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, <i>i <sub>c</sub></i>. (The critical interval <i>i <sub>c</sub></i> varies systematically with both the background luminance and the number of flashes.) Second, as the interval increases beyond <i>i <sub>c</sub></i> threshold energy increases to a maximum, at interval <i>i <sub>M</sub></i>, 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 <i>i <sub>M</sub></i> and the threshold luminance increment (Δ<i>I</i>) at <i>i <sub>M</sub></i> are constant. Also, the increment Δ<i>I</i> at <i>i <sub>M</sub></i> 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 <i>i <sub>M</sub></i>, 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.

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  1. R. M. Herrick, J. Opt. Soc. Am. 62, 104 (1972).
  2. R. M. Herrick and C. J. Theisen, Jr., J. Opt. Soc. Am. 62, 588 (1972).
  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).
  5. C. H. Graham and E. H. Kemp, J. Gen. Physiol. 21, 635 (1938).
  6. Margaret Keller, J. Exp. Psychol. 28, 407 (1941).
  7. R. M. Herrick, J. Comp. Physiol. Psychol. 49, 437 (1956).
  8. The intervals i1 selected in the auxiliary study were slightly longer than the i1 values corresponding to the second straight line of the TEpee plot. However, (a) knowing the true logT M, 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 logT M 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 T M. 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).
  11. In the study on two identical flashes (Ref. 1) it was concluded that (logE M-logE p) 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).
  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).
  14. M. Ikeda and T. Fujii, J. Opt. Soc. Am. 56, 1129 (1966).
  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, t1, ΔI1, and T constant, Erdmann determined the probability of detection while simultaneously varying n and i1.
  16. The following two plots help portray these and other points of agreement between the present study and CFF experiments: (a) threshold logA L (mL) vs log frequency (Hz), with frequency = 1000/(t1 + il); (b) threshold logΔIl vs 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.

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, t1, ΔI1, and T constant, Erdmann determined the probability of detection while simultaneously varying n and i1.

Fujii, T.

M. Ikeda and T. Fujii, J. Opt. Soc. Am. 56, 1129 (1966).

Graham, C. H.

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

Herrick, R. M.

R. M. Herrick, J. Opt. Soc. Am. 62, 104 (1972).

R. M. Herrick and C. J. Theisen, Jr., J. Opt. Soc. Am. 62, 588 (1972).

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

R. M. Herrick, J. Comp. Physiol. Psychol. 49, 437 (1956).

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).

Ikeda, M.

M. Ikeda and T. Fujii, J. Opt. Soc. Am. 56, 1129 (1966).

Keller, Margaret

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

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).

Theisen, Jr., C. J.

R. M. Herrick and C. J. Theisen, Jr., J. Opt. Soc. Am. 62, 588 (1972).

Other (17)

R. M. Herrick, J. Opt. Soc. Am. 62, 104 (1972).

R. M. Herrick and C. J. Theisen, Jr., J. Opt. Soc. Am. 62, 588 (1972).

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.

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

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

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

R. M. Herrick, J. Comp. Physiol. Psychol. 49, 437 (1956).

The intervals i1 selected in the auxiliary study were slightly longer than the i1 values corresponding to the second straight line of the TEpee plot. However, (a) knowing the true logT M, 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 logT M values were estimated from the data of the main experiment.

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 T M. 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).

In the study on two identical flashes (Ref. 1) it was concluded that (logE M-logE p) 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.

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).

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).

M. Ikeda and T. Fujii, J. Opt. Soc. Am. 56, 1129 (1966).

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, t1, ΔI1, and T constant, Erdmann determined the probability of detection while simultaneously varying n and i1.

The following two plots help portray these and other points of agreement between the present study and CFF experiments: (a) threshold logA L (mL) vs log frequency (Hz), with frequency = 1000/(t1 + il); (b) threshold logΔIl vs 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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