Abstract

To determine threshold luminance as a function of the interval separating successive subliminal flashes, 2, 3, 6, and 100 5-ms flashes were added to a centrally fixated background luminance. The interval separating successive flashes was varied from 0 to 150 ms, and four background luminances were used. At any background luminance, for any number of flashes, four empirical laws, collectively termed the TEpee effect, describe the results. First, as the interval increases from 0 the threshold total energy required in the flashes remains constant up to a critical interval, iC. (The critical interval iC varies systematically with both the background luminance and the number of flashes.) Second, as the interval increases beyond iC, threshold energy increases to a maximum, at interval iM, following the rule that the average luminance during the total display time remains constant. [At any given background luminance, for any number of flashes, both iM and the threshold luminance increment (ΔI) at iM are constant. Also, the increment ΔI at iM for any number of 5-ms flashes is slightly greater than that required for a single 5-ms flash.] Third, as the interval increases beyond iM, threshold energy decreases following the rule that the threshold energy times the total display time equals a constant. This decrease continues until a threshold-energy level predicted by the probability-summation hypothesis is reached. Fourth, with further increases in the interval the threshold energy remains constant. The findings are related to results of variable-duration, single-flash experiments and to results of critical-flicker-frequency experiments.

© 1973 Optical Society of America

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  1. R. M. Herrick, J. Opt. Soc. Am. 62, 104 (1972).
    [CrossRef] [PubMed]
  2. R. M. Herrick and C. J. Theisen, J. Opt. Soc. Am. 62, 588 (1972).
    [CrossRef] [PubMed]
  3. With test and background fields of the same size or different sizes, the results for two flashes are the same, as indicated in Ref. 1.
  4. R. M. Herrick, Percept. Psychophys. 13, 548 (1973).
    [CrossRef]
  5. C. H. Graham and E. H. Kemp, J. Gen. Physiol. 21, 635 (1938).
  6. Margaret Keller, J. Exp. Psychol. 28, 407 (1941).
    [CrossRef]
  7. R. M. Herrick, J. Comp. Physiol. Psychol. 49, 437 (1956).
    [CrossRef] [PubMed]
  8. The intervals i1selected in the auxiliary study were slightly longer than the i1values corresponding to the second straight line of the TEpee plot. However, (a) knowing the true logTM, and (b) knowing, from the TEpee effect, that threshold logE is the same at logT values equally greater and less than log TM(see Fig. 6), an experimental point of the third straight line of the TEpee plot may be transferred to the second straight line of the TEpee plot. The true logTM values were estimated from the data of the main experiment.
  9. The finding that critical duration varies with the number of flashes is, of course, contrary to Davy’s [J. Opt. Soc. Am. 42, 937 (1952)] implied conclusion that the critical duration is a fixed value, equal to TCS. Davy’s conclusion, however, is an assumption that cannot be deduced from his data. Whether the critical duration varies with the number of flashes in the periphery, the locus of Davy’s work, as it does in the fovea, is a question that has not yet been answered.
  10. Because of the data-collection procedure, it is not possible to determine if the flashes were more likely to appear as more than one flash as T increased beyond TM. The observor was not asked to estimate the number of flashes. With supraliminal flashes, the number of flashes perceived are fewer than the number presented; see P. G. Cheatham and C. T. White, J. Exp. Psychol. 44, 447 (1952).
    [CrossRef] [PubMed]
  11. In the study on two identical flashes (Ref. 1) it was concluded that (logEM-logEP) varied as a function of background luminance. It appears now, on the basis of various numbers of flashes from 2 to 100, that the earlier conclusion was unwarranted. The earlier, erroneous conclusion was based on a misinterpretation of experimental variability.
  12. M. H. Pirenne, Nature (Lond.) 152, 698 (1943); M. A. Bouman and G. van den Brink, J. Opt. Soc. Am. 42, 617 (1952); G. van den Brink and M. A. Bouman, J. Opt. Soc. Am. 44, 616 (1954); T. Uetsuki and M. Ikeda, J. Opt. Soc. Am. 60, 377 (1970); H. R. Blackwell, J. Opt. Soc. Am. 53, 129 (1963); M. Ikeda, J. Opt. Soc. Am. 55, 1527 (1965).
    [CrossRef] [PubMed]
  13. R. M. Herrick, Percept. Motor Skill. 24, 915 (1967); Percept. Motor Skill. 28, 503 (1969); Percept. Psychophys. 7, 73 (1970); Percept. Psychophys. 8, 61 (1970).
    [CrossRef]
  14. M. Ikeda and T. Fujii, J. Opt. Soc. Am. 56, 1129 (1966).
    [CrossRef] [PubMed]
  15. The complex families of curves of R. L. Erdmann [J. Exp. Psychol. 63, 353 (1962)] can probably be described by reference to curves like those of Fig. 15. With I, ti, ΔI1, and T constant, Erdmann determined the probability of detection while simultaneously varying n and i1.
    [CrossRef] [PubMed]
  16. The following two plots help portray these and other points of agreement between the present study and CFF experiments: (a) threshold logAL(mL) vs log frequency (Hz), with frequency = 1000/(t1+ i1); (b) threshold logΔI1vs log light-time fraction, with light-time fraction = t1/(t1+ i1).
  17. The equation of the line for TCS in Fig. 17 is TCS= 54–20 logI, with TCS, the critical duration of a variable-duration, single-flash experiment, expressed in milliseconds and I, the background luminance, in millilamberts. See Ref. 1, Fig. 10, for a plot of the data.

