Abstract

In optical metrology, state of the art algorithms for background and noise removal of fringe patterns are based on space-frequency analysis. In this Letter, an approach based on variational image decomposition is proposed to remove background and noise from a fringe pattern simultaneously. In the proposed method, a fringe image is directly decomposed into three components: a first one containing background, a second one fringes, and a third one noise, which are described in different function spaces and are solved by minimization of the functional. A simple technical process involved in the minimization algorithm improves the convergence performance. The proposed approach is verified with the simulated and experimental fringe patterns.

© 2013 Optical Society of America

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References

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    [CrossRef]

2012

2011

P. Maurel, J. Aujol, and G. Peyre, SIAM J. Imaging Sci. 4, 413 (2011).
[CrossRef]

2007

M. Bernini, G. Galizzi, A. Federico, and G. Kaufmann, Opt. Lasers Eng. 45, 723 (2007).
[CrossRef]

2005

J. Aujol and A. Chambolle, Int. J. Comput. Vis. 63, 85 (2005).
[CrossRef]

J. Zhong and J. Weng, Opt. Lett. 30, 2560 (2005).
[CrossRef]

2004

Q. Kemao, Appl. Opt. 43, 2695 (2004).
[CrossRef]

J. Zhong and J. Weng, Opt. Eng. 43, 895 (2004).
[CrossRef]

1983

Aujol, J.

P. Maurel, J. Aujol, and G. Peyre, SIAM J. Imaging Sci. 4, 413 (2011).
[CrossRef]

J. Aujol and A. Chambolle, Int. J. Comput. Vis. 63, 85 (2005).
[CrossRef]

Bernini, M.

M. Bernini, G. Galizzi, A. Federico, and G. Kaufmann, Opt. Lasers Eng. 45, 723 (2007).
[CrossRef]

Chambolle, A.

J. Aujol and A. Chambolle, Int. J. Comput. Vis. 63, 85 (2005).
[CrossRef]

Federico, A.

M. Bernini, G. Galizzi, A. Federico, and G. Kaufmann, Opt. Lasers Eng. 45, 723 (2007).
[CrossRef]

Galizzi, G.

M. Bernini, G. Galizzi, A. Federico, and G. Kaufmann, Opt. Lasers Eng. 45, 723 (2007).
[CrossRef]

Kaufmann, G.

M. Bernini, G. Galizzi, A. Federico, and G. Kaufmann, Opt. Lasers Eng. 45, 723 (2007).
[CrossRef]

Kemao, Q.

Maurel, P.

P. Maurel, J. Aujol, and G. Peyre, SIAM J. Imaging Sci. 4, 413 (2011).
[CrossRef]

Meyer, Y.

Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations (AMS, 2001).

Mutoh, K.

Peyre, G.

P. Maurel, J. Aujol, and G. Peyre, SIAM J. Imaging Sci. 4, 413 (2011).
[CrossRef]

Podoleanu, A.

Takeda, M.

Weng, J.

J. Zhong and J. Weng, Opt. Lett. 30, 2560 (2005).
[CrossRef]

J. Zhong and J. Weng, Opt. Eng. 43, 895 (2004).
[CrossRef]

Yang, T.

Yang, Z.

Zhao, H.

Zhong, J.

J. Zhong and J. Weng, Opt. Lett. 30, 2560 (2005).
[CrossRef]

J. Zhong and J. Weng, Opt. Eng. 43, 895 (2004).
[CrossRef]

Zhou, X.

Zou, H.

Appl. Opt.

Int. J. Comput. Vis.

J. Aujol and A. Chambolle, Int. J. Comput. Vis. 63, 85 (2005).
[CrossRef]

Opt. Eng.

J. Zhong and J. Weng, Opt. Eng. 43, 895 (2004).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

M. Bernini, G. Galizzi, A. Federico, and G. Kaufmann, Opt. Lasers Eng. 45, 723 (2007).
[CrossRef]

Opt. Lett.

SIAM J. Imaging Sci.

P. Maurel, J. Aujol, and G. Peyre, SIAM J. Imaging Sci. 4, 413 (2011).
[CrossRef]

Other

Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations (AMS, 2001).

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Figures (2)

Fig. 1.
Fig. 1.

Decomposition of a simulated fringe pattern. (a) Simulated noisy fringe pattern, (b) ideal background, (c) ideal fringes, (d)–(f) extracted background of (a) by MO-BEMD-LP, MO-BEMD-DWT and IVID, and (g)–(i) extracted fringes of (a) by MO-BEMD-LP, MO-BEMD-DWT, and IVID.

Fig. 2.
Fig. 2.

Decomposition of two real fringe patterns. (a) First projected fringe pattern, (b) second projected fringe pattern, (c) extracted background of (a) by IVID, (d) extracted background of (b) by IVID, (e) extracted fringes of (a) by IVID, and (f) extracted fringes of (b) by IVID. Fig. 2(a) is downloaded from http://www.ljmu.ac.uk/GERI/98301.htm with permission of Professor David R. Burton, and Fig. 2(b) is available in [7].

Equations (8)

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

I(x,y)=a(x,y)+b(x,y)cos(ϕ(x,y))+noise,
(u,v,ξ)=argminu˜,v˜,ξ˜λu˜TV+μv˜ξ˜2+12fu˜v˜L22,w=fuv,
ξ=argminξ˜Cv˜ξ˜2=argminξ˜CΓ(ξ˜)ψvL22,
u=argminu˜λu˜TV+12yu˜L22.
u=proxλJ(y),
v=argminv˜12fuv˜L22+μΓ(ξ)ψvL22.
(2μψ*Γ2ψ+I)v=(fu).
I(x,y)=acos(116πx+2p(x,y))+bδp(x,y)δx+noise,

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