Abstract

Using an example of vector Gaussian Schell-model beam, we demonstrate and analyze the dependence of the spatial frequency resolution in optical Fourier transforming system on the intrinsic coherence-polarization structure of illumination.

© 2011 Optical Society of America

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  1. F. Gori, Opt. Lett. 23, 241 (1998).
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  2. E. Wolf, Phys. Lett. A 312, 263 (2003).
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  3. J. Tervo, T. Setälä, and A. T. Friberg, J. Opt. Soc. Am. A 21, 2205 (2004).
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    [CrossRef] [PubMed]
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
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  13. M. Salem and E. Wolf, Opt. Lett. 33, 1180 (2008).
    [CrossRef] [PubMed]
  14. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  15. F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, Opt. Lett. 31, 688 (2006).
    [CrossRef] [PubMed]
  16. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. (Academic Press, 1994).
  17. A. S. Ostrovsky and E. Pino-Mota, Opt. Rev. 5, 219 (1998).
    [CrossRef]
  18. A. S. Ostrovsky, E. Pino-Mota, and J. I. Palma-Cuatianquiz, Opt. Lasers Eng. 40/12, 43 (2003).
    [CrossRef]
  19. H. Stark, in Applications of Optical Fourier Transforms, H.Stark, ed. (Academic Press, 1982).
  20. T. Shirai, O. Korotkova, and E. Wolf, Pure Appl. Opt 7, 232 (2005).
    [CrossRef]
  21. G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, Opt. Commun. 208, 9 (2002).
    [CrossRef]
  22. A. S. Ostrovsky, G. Martinez-Niconoff, V. Arrizón, P. Martinez-Vara, M. Á. Olvera-Santamaría, and C. Rickenstorff-Parrao, Opt. Express 17, 5257 (2009).
    [CrossRef] [PubMed]
  23. A. S. Ostrovsky, G. Rodríguez-Zurita, C. Meneses-Fabián, M. Á. Olvera-Santamaría, and C. Rickenstorff-Parrao, Opt. Express 18, 12864 (2010).
    [CrossRef] [PubMed]

2011 (1)

2010 (1)

2009 (1)

2008 (2)

2007 (1)

2006 (1)

2005 (3)

2004 (1)

2003 (3)

A. S. Ostrovsky, E. Pino-Mota, and J. I. Palma-Cuatianquiz, Opt. Lasers Eng. 40/12, 43 (2003).
[CrossRef]

E. Wolf, Opt. Lett. 28, 1078 (2003).
[CrossRef] [PubMed]

E. Wolf, Phys. Lett. A 312, 263 (2003).
[CrossRef]

2002 (1)

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, Opt. Commun. 208, 9 (2002).
[CrossRef]

1998 (2)

F. Gori, Opt. Lett. 23, 241 (1998).
[CrossRef]

A. S. Ostrovsky and E. Pino-Mota, Opt. Rev. 5, 219 (1998).
[CrossRef]

Arrizón, V.

Borghi, R.

F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, Opt. Lett. 31, 688 (2006).
[CrossRef] [PubMed]

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, Opt. Commun. 208, 9 (2002).
[CrossRef]

Friberg, A. T.

Gamiz, V. L.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

J. W. Goodman, Statistical Optics (Wiley, 1985).

Gori, F.

F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, Opt. Lett. 31, 688 (2006).
[CrossRef] [PubMed]

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, Opt. Commun. 208, 9 (2002).
[CrossRef]

F. Gori, Opt. Lett. 23, 241 (1998).
[CrossRef]

Goudail, F.

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. (Academic Press, 1994).

Hanson, S. G.

Hoover, B. G.

Jakobsen, M.

Korotkova, O.

Luis, A.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

Martinez-Niconoff, G.

Martínez-Niconoff, G.

A. S. Ostrovsky, P. Martínez-Vara, M. Á. Olvera-Santamaría, and G. Martínez-Niconoff, in Recent Research Developments in Optics, A.Gayathri, ed. (Research Signpost, 2009).

