Abstract

Phase retrieval is carried out using sequential intensity measurements of a volume speckle field and a wave propagation equation. Retrieved phases and phase subtraction facilitate the analysis of wavefronts before and after undergoing a small rotation. Angular displacement between incident planar wavefronts is determined from the unwrapped phase difference, phase diffuser aperture diameter, and the light source wavelength. Numerical simulations confirm the experimental results.

© 2008 Optical Society of America

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References

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2008 (2)

E.-T. Hwu, S.-K. Hung, C.-W. Yang, K.-Y. Huang, and I.-S. Hwang, Nanotechnology 19, 115501 (2008).
[CrossRef] [PubMed]

P. F. Almoro and S. G. Hanson, Appl. Opt. 47, 2979 (2008).
[CrossRef] [PubMed]

2007 (2)

2006 (1)

C. Park, Y. Melikhov, and S. Lee, Appl. Phys. Lett. 88, 181116 (2006).
[CrossRef]

2005 (1)

2004 (1)

C. Zhang and X. Wang, Opt. Eng. (Bellingham) 43, 3008 (2004).
[CrossRef]

1992 (1)

1984 (1)

G. G. Luther and R. D. Deslattes, Rev. Sci. Instrum. 55, 747 (1984).
[CrossRef]

1970 (1)

Almoro, P.

Almoro, P. F.

Anand, A.

Cao, Z.

Chen, F.

Deslattes, R. D.

G. G. Luther and R. D. Deslattes, Rev. Sci. Instrum. 55, 747 (1984).
[CrossRef]

Feng, Y.

Hanson, S. G.

Harris, O.

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison Wesley, 2002).

Huang, K.-Y.

E.-T. Hwu, S.-K. Hung, C.-W. Yang, K.-Y. Huang, and I.-S. Hwang, Nanotechnology 19, 115501 (2008).
[CrossRef] [PubMed]

Huang, P. S.

Hung, S.-K.

E.-T. Hwu, S.-K. Hung, C.-W. Yang, K.-Y. Huang, and I.-S. Hwang, Nanotechnology 19, 115501 (2008).
[CrossRef] [PubMed]

Hwang, I.-S.

E.-T. Hwu, S.-K. Hung, C.-W. Yang, K.-Y. Huang, and I.-S. Hwang, Nanotechnology 19, 115501 (2008).
[CrossRef] [PubMed]

Hwu, E.-T.

E.-T. Hwu, S.-K. Hung, C.-W. Yang, K.-Y. Huang, and I.-S. Hwang, Nanotechnology 19, 115501 (2008).
[CrossRef] [PubMed]

Kamada, O.

Kiyono, S.

Lee, S.

C. Park, Y. Melikhov, and S. Lee, Appl. Phys. Lett. 88, 181116 (2006).
[CrossRef]

Lin, K.

S. Lin, K. Lin, and W. Syu, Opt. Commun. 277, 251 (2007).
[CrossRef]

Lin, S.

S. Lin, K. Lin, and W. Syu, Opt. Commun. 277, 251 (2007).
[CrossRef]

Luther, G. G.

G. G. Luther and R. D. Deslattes, Rev. Sci. Instrum. 55, 747 (1984).
[CrossRef]

Malacara, D.

Melikhov, Y.

C. Park, Y. Melikhov, and S. Lee, Appl. Phys. Lett. 88, 181116 (2006).
[CrossRef]

Osten, W.

Park, C.

C. Park, Y. Melikhov, and S. Lee, Appl. Phys. Lett. 88, 181116 (2006).
[CrossRef]

Pedrini, G.

Shen, Q.

Syu, W.

S. Lin, K. Lin, and W. Syu, Opt. Commun. 277, 251 (2007).
[CrossRef]

Wang, X.

C. Zhang and X. Wang, Opt. Eng. (Bellingham) 43, 3008 (2004).
[CrossRef]

Yang, C.-W.

E.-T. Hwu, S.-K. Hung, C.-W. Yang, K.-Y. Huang, and I.-S. Hwang, Nanotechnology 19, 115501 (2008).
[CrossRef] [PubMed]

Zhang, C.

C. Zhang and X. Wang, Opt. Eng. (Bellingham) 43, 3008 (2004).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. Lett. (1)

C. Park, Y. Melikhov, and S. Lee, Appl. Phys. Lett. 88, 181116 (2006).
[CrossRef]

Nanotechnology (1)

E.-T. Hwu, S.-K. Hung, C.-W. Yang, K.-Y. Huang, and I.-S. Hwang, Nanotechnology 19, 115501 (2008).
[CrossRef] [PubMed]

Opt. Commun. (1)

S. Lin, K. Lin, and W. Syu, Opt. Commun. 277, 251 (2007).
[CrossRef]

Opt. Eng. (Bellingham) (1)

C. Zhang and X. Wang, Opt. Eng. (Bellingham) 43, 3008 (2004).
[CrossRef]

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

G. G. Luther and R. D. Deslattes, Rev. Sci. Instrum. 55, 747 (1984).
[CrossRef]

Other (1)

E. Hecht, Optics, 4th ed. (Addison Wesley, 2002).

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Figures (4)

Fig. 1
Fig. 1

Setup for measuring angular displacement of test wavefronts. Inset, the reconstructed planar wavefronts with OPD.

Fig. 2
Fig. 2

Phase subtraction of planar wavefronts from (a) simulations and (b) experiments.

Fig. 3
Fig. 3

Wrapped and unwrapped phase differences showing the multiple scans taken at nearby points along the aperture diameter.

Fig. 4
Fig. 4

(a) Phase differences with respect to a reference initial phase for increasing PZT translation. Angular displacement Δ θ (not drawn to scale) is also depicted for the various pairs of wave vectors. (b) Plot of Δ θ for increasing PZT translation.

Equations (1)

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Δ θ = λ 2 π D Δ ϕ .

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