Abstract

Binocular probability of seeing, P(B), was measured as a function of the time between onsets of 2-msec, 35-min visual angle flashes to corresponding locations 7° horizontally displaced from the foveas of both eyes of dark-adapted subjects. P(B) was greater than the value that would be predicted if the two eyes were independent detectors [P′(B)] for interstimulus intervals below 100 msec. Two peak values of P(B) were observed, one occurring close to zero and the other close to 90 msec. P(B) and P′(B) were indistinguishable for interstimulus intervals above 100 msec. It is concluded that the largest barrier to seeing at threshold lies in a pathway common to the two eyes.

© 1962 Optical Society of America

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  1. H. Piper, Z. f. Psychol. u. Physiol. D. Sinnesorg. 31, 161 (1903); W. Lohmann, Arch. Augenheilk 74, 110 (1915); W. DeW. Abney and W. Watson, Phil. Trans. Roy. Soc. London A216, 91 (1916); E. Muller, Arch. ges. Physiol. Pflüger’s 193, 427 (1921); D. A. Laird, J. Exptl. Psychol. 7, 276 (1924); C. H. Graham, J. Gen. Psychol. 3, 494 (1930) J. Gen. Psychol. 5, 311 (1931); C. B. Hewson, “An Experimental Study of ‘Binocular Stimulus Summation,’” unpublished Master’s thesis, University of Virginia (1931); T. W. Cook, Psychol. Monogr. 45, No. 3 (1934); D. Shaad, J. Exptl. Psychol. 18, 391 (1935); R. J. Lythgoe and L. R. Phillips, J. Physiol. London 91, 427 (1938); N. R. Bartlett and R. M. Gagne, J. Exptl. Psychol. 25, 91 (1939); W. J. Crozier and A. H. Holway, J. Gen. Physiol. 23, 101 (1939); B. H. Crawford, Proc. Roy. Soc. (London) B128, 552 (1940); L. M. Forbes and F. A. Mote, J. Comp. and Physiol. Psychol. 49, 431 (1956).
    [CrossRef]
  2. In any system we may talk about Y as the largest barrier between input and output if the following holds: (1) there are signals from the input which reach Y but do not go beyond Y; (2) any signal which does go beyond Y reaches the output. Of course, it should be recognized that the location of the largest barrier may be itself a stochastic variable for fixed conditions of stimulation, or vary as a function of conditions of stimulation. With regard to the latter possibility see reference 7.
  3. M. H. Pirenne, Nature 152, 698 (1943).
    [CrossRef]
  4. M. H. Pirenne and F. H. C. Marriott, The Quantum Theory of Light and the Psycho-Physiology of Vision in Psychology: A Study of a Science, edited by S. Koch (McGraw-Hill Book Company, Inc., New York, 1959), Study 1, Vol. I.
  5. R. C. Casperson and H. Schlosberg, J. Exptl. Psychol. 40, 81 (1950).
    [CrossRef]
  6. G. Collier, J. Exptl. Psychol. 47, 75 (1954).
    [CrossRef]
  7. L. Matin, “Corresponding Points, Correlated Measurements, and Binocular Summation” (to be published).
  8. R. G. Roush and E. T. Urbanski, Electronics 26, 154 (1953).
  9. B. Buchmann-Olsen and A. M. Rosenfalck, J. Opt. Soc. Am. 47, 30 (1957).
    [CrossRef] [PubMed]
  10. Statistical time lag of the glow modulator tube was reduced to negligible values (i.e., less than 2 µ sec) by continuously irradiating its cathode with ultraviolet radiation derived from a General Electric argon glow lamp AR-3 (U, Fig. 2; see also Fig. 1) whose output was filtered by Corning filter 5860 (T, Fig. 2) so as to pass only wavelengths below 390 mμ. A Kodak No. 4 filter (D, Fig. 2) plus the high-flint component of achromatic lenses B and G prevented the ultraviolet from reaching the subject’s eye.
  11. K. H. Ogle, Researches in Binocular Vision (W. B. Saunders Company, Philadelphia, 1950).
  12. We have called this effect “Binocular Flash Diplopia.” A detailed study of the phenomenon will be reported elsewhere.
  13. For subject 1, this resulted in an intertrial interval which could range from 20 to 40 sec; for subject 2 the intertrial interval could range from 10 to 30 sec. The actual range for all responses, however, was 25 to 35 sec for subject 1 and 15 to 25 sec for subject 2.
  14. Values of χ2 were computed for each experiment with P′(B) as the theoretical value and P(B) at the different values of ITI as the observed values. They were significant in each experiment beyond the .0001 level of confidence. Since P′(B) is an efficient estimate of its population value and since sufficiently large numbers of measurements were taken the use of P′(B) as a population estimate is reasonable: cf., G. U. Yule and M. G. Kendall, Theory of Statistics (Charles Griffin and Company, London, 1940), p. 428.
  15. L. A. Riggs and F. A. Ratliff, Science 114, 17 (1951).
    [CrossRef] [PubMed]
  16. J. Krauskopf, T. N. Cornsweet, and L. A. Riggs, J. Opt. Soc. Am. 50, 572 (1960).
    [CrossRef] [PubMed]
  17. M. A. Bouman and G. Van den Brink, J. Opt. Soc. Am. 42, 617 (1952).
    [CrossRef] [PubMed]
  18. J. C. R. Licklider, “Basic Correlates of the Auditory Stimulus” in Handbook of Experimental Psychology, edited by S. S. Stevens (John Wiley & Sons, Inc., New York, 1951).
  19. S. Hecht, S. Shalaer, and M. H. Pirenne, J. Gen. Physiol. 25, 819 (1942).
  20. C. H. Graham, R. H. Brown, and F. A. Mote, J. Exptl. Psychol. 24, 555 (1939).
    [CrossRef]
  21. C. H. Graham and R. Margaria, Am. J. Physiol. 113, 299 (1935).
  22. E. D. Adrian and R. Matthews, J. Physiol. (London) 64, 279 (1927); H. K. Hartline, J. Cell. Comp. Physiol. 5, 222 (1934).
    [CrossRef]
  23. D. B. Judd, Am. J. Psychol. 38, 507 (1927).
    [CrossRef]
  24. R. Dittler and J. Eisenmeier, Arch. ges. Physiol. Pflüger’s 126, 610 (1909).
    [CrossRef]
  25. S. H. Bartley, J. Exptl. Psychol. 30, 125 (1942).
    [CrossRef]
  26. S. H. Bartley, J. Psychol.,  35, 299 (1953).
    [CrossRef]

