavelengths. This method has a rapid convergence, and a high immunity to noise and environmental disturbance. The wrap-free phase measurement range is also extended based on the principle of two-wavelength interferometry. Simulation and experimental results are presented to demonstrate the approach.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. D. Gabor, Nature (London) 161, 777 (1947).
    [CrossRef]
  2. S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, Nature (London) 432, 885 (2004).
    [CrossRef]
  3. R. W. Gerchberg and W. O. Saxton, Optik (Jena) 35, 237 (1972).
  4. B. Gu and G. Yang, Acta Opt. Sin. 1, 517 (1981).
  5. J. R. Fienup, Opt. Lett. 3, 27 (1978).
    [CrossRef] [PubMed]
  6. H. M. L. Faulkner and J. M. Rodenburg, Phys. Rev. Lett. 93, 023903 (2004).
    [CrossRef] [PubMed]
  7. 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]
  8. Y. Zhang, G. Pedrini, W. Osten, and H. Tiziani, Opt. Express 11, 3234 (2003).
    [CrossRef] [PubMed]
  9. P. Almoro, G. Pedrini, and W. Osten, Appl. Opt. 45, 8596 (2006).
    [CrossRef] [PubMed]
  10. F. Zhang, G. Pedrini, and W. Osten, Phys. Rev. A 75, 043805 (2007).
    [CrossRef]
  11. J. R. Fienup, R. G. Paxman, M. F. Reiley, and B. J. Thelen, Proc. SPIE 3815, 60 (1999).
    [CrossRef]
  12. T. H. Demetrakopoulos and R. Mittra, Appl. Opt. 13, 665 (1974).
    [CrossRef] [PubMed]
  13. J. C. Wyant, Appl. Opt. 10, 2113 (1971).
    [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]

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

2006

2004

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

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

2003

1999

J. R. Fienup, R. G. Paxman, M. F. Reiley, and B. J. Thelen, Proc. SPIE 3815, 60 (1999).
[CrossRef]

1981

B. Gu and G. Yang, Acta Opt. Sin. 1, 517 (1981).

1978

1974

1972

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

1971

1947

D. Gabor, Nature (London) 161, 777 (1947).
[CrossRef]

Acta Opt. Sin.

B. Gu and G. Yang, Acta Opt. Sin. 1, 517 (1981).

Appl. Opt.

Nature (London)

D. Gabor, Nature (London) 161, 777 (1947).
[CrossRef]

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

Opt. Express

Opt. Lett.

Optik (Jena)

R. W. Gerchberg and W. O. Saxton, Optik (Jena) 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]

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]

Proc. SPIE

J. R. Fienup, R. G. Paxman, M. F. Reiley, and B. J. Thelen, Proc. SPIE 3815, 60 (1999).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Schematic of the algorithm for phase retrieval: k is the iteration number, U is the calculated amplitude, and I is the recorded intensity.

Fig. 2
Fig. 2

Simulation result. Test (a) amplitude and (b) phase. Retrieved (c) amplitude and (d) phase.

Fig. 3
Fig. 3

Convergence performance: (a) different numbers of intensity recordings M = 6 , 10, and 20; and (b) different tuning ranges ( TR ) = 2 and 10 nm .

Fig. 4
Fig. 4

Experiment result. (a) Recorded diffraction pattern with 750 nm illumination beam, retrieved (b) amplitude, and (c) phase.

Equations (3)

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

Δ φ m ( x ) = 2 π Δ h ( x ) λ m ( n obj n air ) ,
Λ = λ m λ n λ m λ n ,
SSE = m , n [ U ( m , n ) U ¯ ( m , n ) ] 2 m , n U ( m , n ) 2 ,

Metrics