Abstract

we propose the oriented spatial filter masks for filtering in electronic speckle pattern interferometry (ESPI) phase fringe patterns. We establish the oriented derivative operator that only highlights noise without edges of an image. The noise in the image can be removed while still preserving the edges simply by subtracting the oriented derivative image from original image, which can be implemented with one pass of the oriented spatial filter mask. Further, we make an improvement on the oriented spatial filter mask for enhancing the smoothness. The performance of the oriented spatial filter masks is demonstrated via application to a simulated speckle phase fringe pattern and an experimentally obtained phase fringe pattern and comparison with other directional filtering methods.

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References

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2010

2009

2008

2007

2006

N. A. Kampanis and J. A. Ekaterinaris, “A staggered grid, high-order accurate method for the incompressible Navier–Stokes equations,” J. Comput. Phys. 215(2), 589–613 (2006).
[CrossRef]

2002

1985

Chang, Y.

Creath, K.

Cui, X.

De la Rosa, I.

Ekaterinaris, J. A.

N. A. Kampanis and J. A. Ekaterinaris, “A staggered grid, high-order accurate method for the incompressible Navier–Stokes equations,” J. Comput. Phys. 215(2), 589–613 (2006).
[CrossRef]

Gao, T.

Gao, W.

Gu, X.

Han, L.

Kampanis, N. A.

N. A. Kampanis and J. A. Ekaterinaris, “A staggered grid, high-order accurate method for the incompressible Navier–Stokes equations,” J. Comput. Phys. 215(2), 589–613 (2006).
[CrossRef]

Kemao, Q.

Lin, F.

Liu, X.

Nakadate, S.

Qiu, Z.

Quiroga, J. A.

Ren, H.

Saito, H.

Seah, H. S.

Sun, X.

Tang, C.

Tang, K.

Villa, J.

Wang, H.

Wang, L.

Wang, W.

Wang, X.

Wang, Z.

Wu, J.

Yan, H.

Yan, S.

Yu, Q.

Zhou, D.

Appl. Opt.

J. Comput. Phys.

N. A. Kampanis and J. A. Ekaterinaris, “A staggered grid, high-order accurate method for the incompressible Navier–Stokes equations,” J. Comput. Phys. 215(2), 589–613 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Other

R. C. Gonzalez, and R. E. Woods, Digital image processing.2nd ed. (Publishing House of Electronics Industry, Beijing, 2002).

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Figures (2)

Fig. 1
Fig. 1

A simulated phase pattern and its filtered images. (a) Initial image. (b) ORQCF with λ = 0.01 , μ = 12 . (c) OCPDE with time step Δ t = 0.8 . (d) IOSFM with α = 0.35 , β = 1 / 33 .

Fig. 2
Fig. 2

A real phase pattern and its filtered images. (a) Initial image. (b) ORQCF λ = 0.01 , μ = 10 . (c) OCPDE with time step Δ t = 0.8 .(d) IOSFM with α = 0.3 , β = 1 / 10 .

Equations (19)

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g ( x , y ) = f ( x , y ) α 2 f ( x , y )
g ( x , y ) = f ( x , y ) + α 2 f ( x , y )
2 ρ f = 2 f ρ 2
g ( x , y ) = f ( x , y ) + α ρ 2 f
f ρ = f ρ = f x cos θ + f y sin θ
2 ρ f = f x x cos 2 θ + 2 f x y cos θ sin θ + f y y sin 2 θ
f x = f ( x 2 , y ) 8 f ( x 1 , y ) + 8 f ( x + 1 , y ) f ( x + 2 , y ) 12
f y = f ( x , y 2 ) 8 f ( x , y 1 ) + 8 f ( x , y + 1 ) f ( x , y + 2 ) 12
f x x = f ( x 2 , y ) + 16 f ( x 1 , y ) 30 f ( x , y ) + 16 f ( x + 1 , y ) f ( x + 2 , y ) 12
f y y = f ( x , y 2 ) + 16 f ( x , y 1 ) 30 f ( x , y ) + 16 f ( x , y + 1 ) f ( x , y + 2 ) 12
f x y = f x ( x , y 2 ) 8 f x ( x , y 1 ) + 8 f x ( x , y + 1 ) f x ( x , y + 2 ) 12
g ( x , y ) = s = 2 2 t = 2 2 F o r ( s , t ) f ( x + s , y + t )
F o r = α 72 ( cos θ sin θ 8 cos θ sin θ 6 cos 2 θ 8 cos θ sin θ cos θ sin θ 8 cos θ sin θ 64 cos θ sin θ 96 cos 2 θ 64 cos θ sin θ 8 cos θ sin θ 6 sin 2 θ 96 sin 2 θ 72 / α 180 96 sin 2 θ 6 sin 2 θ 8 cos θ sin θ 64 cos θ sin θ 96 cos 2 θ 64 cos θ sin θ 8 cos θ sin θ cos θ sin θ 8 cos θ sin θ 6 cos 2 θ 8 cos θ sin θ cos θ sin θ )
g ( x , y ) = f ( x , y ) + α 2 ρ f ( x , y ) + β F G ( x , y )
F G ( x , y ) = s = 2 2 t = 2 2 M G ( s , t ) f ( x + s , y + t )
M G = 1 52 ( 1 1 2 1 1 1 2 4 2 1 2 4 8 4 2 1 2 4 2 1 1 1 2 1 1 ) .
g ( x , y ) = s = 2 2 t = 2 2 F i m ( s , t ) f ( x + s , y + t )
F i m = ( α cos θ sin θ 72 + β 52 α cos θ sin θ 9 + β 52 α cos 2 θ 12 + β 26 α cos θ sin θ 9 + β 52 α cos θ sin θ 72 + β 52 α cos θ sin θ 9 + β 52 8 α cos θ sin θ 9 + β 26 4 α cos 2 θ 3 + β 13 8 α cos θ sin θ 9 + β 26 α cos θ sin θ 9 + β 52 α sin 2 θ 12 + β 26 4 α sin 2 θ 3 + β 13 1 5 α 2 + 2 β 13 4 α sin 2 θ 3 + β 13 α sin 2 θ 12 + β 26 α cos θ sin θ 9 + β 52 8 α cos θ sin θ 9 + β 26 4 α cos 2 θ 3 + β 13 8 α cos θ sin θ 9 + β 26 α cos θ sin θ 9 + β 52 α cos θ sin θ 72 + β 52 α cos θ sin θ 9 + β 52 α cos 2 θ 12 + β 26 α cos θ sin θ 9 + β 52 α cos θ sin θ 72 + β 52 )
θ ( x , y ) = 1 2 tan 1 ( k l E ( ω k , ω l ) sin ( 2 θ k , l ) k l E ( ω k , ω l ) cos ( 2 θ k , l ) )

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