Abstract

In a theoretical eye with spherical and aspheric surfaces, the retinal illumination is calculated if a Ganzfeld luminance field is used. The resulting retinal light distribution is nearly homogeneous over the whole retina. The homogeneity is not much influenced by the size of the pupil or the shape of the optical surfaces. The corresponding retinal area and the luminous flux entering the eye are calculated as functions of the size of the visual field. The values of the length of the light path through the crystalline lens and of the angle of incidence on the retina are described as functions of the angle in the visual field.

© 1983 Optical Society of America

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References

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  1. P. Gouras, "Electroretinography: some basic principles," Invest. Ophthalmol. 9, 557–569 (1970).
    [PubMed]
  2. G. H. M. Van Lith, J. Meininger, and G. W. Van Marle, "Electrophysiological equipment for total and local retinal stimulation," Doc. Ophthalmol. 2, 213–218 (1973).
  3. H. Goldman, "Ein selbstregistrierendes Projektions Kugelperimeter," Ophthalmologica 109, 71–79 (1945).
    [CrossRef]
  4. I. M. Siegel, "A Ganzfeld contact lens electrode," Am. J. Ophthalmol. 80, 296–298 (1975).
    [PubMed]
  5. A. C. Kooijman and A. Damhof, "ERG lens with built in Ganzfeld light source for stimulation and adaptation," Invest. Ophthalmol. Visual Sci. 19, 315–318 (1980).
  6. H. E. Bedell and L. M. Katz, "On the necessity of correcting peripheral target luminance for pupillary area," Am. J. Optom. Physiol. Opt. 59, 767–769 (1982).
    [CrossRef] [PubMed]
  7. B. S. Jay, "The effective pupillary area at varying perimeter angles," Vision Res. 1, 418–424 (1962).
    [CrossRef]
  8. N. Drasdo and C. W. Fowler, "Non-linear projection on the retinal image in a wide-angle schematic eye," Br. J. Ophthalmol. 58, 709–714 (1974).
  9. M. L. Hoffman, E. Zrenner, and H. J. Langhof, "Die Wirkung der Pupille als Apertur- und Bildfeldblende auf die verschiedene Komponenten des menschlichen Electroretinograms," Albrecht von Graefes Arch. Klin. Exp. Ophthalmol. 206, 237–245 (1978).
  10. K. Gross, "Uber vergleichende Helligkeitsmessungen am albinotischen Kaninchenauge," Z. Sinnephysiologie 62, 38–43 (1932).
  11. R. W. Young, "A theory of central retinal disease," in New Directions in Ophthalmic Research, M. L. Sears, ed. (Yale U. Press, New Haven, Conn., 1981).
  12. Y. Le Grand, "Optique physiologique. La dioptrique de l'oeil et sa correction," Rev. Opt. (Paris) 25 (1946).
  13. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).
  14. J. M. Enoch and A. M. Laties, "An analysis of retinal receptor orientation. II. Predictions for psychophysical tests," Invest. Ophthalmol. 10, 959–970 (1971).
    [PubMed]
  15. H. E. Bedell and J. M. Enoch, "An apparent failure of the photoreceptor alignment mechanism in a human observer," Arch. Ophthalmol. 98, 2023–2026 (1980).
    [CrossRef] [PubMed]
  16. F. S. Said and R. A. Weale, "The variation with age of the spectral transmissivity of the living human crystalline lens," Gerontologia 3, 213–231 (1959).
    [CrossRef] [PubMed]
  17. D. Van Norren and J. J. Vos, "Spectral transmission of the human ocular media," Vision Res. 14, 1237–1244 (1974).
    [CrossRef]
  18. W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966).
  19. R. B. Mandell and R. St. Helen, "Mathematical model for the corneal contour," Br. J. Physiol. Opt. 26, 183–197 (1971).
  20. N. Drasdo and W. C. Peaston, "Sampling systems for visual field assesment and computerised perimetry," Br. J. Ophthalmol. 64, 705–712 (1980).
  21. M. J. Howcroft and J. A. Parker, "Aspheric curvatures for the human lens," Vision Res. 17, 1217–1223 (1977).
    [CrossRef] [PubMed]
  22. H. Von Helmholtz, Handbuch der Physiologischen Optik I (Verlag von Leopold Voss, Hamburg, 1909), p. 9.
  23. K. H. Spring and W. H. Stiles, "Apparent shape and size of the pupil viewed obliquely," Br. J. Ophthalmol. 32, 347–354 (1948).
  24. J. A. M. Jennings and W. N. Charman, "Off-axis quality in the human eye," Vision Res. 21, 445–455 (1981).
    [CrossRef]

