Abstract

An efficient method is proposed to reduce the noise from electrical speckle pattern interferometry (ESPI) phase fringe patterns obtained by any technique. We establish the filtering windows along the tangent direction of phase fringe patterns. The x and y coordinates of each point in the established filtering windows are defined as the sine and cosine of the half-wrapped phase multiplied by a random quantity, then phase value is calculated using these points' coordinates based on a least-squares fitting algorithm. We tested the proposed methods on the computer-simulated speckle phase fringe patterns and the experimentally obtained phase fringe pattern, respectively, and compared them with the improved sine∕cosine average filtering method [Opt. Commun. 162, 205 (1999)] and the least-squares phase-fitting method [Opt. Lett. 20, 931 (1995)], which may be the most efficient methods. In all cases, our results are even better than the ones obtained with the two methods. Our method can overcome the main disadvantages encountered by the two methods.

© 2007 Optical Society of America

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References

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  1. X. Su and W. Chen, "Fourier transform profilometry: a review," Opt. Laser Eng. 35, 263-284 (2001).
    [CrossRef]
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    [CrossRef]
  5. M. Servin, J. L. Marroquin, and F. J. Cuevas, "Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms," J. Opt. Soc. Am. A 18, 689-695 (2001).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. C. Tang, F. Zhang, and Z. Chen, "Contrast enhancement for electronic speckle pattern interferometry fringes by the differential equation enhancement method," Appl. Opt. 45, 2287-2294 (2006).
    [CrossRef] [PubMed]
  15. Q. F. Yu, X. L. Liu, and K. Andresen, "New spin filters for interferometric fringe patterns and grating patterns," Appl. Opt. 33, 3705-3711 (1994).
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  16. A. Federico and G. H. Kaufmann, "Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes," Opt. Eng. 40, 2598-2604 (2001).
    [CrossRef]
  17. A. Dávila, G. H. Kaufmann, and D. Kerr, "Scale-space filter for smoothing electronic speckle pattern interferometry fringes," Opt. Eng. 35, 3549-3554 (1996).
    [CrossRef]

2006

C. Tang, F. Zhang, H. Yan, and Z. Chen, "Denoising in electronic speckle pattern interferometry fringes by the filtering method based on partial differential equations," Opt. Commun. 260, 91-96 (2006).
[CrossRef]

C. Tang, F. Zhang, and Z. Chen, "Contrast enhancement for electronic speckle pattern interferometry fringes by the differential equation enhancement method," Appl. Opt. 45, 2287-2294 (2006).
[CrossRef] [PubMed]

2005

2003

2002

F. J. Cuevas, J. H. Sossa-Azuela, and M. Servin, "A parametric method applied to phase recovery from a fringe pattern based on a genetic algorithm," Opt. Commun. 203, 213-223 (2002).
[CrossRef]

2001

X. Su and W. Chen, "Fourier transform profilometry: a review," Opt. Laser Eng. 35, 263-284 (2001).
[CrossRef]

A. Federico and G. H. Kaufmann, "Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes," Opt. Eng. 40, 2598-2604 (2001).
[CrossRef]

M. Servin, J. L. Marroquin, and F. J. Cuevas, "Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms," J. Opt. Soc. Am. A 18, 689-695 (2001).
[CrossRef]

P. Picart, J. C. Pascal, and J. M. Breteau, "Systematic errors of phase-shifting speckle interferometry," Appl. Opt. 40, 2107-2116 (2001).
[CrossRef]

1999

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

1998

1997

1996

A. Dávila, G. H. Kaufmann, and D. Kerr, "Scale-space filter for smoothing electronic speckle pattern interferometry fringes," Opt. Eng. 35, 3549-3554 (1996).
[CrossRef]

1995

1994

1984

K. H. Womack, "Interferometric phase measurement using spatial synchronous detection," Opt. Eng. 23, 391-395 (1984).

Aebischer, H. A.

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

Andresen, K.

Breteau, J. M.

Chang, S. W.

Chen, W.

X. Su and W. Chen, "Fourier transform profilometry: a review," Opt. Laser Eng. 35, 263-284 (2001).
[CrossRef]

Chen, Z.

C. Tang, F. Zhang, and Z. Chen, "Contrast enhancement for electronic speckle pattern interferometry fringes by the differential equation enhancement method," Appl. Opt. 45, 2287-2294 (2006).
[CrossRef] [PubMed]

C. Tang, F. Zhang, H. Yan, and Z. Chen, "Denoising in electronic speckle pattern interferometry fringes by the filtering method based on partial differential equations," Opt. Commun. 260, 91-96 (2006).
[CrossRef]

Cuevas, F. J.

F. J. Cuevas, J. H. Sossa-Azuela, and M. Servin, "A parametric method applied to phase recovery from a fringe pattern based on a genetic algorithm," Opt. Commun. 203, 213-223 (2002).
[CrossRef]

M. Servin, J. L. Marroquin, and F. J. Cuevas, "Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms," J. Opt. Soc. Am. A 18, 689-695 (2001).
[CrossRef]

Dávila, A.

