Abstract

A general method of extracting the arbitrary unknown and unequal phase steps in phase-shift interferometry from interferograms recorded on the diffraction field of an object and then reconstructing the object wave front digitally with our derived formulas is proposed. The phase steps are first calculated based on the statistical nature of the diffraction field and are further improved by an iterative approach. This method is simple, highly accurate, and usable for any frame number N (N3) and for both smooth and diffusing objects, as is verified by a series of computer simulations.

© 2004 Optical Society of America

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References

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2003 (1)

2002 (1)

2001 (2)

2000 (1)

1998 (2)

B. Gutman and H. Weber, Appl. Opt. 37, 7624 (1998).
[CrossRef]

N. A. Ochoa and J. M. Huntley, Opt. Eng. 37, 2501 (1998).
[CrossRef]

1997 (2)

I. Yamaguchi and T. Zhang, Opt. Lett. 22, 1268 (1997).
[CrossRef] [PubMed]

G. Stoilov and T. Dragostinov, Opt. Lasers Eng. 28, 61 (1997).
[CrossRef]

1994 (2)

G. D. Lassahn, J. K. Lassahn, P. L. Taylor, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
[CrossRef]

G.-S. Han and S.-W. Kim, Appl. Opt. 33, 7321 (1994).
[CrossRef] [PubMed]

1991 (1)

1984 (1)

J. E. Greivenkamp, Opt. Eng. 23, 350 (1984).
[CrossRef]

1974 (1)

1969 (1)

R. Crane, Appl. Opt. 8, 528 (1969).

Bitoh, Y.

Brangaccio, D. J.

Bruning, J. H.

Cai, L. Z.

Chen, X.

Crane, R.

R. Crane, Appl. Opt. 8, 528 (1969).

Deason, V. A.

G. D. Lassahn, J. K. Lassahn, P. L. Taylor, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
[CrossRef]

Dragostinov, T.

G. Stoilov and T. Dragostinov, Opt. Lasers Eng. 28, 61 (1997).
[CrossRef]

Gallagher, J. E.

Gramaglia, M.

Greivenkamp, J. E.

J. E. Greivenkamp, Opt. Eng. 23, 350 (1984).
[CrossRef]

Guo, C. S.

Gutman, B.

Han, G.-S.

Herriott, D. R.

Huntley, J. M.

N. A. Ochoa and J. M. Huntley, Opt. Eng. 37, 2501 (1998).
[CrossRef]

Kadono, H.

Kato, J.

Kim, S.-W.

Lai, G.

Lassahn, G. D.

G. D. Lassahn, J. K. Lassahn, P. L. Taylor, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
[CrossRef]

Lassahn, J. K.

G. D. Lassahn, J. K. Lassahn, P. L. Taylor, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
[CrossRef]

Liao, J.

Liu, Q.

Mizuno, J.

Ochoa, N. A.

N. A. Ochoa and J. M. Huntley, Opt. Eng. 37, 2501 (1998).
[CrossRef]

Ohta, S.

Rastogi, P. K.

P. K. Rastogi, Holographic Interferometry (Springer-Verlag, Berlin, 1994).
[CrossRef]

Rosenfeld, D. P.

Stoilov, G.

G. Stoilov and T. Dragostinov, Opt. Lasers Eng. 28, 61 (1997).
[CrossRef]

Taylor, P. L.

G. D. Lassahn, J. K. Lassahn, P. L. Taylor, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
[CrossRef]

Toyoka, S.

Wang, H. T.

Wang, Y. R.

Weber, H.

White, A. D.

Yamaguchi, I.

Yang, X. L.

Yatagai, T.

Yeazell, J. A.

Zhang, L.

Zhang, T.

Zhu, Y. Y.

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Tables (2)

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Table 1 Phase Step Retrieval Results for a Surface of Radius R=0.2 ma

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Table 2 Phase Step Retrieval Results for a Surface of Radius R=2 m

Equations (15)

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I1x,y=Ar2+Ao2x,y+2ArAox,ycosφx,y,
I2x,y=Ar2+Ao2x,y+2ArAox,ycosφx,y-α1,
I3x,y=Ar2+Ao2x,y+2ArAox,ycosφx,y-α1-α2,
p=I2-I1=4ArAo sinφ-α1/2sinα1/2,
q=I3-I2=4ArAo sinφ-α1-α2/2sinα2/2,
r=I3-I1=4ArAo sinφ-α1+α2/2sinα1+α2/2,
p=c sinα1/2, q=c sinα2/2, r=c sinα1+α2/2.
c=2pqr2p2q2+p2r2+q2r2-p4+q4+r4-1/2
α1=2 arcsinp/c, α2=2 arcsinq/c.
A0 expiφ=14Ar sinα2/2expiα1/2sinα1+α2/2I1-I3-expiα1+α2/2sinα1/2I1-I2,
=I1-Ar2+Ao2+2ArAo cos φ+I2-Ar2+Ao2+2ArAo cosφ-α1+I3-Ar2+Ao2+2ArAo cosφ-α1-α2,
I4x,y=Ar2+Ao2x,y+2ArAox,y×cosφox,y-α1-α2-α3,
s=I4-I3=4AoAr sinφ-α1-α2-α3/2sinα3/2=c sinα3/2,
Ao expiφ=14Ar sinα1+α3/2×expiα1+α2/2sinα2+α3/2I2-I4-expiα1+α2/2+α3/2sinα1+α2/2I1-I3.
=I4-Ar2+Ao2+2ArAo cosφ-α1-α2-α3,

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