Abstract

Low-resolution optical systems are more tolerant to defocus than are high-resolution systems. We wished to determine whether this principle applies to human vision. We used psychophysical methods to measure the effects of defocus in normal eyes under low-resolution conditions. Modulation transfer of sine-wave gratings was measured as a function of dioptric defocus at low and medium spatial frequencies. We defined the depth of focus at a given spatial frequency to be the dioptric range for which the modulation transfer exceeds 50% of its peak value. For dilated pupils, depth of focus increased from about 2.5 diopters (D) at 3.5 cycles/deg to about 17 D at 0.25 cycles/deg. From our results we predicted that tasks requiring only low spatial frequencies will be more tolerant to defocus than tasks requiring higher spatial frequencies. This prediction was confirmed in a letter-recognition experiment. The increasing tolerance to defocus at low spatial frequencies also implies that individuals with low acuity will be more tolerant to defocus than people with normal vision. We confirmed this prediction by measuring tolerance to defocus in 30 low-vision eyes.

© 1987 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–103 (1955).
    [CrossRef]
  2. F. W. Campbell, “The depth of field of the human eye,” Opt. Acta. 4, 157–164 (1957).
    [CrossRef]
  3. F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,”J. Physiol. (London) 181, 576–593 (1965).
  4. D. G. Green, F. W. Campbell, “Effect of focus on the visual response to a sinusoidally modulated spatial stimulus,”J. Opt. Soc. Am. 55, 1154–1157 (1965).
    [CrossRef]
  5. W. N. Charman, “Effect of refractive error in visual tests with sinusoidal gratings,” Br. J. Physiol. Opt. 33, 10–20 (1979).
    [PubMed]
  6. E. E. Reese, G. A. Fry, “The effect of fogging lenses on accommodation,”J. Optom. Arch. Am. Acad. Optom. 18, 9–16 (1941).
    [CrossRef]
  7. J. H. Prince, G. A. Fry, “The effect of errors of refraction on visual acuity,” Am. J. Optom. Arch. Am. Acad. Optom. 33, 353–373 (1956).
    [PubMed]
  8. K. N. Ogle, J. T. Schwartz, “Depth of focus of the human eye,”J. Opt. Soc. Am. 49, 273–280 (1959).
    [CrossRef] [PubMed]
  9. J. Tucker, W. N. Charman, “The depth of focus of the human eye for Snellen letters,” Am. J. Optom. Physiol. Opt. 52, 3–21 (1975).
    [CrossRef] [PubMed]
  10. G. von Bahr, “Studies on the depth of focus of the eye,” Acta Ophthalmol. 30, 39–44 (1952).
  11. W. N. Charman, H. Whitefoot, “Pupil diameter and the depth-of-field of the human eye as measured by laser speckle,” Opt. Acta 24, 1211–1216 (1977).
    [CrossRef]
  12. W. N. Charman, J. A. M. Jennings, “The optical quality of the monochromatic retinal image as a function of focus,” Br. J. Physiol. Opt. 31, 119–134 (1976).
    [PubMed]
  13. The optical transfer of a target sine wave into an image sine wave holds only for small “ isoplanative patches ”47 within which imaging properties of the visual field are uniform. It is well known that dioptric properties of the human eye vary somewhat across the visual field.
  14. G. Westheimer, “Pupil size and visual resolution,” Vision Res. 4, 39–45 (1964).
    [CrossRef] [PubMed]
  15. W. N. Charman, G. Heron, “Spatial frequency and the dynamics of the accommodation response,” Opt. Acta 26, 217–228 (1979).
    [CrossRef]
  16. G. E. Legge, D. G. Pelli, G. S. Rubin, M. M. Schleske, “Psychophysics of reading. I. Normal vision,” Vision Res. 25, 239–252 (1985).
    [CrossRef]
  17. G. S. Rubin, K. Siegel, “Recognition of low-pass filtered faces and letters,” Invest. Ophthalmol. Vis. Sci. Suppl. 25, 71 (1984).
  18. K. J. Ciuffreda, S. C. Hokoda, C. K. Hung, J. L. Semmlow, A. Selenow, “Static aspects of accommodation in human amblyopia,” Am. J. Optom. Physiol. Opt. 60, 436–449 (1983).
    [CrossRef] [PubMed]
  19. M. K. Powers, V. Dobson, “Effect of focus on visual acuity of human infants,” Vision Res. 22, 521–528 (1982).
    [CrossRef] [PubMed]
  20. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  21. G. Smith, “Ocular defocus, spurious resolution and contrast reversal,” Ophthalmol. Physiol. Opt. 2, 5–23 (1982).
  22. Suppose a lens of power P(in diopters) is located at a distance d(in meters) from the eye. An object is located a distance d′ (in meters) from the lens. Define D′ as the dioptric distance of the object: D′ = 1/d′. For an eye focused at optical infinity, this arrangement produces defocus with an equivalent power Pe given by Pe=(P-D′)/[1-d(P-D′)].The corresponding magnification M is M=(dD′+1)/[1-d(P-D′)].In the figures, defocus refers to values of Pe. Values of spatial frequency cited in the Results section reflect a correction for lens magnification.
  23. F. W. Campbell, “A retinal acuity direction effect,”J. Physiol. 144, 25P–26P (1958).
  24. D. G. Green, “Visual resolution when light enters the eye through different parts of the pupil,”J. Physiol. 190, 583–593 (1967).
    [PubMed]
  25. A. van Meeteren, “Calculations on the optical modulation transfer function of the human eye for white light,” Opt. Acta 21, 395–412 (1974).
    [CrossRef]
