Abstract

A psychophysical method has been used to measure the modulation transfer function (MTF) of the defocused optical system of the human eye for incoherent monochromatic light (514 nm) and for various pupil diameters. The results have been compared with theoretical calculations based on aberration coefficients found previously. MTF’s have been computed for white light with the help of the measurements obtained for monochromatic light.

© 1980 Optical Society of America

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References

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  1. H. von Helmholtz, Helmholtz’s Treatise on Physiological Optics (Dover, New York, 1962), Vols. I and II.
  2. A. C. S. van Heel, “Correcting spherical and chromatic aberrations of the eye,” J. Opt. Soc. Am. 36, 237–241 (1946).
    [PubMed]
  3. J. Krauskopf, “Further measurements of human retinal images,” J. Opt. Soc. Am. 54, 715–716 (1964).
    [Crossref]
  4. A. van Meeteren, “Calculations on the optical modulation transfer function of the human eye for white light,” Opt. Acta 21, 395–412 (1974).
    [Crossref]
  5. W. M. Charman and J. A. M. Jenings, “The optical quality of the monochromatic retinal image as a function of focus,” Brit. J. Physiol. Opt. 31, 119–134 (1976).
    [PubMed]
  6. H. S. Smirnov, “Measurements of wave aberrations in the human eye,” Biophys. 6, 52–66 (1961).
  7. M. Tschernig, “Die monochromatischen Aberrationen des menslichen Auges,” A. Psychol. Physiol. Sinn 6, 456–471 (1894).
  8. H. Schober, H. Munker, and F. Zolleis, “Die Aberration des menslichen Auges und ihre Messung,” Opt. Acta 15, 47–57 (1968).
    [Crossref]
  9. G. van den Brink, “Measurements of the geometrical aberrations of the eye,” Vision Res. 2, 233–244 (1962).
    [Crossref]
  10. A. Ivanoff, “Les aberrations de l’oeil,” ed. de la Revue d’Optique Theorique et Instrumentale (Paris, 1953).
  11. H. C. Howland and B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,” J. Opt. Soc. Am. 67, 1508–1518 (1977).
    [Crossref] [PubMed]
  12. R. Rohler, “Die Abbildungseigenschaften der Augenmedien,” Vision Res. 2, 291–429 (1962).
    [Crossref]
  13. M. Koomen, R. Tousey, and R. Scolnik, “The spherical aberration of the eye,” J. Opt. Soc. Am. 55, 370–376 (1949).
    [Crossref]
  14. M. Françon, “Aberration sphérique chromatisme et pouvoir séparateur de l’oeil,” Rev. d’Optique 30, 71–80 (1951).
  15. F. W. Campbell and D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. 181, 576–593 (1965).
  16. A. Arnulf and O. Dupuy, “La transmission des contrastes par la système optique de l’oeil et les seuils de contrastes rétiniens,” C. R. Acad. Sci. 250, 2757–2760 (1960).
  17. C. R. Ingling, “Luminance and opponent color contributions to visual detection and to temporal and spatial integration: comment,” J. Opt. Soc. Am. 68, 1143–1147 (1978).
    [Crossref] [PubMed]
  18. H. H. Hopkins, “The numerical evaluation of the frequency response of optical systems,” Proc. Phys. Soc. B 70, 1002–1005 (1957).
    [Crossref]
  19. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

1978 (1)

1977 (1)

1976 (1)

W. M. Charman and J. A. M. Jenings, “The optical quality of the monochromatic retinal image as a function of focus,” Brit. J. Physiol. Opt. 31, 119–134 (1976).
[PubMed]

1974 (1)

A. van Meeteren, “Calculations on the optical modulation transfer function of the human eye for white light,” Opt. Acta 21, 395–412 (1974).
[Crossref]

1968 (1)

H. Schober, H. Munker, and F. Zolleis, “Die Aberration des menslichen Auges und ihre Messung,” Opt. Acta 15, 47–57 (1968).
[Crossref]

1965 (1)

F. W. Campbell and D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. 181, 576–593 (1965).

1964 (1)

1962 (2)

G. van den Brink, “Measurements of the geometrical aberrations of the eye,” Vision Res. 2, 233–244 (1962).
[Crossref]

R. Rohler, “Die Abbildungseigenschaften der Augenmedien,” Vision Res. 2, 291–429 (1962).
[Crossref]

1961 (1)

H. S. Smirnov, “Measurements of wave aberrations in the human eye,” Biophys. 6, 52–66 (1961).

1960 (1)

A. Arnulf and O. Dupuy, “La transmission des contrastes par la système optique de l’oeil et les seuils de contrastes rétiniens,” C. R. Acad. Sci. 250, 2757–2760 (1960).