1982

H. E. Bedell and L. M. Katz, "On the necessity of correcting peripheral target luminance for pupillary area," Am. J. Optom. Physiol. Opt. 59, 767–769 (1982).
[CrossRef] [PubMed]

1981

J. A. M. Jennings and W. N. Charman, "Off-axis quality in the human eye," Vision Res. 21, 445–455 (1981).
[CrossRef]

1980

A. C. Kooijman and A. Damhof, "ERG lens with built in Ganzfeld light source for stimulation and adaptation," Invest. Ophthalmol. Visual Sci. 19, 315–318 (1980).

H. E. Bedell and J. M. Enoch, "An apparent failure of the photoreceptor alignment mechanism in a human observer," Arch. Ophthalmol. 98, 2023–2026 (1980).
[CrossRef] [PubMed]

N. Drasdo and W. C. Peaston, "Sampling systems for visual field assesment and computerised perimetry," Br. J. Ophthalmol. 64, 705–712 (1980).

1978

M. L. Hoffman, E. Zrenner, and H. J. Langhof, "Die Wirkung der Pupille als Apertur- und Bildfeldblende auf die verschiedene Komponenten des menschlichen Electroretinograms," Albrecht von Graefes Arch. Klin. Exp. Ophthalmol. 206, 237–245 (1978).

1977

M. J. Howcroft and J. A. Parker, "Aspheric curvatures for the human lens," Vision Res. 17, 1217–1223 (1977).
[CrossRef] [PubMed]

1975

I. M. Siegel, "A Ganzfeld contact lens electrode," Am. J. Ophthalmol. 80, 296–298 (1975).
[PubMed]

1974

N. Drasdo and C. W. Fowler, "Non-linear projection on the retinal image in a wide-angle schematic eye," Br. J. Ophthalmol. 58, 709–714 (1974).

D. Van Norren and J. J. Vos, "Spectral transmission of the human ocular media," Vision Res. 14, 1237–1244 (1974).
[CrossRef]

1973

G. H. M. Van Lith, J. Meininger, and G. W. Van Marle, "Electrophysiological equipment for total and local retinal stimulation," Doc. Ophthalmol. 2, 213–218 (1973).

1971

R. B. Mandell and R. St. Helen, "Mathematical model for the corneal contour," Br. J. Physiol. Opt. 26, 183–197 (1971).

J. M. Enoch and A. M. Laties, "An analysis of retinal receptor orientation. II. Predictions for psychophysical tests," Invest. Ophthalmol. 10, 959–970 (1971).
[PubMed]

1970

P. Gouras, "Electroretinography: some basic principles," Invest. Ophthalmol. 9, 557–569 (1970).
[PubMed]

1962

B. S. Jay, "The effective pupillary area at varying perimeter angles," Vision Res. 1, 418–424 (1962).
[CrossRef]

1959

F. S. Said and R. A. Weale, "The variation with age of the spectral transmissivity of the living human crystalline lens," Gerontologia 3, 213–231 (1959).
[CrossRef] [PubMed]

1948

K. H. Spring and W. H. Stiles, "Apparent shape and size of the pupil viewed obliquely," Br. J. Ophthalmol. 32, 347–354 (1948).