  26. M. Alpern, “The eyes and vision,” in Handbook of Optics, W. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), pp. (12-1)–(12-39).
  27. L. Levi, R. H. Austing, “Tables of the modulation transfer function of a defocused perfect lens,” Appl. Opt. 7, 967–974 (1968).
    [CrossRef] [PubMed]
  28. G. Strong, G. C. Woo, “A distance visual acuity chart incorporating some new design features,” Arch. Ophthalmol. 103, 44–46 (1985).
    [CrossRef] [PubMed]
  29. G. Woo, “Use of low magnification telescopes in low vision,” Optom. Monthly 69, 529–533. (1978).
  30. R. A. Williams, P. G. Boothe, “Effects of defocus on monkey (macaca nemestrina) contrast sensitivity: behavioral measurements and predictions,” Am. J. Optom. Physiol. Opt. 60, 106–111 (1983).
    [CrossRef] [PubMed]
  31. D. G. Green, M. K. Powers, M. S. Banks, “Depth of focus, eye size and visual acuity,” Vision Res. 20, 827–835 (1980).
    [CrossRef] [PubMed]
  32. F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,”J. Physiol. (London) 186, 558–578 (1966).
  33. According to this method, modulation transfer is calculated for wavelengths taken in small steps across the visible spectrum, taking into account the different degrees of defocus resulting from chromatic aberration. A weighted superposition of the values is taken, with the weights determined by the target luminance at each wavelength. To perform this calculation for gratings displayed on a P31 phosphor, we used the radiometric spectral data compiled by Bell.48
  34. F. W. Campbell, R. W. Gubisch, “The effect of chromatic aberration on visual acuity,”J. Physiol.192, 345–358 (1967).
    [PubMed]
  35. The high-frequency cutoffs were measured with slightly different conditions for the two observers. Intersubject comparisons are not meaningful, but horizontal-versus-vertical comparisons for a given subject are.
  36. Inequality in the spherical correction for horizontal and vertical axes (astigmatism) would not produce this pattern of results. Astigmatism would affect the location of the peaks of curves like those in Figs. 3 and 4 but would not affect the breadth of the curves.
  37. According to geometrical optics, there is a reciprocal relationship between spatial frequency and defocus in the specification of zeros of the transfer function. From Ref. 21, the spatial frequency f at which the first zero occurs is f= 21.19/PD, where P is pupil diameter in millimeters and D is defocus in diopters. At low spatial frequencies or for large defocus, values predicted from wave optics are quite similar.
  38. For this comparison, we took the first zero contour as the location for data points in Fig. 8A and the second zero contour for data points in Fig. 8B.
  39. H. C. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,”J. Opt. Soe. An. 67, 1508–1518 (1977).
    [CrossRef]
  40. G. Black, E. H. Linfoot, “Spherical aberration and the information content of optical images,” Proc. R. Soc. London Ser. A 239, 522–540 (1957).
    [CrossRef]
  41. M. Mino, Y. Okano, “Improvement in the OTF of a defocused optical system through the use of shaded apertures,” Appl. Opt. 10, 2219–2225 (1971)
    [CrossRef] [PubMed]
  42. G. E. Legge, “A power law for contrast discrimination,” Vision Res. 21, 457–467 (1981).
    [CrossRef] [PubMed]
  43. It might be argued that small errors in focus produce increasingly large contrast decrements at higher spatial frequencies.25 Hence observers should rely on high spatial frequencies for blur detection, not on the output of a 4-c/deg channel. Although this argument may be true for aberration-free optical systems, the data of Fig. 5 indicate that the human eye has a relatively constant depth of focus at moderate and high spatial frequencies. Moreover, the high-frequency decline in contrast sensitivity combined with the rolloff in the amplitude spectra of most real-world objects probably makes blur detection based on high spatial frequencies unreliable.
  44. Spurious resolution complicates this analogy. Moreover, for an ideal lens, the high-frequency cutoff, beyond which there is no further transfer, positive or negative, is unaffected by defocus.
  45. Legge et al.16 used a 1/e definition rather than a half-amplitude definition of filter bandwidth. They referred to bandwidths in units of cycles per character rather than cycles per degree. If the former is divided by character size in degrees, it gives the latter.
  46. According to Fig. 11, critical bandwidths for 0.1-deg characters are 6 c/deg (letter recognition) and 15 c/deg (reading). These bandwidths correspond to just 0.6 and 1.5 cycles per character, respectively. Perhaps the half-amplitude definition gives misleadingly low estimates because information passed by the ground-glass diffuser at spatial frequencies higher than the half-amplitude frequency may be used by subjects in performing the tasks.
  47. E. H. Linfoot, Fourier Methods in Optical Image Evaluation (Focal, New York, 1964).
  48. R. A. Bell, Principles of Cathode-Ray Tubes, Phosphors and High-Speed Oscillography, Application Note 115 (Hewlett-Packard, Colorado Springs, Colo., 1970).

