Abstract

A robust procedure for analyzing fringe patterns obtained from speckle interferometric techniques is proposed. The fringes generally are observed only in a region S of a rectangular lattice L. We give a method for computing (from S) the region R, where the unwrapped phase is to be computed; this computation is done by use of a morphological filter (in particular, a closing filter). We then use a fast-unwrapping algorithm to compute the phase: a preconditioned conjugate-gradient algorithm that uses the discrete Fourier transform.

© 1997 Optical Society of America

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References

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  1. J. L. Marroquín, M. Rivera, “Quadratic regularization phase functional for phase unwrapping,” J. Opt. Soc. Am. A 12, 2393–2400 (1995).
    [CrossRef]
  2. M. Rivera, J. L. Marroquin, M. Servin, R. Rodriguez-Vera, “Fast algorithm for integrating inconsistent gradient fields,” Appl. Opt. 36, 8381–8390 (1997).
    [CrossRef]
  3. K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. 24, 3053–3058 (1985).
    [CrossRef] [PubMed]
  4. J. Serra, Image Analysis and Mathematical Morphology (Academic, New York, 1982).
  5. R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, Cambridge, 1989).
    [CrossRef]
  6. D. Kerr, F. Mendoza Santoyo, J. R. Tyrer, “Manipulation of the Fourier components of speckle fringe patterns as part of an interferometric analysis process,” J. Mod. Opt. 36, 195–203 (1989).
    [CrossRef]
  7. A. Davila, G. H. Kaufmann, D. Kerr, “An evaluation of synthetic aperture radar noise reduction for the smoothing of electronic speckle pattern interferometry fringes,” J. Mod. Opt. 42, 1795–1804 (1995).
    [CrossRef]
  8. H. A. Vrooman, A. A. M. Maas, “Image processing algorithms for the analysis of phase-shifted speckle interference patterns,” Appl. Opt. 30, 1636–1641 (1991).
    [CrossRef] [PubMed]
  9. K. Itoh, “Analysis of the phase unwrapping algorithm,” Appl. Opt. 21, 2470 (1982).
    [CrossRef] [PubMed]
  10. K. A. Stetson, “Noise-immune method for locating wrap regions in phase-step interferometry,” Opt. Lett. 21, 1268–1270 (1996).
    [CrossRef] [PubMed]
  11. J. M. Huntley, H. Sander, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993).
    [CrossRef] [PubMed]

1997 (1)

1996 (1)

1995 (2)

J. L. Marroquín, M. Rivera, “Quadratic regularization phase functional for phase unwrapping,” J. Opt. Soc. Am. A 12, 2393–2400 (1995).
[CrossRef]

A. Davila, G. H. Kaufmann, D. Kerr, “An evaluation of synthetic aperture radar noise reduction for the smoothing of electronic speckle pattern interferometry fringes,” J. Mod. Opt. 42, 1795–1804 (1995).
[CrossRef]

1993 (1)

1991 (1)

1989 (1)

D. Kerr, F. Mendoza Santoyo, J. R. Tyrer, “Manipulation of the Fourier components of speckle fringe patterns as part of an interferometric analysis process,” J. Mod. Opt. 36, 195–203 (1989).
[CrossRef]

1985 (1)

1982 (1)

Creath, K.

Davila, A.

A. Davila, G. H. Kaufmann, D. Kerr, “An evaluation of synthetic aperture radar noise reduction for the smoothing of electronic speckle pattern interferometry fringes,” J. Mod. Opt. 42, 1795–1804 (1995).
[CrossRef]

Huntley, J. M.

Itoh, K.

Jones, R.

R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, Cambridge, 1989).
[CrossRef]

Kaufmann, G. H.

A. Davila, G. H. Kaufmann, D. Kerr, “An evaluation of synthetic aperture radar noise reduction for the smoothing of electronic speckle pattern interferometry fringes,” J. Mod. Opt. 42, 1795–1804 (1995).
[CrossRef]

Kerr, D.

A. Davila, G. H. Kaufmann, D. Kerr, “An evaluation of synthetic aperture radar noise reduction for the smoothing of electronic speckle pattern interferometry fringes,” J. Mod. Opt. 42, 1795–1804 (1995).
[CrossRef]

D. Kerr, F. Mendoza Santoyo, J. R. Tyrer, “Manipulation of the Fourier components of speckle fringe patterns as part of an interferometric analysis process,” J. Mod. Opt. 36, 195–203 (1989).
[CrossRef]

Maas, A. A. M.

