Abstract

This paper reports experimental results showing the effect of mean retinal illuminance on the modulation transfer function (MTF). The line spread function of the human visual system was computed. The test pattern in which the luminance varied sinusoidally in the horizontal direction was generated on the face of an oscilloscope by modulating the intensity of the beam.

The behavior of the system changes with the mean retinal illuminance. At the highest mean retinal illuminance (1000 td) the MTF shows two peaks which gradually disappear at lower mean retinal illuminances. The line spread function of the entire visual system also exhibits a change in shape dependent on the mean retinal illuminance. In particular, what are deemed inhibitory influences become less prominent at lower mean retinal illuminance. From the line spread function of the optical part up to the retina, the line spread function of the physiological part of the visual system is also evaluated.

A common asymptote appears at high frequencies when the characteristics are plotted in terms of absolute deviation from the mean versus spatial frequency for threshold perception. The asymptote provides an upper bound for the behavior of visual acuity at any retinal illuminance.

© 1966 Optical Society of America

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References

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  1. E. W. H. Selwyn, Phot. J. B88, 6 (1948).
  2. O. H. Schade, J. Opt. Soc. Am. 46, 721 (1956).
    [Crossref] [PubMed]
  3. K. J. Rosenbruch, Optik 16, 135 (1959).
  4. G. Westheimer, J. Physiol. 152, 67 (1960).
  5. E. M. Lowry and J. J. DePalma, J. Opt. Soc. Am. 51, 740 (1961).
    [Crossref] [PubMed]
  6. J. J. DePalma and E. M. Lowry, J. Opt. Soc. Am. 52, 328 (1962).
    [Crossref]
  7. J. G. Robson and F. W. Campbell, “The Physiological Basis for Form Discrimination,” Symposium at Walter S. Hunter Laboratory of Psychology, Brown University, 23–24 January 1964.
  8. A note [J. Opt. Soc. Am. 51, 1441 (1961)] announced the decision of ICO subcommittee for Image Assessment Problems to use this term when phase is not pertinent in the complex optical transfer function.
  9. S. Shlaer, J. Gen. Physiol. 21, 165 (1937–38).
    [Crossref]
  10. R. C. Jones, J. Opt. Soc. Am. 48, 1934 (1958).
    [Crossref]
  11. R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover Publications Inc., New York, 1959).
  12. F. Flamant, Rev. Optique 34, 433 (1955).
  13. G. Westheimer and F. W. Campbell, J. Opt. Soc. Am. 52, 1040 (1962).
    [Crossref] [PubMed]
  14. J. Krauskopf, J. Opt. Soc. Am. 52, 1046 (1962).
    [Crossref]
  15. R. J. Beitel, J. Gen. Psychol. 14, 31 (1936).
    [Crossref]
  16. G. A. Fry, Am. J. Optom. 25, 162 (1948).
    [Crossref]
  17. G. A. Fry, J. Opt. Soc. Am. 53, 94 (1963).
    [Crossref] [PubMed]
  18. G. V. Bekesy, J. Opt. Soc. Am. 50, 1060 (1960).
    [Crossref] [PubMed]
  19. S. W. Kuffler, J. Neurophysiol. 16, 37 (1953).
    [PubMed]
  20. H. B. Barlow, R. Fitzhugh, and S. W. Kuffler, J. Physiol. 137, 338 (1957).
  21. A. Rochon-Duvigneaud, Arch. Anat. Micro. 9, 315 (1906–07).
  22. S. L. Polyak, The Retina (Chicago University Press, 1941).
  23. The details and notations of F test and S method presented here are given in the book The Analysis of Variance by H. Scheffe (John Wiley & Sons, Inc., New York, 1959).
  24. The details and notations of this test are given in the book Probability Theory and Mathematical Statistics by M. Fisz (John Wiley & Sons, Inc., New York, 1963).

1963 (1)

1962 (3)

1961 (2)

1960 (2)

G. V. Bekesy, J. Opt. Soc. Am. 50, 1060 (1960).
[Crossref] [PubMed]

G. Westheimer, J. Physiol. 152, 67 (1960).

1959 (1)

K. J. Rosenbruch, Optik 16, 135 (1959).

1958 (1)

R. C. Jones, J. Opt. Soc. Am. 48, 1934 (1958).
[Crossref]

1957 (1)

H. B. Barlow, R. Fitzhugh, and S. W. Kuffler, J. Physiol. 137, 338 (1957).

1956 (1)

1955 (1)

F. Flamant, Rev. Optique 34, 433 (1955).

1953 (1)

S. W. Kuffler, J. Neurophysiol. 16, 37 (1953).
[PubMed]

1948 (2)

G. A. Fry, Am. J. Optom. 25, 162 (1948).
[Crossref]

E. W. H. Selwyn, Phot. J. B88, 6 (1948).

1936 (1)

R. J. Beitel, J. Gen. Psychol. 14, 31 (1936).
[Crossref]

Barlow, H. B.

H. B. Barlow, R. Fitzhugh, and S. W. Kuffler, J. Physiol. 137, 338 (1957).

Beitel, R. J.

R. J. Beitel, J. Gen. Psychol. 14, 31 (1936).
[Crossref]

Bekesy, G. V.

Blackman, R. B.

R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover Publications Inc., New York, 1959).

Campbell, F. W.

G. Westheimer and F. W. Campbell, J. Opt. Soc. Am. 52, 1040 (1962).
[Crossref] [PubMed]

J. G. Robson and F. W. Campbell, “The Physiological Basis for Form Discrimination,” Symposium at Walter S. Hunter Laboratory of Psychology, Brown University, 23–24 January 1964.

