Abstract

An approach based on two-dimensional iterative nonlinear regression for retrieving phase information from single-frame interferograms was formulated and tested for fluid- and heat-flow measurements. Even though an initial crude phase assignment—i.e., fringe-order numbers at limited data points—is needed, the approach does not require complete phase unwrapping as in conventional techniques. Testing of computer-simulated and real interferometric data shows stable convergence and accurate phase extraction. The method works well under a high noise level, including broken fringes or contaminated regions, with a good noise-cleansing capacity. It provides accuracy at image- or opaque-object boundaries and directly offers spatial-gradient values. A weakness, however, can be intensive computation in the iterative estimation. The method is a good candidate for single-frame interferogram reduction.

© 1998 Optical Society of America

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References

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  1. G. T. Reid, “Automatic fringe pattern analysis: a review,” Opt. Lasers Eng. 7, 37–38 (1987).
    [CrossRef]
  2. J. S. Slepicka, S. S. Cha, “Stabilized nonlinear regression for interferogram analysis,” Appl. Opt. 34, 5039–5044 (1995).
    [CrossRef] [PubMed]
  3. L. W. Carr, Y. H. Yu, “The use of interferometry in the study of rotorcraft aerodynamics,” Opt. Lasers Eng. 17, 121–146 (1992).
    [CrossRef]
  4. J. A. Cobbett, S. S. Cha, “Radiative thermal loading of pyrotechnical energy pumping on phosphate laser glass,” Exp. Heat Transfer 10, 451–462 (1997).
    [CrossRef]
  5. F. Becker, Y. H. Yu, “Digital fringe reduction techniques applied to the measurement of three-dimensional transonic flow fields,” Opt. Eng. 24, 429–434 (1985).
    [CrossRef]
  6. E. Yu, S. S. Cha, W. Joo, “Use of interferometric directionality for noise reduction,” Opt. Eng. 34, 173–182 (1995).
    [CrossRef]
  7. W. Joo, S. S. Cha, “Automated interferogram analysis based on an integrated expert system,” Appl. Opt. 34, 7486–7496 (1995).
    [CrossRef] [PubMed]
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    [CrossRef]
  9. T. Kreis, “Digital holographic interference-phase measurement using the Fourier-transform method,” J. Opt. Soc. Am. A 3, 847–855 (1986).
    [CrossRef]
  10. T. R. Judge, P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199–239 (1994).
    [CrossRef]

1997 (1)

J. A. Cobbett, S. S. Cha, “Radiative thermal loading of pyrotechnical energy pumping on phosphate laser glass,” Exp. Heat Transfer 10, 451–462 (1997).
[CrossRef]

1995 (3)

1994 (1)

T. R. Judge, P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199–239 (1994).
[CrossRef]

1992 (1)

L. W. Carr, Y. H. Yu, “The use of interferometry in the study of rotorcraft aerodynamics,” Opt. Lasers Eng. 17, 121–146 (1992).
[CrossRef]

1987 (1)

G. T. Reid, “Automatic fringe pattern analysis: a review,” Opt. Lasers Eng. 7, 37–38 (1987).
[CrossRef]

1986 (1)

1985 (1)

F. Becker, Y. H. Yu, “Digital fringe reduction techniques applied to the measurement of three-dimensional transonic flow fields,” Opt. Eng. 24, 429–434 (1985).
[CrossRef]

1982 (1)

Becker, F.

F. Becker, Y. H. Yu, “Digital fringe reduction techniques applied to the measurement of three-dimensional transonic flow fields,” Opt. Eng. 24, 429–434 (1985).
[CrossRef]

Bryanston-Cross, P. J.

T. R. Judge, P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199–239 (1994).
[CrossRef]

Carr, L. W.

L. W. Carr, Y. H. Yu, “The use of interferometry in the study of rotorcraft aerodynamics,” Opt. Lasers Eng. 17, 121–146 (1992).
[CrossRef]

Cha, S. S.

J. A. Cobbett, S. S. Cha, “Radiative thermal loading of pyrotechnical energy pumping on phosphate laser glass,” Exp. Heat Transfer 10, 451–462 (1997).
[CrossRef]

E. Yu, S. S. Cha, W. Joo, “Use of interferometric directionality for noise reduction,” Opt. Eng. 34, 173–182 (1995).
[CrossRef]

J. S. Slepicka, S. S. Cha, “Stabilized nonlinear regression for interferogram analysis,” Appl. Opt. 34, 5039–5044 (1995).
[CrossRef] [PubMed]

W. Joo, S. S. Cha, “Automated interferogram analysis based on an integrated expert system,” Appl. Opt. 34, 7486–7496 (1995).
[CrossRef] [PubMed]

Cobbett, J. A.