1985 (2)

G. E. Legge, D. G. Pelli, G. S. Rubin, M. M. Schleske, “Psychophysics of reading. I. Normal vision,” Vision Res. 25, 239–252 (1985).
[CrossRef]

G. Strong, G. C. Woo, “A distance visual acuity chart incorporating some new design features,” Arch. Ophthalmol. 103, 44–46 (1985).
[CrossRef] [PubMed]

1984 (1)

G. S. Rubin, K. Siegel, “Recognition of low-pass filtered faces and letters,” Invest. Ophthalmol. Vis. Sci. Suppl. 25, 71 (1984).

1983 (2)

K. J. Ciuffreda, S. C. Hokoda, C. K. Hung, J. L. Semmlow, A. Selenow, “Static aspects of accommodation in human amblyopia,” Am. J. Optom. Physiol. Opt. 60, 436–449 (1983).
[CrossRef] [PubMed]

R. A. Williams, P. G. Boothe, “Effects of defocus on monkey (macaca nemestrina) contrast sensitivity: behavioral measurements and predictions,” Am. J. Optom. Physiol. Opt. 60, 106–111 (1983).
[CrossRef] [PubMed]

1982 (2)

M. K. Powers, V. Dobson, “Effect of focus on visual acuity of human infants,” Vision Res. 22, 521–528 (1982).
[CrossRef] [PubMed]

G. Smith, “Ocular defocus, spurious resolution and contrast reversal,” Ophthalmol. Physiol. Opt. 2, 5–23 (1982).

1981 (1)

G. E. Legge, “A power law for contrast discrimination,” Vision Res. 21, 457–467 (1981).
[CrossRef] [PubMed]

1980 (1)

D. G. Green, M. K. Powers, M. S. Banks, “Depth of focus, eye size and visual acuity,” Vision Res. 20, 827–835 (1980).
[CrossRef] [PubMed]

1979 (2)

W. N. Charman, G. Heron, “Spatial frequency and the dynamics of the accommodation response,” Opt. Acta 26, 217–228 (1979).
[CrossRef]

W. N. Charman, “Effect of refractive error in visual tests with sinusoidal gratings,” Br. J. Physiol. Opt. 33, 10–20 (1979).
[PubMed]

1978 (1)

G. Woo, “Use of low magnification telescopes in low vision,” Optom. Monthly 69, 529–533. (1978).

1977 (2)

H. C. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,”J. Opt. Soe. An. 67, 1508–1518 (1977).
[CrossRef]

W. N. Charman, H. Whitefoot, “Pupil diameter and the depth-of-field of the human eye as measured by laser speckle,” Opt. Acta 24, 1211–1216 (1977).
[CrossRef]

1976 (1)

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

1975 (1)

J. Tucker, W. N. Charman, “The depth of focus of the human eye for Snellen letters,” Am. J. Optom. Physiol. Opt. 52, 3–21 (1975).
[CrossRef] [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]

1971 (1)

1968 (1)

1967 (1)

D. G. Green, “Visual resolution when light enters the eye through different parts of the pupil,”J. Physiol. 190, 583–593 (1967).
[PubMed]

1966 (1)

F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,”J. Physiol. (London) 186, 558–578 (1966).

1965 (2)

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

D. G. Green, F. W. Campbell, “Effect of focus on the visual response to a sinusoidally modulated spatial stimulus,”J. Opt. Soc. Am. 55, 1154–1157 (1965).
[CrossRef]

1964 (1)

G. Westheimer, “Pupil size and visual resolution,” Vision Res. 4, 39–45 (1964).
[CrossRef] [PubMed]

1959 (1)

1958 (1)

F. W. Campbell, “A retinal acuity direction effect,”J. Physiol. 144, 25P–26P (1958).

1957 (2)

F. W. Campbell, “The depth of field of the human eye,” Opt. Acta. 4, 157–164 (1957).
[CrossRef]

G. Black, E. H. Linfoot, “Spherical aberration and the information content of optical images,” Proc. R. Soc. London Ser. A 239, 522–540 (1957).
[CrossRef]

1956 (1)

J. H. Prince, G. A. Fry, “The effect of errors of refraction on visual acuity,” Am. J. Optom. Arch. Am. Acad. Optom. 33, 353–373 (1956).
[PubMed]

1955 (1)

H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–103 (1955).
[CrossRef]

1952 (1)

G. von Bahr, “Studies on the depth of focus of the eye,” Acta Ophthalmol. 30, 39–44 (1952).

1941 (1)

E. E. Reese, G. A. Fry, “The effect of fogging lenses on accommodation,”J. Optom. Arch. Am. Acad. Optom. 18, 9–16 (1941).
[CrossRef]

Alpern, M.