A. Dávila, G. H. Kaufmann, and D. Kerr, "Scale-space filter for smoothing electronic speckle pattern interferometry fringes," Opt. Eng. 35, 3549-3554 (1996).
[CrossRef]

Federico, A.

A. Federico and G. H. Kaufmann, "Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes," Opt. Eng. 40, 2598-2604 (2001).
[CrossRef]

He, X.

Hong, C. K.

Kaufmann, G. H.

A. Federico and G. H. Kaufmann, "Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes," Opt. Eng. 40, 2598-2604 (2001).
[CrossRef]

A. Dávila, G. H. Kaufmann, and D. Kerr, "Scale-space filter for smoothing electronic speckle pattern interferometry fringes," Opt. Eng. 35, 3549-3554 (1996).
[CrossRef]

Kerr, D.

A. Dávila, G. H. Kaufmann, and D. Kerr, "Scale-space filter for smoothing electronic speckle pattern interferometry fringes," Opt. Eng. 35, 3549-3554 (1996).
[CrossRef]

Lim, H. C.

Liu, X. L.

Malacara, D.

Marroquin, J. L.

Pascal, J. C.

Picart, P.

Quan, C.

Rodriguez-Vera, R.

Ryu, H. S.

Servin, M.

Sossa-Azuela, J. H.

F. J. Cuevas, J. H. Sossa-Azuela, and M. Servin, "A parametric method applied to phase recovery from a fringe pattern based on a genetic algorithm," Opt. Commun. 203, 213-223 (2002).
[CrossRef]

Su, X.

X. Su and W. Chen, "Fourier transform profilometry: a review," Opt. Laser Eng. 35, 263-284 (2001).
[CrossRef]

Tang, C.

C. Tang, F. Zhang, and Z. Chen, "Contrast enhancement for electronic speckle pattern interferometry fringes by the differential equation enhancement method," Appl. Opt. 45, 2287-2294 (2006).
[CrossRef] [PubMed]

C. Tang, F. Zhang, H. Yan, and Z. Chen, "Denoising in electronic speckle pattern interferometry fringes by the filtering method based on partial differential equations," Opt. Commun. 260, 91-96 (2006).
[CrossRef]

Tay, C. J.

Vera, R. R.

Waldner, S.

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

Womack, K. H.

K. H. Womack, "Interferometric phase measurement using spatial synchronous detection," Opt. Eng. 23, 391-395 (1984).

Yan, H.

C. Tang, F. Zhang, H. Yan, and Z. Chen, "Denoising in electronic speckle pattern interferometry fringes by the filtering method based on partial differential equations," Opt. Commun. 260, 91-96 (2006).
[CrossRef]

Yang, F.

Yu, Q. F.

Yun, H. Y.

Zhang, F.

C. Tang, F. Zhang, and Z. Chen, "Contrast enhancement for electronic speckle pattern interferometry fringes by the differential equation enhancement method," Appl. Opt. 45, 2287-2294 (2006).
[CrossRef] [PubMed]

C. Tang, F. Zhang, H. Yan, and Z. Chen, "Denoising in electronic speckle pattern interferometry fringes by the filtering method based on partial differential equations," Opt. Commun. 260, 91-96 (2006).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Commun.

F. J. Cuevas, J. H. Sossa-Azuela, and M. Servin, "A parametric method applied to phase recovery from a fringe pattern based on a genetic algorithm," Opt. Commun. 203, 213-223 (2002).
[CrossRef]

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

C. Tang, F. Zhang, H. Yan, and Z. Chen, "Denoising in electronic speckle pattern interferometry fringes by the filtering method based on partial differential equations," Opt. Commun. 260, 91-96 (2006).
[CrossRef]

Opt. Eng.

A. Federico and G. H. Kaufmann, "Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes," Opt. Eng. 40, 2598-2604 (2001).
[CrossRef]

A. Dávila, G. H. Kaufmann, and D. Kerr, "Scale-space filter for smoothing electronic speckle pattern interferometry fringes," Opt. Eng. 35, 3549-3554 (1996).
[CrossRef]

K. H. Womack, "Interferometric phase measurement using spatial synchronous detection," Opt. Eng. 23, 391-395 (1984).

Opt. Laser Eng.

X. Su and W. Chen, "Fourier transform profilometry: a review," Opt. Laser Eng. 35, 263-284 (2001).
[CrossRef]

Opt. Lett.

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Figures (7)

Fig. 1
Fig. 1

Distribution of the points whose x and y coordinates are given by Eqs. (8) and (9) within a small filtering window 3 × 7 , where the inclination angle of the line AB is obtained based on Eq. (6) using these points' coordinates.