1957 (1)

H. H. Hopkins, “The numerical evaluation of the frequency response of optical systems,” Proc. Phys. Soc. B 70, 1002–1005 (1957).
[Crossref]

1951 (1)

M. Françon, “Aberration sphérique chromatisme et pouvoir séparateur de l’oeil,” Rev. d’Optique 30, 71–80 (1951).

1949 (1)

M. Koomen, R. Tousey, and R. Scolnik, “The spherical aberration of the eye,” J. Opt. Soc. Am. 55, 370–376 (1949).
[Crossref]

1946 (1)

1894 (1)

M. Tschernig, “Die monochromatischen Aberrationen des menslichen Auges,” A. Psychol. Physiol. Sinn 6, 456–471 (1894).

Arnulf, A.

A. Arnulf and O. Dupuy, “La transmission des contrastes par la système optique de l’oeil et les seuils de contrastes rétiniens,” C. R. Acad. Sci. 250, 2757–2760 (1960).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

Campbell, F. W.

F. W. Campbell and D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. 181, 576–593 (1965).

Charman, W. M.

W. M. Charman and J. A. M. Jenings, “The optical quality of the monochromatic retinal image as a function of focus,” Brit. J. Physiol. Opt. 31, 119–134 (1976).
[PubMed]

Dupuy, O.

A. Arnulf and O. Dupuy, “La transmission des contrastes par la système optique de l’oeil et les seuils de contrastes rétiniens,” C. R. Acad. Sci. 250, 2757–2760 (1960).

Françon, M.

M. Françon, “Aberration sphérique chromatisme et pouvoir séparateur de l’oeil,” Rev. d’Optique 30, 71–80 (1951).

Green, D. G.

F. W. Campbell and D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. 181, 576–593 (1965).

Hopkins, H. H.

H. H. Hopkins, “The numerical evaluation of the frequency response of optical systems,” Proc. Phys. Soc. B 70, 1002–1005 (1957).
[Crossref]

Howland, B.

Howland, H. C.

Ingling, C. R.

Ivanoff, A.

A. Ivanoff, “Les aberrations de l’oeil,” ed. de la Revue d’Optique Theorique et Instrumentale (Paris, 1953).

Jenings, J. A. M.

W. M. Charman and J. A. M. Jenings, “The optical quality of the monochromatic retinal image as a function of focus,” Brit. J. Physiol. Opt. 31, 119–134 (1976).
[PubMed]

Koomen, M.

M. Koomen, R. Tousey, and R. Scolnik, “The spherical aberration of the eye,” J. Opt. Soc. Am. 55, 370–376 (1949).
[Crossref]

Krauskopf, J.

Munker, H.

H. Schober, H. Munker, and F. Zolleis, “Die Aberration des menslichen Auges und ihre Messung,” Opt. Acta 15, 47–57 (1968).
[Crossref]

Rohler, R.

R. Rohler, “Die Abbildungseigenschaften der Augenmedien,” Vision Res. 2, 291–429 (1962).
[Crossref]

Schober, H.

H. Schober, H. Munker, and F. Zolleis, “Die Aberration des menslichen Auges und ihre Messung,” Opt. Acta 15, 47–57 (1968).
[Crossref]

Scolnik, R.

M. Koomen, R. Tousey, and R. Scolnik, “The spherical aberration of the eye,” J. Opt. Soc. Am. 55, 370–376 (1949).
[Crossref]

Smirnov, H. S.

H. S. Smirnov, “Measurements of wave aberrations in the human eye,” Biophys. 6, 52–66 (1961).

Tousey, R.

M. Koomen, R. Tousey, and R. Scolnik, “The spherical aberration of the eye,” J. Opt. Soc. Am. 55, 370–376 (1949).
[Crossref]

Tschernig, M.

M. Tschernig, “Die monochromatischen Aberrationen des menslichen Auges,” A. Psychol. Physiol. Sinn 6, 456–471 (1894).

van den Brink, G.

G. van den Brink, “Measurements of the geometrical aberrations of the eye,” Vision Res. 2, 233–244 (1962).
[Crossref]

van Heel, A. C. S.

van Meeteren, A.

A. van Meeteren, “Calculations on the optical modulation transfer function of the human eye for white light,” Opt. Acta 21, 395–412 (1974).
[Crossref]

von Helmholtz, H.

H. von Helmholtz, Helmholtz’s Treatise on Physiological Optics (Dover, New York, 1962), Vols. I and II.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

Zolleis, F.

H. Schober, H. Munker, and F. Zolleis, “Die Aberration des menslichen Auges und ihre Messung,” Opt. Acta 15, 47–57 (1968).
[Crossref]

A. Psychol. Physiol. Sinn (1)

M. Tschernig, “Die monochromatischen Aberrationen des menslichen Auges,” A. Psychol. Physiol. Sinn 6, 456–471 (1894).

Biophys. (1)

H. S. Smirnov, “Measurements of wave aberrations in the human eye,” Biophys. 6, 52–66 (1961).

Brit. J. Physiol. Opt. (1)

W. M. Charman and J. A. M. Jenings, “The optical quality of the monochromatic retinal image as a function of focus,” Brit. J. Physiol. Opt. 31, 119–134 (1976).
[PubMed]

C. R. Acad. Sci. (1)

A. Arnulf and O. Dupuy, “La transmission des contrastes par la système optique de l’oeil et les seuils de contrastes rétiniens,” C. R. Acad. Sci. 250, 2757–2760 (1960).

