Abstract

A simple but effective approach for the demodulation of a single fringe pattern is proposed. The phase with an undetermined sign is directly obtained by taking the arccosine value of a preprocessed fringe pattern. The local frequencies, also with an undetermined sign, are then estimated by local matching. The sign ambiguity is then removed simply by forcing the continuity of the local frequencies. The priority of sign determination is guided by the value of total local frequency (fringe density) so that the critical points are processed last. The proposed approach is verified by successful demodulation of a simulated fringe pattern and two experimental fringe patterns.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Servin and F. J. Cuevas, in Proc. SPIE 5531, 395 (2004).
    [CrossRef]
  2. M. Servin, J. L. Marroguin, and F. J. Cuevas, Appl. Opt. 36, 4540 (1997).
    [CrossRef] [PubMed]
  3. M. Servin, J. L. Marroguin, and F. J. Cuevas, J. Opt. Soc. Am. A 18, 689 (2001).
    [CrossRef]
  4. M. Servin, J. L. Marroguin, and J. A. Quiroga, J. Opt. Soc. Am. A 21, 411 (2004).
    [CrossRef]
  5. K. G. Larkin, D. J. Bone, and M. A. Oldfield, J. Opt. Soc. Am. A 18, 1862 (2001).
    [CrossRef]
  6. M. Servin, J. L. Marroguin, and J. A. Quiroga, J. Opt. Soc. Am. A 20, 925 (2003).
    [CrossRef]
  7. J. A. Quiroga, M. Servin, and J. L. Marroguin, J. Opt. Soc. Am. A 19, 1524 (2002).
    [CrossRef]
  8. J. A. Quiroga, J. A. Gomez-Pedrero, and A. Garcia-Botella, Opt. Commun. 197, 43 (2001).
    [CrossRef]
  9. Q. Kemao, Opt. Lasers Eng. 45, 304 (2007).
    [CrossRef]
  10. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithm and Software (Wiley, 1998).
  11. K. Qian and S. H. Soon, Opt. Eng. 44, 075601 (2005).
    [CrossRef]

2007 (1)

Q. Kemao, Opt. Lasers Eng. 45, 304 (2007).
[CrossRef]

2005 (1)

K. Qian and S. H. Soon, Opt. Eng. 44, 075601 (2005).
[CrossRef]

2004 (2)

2003 (1)

2002 (1)

2001 (3)

1997 (1)

Bone, D. J.

Cuevas, F. J.

Garcia-Botella, A.

J. A. Quiroga, J. A. Gomez-Pedrero, and A. Garcia-Botella, Opt. Commun. 197, 43 (2001).
[CrossRef]

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithm and Software (Wiley, 1998).

Gomez-Pedrero, J. A.

J. A. Quiroga, J. A. Gomez-Pedrero, and A. Garcia-Botella, Opt. Commun. 197, 43 (2001).
[CrossRef]

Kemao, Q.

Q. Kemao, Opt. Lasers Eng. 45, 304 (2007).
[CrossRef]

Larkin, K. G.

Marroguin, J. L.

Oldfield, M. A.

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithm and Software (Wiley, 1998).

Qian, K.

K. Qian and S. H. Soon, Opt. Eng. 44, 075601 (2005).
[CrossRef]

Quiroga, J. A.

Servin, M.

Soon, S. H.

K. Qian and S. H. Soon, Opt. Eng. 44, 075601 (2005).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. A (5)

Opt. Commun. (1)

J. A. Quiroga, J. A. Gomez-Pedrero, and A. Garcia-Botella, Opt. Commun. 197, 43 (2001).
[CrossRef]

Opt. Eng. (1)

K. Qian and S. H. Soon, Opt. Eng. 44, 075601 (2005).
[CrossRef]

Opt. Lasers Eng. (1)

Q. Kemao, Opt. Lasers Eng. 45, 304 (2007).
[CrossRef]

Proc. SPIE (1)

M. Servin and F. J. Cuevas, in Proc. SPIE 5531, 395 (2004).
[CrossRef]

Other (1)

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithm and Software (Wiley, 1998).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Demodulation of a simulated fringe pattern: (a) simulated fringe pattern, (b) filtered fringe pattern, (c) normalized fringe pattern, (d) phase with undetermined signs, (e) frequency with undetermined signs, (f) TLF, (g) phase with determined signs, (h) simultaneously unwrapped phase, (i) refined phase.

Fig. 2
Fig. 2

Demodulation of an experimental fringe pattern from electronic speckle pattern interferometry: (a) original fringe pattern, (b) preprocessed fringe pattern, (c) TLF, (d) phase distribution obtained using FSD, (e) postprocessed phase distribution, (f) cosine value of (e).

Fig. 3
Fig. 3

Demodulation of an experimental fringe pattern from speckle shearography: (a) original fringe pattern, (b) preprocessed fringe pattern, (c) TLF, (d) phase distribution obtained using FSD, (e) postprocessed phase distribution, (f) cosine value of (e).

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

f ( x , y ) = a ( x , y ) + b ( x , y ) cos [ φ ( x , y ) ] + n ( x , y ) ,
f ( x , y ) = cos [ φ ( x , y ) ] .
φ 0 ( x , y ) = arccos [ f ( x , y ) ] ,
U ( x , y ) = ( ϵ , η ) N x , y { f ( ϵ , η ) cos [ ω x ( x , y ) ( ϵ x ) + ω y ( x , y ) ( η y ) + ϕ 0 ( x , y ) ] } 2 ,
ω x ( x + 1 , y ) ω x ( x , y ) + ω y ( x + 1 , y ) ω y ( x , y ) ω x ( x + 1 , y ) + ω x ( x , y ) + ω y ( x + 1 , y ) + ω y ( x , y ) ,
ω ( x , y ) = ω x 2 ( x , y ) + ω y 2 ( x , y ) .
f ( x , y ) = 1 + cos { i = 1 5 30 exp [ ( x x i ) 2 ( y y i ) 2 2 × 30 2 ] } ,

Metrics