Abstract

It is shown that the structure information for a lattice or periodic pattern can be obtained by measuring the diffracted spectrum of a broadband light source at one spatial position in the far field.

© 2009 Optical Society of America

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References

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  1. S. A. Ponomarenko and E. Wolf, Opt. Lett. 27, 1211 (2002).
    [CrossRef]
  2. P. Han, J. Opt. A 10, 035003 (2008).
    [CrossRef]
  3. J. Pu, C. Cai, and S. Nemoto, Opt. Express 12, 5131 (2004).
    [CrossRef] [PubMed]
  4. E. Wolf and D. F. V. James, Rep. Prog. Phys. 59, 771 (1996).
    [CrossRef]
  5. P. Han, J. Opt. A 11, 015708 (2009).
    [CrossRef]
  6. J. T. Foley and E. Wolf, J. Opt. Soc. Am. A 19, 2510 (2002).
    [CrossRef]
  7. G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2002).
    [CrossRef] [PubMed]
  8. P. Han, J. Opt. Soc. Am. A 26, 473 (2009).
    [CrossRef]

2009 (2)

2008 (1)

P. Han, J. Opt. A 10, 035003 (2008).
[CrossRef]

2004 (1)

2002 (3)

1996 (1)

E. Wolf and D. F. V. James, Rep. Prog. Phys. 59, 771 (1996).
[CrossRef]

Cai, C.

Foley, J. T.

Gbur, G.

G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef] [PubMed]

Han, P.

P. Han, J. Opt. A 11, 015708 (2009).
[CrossRef]

P. Han, J. Opt. Soc. Am. A 26, 473 (2009).
[CrossRef]

P. Han, J. Opt. A 10, 035003 (2008).
[CrossRef]

James, D. F. V.

E. Wolf and D. F. V. James, Rep. Prog. Phys. 59, 771 (1996).
[CrossRef]

Nemoto, S.

Ponomarenko, S. A.

Pu, J.

Visser, T. D.

G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef] [PubMed]

Wolf, E.

G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef] [PubMed]

S. A. Ponomarenko and E. Wolf, Opt. Lett. 27, 1211 (2002).
[CrossRef]

J. T. Foley and E. Wolf, J. Opt. Soc. Am. A 19, 2510 (2002).
[CrossRef]

E. Wolf and D. F. V. James, Rep. Prog. Phys. 59, 771 (1996).
[CrossRef]

J. Opt. A (2)

P. Han, J. Opt. A 10, 035003 (2008).
[CrossRef]

P. Han, J. Opt. A 11, 015708 (2009).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

E. Wolf and D. F. V. James, Rep. Prog. Phys. 59, 771 (1996).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

(a) Geometry and notations for a two-dimensional periodic pattern. (b) Graph of the one-dimensional far-field distribution.

Fig. 2
Fig. 2

(a) Geometry and notations for the calculation of diffracted spectrum of a broadband light source. (b) Normalized far-field diffracted spectrum S ( θ , ω ) (solid curve) and its envelop function (dashed curve).

Equations (6)

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g ( x , y ) = 1 bm [ rect ( x a ) comb ( x b ) ] rect ( x d ) × [ rect ( y l ) comb ( y m ) ] rect ( y n ) ,
G ( f x ) { [ sinc ( π a f x ) ] [ comb ( b f x ) ] } sinc ( π d f x ) .
G ( f x ) sinc ( π a f x ) [ comb ( b f x ) sinc ( π d f x ) ] .
S ( ω ) = exp { [ ( ω ω 0 ) ] 2 Γ 2 } .
S ( p , ω ) ω 2 F ( g ( x , y ) ) 2 [ S ( p , ω ) ] ,
S ( θ , ω ) { ω 2 sinc 2 ( a sin ( θ ) ω 2 c ) [ comb ( b sin ( θ ) ω 2 π c ) sinc ( d sin ( θ ) ω 2 c ) ] 2 } × S ( ω ) .

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