Abstract

Phase unwrapping has been and still is a cumbersome concern that involves the resolution of several different problems. When dealing with two-dimensional phase unwrapping in fringe analysis, the final objective is, in many cases, the realization of that analysis in real time. Many algorithms have been developed to carry out the unwrapping process, with some giving satisfactory results even when high levels of noise are present in the image. However, these algorithms are often time consuming and far removed from the goal of real-time fringe analysis. A new approach to the construction of a simple and fast algorithm for two-dimensional unwrapping that has considerable potential for parallel implementation is presented.

© 1996 Optical Society of America

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References

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  1. A. Oppenheim, R. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), Chap. 10, pp. 507–511.
  2. D. Ghiglia, G. Masting, L. Romero, “Cellular-automata method for phase unwrapping,” J. Opt. Soc. Am. A 4, 267–280 (1987).
  3. D. Towers, T. Judge, P. J. Bryanston-Cross, “A quasi heterodyne holographic technique and automatic algorithms for phase unwrapping,” in Fringe Pattern Analysis, Proc. SPIE 1163, 95–119 (1989).
  4. J. Geirloff, “Phase unwrapping by regions,” in Current Developments in Optical Engineering II, R. E. Fischer, W. J. Smith, eds., Proc. SPIE 818, 2–9 (1987).
  5. J. M. Huntley, “Noise-immune phase unwrapping algorithm,” Appl. Opt. 28, 3268–3270 (1989).
  6. J. M. Huntley, H. Saldner, “Temporal phase unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 17, 3047–3052 (1993).
  7. D. C. Ghiglia, L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. A 11, 107–117 (1994).
  8. T. R. Judge, P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21, 199–239 (1994).
  9. C. A. R. Hoare, “Quicksort,” Comput. J. 5, 10–15 (1962).
  10. P. R. Stephenson, D. R. Burton, M. J. Lalor, “Data validation techniques in a tiled phase unwrapping algorithm,” Opt. Eng. 33, 3703–3708 (1994).

1994

D. C. Ghiglia, L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. A 11, 107–117 (1994).

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

P. R. Stephenson, D. R. Burton, M. J. Lalor, “Data validation techniques in a tiled phase unwrapping algorithm,” Opt. Eng. 33, 3703–3708 (1994).

1993

J. M. Huntley, H. Saldner, “Temporal phase unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 17, 3047–3052 (1993).

1989

D. Towers, T. Judge, P. J. Bryanston-Cross, “A quasi heterodyne holographic technique and automatic algorithms for phase unwrapping,” in Fringe Pattern Analysis, Proc. SPIE 1163, 95–119 (1989).

J. M. Huntley, “Noise-immune phase unwrapping algorithm,” Appl. Opt. 28, 3268–3270 (1989).

1987

1962

C. A. R. Hoare, “Quicksort,” Comput. J. 5, 10–15 (1962).

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).

D. Towers, T. Judge, P. J. Bryanston-Cross, “A quasi heterodyne holographic technique and automatic algorithms for phase unwrapping,” in Fringe Pattern Analysis, Proc. SPIE 1163, 95–119 (1989).

Burton, D. R.

P. R. Stephenson, D. R. Burton, M. J. Lalor, “Data validation techniques in a tiled phase unwrapping algorithm,” Opt. Eng. 33, 3703–3708 (1994).

Geirloff, J.

J. Geirloff, “Phase unwrapping by regions,” in Current Developments in Optical Engineering II, R. E. Fischer, W. J. Smith, eds., Proc. SPIE 818, 2–9 (1987).

Ghiglia, D.

Ghiglia, D. C.

Hoare, C. A. R.

C. A. R. Hoare, “Quicksort,” Comput. J. 5, 10–15 (1962).

Huntley, J. M.

J. M. Huntley, H. Saldner, “Temporal phase unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 17, 3047–3052 (1993).

J. M. Huntley, “Noise-immune phase unwrapping algorithm,” Appl. Opt. 28, 3268–3270 (1989).

Judge, T.