1960 (1)

1957 (1)

1954 (1)

G. Collier, J. Exptl. Psychol. 47, 75 (1954).
[CrossRef]

1953 (2)

R. G. Roush and E. T. Urbanski, Electronics 26, 154 (1953).

S. H. Bartley, J. Psychol.,  35, 299 (1953).
[CrossRef]

1952 (1)

1951 (1)

L. A. Riggs and F. A. Ratliff, Science 114, 17 (1951).
[CrossRef] [PubMed]

1950 (1)

R. C. Casperson and H. Schlosberg, J. Exptl. Psychol. 40, 81 (1950).
[CrossRef]

1943 (1)

M. H. Pirenne, Nature 152, 698 (1943).
[CrossRef]

1942 (2)

S. H. Bartley, J. Exptl. Psychol. 30, 125 (1942).
[CrossRef]

S. Hecht, S. Shalaer, and M. H. Pirenne, J. Gen. Physiol. 25, 819 (1942).

1939 (1)

C. H. Graham, R. H. Brown, and F. A. Mote, J. Exptl. Psychol. 24, 555 (1939).
[CrossRef]

1935 (1)

C. H. Graham and R. Margaria, Am. J. Physiol. 113, 299 (1935).

1927 (2)

E. D. Adrian and R. Matthews, J. Physiol. (London) 64, 279 (1927); H. K. Hartline, J. Cell. Comp. Physiol. 5, 222 (1934).
[CrossRef]

D. B. Judd, Am. J. Psychol. 38, 507 (1927).
[CrossRef]

1909 (1)

