Abstract

The contrast sensitivity of the human eye for sinusoidal illuminance changes in space and time, obtained by means of traveling-wave stimuli, was measured as a function of spatial and temporal frequency for white light. The average retinal illuminance was varied between 0.85 and 850 trolands. The threshold modulation for perception of a moving grating is generally higher than that for detection of brightness changes, in space and/or time, that give rise to flicker phenomena. Flicker-fusion characteristics, as determined from the thresholds for the flicker phenomenon, are found to lose their band-pass-filter resemblance for spatial frequencies of more than 5 cycles per degree of visual angle. The thresholds at flicker fusion for spatial- and temporal-frequency combinations in which not both frequencies are very low, appear to be proportional to the inverse of the square root of mean retinal illuminance, in the investigated range. This suggests a photon-noise-dependent threshold mechanism which is operative in a wider illuminance range than that found with contrast-sensitivity measurements for periodic illuminance variations only in space or only in time.

© 1967 Optical Society of America

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References

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    [Crossref] [PubMed]
  2. O. H. Schade, J. Opt. Soc. Am. 46, 721 (1956). Schade, in an attempt to eliminate the effects of limited stimulus size, determined the contrast-sensitivity function for many illuminances with traveling waves that had a single temporal frequency of approx. 1 Hz.
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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1967 (1)

1966 (3)

J. Nachmias, J. Opt. Soc. Am. 56, 538A (1966)/J. Opt. Soc. Am. 57, 421 (1967).

J. G. Robson, J. Opt. Soc. Am. 56, 1141 (1966).
[Crossref]

D. H. Kelly, J. Opt. Soc. Am. 56, 1628 (1966).
[Crossref]

1965 (1)

1963 (1)

1962 (1)

1961 (1)

L. H. van der Tweel, Ann. New York Acad. Sci. 89, 829 (1961).
[Crossref]

1960 (1)

1958 (1)

1956 (1)

1948 (1)

1943 (1)

H. de Vries, Physica 10, 553 (1943).
[Crossref]

1936 (1)

B. H. Crawford, Proc. Roy. Soc. (London),  B121, 376 (1936).

1920 (1)

Bouman, M. A.

Crawford, B. H.

B. H. Crawford, Proc. Roy. Soc. (London),  B121, 376 (1936).

de Lange, H.

De Palma, J. J.

de Vries, H.

H. de Vries, Physica 10, 553 (1943).
[Crossref]

Denier van der Gon, J. J.

J. J. Denier van der Gon, thesis, Univ. Amsterdam (Amsterdam, 1959).

Hilz, R.

Kelly, D. H.

Le Grand, Y.

Y. Le Grand, Optique Physiologique (Editions Rev. Opt., Paris, 1956), Vol. 2, p. 98.

Lowry, E. M.

Nachmias, J.

J. Nachmias, J. Opt. Soc. Am. 56, 538A (1966)/J. Opt. Soc. Am. 57, 421 (1967).

Reeves, P.

Robson, J. G.

Rose, A.

Schade, O. H.

Schober, H. A. W.

Schouten, J. F.

J. F. Schouten, in Proceedings of the Symposium on Models of the Perception of Speech and Visual Form, Boston, November 1964. (Dept. of the Air Force, Hanscom Field, Bedford, Mass.)

van der Tweel, L. H.

L. H. van der Tweel, Ann. New York Acad. Sci. 89, 829 (1961).
[Crossref]

van Nes, F. L.

Veringa, F.

F. Veringa, thesis, Univ. Amsterdam (Amsterdam, 1961).

Vos, J. J.

Walraven, P. L.

Ann. New York Acad. Sci. (1)

L. H. van der Tweel, Ann. New York Acad. Sci. 89, 829 (1961).
[Crossref]

J. Opt. Soc. Am. (12)

Physica (1)

H. de Vries, Physica 10, 553 (1943).
[Crossref]

Proc. Roy. Soc. (London) (1)

B. H. Crawford, Proc. Roy. Soc. (London),  B121, 376 (1936).

Other (4)

Y. Le Grand, Optique Physiologique (Editions Rev. Opt., Paris, 1956), Vol. 2, p. 98.

J. J. Denier van der Gon, thesis, Univ. Amsterdam (Amsterdam, 1959).

J. F. Schouten, in Proceedings of the Symposium on Models of the Perception of Speech and Visual Form, Boston, November 1964. (Dept. of the Air Force, Hanscom Field, Bedford, Mass.)