M. Alpern, “The eyes and vision,” in Handbook of Optics, W. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), pp. (12-1)–(12-39).

Austing, R. H.

Banks, M. S.

D. G. Green, M. K. Powers, M. S. Banks, “Depth of focus, eye size and visual acuity,” Vision Res. 20, 827–835 (1980).
[CrossRef] [PubMed]

Bell, R. A.

R. A. Bell, Principles of Cathode-Ray Tubes, Phosphors and High-Speed Oscillography, Application Note 115 (Hewlett-Packard, Colorado Springs, Colo., 1970).

Black, G.

G. Black, E. H. Linfoot, “Spherical aberration and the information content of optical images,” Proc. R. Soc. London Ser. A 239, 522–540 (1957).
[CrossRef]

Boothe, P. G.

R. A. Williams, P. G. Boothe, “Effects of defocus on monkey (macaca nemestrina) contrast sensitivity: behavioral measurements and predictions,” Am. J. Optom. Physiol. Opt. 60, 106–111 (1983).
[CrossRef] [PubMed]

Campbell, F. W.

F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,”J. Physiol. (London) 186, 558–578 (1966).

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

D. G. Green, F. W. Campbell, “Effect of focus on the visual response to a sinusoidally modulated spatial stimulus,”J. Opt. Soc. Am. 55, 1154–1157 (1965).
[CrossRef]

F. W. Campbell, “A retinal acuity direction effect,”J. Physiol. 144, 25P–26P (1958).

F. W. Campbell, “The depth of field of the human eye,” Opt. Acta. 4, 157–164 (1957).
[CrossRef]

F. W. Campbell, R. W. Gubisch, “The effect of chromatic aberration on visual acuity,”J. Physiol.192, 345–358 (1967).
[PubMed]

Charman, W. N.

W. N. Charman, “Effect of refractive error in visual tests with sinusoidal gratings,” Br. J. Physiol. Opt. 33, 10–20 (1979).
[PubMed]

W. N. Charman, G. Heron, “Spatial frequency and the dynamics of the accommodation response,” Opt. Acta 26, 217–228 (1979).
[CrossRef]

W. N. Charman, H. Whitefoot, “Pupil diameter and the depth-of-field of the human eye as measured by laser speckle,” Opt. Acta 24, 1211–1216 (1977).
[CrossRef]

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

J. Tucker, W. N. Charman, “The depth of focus of the human eye for Snellen letters,” Am. J. Optom. Physiol. Opt. 52, 3–21 (1975).
[CrossRef] [PubMed]

Ciuffreda, K. J.

K. J. Ciuffreda, S. C. Hokoda, C. K. Hung, J. L. Semmlow, A. Selenow, “Static aspects of accommodation in human amblyopia,” Am. J. Optom. Physiol. Opt. 60, 436–449 (1983).
[CrossRef] [PubMed]

Dobson, V.

M. K. Powers, V. Dobson, “Effect of focus on visual acuity of human infants,” Vision Res. 22, 521–528 (1982).
[CrossRef] [PubMed]

Fry, G. A.

J. H. Prince, G. A. Fry, “The effect of errors of refraction on visual acuity,” Am. J. Optom. Arch. Am. Acad. Optom. 33, 353–373 (1956).
[PubMed]

E. E. Reese, G. A. Fry, “The effect of fogging lenses on accommodation,”J. Optom. Arch. Am. Acad. Optom. 18, 9–16 (1941).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Green, D. G.

D. G. Green, M. K. Powers, M. S. Banks, “Depth of focus, eye size and visual acuity,” Vision Res. 20, 827–835 (1980).
[CrossRef] [PubMed]

D. G. Green, “Visual resolution when light enters the eye through different parts of the pupil,”J. Physiol. 190, 583–593 (1967).
[PubMed]

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

D. G. Green, F. W. Campbell, “Effect of focus on the visual response to a sinusoidally modulated spatial stimulus,”J. Opt. Soc. Am. 55, 1154–1157 (1965).
[CrossRef]

Gubisch, R. W.

F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,”J. Physiol. (London) 186, 558–578 (1966).

