Abstract

The local model fitting (LMF) method is a single-shot surface profiling algorithm. Its measurement principle is based on the assumption that the target surface to be profiled is locally flat, which enables us to utilize the information brought by nearby pixels in the single interference image for robust LMF. Given that the shape and size of the local area is appropriately determined, the LMF method was demonstrated to provide very accurate measurement results. However, the appropriate choice of the local area often requires prior knowledge on the target surface profile or manual parameter tuning. To cope with this problem, we propose a method for automatically determining the shape and size of local regions only from the single interference image. The effectiveness of the proposed method is demonstrated through experiments.

© 2011 Optical Society of America

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References

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2010 (2)

2008 (1)

2007 (2)

2006 (1)

2005 (1)

N. Brock, J. Hayes, B. Kimbrough, J. Millerd, M. North-Morris, M. Novak, and J. C. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 1–10 (2005).

2004 (1)

1997 (1)

1996 (1)

M. Takeda and T. Abe, “Phase unwrapping by a maximum cross-amplitude spanning tree algorithm: a comparative study,” Opt. Eng. 35, 2345–2351 (1996).
[CrossRef]

1991 (1)

D. C. Williams, N. S. Nassar, J. E. Banyard, and M. S. Virdee, “Digital phase-step interferometry: a simplified approach,” Opt. Laser Technol. 23, 147–150 (1991).
[CrossRef]

1982 (1)

1974 (1)

Abe, T.

M. Takeda and T. Abe, “Phase unwrapping by a maximum cross-amplitude spanning tree algorithm: a comparative study,” Opt. Eng. 35, 2345–2351 (1996).
[CrossRef]

Banyard, J. E.

D. C. Williams, N. S. Nassar, J. E. Banyard, and M. S. Virdee, “Digital phase-step interferometry: a simplified approach,” Opt. Laser Technol. 23, 147–150 (1991).
[CrossRef]

Brangaccio, D. J.

Brock, N.

N. Brock, J. Hayes, B. Kimbrough, J. Millerd, M. North-Morris, M. Novak, and J. C. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 1–10 (2005).

Brunning, J. H.

Chen, H. J.

Fang, J.

Gallagher, J. E.

Hayes, J.

N. Brock, J. Hayes, B. Kimbrough, J. Millerd, M. North-Morris, M. Novak, and J. C. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 1–10 (2005).

Herriott, D. R.

Ina, H.

Kato, J.

Kemao, Q.

Kimbrough, B.

N. Brock, J. Hayes, B. Kimbrough, J. Millerd, M. North-Morris, M. Novak, and J. C. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 1–10 (2005).

Kitagawa, K.

Kobayashi, S.

Kurihara, N.

Kuwashima, S.

Lv, D. J.

Millerd, J.

N. Brock, J. Hayes, B. Kimbrough, J. Millerd, M. North-Morris, M. Novak, and J. C. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 1–10 (2005).

Nakamura, T.

Nassar, N. S.

D. C. Williams, N. S. Nassar, J. E. Banyard, and M. S. Virdee, “Digital phase-step interferometry: a simplified approach,” Opt. Laser Technol. 23, 147–150 (1991).
[CrossRef]

North-Morris, M.

N. Brock, J. Hayes, B. Kimbrough, J. Millerd, M. North-Morris, M. Novak, and J. C. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 1–10 (2005).

Novak, M.

N. Brock, J. Hayes, B. Kimbrough, J. Millerd, M. North-Morris, M. Novak, and J. C. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 1–10 (2005).

Ogawa, H.

Rosenfeld, D. P.

Su, W. H.

Sugiyama, M.

Suzuki, K.

Takeda, M.

M. Takeda and T. Abe, “Phase unwrapping by a maximum cross-amplitude spanning tree algorithm: a comparative study,” Opt. Eng. 35, 2345–2351 (1996).
[CrossRef]

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
[CrossRef]

Towers, C. E.

Towers, D. P.

Virdee, M. S.

D. C. Williams, N. S. Nassar, J. E. Banyard, and M. S. Virdee, “Digital phase-step interferometry: a simplified approach,” Opt. Laser Technol. 23, 147–150 (1991).
[CrossRef]

White, A. D.

Williams, D. C.

D. C. Williams, N. S. Nassar, J. E. Banyard, and M. S. Virdee, “Digital phase-step interferometry: a simplified approach,” Opt. Laser Technol. 23, 147–150 (1991).
[CrossRef]

Wyant, J. C.