D. Towers, T. Judge, P. J. Bryanston-Cross, “A quasi heterodyne holographic technique and automatic algorithms for phase unwrapping,” in Fringe Pattern Analysis, Proc. SPIE 1163, 95–119 (1989).

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).

Lalor, M. J.

P. R. Stephenson, D. R. Burton, M. J. Lalor, “Data validation techniques in a tiled phase unwrapping algorithm,” Opt. Eng. 33, 3703–3708 (1994).

Masting, G.

Oppenheim, A.

A. Oppenheim, R. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), Chap. 10, pp. 507–511.

Romero, L.

Romero, L. A.

Saldner, H.

J. M. Huntley, H. Saldner, “Temporal phase unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 17, 3047–3052 (1993).

Schafer, R.

A. Oppenheim, R. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), Chap. 10, pp. 507–511.

Stephenson, P. R.

P. R. Stephenson, D. R. Burton, M. J. Lalor, “Data validation techniques in a tiled phase unwrapping algorithm,” Opt. Eng. 33, 3703–3708 (1994).

Towers, D.

D. Towers, T. Judge, P. J. Bryanston-Cross, “A quasi heterodyne holographic technique and automatic algorithms for phase unwrapping,” in Fringe Pattern Analysis, Proc. SPIE 1163, 95–119 (1989).

Appl. Opt.

J. M. Huntley, “Noise-immune phase unwrapping algorithm,” Appl. Opt. 28, 3268–3270 (1989).

J. M. Huntley, H. Saldner, “Temporal phase unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 17, 3047–3052 (1993).

Comput. J.

C. A. R. Hoare, “Quicksort,” Comput. J. 5, 10–15 (1962).

Fringe Pattern Analysis

D. Towers, T. Judge, P. J. Bryanston-Cross, “A quasi heterodyne holographic technique and automatic algorithms for phase unwrapping,” in Fringe Pattern Analysis, Proc. SPIE 1163, 95–119 (1989).

J. Opt. Soc. Am. A

Opt. Eng.

P. R. Stephenson, D. R. Burton, M. J. Lalor, “Data validation techniques in a tiled phase unwrapping algorithm,” Opt. Eng. 33, 3703–3708 (1994).

Opt. Lasers Eng.

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

Other

A. Oppenheim, R. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), Chap. 10, pp. 507–511.

J. Geirloff, “Phase unwrapping by regions,” in Current Developments in Optical Engineering II, R. E. Fischer, W. J. Smith, eds., Proc. SPIE 818, 2–9 (1987).

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Figures (12)

Fig. 1
Fig. 1

Unwrapping of a 2 × 2 pixel matrix.

Fig. 2
Fig. 2

Image subdivided into four parts. Each part is independently unwrapped.

Fig. 3
Fig. 3

Pixels at the junction of two sections.

Fig. 4
Fig. 4

Region with one masked subarea (number 2).

Fig. 5
Fig. 5

Masked junctions. The shaded areas that border subarea adjacencies represent the masked junctions.

Fig. 6
Fig. 6

Two different subareas from Fig. 5 that can be unwrapped. A decision must be made by the unwrapping algorithm.

Fig. 7
Fig. 7

Example of overmasking produced because the connections between subareas cannot be established.

Fig. 8
Fig. 8

Points within larger areas: (a) one pixel (shaded square) within a larger area, and (b) a large area that is being built up from its recursive components [the shaded square represents the pixel from (a)].

Fig. 9
Fig. 9

Pixel (shaded square) placed between the first junctions to be decomposed.

Fig. 10
Fig. 10

(a) Representation of a fringe break within an area. The dashed part of the line represents the break. (b) Location of the fringe-break area in (a) within the whole image.

Fig. 11
Fig. 11

Representation (boldface line segments) of the junctions that are to be checked.

Fig. 12
Fig. 12

Results obtained by the use of the unwrapping algorithm presented here: (a), (b), and (c) depict the wrapped phase distributions, whereas (d), (e), and (f) present their phase distributions, respectively, after the unwrapping process has been applied. The phase distributions are displayed in normalized form with a gray scale, in which black represents the minimum and white the maximum phase values.

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