Abstract

Beckmann’s theory of scattering from rough surfaces is applied to obtain, from the experimental veiling glare functions, a diffuser that when placed at the pupil plane would produce the same scattering halo as the ocular media. This equivalent diffuser is introduced in a schematic eye model, and its influence on the point-spread function and the modulation-transfer function of the eye is analyzed.

© 1985 Optical Society of America

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References

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  1. L. L. Holladay, “Action of a light source in the field of view in lowering visibility,” J. Opt. Soc. Am. 14, 1–15 (1927).
    [CrossRef]
  2. Y. Le Grand, “Recherches sur la diffusion de la lumiére dans l’oeil humain,” Rev. Opt. 16, 240–266 (1937).
  3. W. S. Stiles, B. H. Crawford, “The effect of a glaring light source on extrafoveal vision,” Proc. R. Soc. London B 122, 255–280 (1937).
    [CrossRef]
  4. G. A. Fry, M. Alpern, “The effect of a peripheral glare source upon the apparent brightness of an object,” J. Opt. Soc. Am. 43, 189–195 (1953).
    [CrossRef] [PubMed]
  5. J. J. Vos, M. A. Bouman, “Contribution of the retina to entopic scatter,” J. Opt. Soc. Am. 54, 95–100 (1963).
    [CrossRef]
  6. J. Walraven, “Spatial characteristics of chromatic induction; the segregation of lateral effects from stray light artifacts,” Vision Res. 13, 1739–1753 (1973).
    [CrossRef] [PubMed]
  7. J. J. Vos, J. Walraven, A. Van Meeteren, “Light profiles of the foveal image of a point source,” Vision Res. 16, 215–219 (1976).
    [CrossRef] [PubMed]
  8. P. J. Chandley, W. T. Welford, “A re-formulation of some results of P. Beckmann for scattering from rough surfaces,” Opt. Quantum Electron. 7, 393–397 (1975).
    [CrossRef]
  9. P. Beckmann, “The scattering of electromagnetic waves from rough surfaces,” Prog. Opt. 6, 55–59 (1967).
  10. The schematic eye as well as the computing of the PSF is described in R. Navarro, J. Santamaría, J. Bescós, “Accomodation-dependent model of the human eye with aspherics,” J. Opt. Soc. Am. A 2, 1273–1281 (1985).
    [CrossRef] [PubMed]

1985 (1)

1976 (1)

J. J. Vos, J. Walraven, A. Van Meeteren, “Light profiles of the foveal image of a point source,” Vision Res. 16, 215–219 (1976).
[CrossRef] [PubMed]

1975 (1)

P. J. Chandley, W. T. Welford, “A re-formulation of some results of P. Beckmann for scattering from rough surfaces,” Opt. Quantum Electron. 7, 393–397 (1975).
[CrossRef]

1973 (1)

J. Walraven, “Spatial characteristics of chromatic induction; the segregation of lateral effects from stray light artifacts,” Vision Res. 13, 1739–1753 (1973).
[CrossRef] [PubMed]

1967 (1)

P. Beckmann, “The scattering of electromagnetic waves from rough surfaces,” Prog. Opt. 6, 55–59 (1967).

1963 (1)

1953 (1)

1937 (2)

Y. Le Grand, “Recherches sur la diffusion de la lumiére dans l’oeil humain,” Rev. Opt. 16, 240–266 (1937).

W. S. Stiles, B. H. Crawford, “The effect of a glaring light source on extrafoveal vision,” Proc. R. Soc. London B 122, 255–280 (1937).
[CrossRef]

1927 (1)

Alpern, M.

Beckmann, P.

P. Beckmann, “The scattering of electromagnetic waves from rough surfaces,” Prog. Opt. 6, 55–59 (1967).

Bescós, J.

Bouman, M. A.

Chandley, P. J.

P. J. Chandley, W. T. Welford, “A re-formulation of some results of P. Beckmann for scattering from rough surfaces,” Opt. Quantum Electron. 7, 393–397 (1975).
[CrossRef]

Crawford, B. H.

W. S. Stiles, B. H. Crawford, “The effect of a glaring light source on extrafoveal vision,” Proc. R. Soc. London B 122, 255–280 (1937).
[CrossRef]

Fry, G. A.

Holladay, L. L.

Le Grand, Y.

Y. Le Grand, “Recherches sur la diffusion de la lumiére dans l’oeil humain,” Rev. Opt. 16, 240–266 (1937).

Navarro, R.

Santamaría, J.

Stiles, W. S.