1945

H. Goldman, "Ein selbstregistrierendes Projektions Kugelperimeter," Ophthalmologica 109, 71–79 (1945).
[CrossRef]

1932

K. Gross, "Uber vergleichende Helligkeitsmessungen am albinotischen Kaninchenauge," Z. Sinnephysiologie 62, 38–43 (1932).

Bedell, H. E.

H. E. Bedell and L. M. Katz, "On the necessity of correcting peripheral target luminance for pupillary area," Am. J. Optom. Physiol. Opt. 59, 767–769 (1982).
[CrossRef] [PubMed]

H. E. Bedell and J. M. Enoch, "An apparent failure of the photoreceptor alignment mechanism in a human observer," Arch. Ophthalmol. 98, 2023–2026 (1980).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

Charman, W. N.

J. A. M. Jennings and W. N. Charman, "Off-axis quality in the human eye," Vision Res. 21, 445–455 (1981).
[CrossRef]

Damhof, A.

A. C. Kooijman and A. Damhof, "ERG lens with built in Ganzfeld light source for stimulation and adaptation," Invest. Ophthalmol. Visual Sci. 19, 315–318 (1980).

Drasdo, N.

N. Drasdo and W. C. Peaston, "Sampling systems for visual field assesment and computerised perimetry," Br. J. Ophthalmol. 64, 705–712 (1980).

N. Drasdo and C. W. Fowler, "Non-linear projection on the retinal image in a wide-angle schematic eye," Br. J. Ophthalmol. 58, 709–714 (1974).

Enoch, J. M.

H. E. Bedell and J. M. Enoch, "An apparent failure of the photoreceptor alignment mechanism in a human observer," Arch. Ophthalmol. 98, 2023–2026 (1980).
[CrossRef] [PubMed]

J. M. Enoch and A. M. Laties, "An analysis of retinal receptor orientation. II. Predictions for psychophysical tests," Invest. Ophthalmol. 10, 959–970 (1971).
[PubMed]

Fowler, C. W.

N. Drasdo and C. W. Fowler, "Non-linear projection on the retinal image in a wide-angle schematic eye," Br. J. Ophthalmol. 58, 709–714 (1974).

Goldman, H.

H. Goldman, "Ein selbstregistrierendes Projektions Kugelperimeter," Ophthalmologica 109, 71–79 (1945).
[CrossRef]

Gouras, P.

P. Gouras, "Electroretinography: some basic principles," Invest. Ophthalmol. 9, 557–569 (1970).
[PubMed]

Gross, K.

K. Gross, "Uber vergleichende Helligkeitsmessungen am albinotischen Kaninchenauge," Z. Sinnephysiologie 62, 38–43 (1932).

Helen, R. St.

R. B. Mandell and R. St. Helen, "Mathematical model for the corneal contour," Br. J. Physiol. Opt. 26, 183–197 (1971).

Hoffman, M. L.

M. L. Hoffman, E. Zrenner, and H. J. Langhof, "Die Wirkung der Pupille als Apertur- und Bildfeldblende auf die verschiedene Komponenten des menschlichen Electroretinograms," Albrecht von Graefes Arch. Klin. Exp. Ophthalmol. 206, 237–245 (1978).

Howcroft, M. J.

M. J. Howcroft and J. A. Parker, "Aspheric curvatures for the human lens," Vision Res. 17, 1217–1223 (1977).
[CrossRef] [PubMed]

Jay, B. S.

B. S. Jay, "The effective pupillary area at varying perimeter angles," Vision Res. 1, 418–424 (1962).
[CrossRef]

Jennings, J. A. M.

J. A. M. Jennings and W. N. Charman, "Off-axis quality in the human eye," Vision Res. 21, 445–455 (1981).
[CrossRef]

Katz, L. M.

H. E. Bedell and L. M. Katz, "On the necessity of correcting peripheral target luminance for pupillary area," Am. J. Optom. Physiol. Opt. 59, 767–769 (1982).
[CrossRef] [PubMed]

Kooijman, A. C.