DePalma, J. J.

Fisz, M.

The details and notations of this test are given in the book Probability Theory and Mathematical Statistics by M. Fisz (John Wiley & Sons, Inc., New York, 1963).

Fitzhugh, R.

H. B. Barlow, R. Fitzhugh, and S. W. Kuffler, J. Physiol. 137, 338 (1957).

Flamant, F.

F. Flamant, Rev. Optique 34, 433 (1955).

Fry, G. A.

Jones, R. C.

R. C. Jones, J. Opt. Soc. Am. 48, 1934 (1958).
[Crossref]

Krauskopf, J.

Kuffler, S. W.

H. B. Barlow, R. Fitzhugh, and S. W. Kuffler, J. Physiol. 137, 338 (1957).

S. W. Kuffler, J. Neurophysiol. 16, 37 (1953).
[PubMed]

Lowry, E. M.

Polyak, S. L.

S. L. Polyak, The Retina (Chicago University Press, 1941).

Robson, J. G.

J. G. Robson and F. W. Campbell, “The Physiological Basis for Form Discrimination,” Symposium at Walter S. Hunter Laboratory of Psychology, Brown University, 23–24 January 1964.

Rochon-Duvigneaud, A.

A. Rochon-Duvigneaud, Arch. Anat. Micro. 9, 315 (1906–07).

Rosenbruch, K. J.

K. J. Rosenbruch, Optik 16, 135 (1959).

Schade, O. H.

Scheffe, H.

The details and notations of F test and S method presented here are given in the book The Analysis of Variance by H. Scheffe (John Wiley & Sons, Inc., New York, 1959).

Selwyn, E. W. H.

E. W. H. Selwyn, Phot. J. B88, 6 (1948).

Shlaer, S.

S. Shlaer, J. Gen. Physiol. 21, 165 (1937–38).
[Crossref]

Tukey, J. W.

R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover Publications Inc., New York, 1959).

Westheimer, G.

Am. J. Optom. (1)

G. A. Fry, Am. J. Optom. 25, 162 (1948).
[Crossref]

Arch. Anat. Micro. (1)

A. Rochon-Duvigneaud, Arch. Anat. Micro. 9, 315 (1906–07).

J. Gen. Physiol. (1)

S. Shlaer, J. Gen. Physiol. 21, 165 (1937–38).
[Crossref]

J. Gen. Psychol. (1)

R. J. Beitel, J. Gen. Psychol. 14, 31 (1936).
[Crossref]

J. Neurophysiol. (1)

S. W. Kuffler, J. Neurophysiol. 16, 37 (1953).
[PubMed]

J. Opt. Soc. Am. (9)

J. Physiol. (2)

G. Westheimer, J. Physiol. 152, 67 (1960).

H. B. Barlow, R. Fitzhugh, and S. W. Kuffler, J. Physiol. 137, 338 (1957).

Optik (1)

K. J. Rosenbruch, Optik 16, 135 (1959).

Phot. J. (1)

E. W. H. Selwyn, Phot. J. B88, 6 (1948).

Rev. Optique (1)

F. Flamant, Rev. Optique 34, 433 (1955).

Other (5)

J. G. Robson and F. W. Campbell, “The Physiological Basis for Form Discrimination,” Symposium at Walter S. Hunter Laboratory of Psychology, Brown University, 23–24 January 1964.

R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover Publications Inc., New York, 1959).

S. L. Polyak, The Retina (Chicago University Press, 1941).

The details and notations of F test and S method presented here are given in the book The Analysis of Variance by H. Scheffe (John Wiley & Sons, Inc., New York, 1959).

The details and notations of this test are given in the book Probability Theory and Mathematical Statistics by M. Fisz (John Wiley & Sons, Inc., New York, 1963).

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Figures (4)

Fig. 1
Fig. 1

The modulation transfer functions for the visual system at four different mean retinal illuminances. Subject DR.

Fig. 2
Fig. 2

The line spread functions for the visual system. Curves A, B, C, and D correspond to mean retinal illuminances of 1000, 100, 10, and 3 td, respectively. Curve R represents the line spread function of the optical system up to the retina. Each curve is symmetric with respect to the vertical axis.

Fig. 3
Fig. 3

The line spread functions for the physiological part of the visual system (relating the retinal image to the psychic image) perceived by the observer. Curves A, B, C, and D correspond to mean retinal illuminance of 1000, 100, 10, and 3 td, respectively.

Fig. 4
Fig. 4

Absolute deviation CBav versus spatial frequency for threshold perception. Each curve in Fig. 1 is in effect translated downward by an amount proportional to log mean retinal illuminance; their order is now reversed in absolute units.

Tables (1)

Tables Icon

Table I Threshold contrast readings in the region of second peak in MTF for 1000 td. Subject DR. Threshold contrast is given in arbitrary units (number of turns of potentiometer, 1 turn=0.0364%). The first column is f in cycles/mm.

Equations (9)

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C = ( B max - B min ) / ( B max + B min ) ,
A ( x ) = 2 0 G ( f ) cos 2 π f x d f ,
- A ( x ) d x = G ( 0 )
G ( f ) = G 1 ( f ) · G 2 ( f ) .
ψ ˆ - S σ ˆ ψ ˆ ψ ψ ˆ + S σ ˆ ψ ˆ ,
S 2 = ( I - 1 ) F α : I - 1 , n - I .
F 1 ( x ) F 2 ( x ) .
V = [ U - E ( U ) ] / [ D 2 ( U ) ] 1 2 ,
D 2 ( U ) = n 1 n 2 ( n 1 + n 2 + 1 ) / 12.