Abstract

We present the first account (to our knowledge) of interaction between stochastic light and the crystalline human eye lens. In particular, the spectral density and the spectral degree of polarization of light focused by the crystalline lens onto the eye’s back wall are examined. We find that the correlation properties of the incident light play the important role in the process of image formation by the eye and in its perception of polarization features of the incoming radiation.

© 2011 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  9. S. A. Collins Jr., J. Opt. Soc. Am. A 60, 1168 (1970).
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  10. A. T. Friberg and J. Turunen, J. Opt. Soc. Am. A 5, 713 (1988).
    [CrossRef]
  11. B. Lu and L. Pan, Opt. Commun. 205, 7 (2002).
    [CrossRef]
  12. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).
  13. H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
    [CrossRef]

2008

2006

Y. Huang and D. T. Moore, Proc. SPIE 6324, 63420D-1 (2006).

M. T. Flores-Arias, M. V. Perez, C. Bao, A. Castelo, and C. Gomez-Reino, J. Mod. Opt. 53, 495 (2006).
[CrossRef]

2005

M. V. Perez, C. Bao, M. T. Flores-Arias, M. A. Rama, and C. G. Reino, J. Opt. A 7, 103 (2005).
[CrossRef]

M. A. Rama, M. V. Perez, C. Bao, M. T. Flores-Arias, and C. G. Reino, Opt. Commun. 249, 595 (2005).
[CrossRef]

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
[CrossRef]

2002

B. Lu and L. Pan, Opt. Commun. 205, 7 (2002).
[CrossRef]

1992

1988

1970

S. A. Collins Jr., J. Opt. Soc. Am. A 60, 1168 (1970).
[CrossRef]

1880

L. Matthiessen, Pfluegers Arch. Gesamte Physiol. Menschen Tiere 21, 287 (1880).
[CrossRef]

Atchison, D. A.

Bao, C.

M. T. Flores-Arias, M. V. Perez, C. Bao, A. Castelo, and C. Gomez-Reino, J. Mod. Opt. 53, 495 (2006).
[CrossRef]

M. V. Perez, C. Bao, M. T. Flores-Arias, M. A. Rama, and C. G. Reino, J. Opt. A 7, 103 (2005).
[CrossRef]

M. A. Rama, M. V. Perez, C. Bao, M. T. Flores-Arias, and C. G. Reino, Opt. Commun. 249, 595 (2005).
[CrossRef]

Castelo, A.

M. T. Flores-Arias, M. V. Perez, C. Bao, A. Castelo, and C. Gomez-Reino, J. Mod. Opt. 53, 495 (2006).
[CrossRef]

Collins, S. A.

S. A. Collins Jr., J. Opt. Soc. Am. A 60, 1168 (1970).
[CrossRef]

Diaz, J. A.

Flores-Arias, M. T.

M. T. Flores-Arias, M. V. Perez, C. Bao, A. Castelo, and C. Gomez-Reino, J. Mod. Opt. 53, 495 (2006).
[CrossRef]

M. A. Rama, M. V. Perez, C. Bao, M. T. Flores-Arias, and C. G. Reino, Opt. Commun. 249, 595 (2005).
[CrossRef]

M. V. Perez, C. Bao, M. T. Flores-Arias, M. A. Rama, and C. G. Reino, J. Opt. A 7, 103 (2005).
[CrossRef]

Friberg, A. T.

Gomez-Reino, C.

M. T. Flores-Arias, M. V. Perez, C. Bao, A. Castelo, and C. Gomez-Reino, J. Mod. Opt. 53, 495 (2006).
[CrossRef]

Gullstrand, A.

A. Gullstrand, Helmholtz’s Handbuch der Physiologischen Optik, J.P.Southall, ed. (Optical Society of America, 1924), 3rd ed., Vol.  1, Appendix II, p. 301.

Huang, Y.

Y. Huang and D. T. Moore, Proc. SPIE 6324, 63420D-1 (2006).

Korotkova, O.

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
[CrossRef]

Lu, B.

B. Lu and L. Pan, Opt. Commun. 205, 7 (2002).
[CrossRef]

Matthiessen, L.

L. Matthiessen, Pfluegers Arch. Gesamte Physiol. Menschen Tiere 21, 287 (1880).
[CrossRef]

Moore, D. T.

Y. Huang and D. T. Moore, Proc. SPIE 6324, 63420D-1 (2006).

Pan, L.

B. Lu and L. Pan, Opt. Commun. 205, 7 (2002).
[CrossRef]

Perez, M. V.

M. T. Flores-Arias, M. V. Perez, C. Bao, A. Castelo, and C. Gomez-Reino, J. Mod. Opt. 53, 495 (2006).
[CrossRef]

M. A. Rama, M. V. Perez, C. Bao, M. T. Flores-Arias, and C. G. Reino, Opt. Commun. 249, 595 (2005).
[CrossRef]

M. V. Perez, C. Bao, M. T. Flores-Arias, M. A. Rama, and C. G. Reino, J. Opt. A 7, 103 (2005).
[CrossRef]

Piercionek, B. K.

Rama, M. A.

M. V. Perez, C. Bao, M. T. Flores-Arias, M. A. Rama, and C. G. Reino, J. Opt. A 7, 103 (2005).
[CrossRef]

M. A. Rama, M. V. Perez, C. Bao, M. T. Flores-Arias, and C. G. Reino, Opt. Commun. 249, 595 (2005).
[CrossRef]

Reino, C. G.