A. C. Kooijman and A. Damhof, "ERG lens with built in Ganzfeld light source for stimulation and adaptation," Invest. Ophthalmol. Visual Sci. 19, 315–318 (1980).

Langhof, H. J.

M. L. Hoffman, E. Zrenner, and H. J. Langhof, "Die Wirkung der Pupille als Apertur- und Bildfeldblende auf die verschiedene Komponenten des menschlichen Electroretinograms," Albrecht von Graefes Arch. Klin. Exp. Ophthalmol. 206, 237–245 (1978).

Laties, A. M.

J. M. Enoch and A. M. Laties, "An analysis of retinal receptor orientation. II. Predictions for psychophysical tests," Invest. Ophthalmol. 10, 959–970 (1971).
[PubMed]

Le Grand, Y.

Y. Le Grand, "Optique physiologique. La dioptrique de l'oeil et sa correction," Rev. Opt. (Paris) 25 (1946).

Mandell, R. B.

R. B. Mandell and R. St. Helen, "Mathematical model for the corneal contour," Br. J. Physiol. Opt. 26, 183–197 (1971).

Meininger, J.

G. H. M. Van Lith, J. Meininger, and G. W. Van Marle, "Electrophysiological equipment for total and local retinal stimulation," Doc. Ophthalmol. 2, 213–218 (1973).

Parker, J. A.

M. J. Howcroft and J. A. Parker, "Aspheric curvatures for the human lens," Vision Res. 17, 1217–1223 (1977).
[CrossRef] [PubMed]

Peaston, W. C.

N. Drasdo and W. C. Peaston, "Sampling systems for visual field assesment and computerised perimetry," Br. J. Ophthalmol. 64, 705–712 (1980).

Said, F. S.

F. S. Said and R. A. Weale, "The variation with age of the spectral transmissivity of the living human crystalline lens," Gerontologia 3, 213–231 (1959).
[CrossRef] [PubMed]

Siegel, I. M.

I. M. Siegel, "A Ganzfeld contact lens electrode," Am. J. Ophthalmol. 80, 296–298 (1975).
[PubMed]

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966).

Spring, K. H.

K. H. Spring and W. H. Stiles, "Apparent shape and size of the pupil viewed obliquely," Br. J. Ophthalmol. 32, 347–354 (1948).

Stiles, W. H.

K. H. Spring and W. H. Stiles, "Apparent shape and size of the pupil viewed obliquely," Br. J. Ophthalmol. 32, 347–354 (1948).

Van Lith, G. H. M.

G. H. M. Van Lith, J. Meininger, and G. W. Van Marle, "Electrophysiological equipment for total and local retinal stimulation," Doc. Ophthalmol. 2, 213–218 (1973).

Van Marle, G. W.

G. H. M. Van Lith, J. Meininger, and G. W. Van Marle, "Electrophysiological equipment for total and local retinal stimulation," Doc. Ophthalmol. 2, 213–218 (1973).

Van Norren, D.

D. Van Norren and J. J. Vos, "Spectral transmission of the human ocular media," Vision Res. 14, 1237–1244 (1974).
[CrossRef]

Von Helmholtz, H.

H. Von Helmholtz, Handbuch der Physiologischen Optik I (Verlag von Leopold Voss, Hamburg, 1909), p. 9.

Vos, J. J.

D. Van Norren and J. J. Vos, "Spectral transmission of the human ocular media," Vision Res. 14, 1237–1244 (1974).
[CrossRef]

Weale, R. A.

F. S. Said and R. A. Weale, "The variation with age of the spectral transmissivity of the living human crystalline lens," Gerontologia 3, 213–231 (1959).
[CrossRef] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

Young, R. W.

R. W. Young, "A theory of central retinal disease," in New Directions in Ophthalmic Research, M. L. Sears, ed. (Yale U. Press, New Haven, Conn., 1981).

Zrenner, E.

M. L. Hoffman, E. Zrenner, and H. J. Langhof, "Die Wirkung der Pupille als Apertur- und Bildfeldblende auf die verschiedene Komponenten des menschlichen Electroretinograms," Albrecht von Graefes Arch. Klin. Exp. Ophthalmol. 206, 237–245 (1978).

