Abstract

Visual stimuli consisting of two alternating trains of high-frequency square-wave pulses of the same time-average luminance were presented monocularly to human observers. Two stimulus sizes were used, which subtended visual angles of 12° and 4.3°. In many cases the observers perceived flicker even when each train of pulses by itself appeared fused. The results of the present experiments show that perception of flicker with this type of stimulus pattern depends critically on two variables: (1) the difference t1t2, where t1 and t2 denote the periods of single pulses in the two trains; (2) the combinations of T1 and T2, where T1 and T2 denote the durations of the two trains. The results with the 12° field show some remarkable differences from the results with the 4.3° field, thus, confirming the findings of numerous earlier studies that in many visual tasks the central fovea behaves differently from larger areas around it. The model of de Lange was checked by Fourier analysis of the data. This analysis shows that de Lange’s model can be adequately fitted to the data for the 4.3° field, but not for the 12° field. In the case of the 4.3° field, the amplitudes of the second Fourier component are, for many of the data, at or near the threshold values of their corresponding fundamental components. This means that the possibility of a contribution from the higher harmonics to the threshold of flicker cannot be neglected.

© 1964 Optical Society of America

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References

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  1. D. M. Forsyth and C. R. Brown, Science 134, 612 (1961).
    [Crossref] [PubMed]
  2. The word enclosed in square brackets has been supplied by the present author.
  3. D. H. Kelly, J. Opt. Soc. Am. 49, 730 (1959).
    [Crossref] [PubMed]
  4. W. J. Crozier, E. Wolf, and G. Zerrahn-Wolf, J. Gen. Physiol. 22, 451 (1939).
  5. S. Hecht, in Handbook of General Experimental Psychology, edited by C. Murchison (Clark University Press, Worcester, Massachusetts, 1934), Chap. 14, p. 704.
    [Crossref]
  6. H. de Lange, thesis, Technical University, Delft, Holland (1957).
  7. H. de Lange, J. Opt. Soc. Am. 48, 777 (1958).
    [Crossref]
  8. H. E. Ives, J. Opt. Soc. Am. 6, 254 (1922).
    [Crossref]
  9. D. H. Kelly, J. Opt. Soc. Am. 51, 422 (1961).
    [Crossref] [PubMed]
  10. D. H. Kelly, J. Opt. Soc. Am. 51, 747 (1961).
    [Crossref]
  11. D. H. Kelly, J. Opt. Soc. Am. 52, 940 (1962).
    [Crossref] [PubMed]
  12. R. T. Ross, J. Gen. Psychol. 29, 129 (1943).
    [Crossref]
  13. P. Winchell and E. Simonson, J. Appl. Physiol. 4, 188 (1951).
    [PubMed]
  14. L. Matin, Science 136, 983 (1962).
    [Crossref] [PubMed]
  15. B. S. Hylkema, Acta Ophthalmol. 20, 181 (1942).
    [Crossref]
  16. J. Levinson, Science 131, 1438 (1960).
    [Crossref] [PubMed]

1962 (2)

1961 (3)

1960 (1)

J. Levinson, Science 131, 1438 (1960).
[Crossref] [PubMed]

1959 (1)

1958 (1)

1951 (1)

P. Winchell and E. Simonson, J. Appl. Physiol. 4, 188 (1951).
[PubMed]

1943 (1)

R. T. Ross, J. Gen. Psychol. 29, 129 (1943).
[Crossref]

1942 (1)

B. S. Hylkema, Acta Ophthalmol. 20, 181 (1942).
[Crossref]

1939 (1)

W. J. Crozier, E. Wolf, and G. Zerrahn-Wolf, J. Gen. Physiol. 22, 451 (1939).

1922 (1)

Brown, C. R.

D. M. Forsyth and C. R. Brown, Science 134, 612 (1961).
[Crossref] [PubMed]

Crozier, W. J.

W. J. Crozier, E. Wolf, and G. Zerrahn-Wolf, J. Gen. Physiol. 22, 451 (1939).

de Lange, H.

H. de Lange, J. Opt. Soc. Am. 48, 777 (1958).
[Crossref]

H. de Lange, thesis, Technical University, Delft, Holland (1957).

Forsyth, D. M.

D. M. Forsyth and C. R. Brown, Science 134, 612 (1961).
[Crossref] [PubMed]

Hecht, S.

S. Hecht, in Handbook of General Experimental Psychology, edited by C. Murchison (Clark University Press, Worcester, Massachusetts, 1934), Chap. 14, p. 704.
[Crossref]

Hylkema, B. S.

B. S. Hylkema, Acta Ophthalmol. 20, 181 (1942).
[Crossref]

Ives, H. E.

Kelly, D. H.

Levinson, J.

J. Levinson, Science 131, 1438 (1960).
[Crossref] [PubMed]

Matin, L.

L. Matin, Science 136, 983 (1962).
[Crossref] [PubMed]

Ross, R. T.