Fig. 2
Fig. 2

Eight quantified directions: (a)–(h) directions 0–7 in a given mask (size 7 × 7 ), where the center point of the mask just corresponds to the current pixel (i, j).

Fig. 3
Fig. 3

Filtering window along the tangent direction.

Fig. 4
Fig. 4

Computer-simulated phase pattern corresponding to Eq. (14) and its filtered images: (a) Original image. (b) The filtered image by TLSFF with a 3 × 7 window for three iterations. (c1), (c2) The filtered images by ISCAF with 3 × 7 and 7 × 3 windows for three iterations. (d1), (d2) The filtered images by LSF with 3 × 7 and 7 × 3 windows.

Fig. 5
Fig. 5

Computer-simulated phase pattern corresponding to Eq. (15) and its filtered images: (a) Original image. (b) The filtered image by TLSFF with a 3 × 7 window for three iterations. (c1), (c2) The filtered images by ISCAF with 3 × 7 and 7 × 3 windows for three iterations. (d1), (d2) The filtered images by LSF with 3 × 7 and 7 × 3 windows.

Fig. 6
Fig. 6

Computer-simulated phase pattern corresponding to Eq. (16) and its filtered images: (a) Original image. (b) The filtered image by TLSFF with a 3 × 7 window for two iterations. (c1), (c2) The filtered images by ISCAF with 3 × 7 and 7 × 3 windows for two iterations. (d1), (d2) The filtered images by LSF with 3 × 7 and 7 × 3 windows.

Fig. 7
Fig. 7

Experimentally obtained phase fringe pattern and its filtered images: (a) Original image. (b) The filtered image by TLSFF with a 3 × 7 window for three iterations. (c1), (c2) The filtered images by ISCAF with 3 × 7 and 7 × 3 windows for three iterations. (d1), (d2) The filtered images by LSF with 3 × 7 and 7 × 3 windows.

Tables (1)

Tables Icon

Table 1 Performance Evaluation Results Based on Phase Patterns Shown in Figs. 4–7

Equations (24)

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I 1 , i , j = I 0 , i , j + I r , i , j + 2 I 0 , i , j I r , i , j   cos   φ i , j + n 0 , i , j ,
I 2 , i , j = I 0 , i , j + I r , i , j + 2 I 0 , i , j I r , i , j   cos ( φ i , j + π 2 ) + n 0 , i , j ,
I 3 , i , j = I 0 , i , j + I r , i , j + 2 I 0 , i , j I r , i , j   cos ( φ i , j + ψ i , j + π 2 ) + n 0 , i , j ,
I 4, i , j = I 0 , i , j + I r , i , j + 2 I 0 , i , j I r , i , j   cos ( φ i , j + ψ i , j + π ) + n 0 , i , j ,
ψ i , j = 2 tan 1 ( I 2 , i , j I 3 , i , j I 1 , i , j I 4, i , j ) .
x i , j = I 1 , i , j I 4, i , j = 4 I r , i , j I 0 , i , j   cos [ φ i , j + ψ i , j / 2 ] × cos [ ψ i , j / 2 ] ,
y i , j = I 2 , i , j I 3, i , j = 4 I r , i , j I 0 , i , j   cos [ φ i , j + ψ i , j / 2 ] × sin [ ψ i , j / 2 ] .
k , l ( ϕ ) = k , l ( x k , l 2 sin 2 ϕ 2 x k , l y k , l   sin   ϕ   cos   ϕ + y k , l 2 cos 2 ϕ ) ,
( ϕ ) ϕ = 0.
ϕ i , j = 1 2 tan 1 [ 2 k , l x k , l y k , l k , l ( x k , l 2 y k , l 2 ) ] .
ψ i , j = 2 ϕ i , j .
x i , j = R i , j × cos ( ψ i , j / 2 ) ,
y i , j = R i , j × sin ( ψ i , j / 2 ) ,
ψ i , j = 2 tan 1 ( y i , j x i , j ) .
A i , j d = 1 m l = 1 m f l d ,
C i , j d = l = 1 m | f l d A i j d | ,
d * = ( d + 4 ) mod 8.
ψ i , j = 30 × { exp [ ( i 0 .5 M ) 2 + j 2 10000 ] exp [ ( i 0.5 M ) 2 + ( j N ) 2 10000 ] } ,
M = 244 ,   N = 244 ,   I n = 80 ;
ψ i , j = 25 × { exp [ ( 1.4 i 7 8 ) 2 ( j 78 ) 2 45000 ] + exp [ ( 1.4 i 1 2 8 ) 2 ( j 1 9 2 ) 2 45000 ] } ,
M = 244 ,   N = 244 ,   I n = 70 ;
ψ i , j = 2 π [ ( 6 × i 0.5 M M ) 2 + ( 6 × j 0.5 N N ) 2 ] ,
M = 244 ,   N = 244 ,   I n = 20 ,
f = 1 ( I 0 I ) 2 I 0 2 ,

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