Albrecht von Graefes Arch. Klin. Exp. Ophthalmol.

M. L. Hoffman, E. Zrenner, and H. J. Langhof, "Die Wirkung der Pupille als Apertur- und Bildfeldblende auf die verschiedene Komponenten des menschlichen Electroretinograms," Albrecht von Graefes Arch. Klin. Exp. Ophthalmol. 206, 237–245 (1978).

Am. J. Ophthalmol.

I. M. Siegel, "A Ganzfeld contact lens electrode," Am. J. Ophthalmol. 80, 296–298 (1975).
[PubMed]

Am. J. Optom. Physiol. Opt.

H. E. Bedell and L. M. Katz, "On the necessity of correcting peripheral target luminance for pupillary area," Am. J. Optom. Physiol. Opt. 59, 767–769 (1982).
[CrossRef] [PubMed]

Arch. Ophthalmol.

H. E. Bedell and J. M. Enoch, "An apparent failure of the photoreceptor alignment mechanism in a human observer," Arch. Ophthalmol. 98, 2023–2026 (1980).
[CrossRef] [PubMed]

Br. J. Ophthalmol.

N. Drasdo and C. W. Fowler, "Non-linear projection on the retinal image in a wide-angle schematic eye," Br. J. Ophthalmol. 58, 709–714 (1974).

N. Drasdo and W. C. Peaston, "Sampling systems for visual field assesment and computerised perimetry," Br. J. Ophthalmol. 64, 705–712 (1980).

K. H. Spring and W. H. Stiles, "Apparent shape and size of the pupil viewed obliquely," Br. J. Ophthalmol. 32, 347–354 (1948).

Br. J. Physiol. Opt.

R. B. Mandell and R. St. Helen, "Mathematical model for the corneal contour," Br. J. Physiol. Opt. 26, 183–197 (1971).

Doc. Ophthalmol.

G. H. M. Van Lith, J. Meininger, and G. W. Van Marle, "Electrophysiological equipment for total and local retinal stimulation," Doc. Ophthalmol. 2, 213–218 (1973).

Gerontologia

F. S. Said and R. A. Weale, "The variation with age of the spectral transmissivity of the living human crystalline lens," Gerontologia 3, 213–231 (1959).
[CrossRef] [PubMed]

Invest. Ophthalmol.

P. Gouras, "Electroretinography: some basic principles," Invest. Ophthalmol. 9, 557–569 (1970).
[PubMed]

J. M. Enoch and A. M. Laties, "An analysis of retinal receptor orientation. II. Predictions for psychophysical tests," Invest. Ophthalmol. 10, 959–970 (1971).
[PubMed]

Invest. Ophthalmol. Visual Sci.

A. C. Kooijman and A. Damhof, "ERG lens with built in Ganzfeld light source for stimulation and adaptation," Invest. Ophthalmol. Visual Sci. 19, 315–318 (1980).

Ophthalmologica

H. Goldman, "Ein selbstregistrierendes Projektions Kugelperimeter," Ophthalmologica 109, 71–79 (1945).
[CrossRef]

Vision Res.

B. S. Jay, "The effective pupillary area at varying perimeter angles," Vision Res. 1, 418–424 (1962).
[CrossRef]

D. Van Norren and J. J. Vos, "Spectral transmission of the human ocular media," Vision Res. 14, 1237–1244 (1974).
[CrossRef]

M. J. Howcroft and J. A. Parker, "Aspheric curvatures for the human lens," Vision Res. 17, 1217–1223 (1977).
[CrossRef] [PubMed]

J. A. M. Jennings and W. N. Charman, "Off-axis quality in the human eye," Vision Res. 21, 445–455 (1981).
[CrossRef]

Z. Sinnephysiologie

K. Gross, "Uber vergleichende Helligkeitsmessungen am albinotischen Kaninchenauge," Z. Sinnephysiologie 62, 38–43 (1932).

