Abstract

An advanced random phase-shifting algorithm to extract phase distributions from randomly phase-shifted interferograms is proposed. The algorithm is based on a least-squares iterative procedure, but it copes with the limitation of the existing iterative algorithms by separating a frame-to-frame iteration from a pixel-to-pixel iteration. The algorithm provides stable convergence and accurate phase extraction with as few as three interferograms, even when the phase shifts are completely random. The algorithm is simple, fast, and fully automatic. A computer simulation is conducted to prove the concept.

© 2004 Optical Society of America

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References

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    [CrossRef]
  2. J. Greivenkamp, Opt. Eng. 23, 350 (1984).
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    [CrossRef]
  4. G. S. Han and S. W. Kim, Appl. Opt. 33, 7321 (1994).
    [CrossRef] [PubMed]
  5. S. W. Kim, M. Kang, and G. S. Han, Opt. Eng. 36, 3101 (1997).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2001

1999

C. Wei, M. Chen, and Z. Wang, Opt. Eng. 38, 1357 (1999).
[CrossRef]

1997

S. W. Kim, M. Kang, and G. S. Han, Opt. Eng. 36, 3101 (1997).
[CrossRef]

1994

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

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

1991

K. Okada, A. Sato, and J. Tsujiuchi, Opt. Commun. 84, 118 (1991).
[CrossRef]

1984

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

Chen, M.

C. Wei, M. Chen, and Z. Wang, Opt. Eng. 38, 1357 (1999).
[CrossRef]

Creath, K.

K. Creath, in Interferogram Analysis, D. Robinson and G. Reid, eds. (IOP Publishing, London, 1993), p. 95.

Deason, V.

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

Greivenkamp, J.

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

Han, G. S.

S. W. Kim, M. Kang, and G. S. Han, Opt. Eng. 36, 3101 (1997).
[CrossRef]

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

Kang, M.

S. W. Kim, M. Kang, and G. S. Han, Opt. Eng. 36, 3101 (1997).
[CrossRef]

Kim, S. W.

S. W. Kim, M. Kang, and G. S. Han, Opt. Eng. 36, 3101 (1997).
[CrossRef]

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

Larkin, K.

Lassaahn, J.

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

Lassahn, G.

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

Okada, K.

K. Okada, A. Sato, and J. Tsujiuchi, Opt. Commun. 84, 118 (1991).
[CrossRef]

Sato, A.

K. Okada, A. Sato, and J. Tsujiuchi, Opt. Commun. 84, 118 (1991).
[CrossRef]

Taylor, P.

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

Tsujiuchi, J.

K. Okada, A. Sato, and J. Tsujiuchi, Opt. Commun. 84, 118 (1991).
[CrossRef]

Wang, Z.

C. Wei, M. Chen, and Z. Wang, Opt. Eng. 38, 1357 (1999).
[CrossRef]

Wei, C.

C. Wei, M. Chen, and Z. Wang, Opt. Eng. 38, 1357 (1999).
[CrossRef]

Appl. Opt.

Opt. Commun.

K. Okada, A. Sato, and J. Tsujiuchi, Opt. Commun. 84, 118 (1991).
[CrossRef]

Opt. Eng.

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

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

S. W. Kim, M. Kang, and G. S. Han, Opt. Eng. 36, 3101 (1997).
[CrossRef]

C. Wei, M. Chen, and Z. Wang, Opt. Eng. 38, 1357 (1999).
[CrossRef]

Opt. Express

Other

K. Creath, in Interferogram Analysis, D. Robinson and G. Reid, eds. (IOP Publishing, London, 1993), p. 95.

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Figures (1)

Fig. 1
Fig. 1

Computer-generated phase map with random noise ranging from -π/4 to π/4.

Tables (2)

Tables Icon

Table 1 Comparison of Simulation Results of the Proposed Advanced Iterative Algorithm (AIA) and Okada’s Algorithm for Four-Frame Phase Shiftinga

Tables Icon

Table 2 Simulation Results of the Proposed Advanced Iterative Algorithm (AIA) for Three-Frame Phase Shifting

Equations (17)

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Iijt=Aij+Bij cosϕj+δi,
Iijt=aj+bj cos δi+cj sin δi.
Sj=i=1MIijt-Iij2=i=1Maj+bj cos δi+cj sin δi-Iij2,
Sj/aj=0,  Sj/bj=0,  Sj/cj=0.
Xj=A-1Bj,
A=Mi=1Mcos δii=1Msin δii=1Mcos δii=1Mcos2 δii=1Mcos δi sin δii=1Msin δii=1Msin δi cos δii=1Msin2 δi,
Xj=aj bj cjT,
Bj=i=1MIij i=1MIij cos δi i=1MIij sin δiT.
ϕj=tan-1-cj/bj.
Iijt=ai+bi cos ϕj+ci sin ϕj.
Si=j=1NIijt+Iij2=j=1Nai+bi cos ϕj+ci sin ϕj-Iij2.
Xi=A-1Bi,
A=Nj=1Ncos ϕjj=1Nsin ϕjj=1Ncos ϕjj=1Ncos2 ϕjj=1Ncos ϕj sin ϕjj=1Nsin ϕjj=1Nsin ϕj cos ϕjj=1Nsin2 ϕj,
Xi=ai bi ciT,
Bi=j=1NIij j=1NIij cos ϕj j=1NIij sin ϕjT.
δi=tan-1-ci/bi.
δik-δ1k-δik-1-δ1k-1<,

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