J. Opt. Soc. Am. (5)

J. Physiol. (1)

F. W. Campbell and D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. 181, 576–593 (1965).

Opt. Acta (2)

A. van Meeteren, “Calculations on the optical modulation transfer function of the human eye for white light,” Opt. Acta 21, 395–412 (1974).
[Crossref]

H. Schober, H. Munker, and F. Zolleis, “Die Aberration des menslichen Auges und ihre Messung,” Opt. Acta 15, 47–57 (1968).
[Crossref]

Proc. Phys. Soc. B (1)

H. H. Hopkins, “The numerical evaluation of the frequency response of optical systems,” Proc. Phys. Soc. B 70, 1002–1005 (1957).
[Crossref]

Rev. d’Optique (1)

M. Françon, “Aberration sphérique chromatisme et pouvoir séparateur de l’oeil,” Rev. d’Optique 30, 71–80 (1951).

Vision Res. (2)

R. Rohler, “Die Abbildungseigenschaften der Augenmedien,” Vision Res. 2, 291–429 (1962).
[Crossref]

G. van den Brink, “Measurements of the geometrical aberrations of the eye,” Vision Res. 2, 233–244 (1962).
[Crossref]

Other (3)

A. Ivanoff, “Les aberrations de l’oeil,” ed. de la Revue d’Optique Theorique et Instrumentale (Paris, 1953).

H. von Helmholtz, Helmholtz’s Treatise on Physiological Optics (Dover, New York, 1962), Vols. I and II.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

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Figures (7)

FIG. 1
FIG. 1

Schematic layout of the apparatus in experiment I. PL: half-wave plate; F: Forster prism; B1, B2: beamsplitters; M1, M2: movable mirrors; M2–M5: mirrors; P: Glan-Thompson prism; N: neutral-density filter; D1: diaphragm; D2: artificial pupil; L1: lens, f = 1 cm; L2, L3: lenses, f = 12 cm; L4: correction lens; RD: white diffuse rotating disk.

FIG. 2
FIG. 2

Schematic layout of the apparatus in experiment II. PL: half-wave plate; PL2: rotating fused silica plate; B1, B2: beamsplitters; M1: movable mirror; M2, M3: mirrors; F: Forster prism; P: Glan-Thompson prism; N: neutral-density filter; D: diaphragm; L1, L2: lenses, f = 12 cm; L3: lens, f = 2.5 cm.

FIG. 3
FIG. 3

Measured isomodulation curves for different spatial frequencies as a function of defocus. Positive defocus means focusing of the target before the retina. The isomodulation curves represent the contrast of the image at the fovea when the sine-wave target has a contrast of 100 %. The symbol ✡ represents 56% of contrast. The distance between each successive line is 0.25 log unit. Measurements were made at 46 points along the horizontal axis and at 7 points along the vertical axis. The eye was paralyzed with 1 % atropine. The subject’s age was 29 years.

FIG. 4
FIG. 4

Theoretical isomodulation curves based on the mean values of the aberration coefficients found by Howland and Howland11 (see Mathematical). For other data see comment on Fig. 3.

FIG. 5
FIG. 5

Contrast of a sine-wave target, as a function of the spatial frequency when the stimulus is just not visible. The symbol Δ represents the threshold of the fovea derived from the measurements done for an artificial pupil with a diameter of 1 mm, supposing that at optimum focus the optical system is only diffraction-limited. The symbol □ represents the threshold of the fovea measured—bypassing the optics of the eye—with an interference pattern. The symbols ●, ■, ▲ represent the threshold of the fovea done for an artificial pupil with a diameter of, respectively 2, 3, and 5 mm at optimum focus. The eye was corrected for astigmation and myopia; 2 dB equals 0.1 log unit.

FIG. 6
FIG. 6

Contrast at the fovea of a defocused 10 cpd sine-wave target of 100% contrast as a function of an eccentricly placed pupil with a diameter of 1 mm. Measurements are represented by the symbols. The continuous line shows the theoretical calculations. In Fig. 6(a) the results are shown for +2.3 Diopter defocusing; Fig. 6(b) shows them for −2.3 Diopter defocusing. The vertical dashed curve indicates the position of the viewing axis; 2 dB equals 0.1 log unit.

FIG. 7
FIG. 7

Calculated isomodulation curves for polychromatic light (flat spectrum; 480–780 nm), derived from the measurements for monochromatic light. Each wavelength of the spectrum is weighted according the Vλ curve (see text). For other data see comment on Fig. 3.

Equations (3)

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M = I max I min I max + I min = ( 1 cos 2 α ) 2 .
W ( x , y ) = A + B x + C y + D x 2 + E x y + F y 2 + G x 3 + H x 2 y + I x y 2 + J y 3 + K x 4 + L x 3 y + M x 2 y 2 + N x y 3 + O y 4 .
W ( x , y ) = A + B x + D x 2 + E x y + G x 3 + H x 2 y + I x y 2 + K x 4 + L x 3 y + M x 2 y 2 + N x y 3 .