F. W. Campbell, R. W. Gubisch, “The effect of chromatic aberration on visual acuity,”J. Physiol.192, 345–358 (1967).
[PubMed]

Heron, G.

W. N. Charman, G. Heron, “Spatial frequency and the dynamics of the accommodation response,” Opt. Acta 26, 217–228 (1979).
[CrossRef]

Hokoda, S. C.

K. J. Ciuffreda, S. C. Hokoda, C. K. Hung, J. L. Semmlow, A. Selenow, “Static aspects of accommodation in human amblyopia,” Am. J. Optom. Physiol. Opt. 60, 436–449 (1983).
[CrossRef] [PubMed]

Hopkins, H. H.

H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–103 (1955).
[CrossRef]

Howland, B.

H. C. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,”J. Opt. Soe. An. 67, 1508–1518 (1977).
[CrossRef]

Howland, H. C.

H. C. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,”J. Opt. Soe. An. 67, 1508–1518 (1977).
[CrossRef]

Hung, C. K.

K. J. Ciuffreda, S. C. Hokoda, C. K. Hung, J. L. Semmlow, A. Selenow, “Static aspects of accommodation in human amblyopia,” Am. J. Optom. Physiol. Opt. 60, 436–449 (1983).
[CrossRef] [PubMed]

Jennings, J. A. M.

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

Legge, G. E.

G. E. Legge, D. G. Pelli, G. S. Rubin, M. M. Schleske, “Psychophysics of reading. I. Normal vision,” Vision Res. 25, 239–252 (1985).
[CrossRef]

G. E. Legge, “A power law for contrast discrimination,” Vision Res. 21, 457–467 (1981).
[CrossRef] [PubMed]

Levi, L.

Linfoot, E. H.

G. Black, E. H. Linfoot, “Spherical aberration and the information content of optical images,” Proc. R. Soc. London Ser. A 239, 522–540 (1957).
[CrossRef]

E. H. Linfoot, Fourier Methods in Optical Image Evaluation (Focal, New York, 1964).

Mino, M.

Ogle, K. N.

Okano, Y.

Pelli, D. G.

G. E. Legge, D. G. Pelli, G. S. Rubin, M. M. Schleske, “Psychophysics of reading. I. Normal vision,” Vision Res. 25, 239–252 (1985).
[CrossRef]

Powers, M. K.

M. K. Powers, V. Dobson, “Effect of focus on visual acuity of human infants,” Vision Res. 22, 521–528 (1982).
[CrossRef] [PubMed]

D. G. Green, M. K. Powers, M. S. Banks, “Depth of focus, eye size and visual acuity,” Vision Res. 20, 827–835 (1980).
[CrossRef] [PubMed]

Prince, J. H.

J. H. Prince, G. A. Fry, “The effect of errors of refraction on visual acuity,” Am. J. Optom. Arch. Am. Acad. Optom. 33, 353–373 (1956).
[PubMed]

Reese, E. E.

E. E. Reese, G. A. Fry, “The effect of fogging lenses on accommodation,”J. Optom. Arch. Am. Acad. Optom. 18, 9–16 (1941).
[CrossRef]

Rubin, G. S.

G. E. Legge, D. G. Pelli, G. S. Rubin, M. M. Schleske, “Psychophysics of reading. I. Normal vision,” Vision Res. 25, 239–252 (1985).
[CrossRef]

G. S. Rubin, K. Siegel, “Recognition of low-pass filtered faces and letters,” Invest. Ophthalmol. Vis. Sci. Suppl. 25, 71 (1984).

Schleske, M. M.

G. E. Legge, D. G. Pelli, G. S. Rubin, M. M. Schleske, “Psychophysics of reading. I. Normal vision,” Vision Res. 25, 239–252 (1985).
[CrossRef]

Schwartz, J. T.

Selenow, A.

K. J. Ciuffreda, S. C. Hokoda, C. K. Hung, J. L. Semmlow, A. Selenow, “Static aspects of accommodation in human amblyopia,” Am. J. Optom. Physiol. Opt. 60, 436–449 (1983).
[CrossRef] [PubMed]

Semmlow, J. L.

K. J. Ciuffreda, S. C. Hokoda, C. K. Hung, J. L. Semmlow, A. Selenow, “Static aspects of accommodation in human amblyopia,” Am. J. Optom. Physiol. Opt. 60, 436–449 (1983).
[CrossRef] [PubMed]

Siegel, K.

G. S. Rubin, K. Siegel, “Recognition of low-pass filtered faces and letters,” Invest. Ophthalmol. Vis. Sci. Suppl. 25, 71 (1984).

Smith, G.

G. Smith, “Ocular defocus, spurious resolution and contrast reversal,” Ophthalmol. Physiol. Opt. 2, 5–23 (1982).

Strong, G.

G. Strong, G. C. Woo, “A distance visual acuity chart incorporating some new design features,” Arch. Ophthalmol. 103, 44–46 (1985).
[CrossRef] [PubMed]

Tucker, J.

