Abstract

The effect of coherence properties of illumination on image resolution, well known in a scalar case, is studied for the case of vector electromagnetic illumination. Using an example of vector Gaussian Schell-model illumination, we analyze the dependence of optical system resolution on the transverse correlation lengths of the orthogonal field components and on the ratio of the powers of these components, each taken separately.

© 2011 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics (Cambridge U., 1999).
  2. J. W. Goodman, Statistical Optics (Wiley, 1985).
  3. W. Wang, A. T. Friberg, and E. Wolf, J. Opt. Soc. Am. A 14, 491 (1997).
    [CrossRef]
  4. A. T. Friberg, T. D. Visser, W. Wang, and E. Wolf, Opt. Commun. 196, 1 (2001).
    [CrossRef]
  5. D. G. Fischer and T. D. Visser, J. Opt. Soc. Am. A 21, 2097 (2004).
    [CrossRef]
  6. F. Gori, Opt. Lett. 23, 241 (1998).
    [CrossRef]
  7. E. Wolf, Phys. Lett. A 312, 263 (2003).
    [CrossRef]
  8. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge U., 2007).
  9. J. Tervo, T. Setälä, and A. T. Friberg, J. Opt. Soc. Am. A 21, 2205 (2004).
    [CrossRef]
  10. A. Luis, J. Opt. Soc. Am. A 24, 1063 (2007).
    [CrossRef]
  11. P. Réfrégier and F. Goudail, Opt. Express 13, 6051 (2005).
    [CrossRef] [PubMed]
  12. A. S. Ostrovsky, P. Martínez-Vara, M. Á. Olvera-Santamaría, and G. Martínez-Niconoff, in Recent Research Developments in Optics, A.Gayathri, eds. (Research Signpost, 2009), pp. 113–132.
  13. E. Wolf, Opt. Lett. 28, 1078 (2003).
    [CrossRef] [PubMed]
  14. O. Korotkova, B. G. Hoover, V. L. Gamiz, and E. Wolf, J. Opt. Soc. Am. A 22, 2547 (2005).
    [CrossRef]
  15. M. Salem and E. Wolf, Opt. Lett. 33, 1180 (2008).
    [CrossRef] [PubMed]
  16. S. G. Hanson, W. Wang, M. Jakobsen, and M. Takeda, J. Opt. Soc. Am. A 25, 2338 (2008).
    [CrossRef]
  17. X. Du and D. Zhao, Phys. Lett. A 373, 4297 (2009).
    [CrossRef]
  18. X. Du and D. Zhao, J. Electromagn. Waves Appl. 24, 521 (2010).
  19. X. Du and D. Zhao, Opt. Commun. 281, 2711 (2008).
    [CrossRef]
  20. K. Lindfors, T. Setälä, M. Kaivola, and A. T. Friberg, J. Opt. Soc. Am. A 22, 561 (2005).
    [CrossRef]
  21. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  22. T. Shirai, O. Korotkova, and E. Wolf, J. Opt. A: Pure Appl. Opt. 7, 232 (2005).
    [CrossRef]
  23. G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, Opt. Commun. 208, 9 (2002).
    [CrossRef]
  24. 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]
  25. A. S. Ostrovsky, G. Rodríguez-Zurita, C. Meneses-Fabián, M. Á. Olvera-Santamaría, and C. Rickenstorff-Parrao, Opt. Express 18, 12864 (2010).
    [CrossRef] [PubMed]

2010 (2)

2009 (2)

2008 (3)

2007 (1)

2005 (4)

2004 (2)

2003 (2)

2002 (1)

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

2001 (1)

A. T. Friberg, T. D. Visser, W. Wang, and E. Wolf, Opt. Commun. 196, 1 (2001).
[CrossRef]

1998 (1)

1997 (1)

Arrizón, V.

Borghi, R.

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

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U., 1999).

Du, X.

X. Du and D. Zhao, J. Electromagn. Waves Appl. 24, 521 (2010).

X. Du and D. Zhao, Phys. Lett. A 373, 4297 (2009).
[CrossRef]

X. Du and D. Zhao, Opt. Commun. 281, 2711 (2008).
[CrossRef]

Fischer, D. G.

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.

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.

Hanson, S. G.

Hoover, B. G.

Jakobsen, M.

Kaivola, M.

Korotkova, O.

O. Korotkova, B. G. Hoover, V. L. Gamiz, and E. Wolf, J. Opt. Soc. Am. A 22, 2547 (2005).
[CrossRef]

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

Lindfors, K.

Luis, A.

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, eds. (Research Signpost, 2009), pp. 113–132.

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, eds. (Research Signpost, 2009), pp. 113–132.

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.

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]

Salem, M.

Santarsiero, M.

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, J. Opt. A: Pure Appl. Opt. 7, 232 (2005).
[CrossRef]

Takeda, M.

Tervo, J.

Visser, T. D.

D. G. Fischer and T. D. Visser, J. Opt. Soc. Am. A 21, 2097 (2004).
[CrossRef]

A. T. Friberg, T. D. Visser, W. Wang, and E. Wolf, Opt. Commun. 196, 1 (2001).
[CrossRef]

Wang, W.

Wolf, E.