N. Brock, J. Hayes, B. Kimbrough, J. Millerd, M. North-Morris, M. Novak, and J. C. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 1–10 (2005).

Yamaguchi, I.

Zhang, J.

Zhang, Z.

Appl. Opt. (6)

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

M. Takeda and T. Abe, “Phase unwrapping by a maximum cross-amplitude spanning tree algorithm: a comparative study,” Opt. Eng. 35, 2345–2351 (1996).
[CrossRef]

Opt. Express (3)

Opt. Laser Technol. (1)

D. C. Williams, N. S. Nassar, J. E. Banyard, and M. S. Virdee, “Digital phase-step interferometry: a simplified approach,” Opt. Laser Technol. 23, 147–150 (1991).
[CrossRef]

Proc. SPIE (1)

N. Brock, J. Hayes, B. Kimbrough, J. Millerd, M. North-Morris, M. Novak, and J. C. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 1–10 (2005).

Other (1)

Toray Co. Engineering, Ltd., “SP-500,” http://www.toray-eng.com/lcd/inspection/lineup/sp-500.html.

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Figures (5)

Fig. 1
Fig. 1

Experimental results for the artificial sharp bump.

Fig. 2
Fig. 2

RMSE g and RMSE ϕ as functions of vicinity size s for the artificial sharp bump.

Fig. 3
Fig. 3

Experimental results for the artificial sphere bump.

Fig. 4
Fig. 4

Experimental results for the artificial fish-shaped object.

Fig. 5
Fig. 5

Actual measurement results.

Equations (17)

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g ( x , y ) a ( x , y ) + b ( x , y ) cos ( ϕ ( x , y ) + 2 π f x x + 2 π f y y ) ,
g ¯ t ( x , y ) a t + b t cos ( ϕ t + 2 π f x x + 2 π f y y ) = a t + ξ t φ ( x , y ) + ζ t ψ ( x , y ) ,
ξ t b t cos ϕ t , φ ( x , y ) cos ( 2 π f x x + 2 π f y y ) , ζ t b t sin ϕ t , ψ ( x , y ) sin ( 2 π f x x + 2 π f y y ) .
( a ^ t , ξ ^ t , ζ ^ t ) argmin ( a t , ξ t , ζ t ) i T t ( g i g ¯ t ( x i , y i ) ) 2 ,
( a ^ t , ξ ^ t , ζ ^ t ) = ( A t A t ) 1 A t g t ,
A t ( 1 φ ( x t 1 , y t 1 ) ψ ( x t 1 , y t 1 ) 1 φ ( x t 2 , y t 2 ) ψ ( x t 2 , y t 2 ) 1 φ ( x | T t | , y | T t | ) ψ ( x | T t | , y | T t | ) ) , g t ( g t 1 g t 2 g | T t | ) .
ϕ ^ ( x t , y t ) arctan ( ζ ^ t / ξ ^ t ) + 2 m t π ,
RMSE ϕ 1 | T | t T ( ϕ ^ ( x t , y t ) ϕ ( x t , y t ) ) 2 ,
RMSE g 1 | T | t T ( g ^ t g t ) 2 .
a ^ t + ξ ^ t φ ( x t , y t ) + ζ ^ t ψ ( x t , y t )
( a t ˜ , ξ ˜ t , ζ ˜ t ) argmin ( a t , ξ t , ζ t ) i T t t ( g i g ¯ t ( x i , y i ) ) 2 ,
g ^ t a t ˜ + ξ ˜ t φ ( x t , y t ) + ζ ˜ t ψ ( x t , y t ) .
( a t ^ , ξ t ^ , ζ t ^ ) argmin ( a t , ξ t , ζ t ) [ i T t w t , i ( g i g ¯ t ( x i , y i ) ) 2 ] ,
( a t ^ , ξ t ^ , ζ t ^ ) = ( A t W t A t ) 1 A t W t g t ,
1 d 2 ( ( x i x t ) 2 + ( y i y t ) 2 ) · ( 1 + c 1 ( ϕ ( x i , y i ) ϕ ( x t , y t ) ) 2 ) 1 ,
w t , i ( 1 ) 1 d 1 2 ( ( x i x t ) 2 + ( y i y t ) 2 ) .
w t , i ( 2 ) 1 d 2 2 ( ( x i x t ) 2 + ( y i y t ) 2 ) · ( 1 + c 1 ( ϕ ˜ ( x i , y i ) ϕ ˜ ( x t , y t ) ) 2 ) 1 ,

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