1973 (1)

R. M. Herrick, Percept. Psychophys. 13, 548 (1973).
[CrossRef]

1972 (2)

1967 (1)

R. M. Herrick, Percept. Motor Skill. 24, 915 (1967); Percept. Motor Skill. 28, 503 (1969); Percept. Psychophys. 7, 73 (1970); Percept. Psychophys. 8, 61 (1970).
[CrossRef]

1966 (1)

1962 (1)

The complex families of curves of R. L. Erdmann [J. Exp. Psychol. 63, 353 (1962)] can probably be described by reference to curves like those of Fig. 15. With I, ti, ΔI1, and T constant, Erdmann determined the probability of detection while simultaneously varying n and i1.
[CrossRef] [PubMed]

1956 (1)

R. M. Herrick, J. Comp. Physiol. Psychol. 49, 437 (1956).
[CrossRef] [PubMed]

1952 (2)

The finding that critical duration varies with the number of flashes is, of course, contrary to Davy’s [J. Opt. Soc. Am. 42, 937 (1952)] implied conclusion that the critical duration is a fixed value, equal to TCS. Davy’s conclusion, however, is an assumption that cannot be deduced from his data. Whether the critical duration varies with the number of flashes in the periphery, the locus of Davy’s work, as it does in the fovea, is a question that has not yet been answered.

Because of the data-collection procedure, it is not possible to determine if the flashes were more likely to appear as more than one flash as T increased beyond TM. The observor was not asked to estimate the number of flashes. With supraliminal flashes, the number of flashes perceived are fewer than the number presented; see P. G. Cheatham and C. T. White, J. Exp. Psychol. 44, 447 (1952).
[CrossRef] [PubMed]

1943 (1)

M. H. Pirenne, Nature (Lond.) 152, 698 (1943); M. A. Bouman and G. van den Brink, J. Opt. Soc. Am. 42, 617 (1952); G. van den Brink and M. A. Bouman, J. Opt. Soc. Am. 44, 616 (1954); T. Uetsuki and M. Ikeda, J. Opt. Soc. Am. 60, 377 (1970); H. R. Blackwell, J. Opt. Soc. Am. 53, 129 (1963); M. Ikeda, J. Opt. Soc. Am. 55, 1527 (1965).
[CrossRef] [PubMed]

1941 (1)

Margaret Keller, J. Exp. Psychol. 28, 407 (1941).
[CrossRef]

1938 (1)

C. H. Graham and E. H. Kemp, J. Gen. Physiol. 21, 635 (1938).

Cheatham, P. G.