Other

R. W. Young, "A theory of central retinal disease," in New Directions in Ophthalmic Research, M. L. Sears, ed. (Yale U. Press, New Haven, Conn., 1981).

Y. Le Grand, "Optique physiologique. La dioptrique de l'oeil et sa correction," Rev. Opt. (Paris) 25 (1946).

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966).

H. Von Helmholtz, Handbuch der Physiologischen Optik I (Verlag von Leopold Voss, Hamburg, 1909), p. 9.

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Figures (10)

Fig. 1
Fig. 1

Schematic eye. Solid lines are spherical surfaces (theoretical eye of Le Grand). Dashed lines are aspheric surfaces as used in this study.

Fig. 2
Fig. 2

Retinal area dRA(φ) corresponding to an annular solid angle of visual field dSA(φ) calculated for various values of φ and with an annular width of 0.5°.

Fig. 3
Fig. 3

Angle of incidence on the retina of the principal ray of a light pencil of parallel rays as a function of angle of incidence in the visual field. A, B, and C refer to the eye models A, B, and C in the caption of Table 1. The numbers 2 and 8 indicate that the eye model had a pupil diameter of 2 or 8 mm.

Fig. 4
Fig. 4

Path length of the principal light ray through the lens. A and B refer to the eye models A and B in the caption of Table 1. L is calculated in an eye with aspheric anterior and posterior lens surfaces. It is the combination of models D and E in the caption of Table 1.

Fig. 5
Fig. 5

Retinal illumination. A, B, and C are calculated in eye models A, B, and C as defined in the caption of Table 1.

Fig. 6
Fig. 6

Relative light flux into the eye with a homogeneous luminance field of limited size. All eye models (irrespective of whether the pupil diameter is 2 or 8 mm) in this study show the same relation between visual field and light flux. With a Ganzfeld with a luminance of 1 cd/m2 the absolute light flux is 212 μlm with an 8-mm pupil and 13 μlm with a 2-mm pupil.

Fig. 7
Fig. 7

Retinal area corresponding with angular field of view. A, B, and C refer to the eye models A, B, and C in the caption of Table 1. The numbers 2 and 8 indicate that the eye model had a pupil diameter of 2 or 8 mm.

Fig. 8
Fig. 8

Retinal area per solid degree in the visual field. B2: Calculated relation in the eye model with aspheric (conic constant p = 0.75) anterior and posterior corneal surfaces and spherical lens and retinal surfaces. Pupil diameter, 2 mm. D&F: Relative values calculated by Drasdo and Fowler8 in an eye model with a single aspheric (conic constant p = 0.5) corneal surface and spherical lens and retinal surfaces.

Fig. 9
Fig. 9

Length of retinal arc between the optic axis and the point of incidence of the principal ray with eccentricity φ. A, B, and C refer to the eye models A, B, and C in the caption of Table 1. The numbers 2 and 8 indicate that the eye model had a pupil diameter of 2 or 8 mm.

Fig. 10
Fig. 10

Corneal arc in the meridional plane, covered by the light rays that pass through the pupil, depends on the angle of incidence and on the size of the pupil. These data are collected with the spherical eye model.

Tables (2)

Tables Icon

Table 2 Apparent Pupil Diameter, Retinal Area per Solid Angle, and Retinal Illumination Resulting from a Ganzfeld Light Source with a Luminance of 1 cd/m2

Equations (5)

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PA ( φ ) = π × PD ( φ ) × PD ( 0 ) / 4.
RI ( φ ) = PA ( φ ) RS ( φ ) × A ,
( x - r p ) 2 + y 2 p = r 2 p , p x 2 - 2 x r + y 2 = 0 ,
| b a - 1 | 1 p = ( b a ) 2 = ( 1 - | b a - 1 | ) 2 }             if a and b are real and b a ,
| b a - 1 | > 1 p = ( b a ) 2 = 1 - | b a - 1 | 2 }             if b is imaginary and a is real .