M. A. Rama, M. V. Perez, C. Bao, M. T. Flores-Arias, and C. G. Reino, Opt. Commun. 249, 595 (2005).
[CrossRef]

M. V. Perez, C. Bao, M. T. Flores-Arias, M. A. Rama, and C. G. Reino, J. Opt. A 7, 103 (2005).
[CrossRef]

Roychowdhury, H.

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
[CrossRef]

Smith, G.

Turunen, J.

Wolf, E.

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

Appl. Opt.

J. Mod. Opt.

M. T. Flores-Arias, M. V. Perez, C. Bao, A. Castelo, and C. Gomez-Reino, J. Mod. Opt. 53, 495 (2006).
[CrossRef]

J. Opt. A

M. V. Perez, C. Bao, M. T. Flores-Arias, M. A. Rama, and C. G. Reino, J. Opt. A 7, 103 (2005).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

B. Lu and L. Pan, Opt. Commun. 205, 7 (2002).
[CrossRef]

M. A. Rama, M. V. Perez, C. Bao, M. T. Flores-Arias, and C. G. Reino, Opt. Commun. 249, 595 (2005).
[CrossRef]

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
[CrossRef]

Pfluegers Arch. Gesamte Physiol. Menschen Tiere

L. Matthiessen, Pfluegers Arch. Gesamte Physiol. Menschen Tiere 21, 287 (1880).
[CrossRef]

Proc. SPIE

Y. Huang and D. T. Moore, Proc. SPIE 6324, 63420D-1 (2006).

Other

A. Gullstrand, Helmholtz’s Handbuch der Physiologischen Optik, J.P.Southall, ed. (Optical Society of America, 1924), 3rd ed., Vol.  1, Appendix II, p. 301.

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

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Figures (3)

Fig. 1
Fig. 1

Illustration of the notations used.

Fig. 2
Fig. 2

Spectral density S ( r , z , ω ) of the beam versus the propagation distance l [m] after the lens for: the coherent beam, δ x x = δ y y = δ x y = δ y x (solid curve), the partially coherent beam δ x x = δ y y = 1.125 × 10 4 m (dotted curve), δ x y = δ y x = 1.25 × 10 4 m , (C), and the nearly incoherent beam δ x x = δ y y = 1.125 × 10 5 m , δ x y = δ y x = 1.25 × 10 5 m (dashed curve).

Fig. 3
Fig. 3

Spectral degree of polarization P ( r , z , ω ) of the beams generated by the same sources as in Fig. 2 versus the propagation distance l [m] after the lens.

Equations (11)

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n ( r , d ) = 0.0062685 ( d d 0 ) 2 + 0.0003834 ( d d 0 ) 3 + 1.406 [ 0.00052375 + 0.00005735 ( d d 0 ) + 0.00027875 ( d d 0 ) 2 ] r 2 0.000066717 r 4 ,
n ( r , d ) = n 0 ( d ) [ 1 g 2 ( d ) r 2 / 2 ] ,
W ( ρ 1 , ρ 2 , ω ) = [ W i j ( ρ 1 , ρ 2 , ω ) ] , ( i , j = x , y ) ,
W i j ( r 1 , r 2 , z , ω ) = ( k 2 π B ) 2 W i j ( ρ 1 , ρ 2 , ω ) × exp { i k 2 B ( z ) [ A ( z ) ( ρ 1 2 ρ 2 2 ) 2 ( r 1 · ρ 1 r 2 · ρ 2 ) + D ( z ) ( r 1 2 r 2 2 ) ] } d ρ 1 d ρ 2 ,
W i j ( ρ 1 , ρ 2 , ω ) = I i I j B i j exp [ ( | ρ 1 | 2 + | ρ 2 | 2 ) / ( 4 σ 2 ) ] × exp [ ( | ρ 1 ρ 2 | 2 ) / ( 2 δ i j 2 ) ] .
W i j ( r 1 , r 2 , z , ω ) = I i I j B i j Q i j exp [ | r 1 | 2 + | r 2 | 2 4 σ 2 Q i j ] × exp [ | r 1 r 2 | 2 2 δ i j 2 Q i j ] exp [ i k ( | r 1 | 2 | r 2 | 2 ) 2 R i j ] ,
S ( r , z , ω ) = Tr W ( r , r , z , ω ) .
P ( r , z , ω ) = 1 4 Det W ( r , r , z , ω ) / [ Tr W ( r , r , z , ω ) ] 2 .
A ( d ) = [ 1 g e 2 d 2 2 + d g ˙ e 2 g e ( 1 g e 2 d 2 6 ) ] P f d ( 1 g e 2 d 2 6 ) n e , B ( d ) = n 1 n e d ( 1 g e 2 d 2 6 ) , C ( d ) = P E ( d ) n 1 , D ( d ) = n 1 n 1 ( [ g e 2 + ( g ˙ e 2 g e ) 2 ] d ( 1 g e 2 d 2 6 ) + P b [ g e 2 + ( g ˙ e 2 g e ) 2 ] d ( 1 g e 2 d 2 6 ) n e ) ,
P E ( d ) = P b H f ( d ) + P f H ˙ a ( d ) + P G ( d ) P b P f H a ( d ) n e = P b [ 1 g e 2 d 2 2 + g ˙ e 2 g e d ( 1 g e 2 d 2 6 ) ] + P f ( [ g e 2 + ( g ˙ e 2 g e ) 2 ] d ( 1 g e 2 d 2 6 ) ) n e [ 1 g e 2 d 2 2 g ˙ e 2 g e d ( 1 g e 2 d 2 6 ) ] P b P f d ( 1 g e 2 d 2 6 ) n e .
( A B C D ) = ( A ( d ) + l C ( d ) B ( d ) + l D ( d ) C ( d ) D ( d ) ) .

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