R. T. Ross, J. Gen. Psychol. 29, 129 (1943).
[Crossref]

Simonson, E.

P. Winchell and E. Simonson, J. Appl. Physiol. 4, 188 (1951).
[PubMed]

Winchell, P.

P. Winchell and E. Simonson, J. Appl. Physiol. 4, 188 (1951).
[PubMed]

Wolf, E.

W. J. Crozier, E. Wolf, and G. Zerrahn-Wolf, J. Gen. Physiol. 22, 451 (1939).

Zerrahn-Wolf, G.

W. J. Crozier, E. Wolf, and G. Zerrahn-Wolf, J. Gen. Physiol. 22, 451 (1939).

Acta Ophthalmol. (1)

B. S. Hylkema, Acta Ophthalmol. 20, 181 (1942).
[Crossref]

J. Appl. Physiol. (1)

P. Winchell and E. Simonson, J. Appl. Physiol. 4, 188 (1951).
[PubMed]

J. Gen. Physiol. (1)

W. J. Crozier, E. Wolf, and G. Zerrahn-Wolf, J. Gen. Physiol. 22, 451 (1939).

J. Gen. Psychol. (1)

R. T. Ross, J. Gen. Psychol. 29, 129 (1943).
[Crossref]

J. Opt. Soc. Am. (6)

Science (3)

D. M. Forsyth and C. R. Brown, Science 134, 612 (1961).
[Crossref] [PubMed]

L. Matin, Science 136, 983 (1962).
[Crossref] [PubMed]

J. Levinson, Science 131, 1438 (1960).
[Crossref] [PubMed]

Other (3)

The word enclosed in square brackets has been supplied by the present author.

S. Hecht, in Handbook of General Experimental Psychology, edited by C. Murchison (Clark University Press, Worcester, Massachusetts, 1934), Chap. 14, p. 704.
[Crossref]

H. de Lange, thesis, Technical University, Delft, Holland (1957).

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Figures (7)

Fig. 1
Fig. 1

A schematic representation of the stimulus pattern used by Forsyth and Brown.

Fig. 2
Fig. 2

Threshold functions for fixed values of t1 and t2. The points on each curve denote the combinations of n1 and n2 for which the observer just perceived the transition between fusion and flicker. The value of t1 for each curve is indicated on the figures. The value of t2 was 1 msec for all cases. The stimulus subtended a visual angle of 4.3° at the center of the retina.

Fig. 3
Fig. 3

Same threshold functions as Fig. 2, but the value of t2 here was 2 msec for all cases.

Fig. 4
Fig. 4

Same threshold functions as Fig. 2, but the stimulus in this case subtended a visual angle of 1 2 ° at the center of the fovea.

Fig. 5
Fig. 5

Threshold functions for fixed values of t1 and T1. The lines show that at threshold the relationship T2=n2×t2 is constant, that is, n2 is linear with 1/t2. The values of t1 and T1 for each line are indicated in the figures.

Fig. 6
Fig. 6

Frequency-response curves for observer HC. Threshold relative amplitudes for the Fourier fundamental are plotted against corresponding frequencies in logarithmic coordinates. Also plotted is one of de Lange’s5 attenuation characteristic functions for his observer V.

Fig. 7
Fig. 7

Frequency-response curves for observer HC showing the relative contributions of the first two Fourier components. Threshold relative amplitudes for the first two Fourier components are plotted against corresponding frequencies in logarithmic coordinates. The hatched area between 12 and 45 cps contains the relative amplitudes of the second Fourier components in about 60% of the cases.

Tables (2)

Tables Icon

Table I Outline of the size and temporal aspects of the stimuli held constant in Experiment I.

Tables Icon

Table II Outline of the size and temporal aspects of the stimuli held constant in Experiment II.

Equations (8)

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f ( t ) = a 0 / 2 + n = 1 ( a n cos n ω t + b n sin n ω t )
= c 0 / 2 + n = 1 c n cos ( n ω t + ϕ n ) ,
c 0 = a 0 ,
c n = ( a n 2 + b n 2 ) 1 2 ,
ϕ n = tan - 1 ( - b n / a n ) ,
a n = c 0 π n ( [ sin n π t 1 n 1 T cos n π t 1 ( 2 n - 1 ) 2 T / cos n π t 1 2 T ] + { sin n π t 2 n 2 T cos n π [ 4 n 1 t 1 + ( 2 n 2 - 1 ) t 2 ] 2 T / cos n π t 2 2 T } ) ,
b n = c 0 π n ( [ sin n π t 1 n 1 T sin n π t 1 ( 2 n 1 - 1 ) 2 T / cos n π t 1 2 T ] + { sin n π t 2 n 2 T sin n π [ 4 n 1 t 1 + ( 2 n 2 - 1 ) t 2 ] 2 T / cos n π t 2 2 T } ) .
r % = [ c 1 / ( c 0 / 2 ) ] × 100.