J. Tucker, W. N. Charman, “The depth of focus of the human eye for Snellen letters,” Am. J. Optom. Physiol. Opt. 52, 3–21 (1975).
[CrossRef] [PubMed]

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 Bahr, G.

G. von Bahr, “Studies on the depth of focus of the eye,” Acta Ophthalmol. 30, 39–44 (1952).

Westheimer, G.

G. Westheimer, “Pupil size and visual resolution,” Vision Res. 4, 39–45 (1964).
[CrossRef] [PubMed]

Whitefoot, H.

W. N. Charman, H. Whitefoot, “Pupil diameter and the depth-of-field of the human eye as measured by laser speckle,” Opt. Acta 24, 1211–1216 (1977).
[CrossRef]

Williams, R. A.

R. A. Williams, P. G. Boothe, “Effects of defocus on monkey (macaca nemestrina) contrast sensitivity: behavioral measurements and predictions,” Am. J. Optom. Physiol. Opt. 60, 106–111 (1983).
[CrossRef] [PubMed]

Woo, G.

G. Woo, “Use of low magnification telescopes in low vision,” Optom. Monthly 69, 529–533. (1978).

Woo, G. C.

G. Strong, G. C. Woo, “A distance visual acuity chart incorporating some new design features,” Arch. Ophthalmol. 103, 44–46 (1985).
[CrossRef] [PubMed]

Acta Ophthalmol. (1)

G. von Bahr, “Studies on the depth of focus of the eye,” Acta Ophthalmol. 30, 39–44 (1952).

Am. J. Optom. Arch. Am. Acad. Optom. (1)

J. H. Prince, G. A. Fry, “The effect of errors of refraction on visual acuity,” Am. J. Optom. Arch. Am. Acad. Optom. 33, 353–373 (1956).
[PubMed]

Am. J. Optom. Physiol. Opt. (3)

J. Tucker, W. N. Charman, “The depth of focus of the human eye for Snellen letters,” Am. J. Optom. Physiol. Opt. 52, 3–21 (1975).
[CrossRef] [PubMed]

K. J. Ciuffreda, S. C. Hokoda, C. K. Hung, J. L. Semmlow, A. Selenow, “Static aspects of accommodation in human amblyopia,” Am. J. Optom. Physiol. Opt. 60, 436–449 (1983).
[CrossRef] [PubMed]

R. A. Williams, P. G. Boothe, “Effects of defocus on monkey (macaca nemestrina) contrast sensitivity: behavioral measurements and predictions,” Am. J. Optom. Physiol. Opt. 60, 106–111 (1983).
[CrossRef] [PubMed]

Appl. Opt. (2)

Arch. Ophthalmol. (1)

G. Strong, G. C. Woo, “A distance visual acuity chart incorporating some new design features,” Arch. Ophthalmol. 103, 44–46 (1985).
[CrossRef] [PubMed]

Br. J. Physiol. Opt. (2)

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

W. N. Charman, “Effect of refractive error in visual tests with sinusoidal gratings,” Br. J. Physiol. Opt. 33, 10–20 (1979).
[PubMed]

Invest. Ophthalmol. Vis. Sci. Suppl. (1)

G. S. Rubin, K. Siegel, “Recognition of low-pass filtered faces and letters,” Invest. Ophthalmol. Vis. Sci. Suppl. 25, 71 (1984).

J. Opt. Soc. Am. (2)

J. Opt. Soe. An. (1)

H. C. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,”J. Opt. Soe. An. 67, 1508–1518 (1977).
[CrossRef]

J. Optom. Arch. Am. Acad. Optom. (1)

E. E. Reese, G. A. Fry, “The effect of fogging lenses on accommodation,”J. Optom. Arch. Am. Acad. Optom. 18, 9–16 (1941).
[CrossRef]

J. Physiol. (2)

F. W. Campbell, “A retinal acuity direction effect,”J. Physiol. 144, 25P–26P (1958).

D. G. Green, “Visual resolution when light enters the eye through different parts of the pupil,”J. Physiol. 190, 583–593 (1967).
[PubMed]

J. Physiol. (London) (2)

F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,”J. Physiol. (London) 186, 558–578 (1966).