W. S. Stiles, B. H. Crawford, “The effect of a glaring light source on extrafoveal vision,” Proc. R. Soc. London B 122, 255–280 (1937).
[CrossRef]

Van Meeteren, A.

J. J. Vos, J. Walraven, A. Van Meeteren, “Light profiles of the foveal image of a point source,” Vision Res. 16, 215–219 (1976).
[CrossRef] [PubMed]

Vos, J. J.

J. J. Vos, J. Walraven, A. Van Meeteren, “Light profiles of the foveal image of a point source,” Vision Res. 16, 215–219 (1976).
[CrossRef] [PubMed]

J. J. Vos, M. A. Bouman, “Contribution of the retina to entopic scatter,” J. Opt. Soc. Am. 54, 95–100 (1963).
[CrossRef]

Walraven, J.

J. J. Vos, J. Walraven, A. Van Meeteren, “Light profiles of the foveal image of a point source,” Vision Res. 16, 215–219 (1976).
[CrossRef] [PubMed]

J. Walraven, “Spatial characteristics of chromatic induction; the segregation of lateral effects from stray light artifacts,” Vision Res. 13, 1739–1753 (1973).
[CrossRef] [PubMed]

Welford, W. T.

P. J. Chandley, W. T. Welford, “A re-formulation of some results of P. Beckmann for scattering from rough surfaces,” Opt. Quantum Electron. 7, 393–397 (1975).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (1)

Opt. Quantum Electron. (1)

P. J. Chandley, W. T. Welford, “A re-formulation of some results of P. Beckmann for scattering from rough surfaces,” Opt. Quantum Electron. 7, 393–397 (1975).
[CrossRef]

Proc. R. Soc. London B (1)

W. S. Stiles, B. H. Crawford, “The effect of a glaring light source on extrafoveal vision,” Proc. R. Soc. London B 122, 255–280 (1937).
[CrossRef]

Prog. Opt. (1)

P. Beckmann, “The scattering of electromagnetic waves from rough surfaces,” Prog. Opt. 6, 55–59 (1967).

Rev. Opt. (1)

Y. Le Grand, “Recherches sur la diffusion de la lumiére dans l’oeil humain,” Rev. Opt. 16, 240–266 (1937).

Vision Res. (2)

J. Walraven, “Spatial characteristics of chromatic induction; the segregation of lateral effects from stray light artifacts,” Vision Res. 13, 1739–1753 (1973).
[CrossRef] [PubMed]

J. J. Vos, J. Walraven, A. Van Meeteren, “Light profiles of the foveal image of a point source,” Vision Res. 16, 215–219 (1976).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Schematic eye with the equivalent diffuser.

Fig. 2
Fig. 2

Adjustment of the veiling glare functions of a) Walraven and b) Le Grand. The figures represent both the empirical functions (dashed lines) and the calculated scattering halos (continuous lines) of the equivalent diffusers. Er is the retinal illuminance normalized to the illuminance E at the pupil plane.

Fig. 3
Fig. 3

PSF’s of the schematic eye computed a) without and b) with the equivalent diffuser for several pupil diameters: 2 mm (●), 3 mm (○), 4 mm (×), 5 mm (△), 6 mm (□), and 8 mm (▲). ρ is the radial coordinate (in micrometers) and α′ the semiaperture angle. Dashed curve corresponds to the aberration-free system.

Tables (2)

Tables Icon

Table 1 Equivalent Diffuser Parameters, φφ and r0, Computed from the Veiling Glare Functions of Walraven and Le Grand

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Table 2 Schematic Eye Parameters

Equations (6)

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L eq = A E ( θ + θ 0 ) n ,
E r = ( 1 R ) π n 2 4 ( D f ) 2 L eq ,
I ( ξ , η ) = S 2 n 2 λ 2 f 2 E exp ( k 2 σ φ 2 ) × { F 0 ( ξ , η ) + 2 π r 0 2 k 2 σ φ 2 S 1 [ 1 + k 2 r 0 2 ( ξ 2 + η 2 ) f 2 ] 3 / 2 } ,
T ( u , υ ) = T 0 ( u , υ ) + 4 π 2 σ φ 2 f 2 S 2 exp [ λ f r 0 ( u 2 + υ 2 ) 1 / 2 ] 1 + 4 π 2 σ φ 2 f 2 S 2 ,
L eq = 29 E ( θ + 0.13 ) 2.8
E r = E ( 0.61 θ 3 + 0.05 θ 1.5 + 0.0002 cos 4 θ )

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