M. Salem and E. Wolf, Opt. Lett. 33, 1180 (2008).
[CrossRef] [PubMed]

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

O. Korotkova, B. G. Hoover, V. L. Gamiz, and E. Wolf, J. Opt. Soc. Am. A 22, 2547 (2005).
[CrossRef]

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

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

A. T. Friberg, T. D. Visser, W. Wang, and E. Wolf, Opt. Commun. 196, 1 (2001).
[CrossRef]

W. Wang, A. T. Friberg, and E. Wolf, J. Opt. Soc. Am. A 14, 491 (1997).
[CrossRef]

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge U., 2007).

M. Born and E. Wolf, Principles of Optics (Cambridge U., 1999).

Zhao, D.

X. Du and D. Zhao, J. Electromagn. Waves Appl. 24, 521 (2010).

X. Du and D. Zhao, Phys. Lett. A 373, 4297 (2009).
[CrossRef]

X. Du and D. Zhao, Opt. Commun. 281, 2711 (2008).
[CrossRef]

J. Electromagn. Waves Appl. (1)

X. Du and D. Zhao, J. Electromagn. Waves Appl. 24, 521 (2010).

J. Opt. A: Pure Appl. Opt. (1)

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

J. Opt. Soc. Am. A (7)

Opt. Commun. (3)

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

X. Du and D. Zhao, Opt. Commun. 281, 2711 (2008).
[CrossRef]

A. T. Friberg, T. D. Visser, W. Wang, and E. Wolf, Opt. Commun. 196, 1 (2001).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Phys. Lett. A (2)

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

X. Du and D. Zhao, Phys. Lett. A 373, 4297 (2009).
[CrossRef]

Other (5)

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge U., 2007).

A. S. Ostrovsky, P. Martínez-Vara, M. Á. Olvera-Santamaría, and G. Martínez-Niconoff, in Recent Research Developments in Optics, A.Gayathri, eds. (Research Signpost, 2009), pp. 113–132.

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

M. Born and E. Wolf, Principles of Optics (Cambridge U., 1999).

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

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Figures (3)

Fig. 1
Fig. 1

Telecentric imaging system (both lenses have the same focal length f).

Fig. 2
Fig. 2

Image of two incoherently illuminated pinholes, plotted in normalized coordinates. The bold-face points show the locations of pinholes corresponding to the Rayleigh resolution limit.

Fig. 3
Fig. 3

Graphical solution of Eq. (14) for the case of (a) arbitrary polarization and for the case of (b) different values of the degree of polarization . The numbering of curves concurs with the numbering of corresponding parameter combinations given in the main text. The roots of Eq. (14) are shown with bold-face dots and their numerical values are given to the right of the plots.

Equations (14)

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W ( x 1 , x 2 ) = ( W x x ( x 1 , x 2 ) W y x ( x 1 , x 2 ) W x y ( x 1 , x 2 ) W y y ( x 1 , x 2 ) ) ,
S ( x ) = Tr W ( x , x ) ,
η ( x 1 , x 2 ) = Tr W ( x 1 , x 2 ) [ Tr W ( x 1 , x 1 ) Tr W ( x 2 , x 2 ) ] 1 / 2 ,
P ( x ) = ( 1 4 Det W ( x , x ) [ Tr W ( x , x ) ] 2 ) 1 / 2 .
W out ( x 1 , x 2 ) = t * ( x 1 ) t ( x 2 ) W in ( x 1 , x 2 ) × h * ( x 1 x 1 ) h ( x 2 x 2 ) d x 1 d x 2 .
S out ( x ) = Tr t * ( x 1 ) t ( x 2 ) W in ( x 1 , x 2 ) × h * ( x 1 x ) h ( x 2 x ) d x 1 d x 2 .
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 ) ,
η ( x 1 , x 2 ) = 1 S 0 x + S 0 y [ S 0 x exp ( ( x 1 x 2 ) 2 2 σ x 2 ) + S 0 y exp ( ( x 1 x 2 ) 2 2 σ y 2 ) ] ,
P ( x ) = | S 0 x S 0 y | S 0 x + S 0 y .
h ( x ) = h ( r ) = π R 2 λ f ( 2 J 1 ( 2 π R r / λ f ) 2 π R r / λ f ) ,
t ( x ) = a δ ( x d / 2 , y ) + a δ ( x + d / 2 , y ) ,
S out ( x ) = ( a π R 2 λ f ) 2 exp ( d 2 8 σ 2 ) ( S 0 x + S 0 y ) × { ( 2 J 1 [ 2 π R ( x d / 2 ) / λ f ] 2 π R ( x d / 2 ) / λ f ) 2 + ( 2 J 1 [ 2 π R ( x + d / 2 ) / λ f ] 2 π R ( x + d / 2 ) / λ f ) 2 + 2 1 S 0 x + S 0 y [ S 0 x exp ( d 2 2 σ x 2 ) + S 0 y exp ( d 2 2 σ y 2 ) ] × ( 2 J 1 [ 2 π R ( x d / 2 ) / λ f ] 2 π R ( x d / 2 ) / λ f ) ( 2 J 1 [ 2 π R ( x + d / 2 ) / λ f ] 2 π R ( x + d / 2 ) / λ f ) } .
S out ( 0 ) S out ( d / 2 ) = 2 ( 2 J 1 ( π R d / λ f ) π R d / λ f ) 2 { 1 + 1 S 0 x + S 0 y × [ S 0 x exp ( d 2 2 σ x 2 ) + S 0 y exp ( d 2 2 σ y 2 ) ] } = 0.735 .

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