Abstract

We present a new technique for the recovery of local phase from multiple phase-stepping fringe images that uses adaptive quadrature filters constructed by use of Bayesian estimation theory and complex-valued Markov random fields as prior models. It is shown that with this technique it is possible to perform accurate phase reconstructions even for extremely noisy fringe images and that the performance of this technique is nearly independent of the particular noise model, as long as the noise spectrum is wideband.

© 1998 Optical Society of America

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References

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  1. J. L. Marroquin, M. Servin, and R. Rodriguez-Vera, J. Opt. Soc. Am. A 14, 1742 (1997).
    [CrossRef]
  2. J. L. Marroquin, M. Servin, and J. E. Figueroa, J. Opt. Soc. Am. A 14, 779 (1997).
    [CrossRef]
  3. M. Takeda, H. Ina, and S. Kobayashi, J. Opt. Soc. Am. 72, 156 (1982).
    [CrossRef]
  4. Th. Kreis, J. Opt. Soc. Am. A 3, 847 (1986).
    [CrossRef]
  5. J. L. Marroquin, Computer Vision Graphics Image Process. 55, 408 (1993).
  6. K. Creath, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. XXVI, pp. 349–393.
    [CrossRef]
  7. R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, 1989).
    [CrossRef]
  8. M. Rivera, R. Rodriguez-Vera, and J. L. Marroquin, Appl. Opt. 36, 8391 (1997).
    [CrossRef]

1997 (3)

1993 (1)

J. L. Marroquin, Computer Vision Graphics Image Process. 55, 408 (1993).

1986 (1)

1982 (1)

Creath, K.

K. Creath, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. XXVI, pp. 349–393.
[CrossRef]

Figueroa, J. E.

Ina, H.

Jones, R.

R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, 1989).
[CrossRef]

Kobayashi, S.

Kreis, Th.

Marroquin, J. L.

Rivera, M.

Rodriguez-Vera, R.

Servin, M.

Takeda, M.

Wykes, C.

R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, 1989).
[CrossRef]

Appl. Opt. (1)

Computer Vision Graphics Image Process. (1)

J. L. Marroquin, Computer Vision Graphics Image Process. 55, 408 (1993).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Other (2)

K. Creath, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. XXVI, pp. 349–393.
[CrossRef]

R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, 1989).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

a–c, Synthetic fringe pattern images generated by the phase shown (wrapped) in d (see text). e, Wrapped phase recovered by the adaptive filter proposed here. f, Wrapped phase recovered by a standard phase-stepping processing scheme.

Fig. 2
Fig. 2

a–d, Phase-shifted electron speckle pattern interferometry images obtained from the thermal deformation of a mechanical part. e, Phase recovered by our technique.

Tables (1)

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Table 1 Schedule for Increasing the Value of λ

Equations (8)

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ϕx=arctanIm fxRe fx.
Udf=xLf x-2gx2
Unf,ω=x, yLf xexp-i/2ωx·x-y-f yexp-i/2ωy·y-x2,
Usω=xLD11ωx2+2D12ωx2+D22ωx2,
Uf,ω=Udf+λUnf,ω+μUsω,
Udf=xLk=1Kf xexpiαk-2gkx2,
gkx=axcosϕx+nx+αk, k=1,2,3,
αk=arctan-xLIm f xgkxxLRe f xgkx.

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