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

Ophthalmol. Physiol. Opt. (1)

G. Smith, “Ocular defocus, spurious resolution and contrast reversal,” Ophthalmol. Physiol. Opt. 2, 5–23 (1982).

Opt. Acta (3)

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

W. N. Charman, H. Whitefoot, “Pupil diameter and the depth-of-field of the human eye as measured by laser speckle,” Opt. Acta 24, 1211–1216 (1977).
[CrossRef]

W. N. Charman, G. Heron, “Spatial frequency and the dynamics of the accommodation response,” Opt. Acta 26, 217–228 (1979).
[CrossRef]

Opt. Acta. (1)

F. W. Campbell, “The depth of field of the human eye,” Opt. Acta. 4, 157–164 (1957).
[CrossRef]

Optom. Monthly (1)

G. Woo, “Use of low magnification telescopes in low vision,” Optom. Monthly 69, 529–533. (1978).

Proc. R. Soc. London Ser. A (2)

H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–103 (1955).
[CrossRef]

G. Black, E. H. Linfoot, “Spherical aberration and the information content of optical images,” Proc. R. Soc. London Ser. A 239, 522–540 (1957).
[CrossRef]

Vision Res. (5)

G. E. Legge, “A power law for contrast discrimination,” Vision Res. 21, 457–467 (1981).
[CrossRef] [PubMed]

G. E. Legge, D. G. Pelli, G. S. Rubin, M. M. Schleske, “Psychophysics of reading. I. Normal vision,” Vision Res. 25, 239–252 (1985).
[CrossRef]

G. Westheimer, “Pupil size and visual resolution,” Vision Res. 4, 39–45 (1964).
[CrossRef] [PubMed]

D. G. Green, M. K. Powers, M. S. Banks, “Depth of focus, eye size and visual acuity,” Vision Res. 20, 827–835 (1980).
[CrossRef] [PubMed]

M. K. Powers, V. Dobson, “Effect of focus on visual acuity of human infants,” Vision Res. 22, 521–528 (1982).
[CrossRef] [PubMed]

Other (16)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Suppose a lens of power P(in diopters) is located at a distance d(in meters) from the eye. An object is located a distance d′ (in meters) from the lens. Define D′ as the dioptric distance of the object: D′ = 1/d′. For an eye focused at optical infinity, this arrangement produces defocus with an equivalent power Pe given by Pe=(P-D′)/[1-d(P-D′)].The corresponding magnification M is M=(dD′+1)/[1-d(P-D′)].In the figures, defocus refers to values of Pe. Values of spatial frequency cited in the Results section reflect a correction for lens magnification.

M. Alpern, “The eyes and vision,” in Handbook of Optics, W. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), pp. (12-1)–(12-39).

According to this method, modulation transfer is calculated for wavelengths taken in small steps across the visible spectrum, taking into account the different degrees of defocus resulting from chromatic aberration. A weighted superposition of the values is taken, with the weights determined by the target luminance at each wavelength. To perform this calculation for gratings displayed on a P31 phosphor, we used the radiometric spectral data compiled by Bell.48

F. W. Campbell, R. W. Gubisch, “The effect of chromatic aberration on visual acuity,”J. Physiol.192, 345–358 (1967).
[PubMed]

The high-frequency cutoffs were measured with slightly different conditions for the two observers. Intersubject comparisons are not meaningful, but horizontal-versus-vertical comparisons for a given subject are.

Inequality in the spherical correction for horizontal and vertical axes (astigmatism) would not produce this pattern of results. Astigmatism would affect the location of the peaks of curves like those in Figs. 3 and 4 but would not affect the breadth of the curves.

According to geometrical optics, there is a reciprocal relationship between spatial frequency and defocus in the specification of zeros of the transfer function. From Ref. 21, the spatial frequency f at which the first zero occurs is f= 21.19/PD, where P is pupil diameter in millimeters and D is defocus in diopters. At low spatial frequencies or for large defocus, values predicted from wave optics are quite similar.

For this comparison, we took the first zero contour as the location for data points in Fig. 8A and the second zero contour for data points in Fig. 8B.

The optical transfer of a target sine wave into an image sine wave holds only for small “ isoplanative patches ”47 within which imaging properties of the visual field are uniform. It is well known that dioptric properties of the human eye vary somewhat across the visual field.

It might be argued that small errors in focus produce increasingly large contrast decrements at higher spatial frequencies.25 Hence observers should rely on high spatial frequencies for blur detection, not on the output of a 4-c/deg channel. Although this argument may be true for aberration-free optical systems, the data of Fig. 5 indicate that the human eye has a relatively constant depth of focus at moderate and high spatial frequencies. Moreover, the high-frequency decline in contrast sensitivity combined with the rolloff in the amplitude spectra of most real-world objects probably makes blur detection based on high spatial frequencies unreliable.

Spurious resolution complicates this analogy. Moreover, for an ideal lens, the high-frequency cutoff, beyond which there is no further transfer, positive or negative, is unaffected by defocus.

Legge et al.16 used a 1/e definition rather than a half-amplitude definition of filter bandwidth. They referred to bandwidths in units of cycles per character rather than cycles per degree. If the former is divided by character size in degrees, it gives the latter.

According to Fig. 11, critical bandwidths for 0.1-deg characters are 6 c/deg (letter recognition) and 15 c/deg (reading). These bandwidths correspond to just 0.6 and 1.5 cycles per character, respectively. Perhaps the half-amplitude definition gives misleadingly low estimates because information passed by the ground-glass diffuser at spatial frequencies higher than the half-amplitude frequency may be used by subjects in performing the tasks.

