Abstract

Most phase unwrapping algorithms shift the 2π phase jump pixels to obtain the unwrapped phases, while most filtering algorithms remove the noisy pixels to avoid the fault of unwrapped phases. Thus, finding the positions of phase jump pixels and noisy pixels is important. This study proposed a modified detection scheme developed from the originally published noise and phase jump detection scheme [Opt. Express 19, 3086 (2011)]. The original detection scheme finds the noise positions and phase jump positions, and then marks these pixels in two maps, namely, the noise map and the phase jump map. One 2π phase jump contains a 2π-high position and a 0-low position. However, the original detection scheme usually finds a 2π-high position and misses a corresponding 0-low position, or usually finds a 0-low position and misses a corresponding 2π-high position. Moreover, the original detection scheme produces detection errors, containing the repeated pixels of phase jump or the wrong pixels generated by noise. Fortunately, the proposed modified detection scheme can find both the 2π-high position and the corresponding 0-low position. Moreover, the detection errors are also reduced by the proposed modified detection scheme. The robustness of the modified detection scheme is demonstrated both numerically and experimentally.

© 2013 Optical Society of America

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2012 (3)

2011 (1)

2010 (1)

2009 (1)

2008 (1)

2007 (2)

Y. Shi, “Robust phase unwrapping by spinning iteration,” Opt. Express 15, 8059–8064 (2007).
[CrossRef]

R. Yamaki and A. Hirose, “Singularity-spreading phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 45, 3240–3251 (2007).
[CrossRef]

2005 (1)

2001 (1)

1999 (1)

H. A. Aebischery and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[CrossRef]

1998 (1)

H. Y. Chang, C. W. Chen, C. K. Lee, and C. P. Hu, “The Tapestry Cellular Automata phase unwrapping algorithm for interferogram analysis,” Opt. Lasers Eng. 30, 487–502 (1998).
[CrossRef]

1997 (3)

1995 (1)

1993 (1)

1991 (1)

A. Spik and D. W. Robinson, “Investigation of the cellular automata method for phase unwrapping and its implementation on an array processor,” Opt. Lasers Eng. 14, 25–37 (1991).
[CrossRef]

1987 (2)

1985 (1)

1983 (1)

Aebischery, H. A.

H. A. Aebischery and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[CrossRef]

Bertani, D.

A. Capanni, L. Pezzati, D. Bertani, M. Cetica, and F. Francini, “Phase-shifting speckle interferometry: a noise reduction filter for phase unwrapping,” Opt. Eng. 36, 2466–2472 (1997).
[CrossRef]

Brady, D.

Capanni, A.

A. Capanni, L. Pezzati, D. Bertani, M. Cetica, and F. Francini, “Phase-shifting speckle interferometry: a noise reduction filter for phase unwrapping,” Opt. Eng. 36, 2466–2472 (1997).
[CrossRef]

Cetica, M.

A. Capanni, L. Pezzati, D. Bertani, M. Cetica, and F. Francini, “Phase-shifting speckle interferometry: a noise reduction filter for phase unwrapping,” Opt. Eng. 36, 2466–2472 (1997).
[CrossRef]

Chang, H. Y.

H. Y. Chang, C. W. Chen, C. K. Lee, and C. P. Hu, “The Tapestry Cellular Automata phase unwrapping algorithm for interferogram analysis,” Opt. Lasers Eng. 30, 487–502 (1998).
[CrossRef]

Chen, C. W.

H. Y. Chang, C. W. Chen, C. K. Lee, and C. P. Hu, “The Tapestry Cellular Automata phase unwrapping algorithm for interferogram analysis,” Opt. Lasers Eng. 30, 487–502 (1998).
[CrossRef]

Cheng, J.

Creath, K.

Eiju, T.

Estrada, J. C.

Fetterman, M.

Flynn, T. J.

Francini, F.

A. Capanni, L. Pezzati, D. Bertani, M. Cetica, and F. Francini, “Phase-shifting speckle interferometry: a noise reduction filter for phase unwrapping,” Opt. Eng. 36, 2466–2472 (1997).
[CrossRef]

Ghiglia, D. C.