Martinez-Vara, P.

Martínez-Vara, P.

A. S. Ostrovsky, P. Martínez-Vara, M. Á. Olvera-Santamaría, and G. Martínez-Niconoff, in Recent Research Developments in Optics, A.Gayathri, ed. (Research Signpost, 2009).

Meneses-Fabián, C.

Mondello, A.

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, Opt. Commun. 208, 9 (2002).
[CrossRef]

Olvera-Santamaría, M. Á.

Ostrovsky, A. S.

A. S. Ostrovsky, M. Á. Olvera-Santamaría, and P. C. Romero-Soría, Opt. Lett. 36, 1677 (2011).
[CrossRef] [PubMed]

A. S. Ostrovsky, G. Rodríguez-Zurita, C. Meneses-Fabián, M. Á. Olvera-Santamaría, and C. Rickenstorff-Parrao, Opt. Express 18, 12864 (2010).
[CrossRef] [PubMed]

A. S. Ostrovsky, G. Martinez-Niconoff, V. Arrizón, P. Martinez-Vara, M. Á. Olvera-Santamaría, and C. Rickenstorff-Parrao, Opt. Express 17, 5257 (2009).
[CrossRef] [PubMed]

A. S. Ostrovsky, E. Pino-Mota, and J. I. Palma-Cuatianquiz, Opt. Lasers Eng. 40/12, 43 (2003).
[CrossRef]

A. S. Ostrovsky and E. Pino-Mota, Opt. Rev. 5, 219 (1998).
[CrossRef]

A. S. Ostrovsky, P. Martínez-Vara, M. Á. Olvera-Santamaría, and G. Martínez-Niconoff, in Recent Research Developments in Optics, A.Gayathri, ed. (Research Signpost, 2009).

Palma-Cuatianquiz, J. I.

A. S. Ostrovsky, E. Pino-Mota, and J. I. Palma-Cuatianquiz, Opt. Lasers Eng. 40/12, 43 (2003).
[CrossRef]

Pino-Mota, E.

A. S. Ostrovsky, E. Pino-Mota, and J. I. Palma-Cuatianquiz, Opt. Lasers Eng. 40/12, 43 (2003).
[CrossRef]

A. S. Ostrovsky and E. Pino-Mota, Opt. Rev. 5, 219 (1998).
[CrossRef]

Piquero, G.

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, Opt. Commun. 208, 9 (2002).
[CrossRef]

Réfrégier, P.

Rickenstorff-Parrao, C.

Rodríguez-Zurita, G.

Romanini, P.

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, Opt. Commun. 208, 9 (2002).
[CrossRef]

Romero-Soría, P. C.

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. (Academic Press, 1994).

Salem, M.

Santarsiero, M.

F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, Opt. Lett. 31, 688 (2006).
[CrossRef] [PubMed]

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, Opt. Commun. 208, 9 (2002).
[CrossRef]

Setälä, T.

Shirai, T.

T. Shirai, O. Korotkova, and E. Wolf, Pure Appl. Opt 7, 232 (2005).
[CrossRef]

Stark, H.

H. Stark, in Applications of Optical Fourier Transforms, H.Stark, ed. (Academic Press, 1982).

Takeda, M.

Tervo, J.

Wang, W.

Wolf, E.

J. Opt. Soc. Am. A (4)

Opt. Commun. (1)

G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, Opt. Commun. 208, 9 (2002).
[CrossRef]

Opt. Express (3)

Opt. Lasers Eng. (1)

A. S. Ostrovsky, E. Pino-Mota, and J. I. Palma-Cuatianquiz, Opt. Lasers Eng. 40/12, 43 (2003).
[CrossRef]

Opt. Lett. (5)

Opt. Rev. (1)

A. S. Ostrovsky and E. Pino-Mota, Opt. Rev. 5, 219 (1998).
[CrossRef]

Phys. Lett. A (1)

E. Wolf, Phys. Lett. A 312, 263 (2003).
[CrossRef]

Pure Appl. Opt (1)

T. Shirai, O. Korotkova, and E. Wolf, Pure Appl. Opt 7, 232 (2005).
[CrossRef]

Other (6)

A. S. Ostrovsky, P. Martínez-Vara, M. Á. Olvera-Santamaría, and G. Martínez-Niconoff, in Recent Research Developments in Optics, A.Gayathri, ed. (Research Signpost, 2009).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

J. W. Goodman, Statistical Optics (Wiley, 1985).

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. (Academic Press, 1994).

