Abstract

The Schlieren technique is a well-known coherent processing method that is usually applied to the visualization of phase objects. In this paper, we demonstrate that, when the Schlieren processing is applied to a light wave modulated in amplitude and possessing some periodicity, the harmonic contents of the resultant image decreases (i.e., the higher harmonics are suppressed). Also, we show that, when the amplitude-modulated (periodic) light wave possesses faults, the Schlieren processing produces an enhancement of the faults relative to the periodic carrier. This technique can be applied to defect detection in periodic structures such as photomasks used for LCD panels, integrated-circuit masks, or semiconductor wafers.

© 2005 Optical Society of America

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References

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2004

2003

2002

G. Serafino, P. Sirotti, “Phase image visualization with white light extended sources: a Fourier-optics-based interpretation,” Opt. Eng. 41, 2549–2555 (2002).
[CrossRef]

1998

E. U. Wagemann, H.-J. Tiziani, “Spatial self-filtering using photorefractive and liquid crystals,” J. Mod. Opt. 45, 1885–1897 (1998).
[CrossRef]

1997

1996

1994

1993

T. Huang, K. H. Wagner, “Photoanisotropic incoherent-to-coherent optical conversion,” Appl. Opt. 32, 1890–1900 (1993).
[CrossRef]

1985

1980

1967

J. B. Brackenridge, J. Peterka, “Criteria for quantitative Schlieren interferometry,” App. Opt. 6, 731–735 (1967).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics 6th ed. (Pergamon, London, 1989), Chap. 8.

Brackenridge, J. B.

J. B. Brackenridge, J. Peterka, “Criteria for quantitative Schlieren interferometry,” App. Opt. 6, 731–735 (1967).
[CrossRef]

DeVelis, J. B.

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, B. J. Thompson, eds., The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE, Bellingham, Wash., 1989).
[CrossRef]

Dubois, F.

Egami, C.

Feinberg, J.

Goodman, J. W.

Hesselink, L.

Huang, T.

T. Huang, K. H. Wagner, “Photoanisotropic incoherent-to-coherent optical conversion,” Appl. Opt. 32, 1890–1900 (1993).
[CrossRef]

Joannes, L.

Kato, J.

Legros, J.-C.

Ochoa, E.

Okamoto, N.

Okamoto, T.

Parrent, G. B.

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, B. J. Thompson, eds., The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE, Bellingham, Wash., 1989).
[CrossRef]

Peterka, J.

J. B. Brackenridge, J. Peterka, “Criteria for quantitative Schlieren interferometry,” App. Opt. 6, 731–735 (1967).
[CrossRef]

Reynolds, G. O.

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, B. J. Thompson, eds., The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE, Bellingham, Wash., 1989).
[CrossRef]

Serafino, G.

G. Serafino, P. Sirotti, “Phase image visualization with white light extended sources: a Fourier-optics-based interpretation,” Opt. Eng. 41, 2549–2555 (2002).
[CrossRef]

Sirotti, P.

G. Serafino, P. Sirotti, “Phase image visualization with white light extended sources: a Fourier-optics-based interpretation,” Opt. Eng. 41, 2549–2555 (2002).
[CrossRef]

Stricker, J.

Sugihara, O.

Suzuki, Y.

Tanaka, H.

Thompson, B. J.

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, B. J. Thompson, eds., The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE, Bellingham, Wash., 1989).
[CrossRef]

Tiziani, H.-J.

E. U. Wagemann, H.-J. Tiziani, “Spatial self-filtering using photorefractive and liquid crystals,” J. Mod. Opt. 45, 1885–1897 (1998).
[CrossRef]

Uemori, T.

Uhrich, C.

Wagemann, E. U.

E. U. Wagemann, H.-J. Tiziani, “Spatial self-filtering using photorefractive and liquid crystals,” J. Mod. Opt. 45, 1885–1897 (1998).
[CrossRef]

Wagner, K. H.

T. Huang, K. H. Wagner, “Photoanisotropic incoherent-to-coherent optical conversion,” Appl. Opt. 32, 1890–1900 (1993).
[CrossRef]

Weisstein, E. W.

E. W. Weisstein, “Hilbert transform,” in MathWorld (Wolfram Research, Champaign, IL, 1999); http://mathworld.wolfram.com/HilbertTransform.html .

Wolf, E.

M. Born, E. Wolf, Principles of Optics 6th ed. (Pergamon, London, 1989), Chap. 8.

Yamagata, K.

Yamaguchi, I.

Zakharin, B.

App. Opt.

J. B. Brackenridge, J. Peterka, “Criteria for quantitative Schlieren interferometry,” App. Opt. 6, 731–735 (1967).
[CrossRef]

Appl. Opt.

J. Mod. Opt.

E. U. Wagemann, H.-J. Tiziani, “Spatial self-filtering using photorefractive and liquid crystals,” J. Mod. Opt. 45, 1885–1897 (1998).
[CrossRef]

Opt. Eng.

G. Serafino, P. Sirotti, “Phase image visualization with white light extended sources: a Fourier-optics-based interpretation,” Opt. Eng. 41, 2549–2555 (2002).
[CrossRef]

Opt. Lett.

Other

M. Born, E. Wolf, Principles of Optics 6th ed. (Pergamon, London, 1989), Chap. 8.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1988).

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, B. J. Thompson, eds., The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE, Bellingham, Wash., 1989).
[CrossRef]

E. W. Weisstein, “Hilbert transform,” in MathWorld (Wolfram Research, Champaign, IL, 1999); http://mathworld.wolfram.com/HilbertTransform.html .

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Figures (5)

Fig. 1
Fig. 1

Schlieren setup with the knife border orthogonal to the x direction. M is the amplitude mask to be tested, K is the knife, C is a CCD camera, and L1, 2 are the Fourier lenses.