J. A. Cobbett, S. S. Cha, “Radiative thermal loading of pyrotechnical energy pumping on phosphate laser glass,” Exp. Heat Transfer 10, 451–462 (1997).
[CrossRef]

Ina, H.

Joo, W.

E. Yu, S. S. Cha, W. Joo, “Use of interferometric directionality for noise reduction,” Opt. Eng. 34, 173–182 (1995).
[CrossRef]

W. Joo, S. S. Cha, “Automated interferogram analysis based on an integrated expert system,” Appl. Opt. 34, 7486–7496 (1995).
[CrossRef] [PubMed]

Judge, T. R.

T. R. Judge, P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199–239 (1994).
[CrossRef]

Kobayashi, S.

Kreis, T.

Reid, G. T.

G. T. Reid, “Automatic fringe pattern analysis: a review,” Opt. Lasers Eng. 7, 37–38 (1987).
[CrossRef]

Slepicka, J. S.

Takeda, M.

Yu, E.

E. Yu, S. S. Cha, W. Joo, “Use of interferometric directionality for noise reduction,” Opt. Eng. 34, 173–182 (1995).
[CrossRef]

Yu, Y. H.

L. W. Carr, Y. H. Yu, “The use of interferometry in the study of rotorcraft aerodynamics,” Opt. Lasers Eng. 17, 121–146 (1992).
[CrossRef]

F. Becker, Y. H. Yu, “Digital fringe reduction techniques applied to the measurement of three-dimensional transonic flow fields,” Opt. Eng. 24, 429–434 (1985).
[CrossRef]

Appl. Opt. (2)

Exp. Heat Transfer (1)

J. A. Cobbett, S. S. Cha, “Radiative thermal loading of pyrotechnical energy pumping on phosphate laser glass,” Exp. Heat Transfer 10, 451–462 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Eng. (2)

F. Becker, Y. H. Yu, “Digital fringe reduction techniques applied to the measurement of three-dimensional transonic flow fields,” Opt. Eng. 24, 429–434 (1985).
[CrossRef]

E. Yu, S. S. Cha, W. Joo, “Use of interferometric directionality for noise reduction,” Opt. Eng. 34, 173–182 (1995).
[CrossRef]

Opt. Lasers Eng. (3)

G. T. Reid, “Automatic fringe pattern analysis: a review,” Opt. Lasers Eng. 7, 37–38 (1987).
[CrossRef]

T. R. Judge, P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199–239 (1994).
[CrossRef]

L. W. Carr, Y. H. Yu, “The use of interferometry in the study of rotorcraft aerodynamics,” Opt. Lasers Eng. 17, 121–146 (1992).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Plots of various values in the analysis of the curved-fringe interferogram with seven fringes at a 20% noise level: (a) Noisy interferogram intensity. (b) Exact phase. (c) Phase reduced by the RM. (d) Phase reduced by the FTM.

Fig. 2
Fig. 2

Plots of various values in the analysis of the mixed-fringe interferogram at a 20% noise level: (a) Noisy interferogram intensity. (b) Exact phase. (c) Phase reduced by the RM. (d) Phase reduced by the FTM.

Fig. 3
Fig. 3

Plots of interferogram and unwrapped phase values: (a) Intensity. (b) Phase extracted by the RM. (c) Phase extracted by the FTM.

Fig. 4
Fig. 4

Plots of interferogram and unwrapped phase values: (a) Intensity. (b) Phase extracted by the RM. (c) Phase extracted by the FTM.

Tables (1)

Tables Icon

Table 1 Phase-Extraction Errors of the RM and the FTM for Computer-Generated Interferograms

Equations (9)

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I x ,   y = B x ,   y + A x ,   y cos P x ,   y ,
F x ,   y i N j M   f ij x i y j ,
B e x ,   y = I x ,   y .
I s x ,   y = I x ,   y - B e x ,   y .
cos P e x ,   y A e x ,   y = I s x ,   y .
cos P e x ,   y = I s x ,   y A e x ,   y
I n = I 0 1.0 + n σ n ,
B x ,   y = 20   ln x + 0.5 y / 150 + 0.15 + 150 , A x ,   y = 50   sin x + 0.14 y - 14 / 53 + 1.0 , P x ,   y = C 1 J 0 0.0090 xy / 150 - 1.0 + C 2 ,
P x ,   y = 20   sin 19 x / 750 + 0.30 J 0 3.0 y / 250 + 8   ln xy / 250 + 8.5 - 23 ,

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