H. Stark, in Applications of Optical Fourier Transforms, H.Stark, ed. (Academic Press, 1982).

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Figures (3)

Fig. 1
Fig. 1

Optical Fourier transforming system.

Fig. 2
Fig. 2

The typical shape of the spectrum given by Eq. (6).

Fig. 3
Fig. 3

Dependence of the normalized spatial frequency resolution on the degree of global coherence (a) and the ratio of the powers of polarization components (b) of the illumination field.

Equations (15)

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W in ( x 1 , x 2 ) = ( W x x in ( x 1 , x 2 ) W x y in ( x 1 , x 2 ) W y x in ( x 1 , x 2 ) W y y in ( x 1 , x 2 ) ) ,
W out ( x 1 , x 2 ) = 1 ( λ f ) 2 exp [ i π λ f ( x 1 2 x 2 2 ) ] t * ( x 1 ) t ( x 2 ) × W in ( x 1 , x 2 ) exp [ i 2 π λ f ( x 1 · x 1 x 2 · x 2 ) ] d x 1 d x 2 .
S out ( p ) = Tr W out ( p , p ) = Tr 1 ( λ f ) 2 t * ( x 1 ) t ( x 2 ) × W in ( x 1 , x 2 ) exp [ i 2 π p · ( x 1 x 2 ) ] d x 1 d x 2 ,
t ( x ) = cos ( 2 π p 0 x ) + cos [ 2 π ( p 0 + Δ p ) x ] ,
W ˜ in ( p 1 , p 2 ) = W in ( x 1 , x 2 ) exp [ i 2 π ( p 1 x 1 + p 2 x 2 ) ] d x 1 d x 2 ,
S out ( p ) | p > 0 = Tr 1 4 ( λ f ) 2 [ W ˜ in ( p p 0 , p + p 0 ) + W ˜ in ( p p 0 Δ p , p + p 0 + Δ p ) ] .
( Δ p ) min = Tr W ˜ in ( p , p ) d p Tr W ˜ in ( 0 , 0 ) .
W in ( x 1 , x 2 ) = ( W x x ( x 1 , x 2 ) 0 0 W y y ( x 1 , x 2 ) ) ,
W i i ( x 1 , x 2 ) = S 0 i exp ( x 1 2 + x 2 2 4 σ 2 ) exp ( ( x 1 x 2 ) 2 2 σ i 2 ) ,
W ˜ i i in ( p , p ) = S 0 i exp ( x 1 2 + x 2 2 4 σ 2 ) exp ( ( x 1 x 2 ) 2 2 σ i 2 ) × exp [ i 2 π p ( x 1 x 2 ) ] d x 1 d x 2 .
ξ = x 1 x 2 , η = x 1 + x 2 2 ,
0 exp ( a 2 u 2 ) d u = π 2 a ( a > 0 ) ,
0 exp ( a 2 u 2 ) exp ( i u v ) d u = π | a | exp ( v 2 4 a 2 ) ,
W ˜ i i in ( p , p ) = 4 π σ 2 S 0 i γ i ( 4 + γ i 2 ) 1 / 2 exp ( 8 π 2 σ 2 γ i 2 4 + γ i 2 p 2 ) .
( Δ p ) min = ( 1 2 2 π σ ) 1 + β γ x ( 4 + γ x 2 ) 1 / 2 + β γ y ( 4 + γ y 2 ) 1 / 2 .

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