Fig. 2
Fig. 2

Computer-simulated intensity distributions along the x axis. (a) Intensity distribution I(x) of a periodic pattern with scratchlike and dustlike defects. (b) Intensity pattern Isch(x) obtained after processing the amplitude according to approximation (19).

Fig. 3
Fig. 3

Chrome-on-glass mask with scratches: (a) unprocessed image; (b) Schlieren processed image showing defect enhancement.

Fig. 4
Fig. 4

Liquid-crystal panel with wool fiber: (a) unprocessed image; (b) Schlieren processed image. In the background, the pixeled structure of the panel is visible. The dashed appearance of the wool fiber is due to the modulation by the periodic carrier.

Fig. 5
Fig. 5

Amplitude mask with concentric rings: (a) unprocessed image; (b) Schlieren processed image. The wool fiber path and other dustlike defects are enhanced.

Equations (20)

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E ( x , y ) = g ( x ) h ( y ) ,
g ( x ) = c 0 + n = 1 N c n cos [ ( 2 π n x / d ) + ϕ n ] ,
I ( x , y ) = E 2 ( x , y ) = { c 0 + n = 1 N c n cos [ ( 2 π n x / d ) + ϕ n ] } 2 h 2 ( y ) .
I ( x , y ) = [ c 0 2 + 2 c 0 n = 1 N c n cos [ ( 2 π n x / d ) + ϕ n ] + n = 1 N c n 2 cos 2 [ ( 2 π n x / d ) + ϕ n ] + k = 1 N 1 n = k + 1 N c n c k ( cos { [ 2 π ( n + k ) x / d ] + ( ϕ n + ϕ k ) } + cos { [ 2 π ( n k ) x / d ) ] + ( ϕ n ϕ k ) } ) ] h 2 ( y ) ,
I ( x , y ) = ( c 0 2 + n = 1 N ( c n 2 / 2 ) + 2 c 0 n = 1 N c n cos [ ( 2 π n x / d ) + ϕ n ] + k = 1 N 1 n = k + 1 N c n c k cos { [ 2 π ( n k ) x / d ] + ( ϕ n ϕ k ) } + k = 1 N 1 n = k + 1 N c n c k cos { [ 2 π ( n + k ) x / d ] + ( ϕ n ϕ k ) } + n = 1 N ( c n 2 / 2 ) cos [ ( 4 π n x / d ) + 2 ϕ n ] ) h 2 ( y ) .
( x , y ) = g ( x ) h ( y ) ,
g ( x ) = c 0 δ ( 0 ) + n = 1 N ( c n 2 ) [ δ ( n / d + x / λ f ) exp ( i ϕ n ) + δ ( n / d x / λ f ) exp ( i ϕ n ) ] ,
E sch ( x , y ) = g sch ( x ) h ( y ) ,
g sch ( x ) = ( c 0 / 2 ) + n = 1 N ( c n / 2 ) exp [ i ( 2 π n x / d + ϕ n ) ] .
I sch ( x , y ) = | E sch ( x , y ) | 2 = | ( c 0 / 2 ) + n = 1 N ( c n / 2 ) exp [ ] i ( 2 π n x / d + ϕ n ) ] | 2 h 2 ( y ) .
I ( x , y ) = ( c 0 2 + n = 1 N c n 2 + 2 c 0 n = 1 N c n cos [ ( 2 π n x / d ) + ϕ n ] + k = 1 N 1 n = K + 1 N c n c k cos { [ 2 π ( n k ) x / d ] + ( ϕ n ϕ k ) } ) h 2 ( y ) .
E ( x , y ) = [ 1 α ( x , m ( x ) ) ] g ( x ) h ( y ) + β ( x , l ( x ) ) ,
α ( x , m ( x ) ) = E 1 rect [ x m 1 ( y ) ɛ 1 ] ,
β ( x , l ( x ) ) = E 2 rect [ x l 1 ( y ) ɛ 2 ] ,
E sch ( x , y ) = E ( x , y ) 2 + 1 2 π i P E ( ξ , y ) d ξ x ξ ,
E sch ( x , y ) = g sch ( x ) h ( y ) α ( x , m ( x ) ) g ( x ) h ( y ) 2 h ( y ) 2 π i P α ( ξ , m ( ξ ) ) g ( ξ ) d ξ x ξ + β ( x , l ( x ) ) 2 + 1 2 π i P β ( ξ , l ( ξ ) ) d ξ x ξ ,
P α ( ξ , m ( ξ ) ) g ( ξ ) d ξ x ξ E 1 g ( m 1 ( y ) ) × log | ( x m 1 ( y ) ) + ( ɛ 1 / 2 ) ( x m 1 ( y ) ) ( ɛ 1 / 2 ) |
P β ( ξ , l ( ξ ) ) d ξ x ξ E 2 × log | ( x l 1 ( y ) ) + ( ɛ 2 / 2 ) ( x l 1 ( y ) ) ( ɛ 2 / 2 ) | .
E sch ( x , y ) g sch ( x ) h ( y ) α ( x , m ( x ) ) g ( x ) h ( y ) 2 E 1 g ( m 1 ( y ) ) h ( y ) 2 π i × log | ( x m 1 ( y ) ) + ( ɛ 1 / 2 ) ( x m 1 ( y ) ) ( ɛ 1 / 2 ) | + β ( x , l ( x ) ) 2 + E 2 2 π i log | ( x l 1 ( y ) ) + ( ɛ 2 / 2 ) ( x l 1 ( y ) ) ( ɛ 2 / 2 ) | .
g ( x ) = 1 ( 1 / 4 ) cos ( 2 π x ) ( 1 / 16 ) cos ( 4 π x ) ,

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