Abstract

It is shown that circular nonmoving targets, detected at threshold, which appear as a “point source” for low values of the subtended visual angle (target diameter), pass smoothly into a subjective annular shape for larger diameters. The annulus is the locale of the luminance gradient and therefore provides the significant visual information. The annulus width is 0.9 min of arc when the adapting luminance B is 102 ft-L and rises to 1.3 min as B falls to 10−3 ft-L. Because of this continuous transition from a point source to an annulus, the “critical visual angle” is at best only an approximation.

Over a range of B from 10−3 to 102 ft-L and a duration of stimulus from 10−2 to 1 sec the threshold energy for a point source rises 140 fold. The corresponding rise in the threshold energy per sq min of annulus area is about 1600 fold.

The trends in threshold energy and in threshold contrast with increasing target size are believed to measure some of the effects of retinal (or neural) interaction and inhibition in the human fovea.

© 1962 Optical Society of America

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References

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  1. H. R. Blackwell and W. D. McCready, “Foveal contrast threshold for various durations of single pulses,” Eng. Research Rept. 2455-13-F, University of Michigan, Ann Arbor, Michigan (1958), pp. 28.
  2. H. R. Blackwell, Illum. Engr. 54, 317–353 (1959).
  3. S. G. de Groot and J. W. Gebhard, J. Opt. Soc. Am. 42, 492–495 (1952).
    [Crossref] [PubMed]
  4. R. Clark Jones, J. Opt. Soc. Am. 49, 645–653 (1959).
    [Crossref]
  5. S. Hecht, S. Shlaer, C. D. Hendley, and E. F. Lamar, J. Opt. Soc. Am. 37, 531–545 (1947). See also M. Nackman, Am. J. Psychol. 70, 211–218 (1957).
    [Crossref]
  6. H. R. Blackwell, J. Opt. Soc. Am. 36, 624–43 (1946)
    [Crossref] [PubMed]
  7. H. K. Hartline and F. Ratliff, J. General Physiol. 40, 357 (1957).
    [Crossref]
  8. K. N. Ogle, J. Opt. Soc. Am. 51, 862–869 (1961).
    [Crossref] [PubMed]

1961 (1)

1959 (2)

H. R. Blackwell, Illum. Engr. 54, 317–353 (1959).

R. Clark Jones, J. Opt. Soc. Am. 49, 645–653 (1959).
[Crossref]

1957 (1)

H. K. Hartline and F. Ratliff, J. General Physiol. 40, 357 (1957).
[Crossref]

1952 (1)

1947 (1)

1946 (1)

Blackwell, H. R.

H. R. Blackwell, Illum. Engr. 54, 317–353 (1959).

H. R. Blackwell, J. Opt. Soc. Am. 36, 624–43 (1946)
[Crossref] [PubMed]

H. R. Blackwell and W. D. McCready, “Foveal contrast threshold for various durations of single pulses,” Eng. Research Rept. 2455-13-F, University of Michigan, Ann Arbor, Michigan (1958), pp. 28.

Clark Jones, R.

de Groot, S. G.

Gebhard, J. W.

Hartline, H. K.

H. K. Hartline and F. Ratliff, J. General Physiol. 40, 357 (1957).
[Crossref]

Hecht, S.

Hendley, C. D.

Lamar, E. F.

McCready, W. D.

H. R. Blackwell and W. D. McCready, “Foveal contrast threshold for various durations of single pulses,” Eng. Research Rept. 2455-13-F, University of Michigan, Ann Arbor, Michigan (1958), pp. 28.

Ogle, K. N.

Ratliff, F.

H. K. Hartline and F. Ratliff, J. General Physiol. 40, 357 (1957).
[Crossref]

Shlaer, S.

Illum. Engr. (1)

H. R. Blackwell, Illum. Engr. 54, 317–353 (1959).

J. General Physiol. (1)

H. K. Hartline and F. Ratliff, J. General Physiol. 40, 357 (1957).
[Crossref]

J. Opt. Soc. Am. (5)

Other (1)

H. R. Blackwell and W. D. McCready, “Foveal contrast threshold for various durations of single pulses,” Eng. Research Rept. 2455-13-F, University of Michigan, Ann Arbor, Michigan (1958), pp. 28.

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Figures (2)

Fig. 1
Fig. 1

Ricco energy constants, R = t E C ( 1 4 π d 2 ), as a function of the adapting luminance B. The curves are for t = l, 1/3, 1/10, and 1/100 sec of target exposure.

Fig. 2
Fig. 2

Threshold energy ΔQ = R + βwπ(ddc) as a function of target diameter (min of arc), at B = 0.1 ft-L, t = 0.01 sec.

Tables (11)

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Table I Retinal illuminance E for several levels of background luminance B.

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Table II Ricco constants R (troland-sec), for various durations of stimulus t (sec), and adapting luminances B (ft-L).

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Table III Threshold energies ΔQ as a function of target diameter at t = 0.01 sec, B = 0.1 ft − L, for values of d from 4 to 60. E = 5.14 trolands. The value of w is calculated to be 1.26.

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Table IV Ring width, w, for 42 combinations of B and t. The unit for w is minutes of visual angle.

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Table V Critical visual angle dc = 4w for 42 combinations of B and t. The unit for dc is minutes of visual angle.

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Table VI Critical visual angle, Blackwell 1946.

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Table VII Dependence of the critical visual angle dc on the pupil diameter p and the Stiles–Crawford factor S.

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Table VIII Coefficient b for various exposure times and adapting luminances, b is expressed in troland-seconds per πw square minutes of annulus subtend of the target.

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Table IX Values of β = b/πw. The units are troland-seconds per square minute of annulus subtend of the target. B is in ft − L, and E is in trolands.

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Table X Threshold limen ΔB vs target diameter d, when B = 10−1ft-L, and t = 0.01 sec.

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Table IV A Smoothed threshold data, 1-sec duration, values of log threshold contrast.

Equations (5)

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Δ Q R = β w ( perimeter π d c ) .
w = AO / EO = AO / ( AO X ) .
X / ( AB 4 w ) = AC / AB .
X / ( AO X ) AB ( AO X ) 4 AO = AC AB .
Δ Q = 2.15 + 0.041 ( d 5.04 ) .