E. H. Linfoot, Fourier Methods in Optical Image Evaluation (Focal, New York, 1964).

R. A. Bell, Principles of Cathode-Ray Tubes, Phosphors and High-Speed Oscillography, Application Note 115 (Hewlett-Packard, Colorado Springs, Colo., 1970).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1

Demonstration of spurious resolution. A, A sinusoidal sunburst pattern has been photographed from a TV screen with a camera in focus. B, The same pattern has been photographed with the camera defocused. The regions of contrast reversal demonstrate spurious resolution. The transitions between these regions demonstrate zeros in the MTF of the defocused optical system. To observe spurious resolution in your own eye, hold Fig. 1A at arm’s length and observe it while focusing much nearer.

Fig. 2
Fig. 2

Schematic diagram of the apparatus used in the matching experiments.

Fig. 3
Fig. 3

Modulation transfer as a function of defocus. Each panel shows mean data from one experiment for subject KTM. One point has been omitted from panel F because it falls off the scale to the right. Within each panel, normalized modulation transfer is proportional to contrast sensitivity, with normalization based on maximum contrast sensitivity. Straight lines have been fitted by eye to all the data to the left and right of the peak and are drawn down to an ordinate value of 0.2. Horizontal dashed lines indicate where transfer has dropped to 50% of its peak. We take the breadth of the curves, measured along these half-amplitude lines, as our definition of depth of focus.

Fig. 4
Fig. 4

Modulation transfer as a function of defocus. Details are as in Fig. 3 except that data are for subject GW.

Fig. 5
Fig. 5

Depth of focus as a function of spatial frequency for experiments with dilated pupils. Each point is the depth of focus estimated from one experiment. Circles and triangles refer to data from this study, open symbols refer to the threshold method, and filled symbols refer to the matching method. ×’s refer to values derived from the data of Green and Campbell,4 and +’s refer to the data of Charman.5 The solid curve labeled ideal lens refers to results to be expected from an aberration-free, diffraction-limited optical system with an 8-mm pupil.

Fig. 6
Fig. 6

Depth of focus as a function of spatial frequency for 2-mm-diameter pupils. Details are as in Fig. 5 except that subjects viewed the stimuli through 2-mm-diameter artificial pupils. The ideal lens curve refers to an optical system with a 2-mm pupil.

Fig. 7
Fig. 7

Depth of focus as a function of pupil diameter for 3.5-c/deg sine-wave gratings.

Fig. 8
Fig. 8

Spurious resolution in the human eye. The data points show our measurements of the spatial frequency and defocus associated with the first zero in modulation transfer function of KTM’s right eye. Circles refer to defocus with positive lenses and triangles to defocus with negative lenses. The lines labeled FIRST ZERO and SECOND ZERO represent combinations of defocus and spatial frequency producing first and second zeros in the transfer functions of an ideal lens. A, 2-mm pupil; B, 8-mm pupil.

Fig. 9
Fig. 9

Acuity is plotted as a function of defocus for four normal subjects (see Table 1). The solid lines are predictions based on our modulation-transfer data and spatial-frequency bandwidth considerations (see the text).

Fig. 10
Fig. 10

Total depth of focus, as defined by Tucker and Charman,9 is plotted as a function of acuity (see the text).

Fig. 11
Fig. 11

Critical bandwidths for reading and letter recognition. The dashed curves summarize the findings of experiments in which the minimum spatial-frequency bandwidths for reading16 and for letter recognitions17 were measured as a function of character size. These bandwidths can be used in relating our modulation-transfer definition of depth of focus to the effects of defocus on acuity.

Fig. 12
Fig. 12

Tolerance to defocus in low vision. Each point refers to one low-vision eye. The positive-lens defocus required to degrade acuity by one line on a chart (0.1 log unit in character size) is plotted as a function of the subject’s acuity. The solid lines are based on predictions from our modulation-transfer data and spatial-frequency filtering considerations.

Tables (3)

Tables Icon

Table 1 Subject Data (Right Eye)

Tables Icon

Table 2 Depth of Focus at 3.5 c/deg: Effects of Wavelength Composition

Tables Icon

Table 3 Depth of Focus at 3.5 c/deg: Effect of Grating Orientation

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

W 20 = ( n / 2 ) ( a z / f 2 ) ,
W 20 = ( a 2 / 2 ) [ D D 0 / ( D + D 0 ) ] ,
Δ = W 20 / ( λ / 4 ) .
T = exp ( - k D ) ,
T = exp [ - ( 0.7 / D 0.5 ) D ] .
D a = ( - D 0.5 / 0.7 ) ln ( T a ) .
Pe=(P-D)/[1-d(P-D)].
M=(dD+1)/[1-d(P-D)].

Metrics