Marroquin, J. L.

Marroquín, J. L.

Mendoza Santoyo, F.

D. Kerr, F. Mendoza Santoyo, J. R. Tyrer, “Manipulation of the Fourier components of speckle fringe patterns as part of an interferometric analysis process,” J. Mod. Opt. 36, 195–203 (1989).
[CrossRef]

Rivera, M.

Rodriguez-Vera, R.

Sander, H.

Serra, J.

J. Serra, Image Analysis and Mathematical Morphology (Academic, New York, 1982).

Servin, M.

Stetson, K. A.

Tyrer, J. R.

D. Kerr, F. Mendoza Santoyo, J. R. Tyrer, “Manipulation of the Fourier components of speckle fringe patterns as part of an interferometric analysis process,” J. Mod. Opt. 36, 195–203 (1989).
[CrossRef]

Vrooman, H. A.

Wykes, C.

R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, Cambridge, 1989).
[CrossRef]

Appl. Opt. (5)

J. Mod. Opt. (2)

D. Kerr, F. Mendoza Santoyo, J. R. Tyrer, “Manipulation of the Fourier components of speckle fringe patterns as part of an interferometric analysis process,” J. Mod. Opt. 36, 195–203 (1989).
[CrossRef]

A. Davila, G. H. Kaufmann, D. Kerr, “An evaluation of synthetic aperture radar noise reduction for the smoothing of electronic speckle pattern interferometry fringes,” J. Mod. Opt. 42, 1795–1804 (1995).
[CrossRef]

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

Opt. Lett. (1)

Other (2)

J. Serra, Image Analysis and Mathematical Morphology (Academic, New York, 1982).

R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2nd ed. (Cambridge U. Press, Cambridge, 1989).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Images of three speckle interferograms recorded with phase shifts of 2π/3 rad: (a) l = -1, (b) l = 0, and (c) l = 1.

Fig. 2
Fig. 2

Enhanced (smoothed) images of the three speckle interferograms shown in Fig. 1: (a) l = -1, (b) l = 0, and (c) l = 1.

Fig. 3
Fig. 3

(a) Calculated wrapped phase. The white areas are where (b) the wrapped phase data are valid, and (c) the unwrapped phase is computed. (d) The unwrapped phase.

Equations (17)

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Ilx, y=ax, y+bx, y×cosϕx, y+nx, y+2π3l
gx, y=tan-1βx, yαx, y,
βx, y3Ĩ-1x, y-Ĩ1x, y, αx, y2˜I0x, y-Ĩ-1x, y-Ĩ1x, y,
Hu, v=DFThx, y,
hx, y1δ2exp-πx2+y2δ2,
Ŝx, y=1bˆx, y>0otherwise,
Rx, y1where ϕˆx, y is computed0otherwise
Rx, y=CŜx, y,
Cfx, yEDfx, y,
Dfx, y=1 ifx=-M/2M/2y=-N/2N/2fx-x, y-y×mx, y>0,0 otherwise,Efx, y=1ifx=-M/2M/2y=-N/2N/2fx-x, y-y×mx, y=x=0M-1y=0N-1mx, y0otherwise,
Uϕˆxx, y, ϕˆyx, y=x, yϕˆxx, y-gxx, y2Ŝxx, y+x, yϕˆyx, y-gyx, y2Ŝyx, y+λx, yΔyBϕˆxx, y-ΔxBϕˆyx, y2+νx, yϕˆxx, y21-Ŝxx, y+νx, yϕˆyx, y21-Ŝyx, y,
gxx, yWΔxBgx, y, gyx, yWΔyBgx, y,
Ŝxx, y=1xŜx, yŜx-1, yXx, y00otherwiseŜyx, y=1yŜx, yŜx, y-1Yx, y00otherwise
gπ/2x, y=tan-1αx, y-βx, y,
Xx, y=0ΔxBgx, y>π,ΔxBgπ/2x, y>π1otherwise,Yx, y=0ΔyBgx, y>π,ΔyBgπ/2x, y>π1otherwise,
ϕˆx, y=i=0xϕˆxi, 0+j=1yϕˆyi,jRx, y,
mk, l=000111000011111110011111110111111111111111111111111111011111110011111110000111000.

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