Because of the data-collection procedure, it is not possible to determine if the flashes were more likely to appear as more than one flash as T increased beyond TM. The observor was not asked to estimate the number of flashes. With supraliminal flashes, the number of flashes perceived are fewer than the number presented; see P. G. Cheatham and C. T. White, J. Exp. Psychol. 44, 447 (1952).
[CrossRef] [PubMed]

Erdmann, R. L.

The complex families of curves of R. L. Erdmann [J. Exp. Psychol. 63, 353 (1962)] can probably be described by reference to curves like those of Fig. 15. With I, ti, ΔI1, and T constant, Erdmann determined the probability of detection while simultaneously varying n and i1.
[CrossRef] [PubMed]

Fujii, T.

Graham, C. H.

C. H. Graham and E. H. Kemp, J. Gen. Physiol. 21, 635 (1938).

Herrick, R. M.

R. M. Herrick, Percept. Psychophys. 13, 548 (1973).
[CrossRef]

R. M. Herrick, J. Opt. Soc. Am. 62, 104 (1972).
[CrossRef] [PubMed]

R. M. Herrick and C. J. Theisen, J. Opt. Soc. Am. 62, 588 (1972).
[CrossRef] [PubMed]

R. M. Herrick, Percept. Motor Skill. 24, 915 (1967); Percept. Motor Skill. 28, 503 (1969); Percept. Psychophys. 7, 73 (1970); Percept. Psychophys. 8, 61 (1970).
[CrossRef]

R. M. Herrick, J. Comp. Physiol. Psychol. 49, 437 (1956).
[CrossRef] [PubMed]

Ikeda, M.

Keller, Margaret

Margaret Keller, J. Exp. Psychol. 28, 407 (1941).
[CrossRef]

Kemp, E. H.

C. H. Graham and E. H. Kemp, J. Gen. Physiol. 21, 635 (1938).

Pirenne, M. H.

M. H. Pirenne, Nature (Lond.) 152, 698 (1943); M. A. Bouman and G. van den Brink, J. Opt. Soc. Am. 42, 617 (1952); G. van den Brink and M. A. Bouman, J. Opt. Soc. Am. 44, 616 (1954); T. Uetsuki and M. Ikeda, J. Opt. Soc. Am. 60, 377 (1970); H. R. Blackwell, J. Opt. Soc. Am. 53, 129 (1963); M. Ikeda, J. Opt. Soc. Am. 55, 1527 (1965).
[CrossRef] [PubMed]

Theisen, C. J.

White, C. T.

Because of the data-collection procedure, it is not possible to determine if the flashes were more likely to appear as more than one flash as T increased beyond TM. The observor was not asked to estimate the number of flashes. With supraliminal flashes, the number of flashes perceived are fewer than the number presented; see P. G. Cheatham and C. T. White, J. Exp. Psychol. 44, 447 (1952).
[CrossRef] [PubMed]

J. Comp. Physiol. Psychol. (1)

R. M. Herrick, J. Comp. Physiol. Psychol. 49, 437 (1956).
[CrossRef] [PubMed]

J. Exp. Psychol. (3)

Margaret Keller, J. Exp. Psychol. 28, 407 (1941).
[CrossRef]

Because of the data-collection procedure, it is not possible to determine if the flashes were more likely to appear as more than one flash as T increased beyond TM. The observor was not asked to estimate the number of flashes. With supraliminal flashes, the number of flashes perceived are fewer than the number presented; see P. G. Cheatham and C. T. White, J. Exp. Psychol. 44, 447 (1952).
[CrossRef] [PubMed]

The complex families of curves of R. L. Erdmann [J. Exp. Psychol. 63, 353 (1962)] can probably be described by reference to curves like those of Fig. 15. With I, ti, ΔI1, and T constant, Erdmann determined the probability of detection while simultaneously varying n and i1.
[CrossRef] [PubMed]

J. Gen. Physiol. (1)

C. H. Graham and E. H. Kemp, J. Gen. Physiol. 21, 635 (1938).

J. Opt. Soc. Am. (4)

Nature (Lond.) (1)