Hariharan, P.

Hirose, A.

R. Yamaki and A. Hirose, “Singularity-spreading phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 45, 3240–3251 (2007).
[CrossRef]

Hu, C. P.

H. Y. Chang, C. W. Chen, C. K. Lee, and C. P. Hu, “The Tapestry Cellular Automata phase unwrapping algorithm for interferogram analysis,” Opt. Lasers Eng. 30, 487–502 (1998).
[CrossRef]

Huntley, J. M.

Ishii, Y.

Javidi, B.

Jiang, J.

Kato, M.

Krishnaswamy, S.

Lee, C. K.

H. Y. Chang, C. W. Chen, C. K. Lee, and C. P. Hu, “The Tapestry Cellular Automata phase unwrapping algorithm for interferogram analysis,” Opt. Lasers Eng. 30, 487–502 (1998).
[CrossRef]

Liu, Z.

Lo, Y. L.

Luong, B.

Macy, W. W.

Mastin, G.

Moon, I.

Navarro, M. A.

Oreb, B. F.

Pezzati, L.

A. Capanni, L. Pezzati, D. Bertani, M. Cetica, and F. Francini, “Phase-shifting speckle interferometry: a noise reduction filter for phase unwrapping,” Opt. Eng. 36, 2466–2472 (1997).
[CrossRef]

Potuluri, P.

Pouet, B. F.

Quiroga, J. A.

Reichard, K.

Robinson, D. W.

A. Spik and D. W. Robinson, “Investigation of the cellular automata method for phase unwrapping and its implementation on an array processor,” Opt. Lasers Eng. 14, 25–37 (1991).
[CrossRef]

Romero, L. A.

Saldner, H.

Saldner, H. O.

Servin, M.

Shi, K.

Shi, Y.

Spik, A.

A. Spik and D. W. Robinson, “Investigation of the cellular automata method for phase unwrapping and its implementation on an array processor,” Opt. Lasers Eng. 14, 25–37 (1991).
[CrossRef]

Su, W. H.

Vargas, J.

Wada, A.

Waldner, S.

H. A. Aebischery and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[CrossRef]

Wang, B.

Weng, J. F.

Yamaki, R.

R. Yamaki and A. Hirose, “Singularity-spreading phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 45, 3240–3251 (2007).
[CrossRef]

Yin, S.

Appl. Opt. (6)

IEEE Trans. Geosci. Remote Sens. (1)

R. Yamaki and A. Hirose, “Singularity-spreading phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 45, 3240–3251 (2007).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Commun. (1)

H. A. Aebischery and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[CrossRef]

Opt. Eng. (1)

A. Capanni, L. Pezzati, D. Bertani, M. Cetica, and F. Francini, “Phase-shifting speckle interferometry: a noise reduction filter for phase unwrapping,” Opt. Eng. 36, 2466–2472 (1997).
[CrossRef]

Opt. Express (7)

Opt. Lasers Eng. (2)

A. Spik and D. W. Robinson, “Investigation of the cellular automata method for phase unwrapping and its implementation on an array processor,” Opt. Lasers Eng. 14, 25–37 (1991).
[CrossRef]

H. Y. Chang, C. W. Chen, C. K. Lee, and C. P. Hu, “The Tapestry Cellular Automata phase unwrapping algorithm for interferogram analysis,” Opt. Lasers Eng. 30, 487–502 (1998).
[CrossRef]

Opt. Lett. (2)

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Figures (11)

Fig. 1.
Fig. 1.

Cross section shown in 3D wrapped phase. Note that one phase jump includes a 2 π -high position (i.e., A1) and a 0-low position (i.e., B1). Note also that two pixels A1, A2 are detected by using Eq. (1), while the pixel B1 is not detected by using Eq. (1). Pixel P is a good pixel without noise.

Fig. 2.
Fig. 2.