F. Veringa, thesis, Univ. Amsterdam (Amsterdam, 1961).

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Figures (9)

F. 1
F. 1

Visual field of the experiments. The traveling waves are generated in the central rectangle. The mean luminance and color in the rectangle are approximately the same as those of the surrounding field, which has an elliptical limitation and contains narrow, horizontal, and broad vertical black bars, to provide a fixation aid of high contrast. All measures are expressed in degrees of subtended visual angle.

F. 2
F. 2

Spatial-threshold modulation curves for perception of gratings as such, at three temporal frequencies and an average retinal illuminance of 850 td, white light. The spatial-frequency unit is the cycle per degree of subtended visual angle, cpd. Each point indicates the mean of three values which, as far as the temporal frequency is concerned, were found by interpolation between two modulation percentages measured on one day for temporal frequencies that were readily obtainable with the traveling-wave technique. ● Hz, ○ 1 Hz, ▲ 10 Hz.

F. 3
F. 3

Temporal-threshold modulation curves for flicker fusion at five spatial frequencies and an average retinal illuminance of 85 td, white light. Each point is the mean of three values found by interpolation, as described in the caption of Fig. 2. □ 0.64 cycles per degree, ▲ 1.66 cpd, ● 4.7 cpd, △ 11.0 cpd, ○ 22.8 cpd.

F. 4
F. 4

Temporal-threshold modulation curves for flicker fusion at a spatial frequency of 0.64 cpd and four average retinal illuminances: 0.85, 8.5, 85, and 850 td. Each point is the mean of three values found by interpolation, as described in the caption of Fig. 2.

F. 5
F. 5

Temporal-threshold modulation curves for flicker fusion at a spatial frequency of 11.0 cpd and four average retinal illuminances: 0.85, 8.5, 85, and 850 td. Each point is the mean of three values found by interpolation, as described in the caption of Fig. 2.

F. 6
F. 6

Dependence of threshold modulation M on retinal illuminance B0 for 8 spatial frequencies and green light, λ=525 nm. Each pair of dots indicates the average values of measured supra-and sub-threshold modulations, respectively. The lines have slopes of −0.5 and 0 (from Ref. 4).

F. 7
F. 7

Dependence of threshold modulation M on retinal illuminance B0 for 7 temporal frequencies and white light. The lines have slopes of −0.5 and 0. ○ 2 Hz, □ 5 Hz, ● 10 Hz (deduced from Ref. 5).

F. 8
F. 8

Spatial (lower graph; left ordinate) and temporal (upper graph; right ordinate) frequency for which the exponent n in Mf=cB0n changes from −0.5 into 0, as a function of B0. Both graphs are straight lines with slopes of 0.5. Mf=cB0n is the empirical relation between the threshold modulation Mf for either a spatial or a temporal frequency and mean retinal illuminance B0.

F. 9
F. 9

Dependence of modulation M at the threshold for the flicker phenomenon on retinal illuminance B0 for three spatial and temporal-frequency combinations (fs,ft) from the reported experiments (open circles; continuous lines) and two combinations from Kelly11 (filled circles; dashed lines). Each open circle represents the mean of three measurements with the indicated average variability. All lines have slopes of −0.5. Graph 1: fs=0.64 cpd, ft=10 Hz. 2: fs=0.64 cpd, ft=18 Hz; shifted downwards by 0.5 decade. 3: fs=4.7 cpd, ft=3.5 Hz; shifted upwards by 2 decades. 4: fs=4.7 cpd, ft=10.7Hz; shifted upwards by 1 decade. Graph 5: fs=11.0 cpd, ft=1 Hz; shifted upwards by 3.5 decades.

Equations (1)

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I = I 0 { 1 + M sin 2 π ( f s x + f t t ) } .