M. H. Pirenne, Nature (Lond.) 152, 698 (1943); M. A. Bouman and G. van den Brink, J. Opt. Soc. Am. 42, 617 (1952); G. van den Brink and M. A. Bouman, J. Opt. Soc. Am. 44, 616 (1954); T. Uetsuki and M. Ikeda, J. Opt. Soc. Am. 60, 377 (1970); H. R. Blackwell, J. Opt. Soc. Am. 53, 129 (1963); M. Ikeda, J. Opt. Soc. Am. 55, 1527 (1965).
[CrossRef] [PubMed]

Percept. Motor Skill. (1)

R. M. Herrick, Percept. Motor Skill. 24, 915 (1967); Percept. Motor Skill. 28, 503 (1969); Percept. Psychophys. 7, 73 (1970); Percept. Psychophys. 8, 61 (1970).
[CrossRef]

Percept. Psychophys. (1)

R. M. Herrick, Percept. Psychophys. 13, 548 (1973).
[CrossRef]

Other (5)

With test and background fields of the same size or different sizes, the results for two flashes are the same, as indicated in Ref. 1.

The intervals i1selected in the auxiliary study were slightly longer than the i1values corresponding to the second straight line of the TEpee plot. However, (a) knowing the true logTM, and (b) knowing, from the TEpee effect, that threshold logE is the same at logT values equally greater and less than log TM(see Fig. 6), an experimental point of the third straight line of the TEpee plot may be transferred to the second straight line of the TEpee plot. The true logTM values were estimated from the data of the main experiment.

In the study on two identical flashes (Ref. 1) it was concluded that (logEM-logEP) varied as a function of background luminance. It appears now, on the basis of various numbers of flashes from 2 to 100, that the earlier conclusion was unwarranted. The earlier, erroneous conclusion was based on a misinterpretation of experimental variability.

The following two plots help portray these and other points of agreement between the present study and CFF experiments: (a) threshold logAL(mL) vs log frequency (Hz), with frequency = 1000/(t1+ i1); (b) threshold logΔI1vs log light-time fraction, with light-time fraction = t1/(t1+ i1).

The equation of the line for TCS in Fig. 17 is TCS= 54–20 logI, with TCS, the critical duration of a variable-duration, single-flash experiment, expressed in milliseconds and I, the background luminance, in millilamberts. See Ref. 1, Fig. 10, for a plot of the data.

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Figures (17)

Fig. 1
Fig. 1

Definitions of symbols vised to describe experimental procedures. I = background luminance; t1,t2,t3, …,tn are durations of first, second, third, …, n flashes; ΔI1, ΔI2, ΔI3, …, ΔIn are luminances of first, second, third, …, n flashes; i1, i2, … are intervals between successive flashes; T is the total display time. In this experiment, t1 = t2 = ⋯ = tn = 5 ms, ΔI1 = ΔI2 = ⋯ = ΔIn, and i1 = i2 = ⋯ = in−1.

Fig. 2
Fig. 2

Threshold energy E as a function of total display time T. Number next to each curve gives the number of identical 5-ms flashes. For clarity, the curves for 3, 6, 12, and 100 flashes have been displaced upward by 0.3, 0.6, 0.9, and 1.2 units, respectively. First point on the left-hand side of each curve represents a case in which the interval i1 = i2 = ⋯ = 0. Each curve gives the data of one session of observer A. L. at a background luminance of 1.02 mL.

Fig. 3
Fig. 3

Threshold energy E as a function of total display time T. Number next to each curve gives the number of identical 5-ms flashes. For clarity, the curves for 3, 6, 12, and 100 flashes have been displaced upward by 0.3, 0.6, 0.9, and 1.2 units, respectively. Each curve gives the data of one session of observer A. L. at a background luminance of 0.1 mL.

Fig. 4
Fig. 4

Threshold energy E as a function of total display time T. Number next to each curve gives the number of identical 5-ms flashes. For clarity, the curves for 3 and 6 flashes have been displaced upward by 0.3 and 0.6 units, respectively. Each curve gives the data of one session of observer A. L. at a background luminance of 45 mL.