(a) Proposed mask composed of three pixels, ϕ P j ( i , j ) , ϕ ( i 1 , j ) , and ϕ ( i + 1 , j ) in row direction. (b) Limitation of the mask in Situation (1).

Fig. 3.
Fig. 3.

Curved wrapped phase map.

Fig. 4.
Fig. 4.

Detection results obtained for curved wrapped phase map in Fig. 3(a) given threshold parameter of σ A = 2.8 : (a) phase jump map using Eq. (1) and (b) modified phase jump map using Situations (1)–(4).

Fig. 5.
Fig. 5.

Phase values in pixel column 91 in curved wrapped phase map with (a) corresponding phase jump positions in Fig. 4(a) and (b) corresponding modified phase jump positions in Fig. 4(b).

Fig. 6.
Fig. 6.

Phase values in pixel column 23 with (a) corresponding phase jump positions in Fig. 4(a) containing regions of PJ1 and PJ2 and (b) corresponding modified phase jump positions in Fig. 4(b) containing regions of PJ1′ and PJ2′.

Fig. 7.
Fig. 7.

Phase values in pixel column 22 (no phase jump) with (a) corresponding phase jump positions in Fig. 4(a) containing region of PJ12 and (b) corresponding modified phase jump positions in Fig. 4(b) containing region of PJ12′.

Fig. 8.
Fig. 8.

Wrapped phase map of TaSiN sample obtained using white-light source, including the residual noise marked in regions D and E.

Fig. 9.
Fig. 9.

Detection results obtained for rough TaSiN sample given white-light source and σ A = 2.8 . (a) Noise map using Eq. (1), (b) phase jump map using Eq. (1), and (c) modified phase jump map using Situations (1)–(4).

Fig. 10.
Fig. 10.

Phase values of pixels in pixel column 200 with (a) phase jump detection result using Eq. (1) and (b) phase jump detection result using Situations (1)–(4).

Fig. 11.
Fig. 11.

(a) Wrapped phase of Fig. 6(a) containing the detection errors (i.e., the repeated pixels). (b) Wrapped phase of Fig. 8(a) containing two detection errors (i.e., the wrong pixels produced by the noise) within the region E′.

Equations (3)

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S 1 ( i , j ) = [ ϕ ( i + 1 , j ) ϕ ( i , j ) σ A 2 π ] + [ ϕ ( i + 1 , j + 1 ) ϕ ( i + 1 , j ) + σ A 2 π ] + [ ϕ ( i , j + 1 ) ϕ ( i + 1 , j + 1 ) σ A 2 π ] + [ ϕ ( i , j ) ϕ ( i , j + 1 ) + σ A 2 π ] , S 2 ( i , j ) = [ ϕ ( i + 1 , j ) ϕ ( i , j ) + σ A 2 π ] + [ ϕ ( i + 1 , j + 1 ) ϕ ( i + 1 , j ) σ A 2 π ] + [ ϕ ( i , j + 1 ) ϕ ( i + 1 , j + 1 ) + σ A 2 π ] + [ ϕ ( i , j ) ϕ ( i , j + 1 ) σ A 2 π ] , S 3 ( i , j ) = [ ϕ ( i + 1 , j ) ϕ ( i , j ) + σ A 2 π ] + [ ϕ ( i + 1 , j + 1 ) ϕ ( i + 1 , j ) + σ A 2 π ] + [ ϕ ( i , j + 1 ) ϕ ( i + 1 , j + 1 ) σ A 2 π ] + [ ϕ ( i , j ) ϕ ( i , j + 1 ) σ A 2 π ] , S 4 ( i , j ) = [ ϕ ( i + 1 , j ) ϕ ( i , j ) σ A 2 π ] + [ ϕ ( i + 1 , j + 1 ) ϕ ( i + 1 , j ) σ A 2 π ] + [ ϕ ( i , j + 1 ) ϕ ( i + 1 , j + 1 ) + σ A 2 π ] + [ ϕ ( i , j ) ϕ ( i , j + 1 ) + σ A 2 π ] ,
| PD | < π σ A .
| PD | π σ A .

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