Abstract

A new phase unwrapping algorithm is proposed which combines noise immunity with computational efficiency. It is based on the requirement that the unwrapped map should be independent of the route by which unwrapping takes place.

© 1989 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, 37–68 (1986/7).
    [CrossRef]
  2. M. Takeda, H. Ina, S. Kobayashi, “Fourier-Transform Method of Fringe-Pattern Analysis for Computer-based Topography and Interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  3. D. C. Ghiglia, G. A. Mastin, L. A. Romero, “Cellular-Automata Method for Phase Unwrapping,” J. Opt. Soc. Am. A 4, 267–280 (1987).
    [CrossRef]
  4. J. J. Gierloff, “Phase Unwrapping by Regions,” Proc. Soc. PhotoOpt. Instrum. Eng. 818, 2–9 (1987).
  5. K. Freischlad, C. L. Koliopoulos, “Wavefront Reconstruction from Noisy Slope or Difference Data Using the Discrete Fourier Transform,” Proc. Soc. Photo-Opt. Instrum. Eng. 551, 74–80 (1985).
  6. J. M. Huntley, J. E. Field, “High Resolution Moire Photography: Application to Dynamic Stress Analysis,” Opt. Eng. 28, (1989), accepted for publication.
    [CrossRef]
  7. D. J. Bone, H.-A. Bachor, R. J. Sandeman, “Fringe-Pattern Analysis Using a 2-D Fourier Transform,” Appl. Opt. 25, 1653–1660 (1986).
    [CrossRef] [PubMed]

1989

J. M. Huntley, J. E. Field, “High Resolution Moire Photography: Application to Dynamic Stress Analysis,” Opt. Eng. 28, (1989), accepted for publication.
[CrossRef]

1987

D. C. Ghiglia, G. A. Mastin, L. A. Romero, “Cellular-Automata Method for Phase Unwrapping,” J. Opt. Soc. Am. A 4, 267–280 (1987).
[CrossRef]

J. J. Gierloff, “Phase Unwrapping by Regions,” Proc. Soc. PhotoOpt. Instrum. Eng. 818, 2–9 (1987).

1986

1985

K. Freischlad, C. L. Koliopoulos, “Wavefront Reconstruction from Noisy Slope or Difference Data Using the Discrete Fourier Transform,” Proc. Soc. Photo-Opt. Instrum. Eng. 551, 74–80 (1985).

1982

Bachor, H.-A.

Bone, D. J.

Field, J. E.

J. M. Huntley, J. E. Field, “High Resolution Moire Photography: Application to Dynamic Stress Analysis,” Opt. Eng. 28, (1989), accepted for publication.
[CrossRef]

Freischlad, K.

K. Freischlad, C. L. Koliopoulos, “Wavefront Reconstruction from Noisy Slope or Difference Data Using the Discrete Fourier Transform,” Proc. Soc. Photo-Opt. Instrum. Eng. 551, 74–80 (1985).

Ghiglia, D. C.

Gierloff, J. J.

J. J. Gierloff, “Phase Unwrapping by Regions,” Proc. Soc. PhotoOpt. Instrum. Eng. 818, 2–9 (1987).

Huntley, J. M.

J. M. Huntley, J. E. Field, “High Resolution Moire Photography: Application to Dynamic Stress Analysis,” Opt. Eng. 28, (1989), accepted for publication.
[CrossRef]

Ina, H.

Kobayashi, S.

Koliopoulos, C. L.

K. Freischlad, C. L. Koliopoulos, “Wavefront Reconstruction from Noisy Slope or Difference Data Using the Discrete Fourier Transform,” Proc. Soc. Photo-Opt. Instrum. Eng. 551, 74–80 (1985).

Mastin, G. A.

Reid, G. T.

G. T. Reid, “Automatic Fringe Pattern Analysis: a Review,” Opt. Lasers Eng. 7, 37–68 (1986/7).
[CrossRef]

Romero, L. A.

Sandeman, R. J.

Takeda, M.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng.

J. M. Huntley, J. E. Field, “High Resolution Moire Photography: Application to Dynamic Stress Analysis,” Opt. Eng. 28, (1989), accepted for publication.
[CrossRef]

Opt. Lasers Eng.

G. T. Reid, “Automatic Fringe Pattern Analysis: a Review,” Opt. Lasers Eng. 7, 37–68 (1986/7).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

K. Freischlad, C. L. Koliopoulos, “Wavefront Reconstruction from Noisy Slope or Difference Data Using the Discrete Fourier Transform,” Proc. Soc. Photo-Opt. Instrum. Eng. 551, 74–80 (1985).

Proc. Soc. PhotoOpt. Instrum. Eng.

J. J. Gierloff, “Phase Unwrapping by Regions,” Proc. Soc. PhotoOpt. Instrum. Eng. 818, 2–9 (1987).

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Figures (4)

Fig. 1
Fig. 1

Crossed moire fringe pattern from high speed photographic sequence showing the impact of a steel ball on a plate of PMMA (spatial frequency of specimen grating = 150 lines mm−1; interframe time = 1 μs).

Fig. 2
Fig. 2

Phase map of the horizontal fringes from Fig. 1 after unwrapping by the conventional algorithm. Phase values have been divided by 2π; each contour represents one fringe.

Fig. 3
Fig. 3

(a) A and B are two alternative paths for unwrapping the phase at data point (m1,n1), given the phase at (m0,n0) (data points are represented by the symbol •). Path C is a closed loop consisting of path B, and path A reversed. (b) Example of a cut made between two discontinuity sources s = +1 at data point (m2,n2) and s =−1 at (m3,n3). The cut is represented by two arrays H and V referred to in the text; nonzero values only are shown here.

Fig. 4
Fig. 4

Phase map of the horizontal fringes from Fig. 1 after unwrapping by the new algorithm. Phase values have been divided by 2π; each contour represents one fringe.

Equations (4)

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d A ( i ) = [ ( Φ A ( i ) Φ A ( i 1 ) ) / 2 π ] ,
S = j = 1 N B d B ( j ) i = 1 N A d A ( i )
s ( m , n ) = [ ( Φ ( m + 1 , n ) Φ ( m , n ) ) / 2 π ] + [ ( Φ ( m + 1 , n + 1 ) Φ ( m + 1 , n ) ) / 2 π ] + [ ( Φ ( m , n + 1 ) Φ ( m + 1 , n + 1 ) ) / 2 π ] + [ ( Φ ( m , n ) Φ ( m , n + 1 ) ) / 2 π ] .
S = m , n s ( m , n ) ,

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