Fig. 5
Fig. 5

Threshold energy E as a function of total display time T. Number next to each curve gives the number of identical 5-ms flashes. For clarity, the curves for 3, 4, 6, and 100 flashes have been displaced upward by 0.3, 0.6, 0.9, and 0.9 units, respectively. Each curve gives the data of one session of observer A. L. at a background luminance of 8.9 mL.

Fig. 6
Fig. 6

Model indicating general relationships between threshold energy E and total time of display T for six identical 5-ms flashes. TEpee effect. EB = 1.0 mL ms and TCS = 80 ms.

Fig. 7
Fig. 7

Constancy of threshold base energy (EB) for different numbers of 5-ms flashes at each of four background luminances, 45, 8.9, 1.02, and 0.1 mL, respectively, from top to bottom. Each point represents logEB of one session of observer A. L.

Fig. 8
Fig. 8

(t1 + iC) as a function of the number of 5-ms flashes on a log-log plot. From top to bottom, the straight lines represent background luminances of 0.1, 1.02, 8.9, and 45 mL, respectively. Each point was derived from the data of one session of observer A. L. Points at iC = 0 were derived from variable-duration, single-flash experiments (see text).

Fig. 9
Fig. 9

Critical duration as a function of (n − 1)/n, where n is the number of flashes. From top to bottom, the straight lines represent background luminances of 0.1, 1.02, 8.9, and 45 mL, respectively. All the points for each line were determined in one session with observer A. L.

Fig. 10
Fig. 10

Threshold logΔI1 as a function of the number of flashes. Each line represents the data of one session of observer A. L. (●) or B. M. (○). From top to bottom, for each pair of lines, the background luminance I and the interval between successive flashes i1 are 45 mL, 30 ms; 8.9 mL, 50 ms; 1.02 mL, 70 ms; 0.1 mL, 90 ms.

Fig. 11
Fig. 11

Relation between TCn and TM as a function of the number of flashes. From top to bottom, the four lines represent background luminances of 45, 8.9, 1.02, and 0.1 mL. For clarity, the curves for 1.02, 8.9, and 45 mL were displaced upward by 2, 4, and 6 units, respectively. Each point represents the data of one session of observer A. L.

Fig. 12
Fig. 12

Mean (logEM − logEP) as a function of the number of 5-ms flashes on a log scale. Each point represents the data of all background luminances. Upper curve, observer A. L.; lower curve, observer B. M.

Fig. 13
Fig. 13

LogΔIP as a function of the number of 5-ms flashes. Points based on Fig. 12 data of observer B. M., with logΔIM = 1.12 at background luminance of 45 mL. Curve is derived from probability-summation hypothesis.

Fig. 14
Fig. 14

Derivation of the psychometric function for a single 5-ms flash from data for 2, 3, 4, 6, 12, and 100 flashes. Based on Fig. 13 and probability-summation hypothesis. (See text.) Vertical scale is cumulative-normal-probability scale.

Fig. 15
Fig. 15

Model showing relationships between the threshold increment (ΔI1) and the interval between flashes (i1). The numbers refer to the number of 5-ms flashes. The point (●) at ΔI1 = 0.60 gives the threshold for one 5-ms flash. EB = 3.0 mL ms and TCS = 66 ms. Curves derived from equations of the TEpee effect plus other relationships described in text.

Fig. 16
Fig. 16

Base threshold energy EB and threshold increment at the maximum (ΔIM) as a function of background luminance. Each point is the mean logEB or logΔIM of all sessions where logEB or log ΔIM was obtained. Data of observers A. L. (□) and B. M. (○).

Fig. 17
Fig. 17

Critical duration as a function of background luminance. The number next to each curve gives the number of identical 5-ms flashes. The term TCS refers to the critical duration of a variable-duration, single-flash experiment.

Tables (1)

Tables Icon

Table I Empirical laws for brightness discrimination when the added luminance is presented in the form of n identical flashes.a

Equations (7)

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E = n t 1 Δ I 1 ,
T = n t 1 + ( n 1 ) i 1 ,
A L = E / T .
T C n = n t 1 + ( n 1 ) i C ,
t 1 + i C = k / n ,
T C n = t 1 + T C S [ ( n 1 ) / n ] .
T M = n T C n + ( n 1 ) t 1 ,