R. Dittler and J. Eisenmeier, Arch. ges. Physiol. Pflüger’s 126, 610 (1909).
[CrossRef]

1903 (1)

H. Piper, Z. f. Psychol. u. Physiol. D. Sinnesorg. 31, 161 (1903); W. Lohmann, Arch. Augenheilk 74, 110 (1915); W. DeW. Abney and W. Watson, Phil. Trans. Roy. Soc. London A216, 91 (1916); E. Muller, Arch. ges. Physiol. Pflüger’s 193, 427 (1921); D. A. Laird, J. Exptl. Psychol. 7, 276 (1924); C. H. Graham, J. Gen. Psychol. 3, 494 (1930) J. Gen. Psychol. 5, 311 (1931); C. B. Hewson, “An Experimental Study of ‘Binocular Stimulus Summation,’” unpublished Master’s thesis, University of Virginia (1931); T. W. Cook, Psychol. Monogr. 45, No. 3 (1934); D. Shaad, J. Exptl. Psychol. 18, 391 (1935); R. J. Lythgoe and L. R. Phillips, J. Physiol. London 91, 427 (1938); N. R. Bartlett and R. M. Gagne, J. Exptl. Psychol. 25, 91 (1939); W. J. Crozier and A. H. Holway, J. Gen. Physiol. 23, 101 (1939); B. H. Crawford, Proc. Roy. Soc. (London) B128, 552 (1940); L. M. Forbes and F. A. Mote, J. Comp. and Physiol. Psychol. 49, 431 (1956).
[CrossRef]

Adrian, E. D.

E. D. Adrian and R. Matthews, J. Physiol. (London) 64, 279 (1927); H. K. Hartline, J. Cell. Comp. Physiol. 5, 222 (1934).
[CrossRef]

Bartley, S. H.

S. H. Bartley, J. Psychol.,  35, 299 (1953).
[CrossRef]

S. H. Bartley, J. Exptl. Psychol. 30, 125 (1942).
[CrossRef]

Bouman, M. A.

Brown, R. H.

C. H. Graham, R. H. Brown, and F. A. Mote, J. Exptl. Psychol. 24, 555 (1939).
[CrossRef]

Buchmann-Olsen, B.

Casperson, R. C.

R. C. Casperson and H. Schlosberg, J. Exptl. Psychol. 40, 81 (1950).
[CrossRef]

Collier, G.

G. Collier, J. Exptl. Psychol. 47, 75 (1954).
[CrossRef]

Cornsweet, T. N.

Dittler, R.

R. Dittler and J. Eisenmeier, Arch. ges. Physiol. Pflüger’s 126, 610 (1909).
[CrossRef]

Eisenmeier, J.

R. Dittler and J. Eisenmeier, Arch. ges. Physiol. Pflüger’s 126, 610 (1909).
[CrossRef]

Graham, C. H.

C. H. Graham, R. H. Brown, and F. A. Mote, J. Exptl. Psychol. 24, 555 (1939).
[CrossRef]

C. H. Graham and R. Margaria, Am. J. Physiol. 113, 299 (1935).

Hecht, S.

S. Hecht, S. Shalaer, and M. H. Pirenne, J. Gen. Physiol. 25, 819 (1942).

Judd, D. B.

D. B. Judd, Am. J. Psychol. 38, 507 (1927).
[CrossRef]

Kendall, M. G.

Values of χ2 were computed for each experiment with P′(B) as the theoretical value and P(B) at the different values of ITI as the observed values. They were significant in each experiment beyond the .0001 level of confidence. Since P′(B) is an efficient estimate of its population value and since sufficiently large numbers of measurements were taken the use of P′(B) as a population estimate is reasonable: cf., G. U. Yule and M. G. Kendall, Theory of Statistics (Charles Griffin and Company, London, 1940), p. 428.

Krauskopf, J.

Licklider, J. C. R.

J. C. R. Licklider, “Basic Correlates of the Auditory Stimulus” in Handbook of Experimental Psychology, edited by S. S. Stevens (John Wiley & Sons, Inc., New York, 1951).

Margaria, R.

C. H. Graham and R. Margaria, Am. J. Physiol. 113, 299 (1935).

Marriott, F. H. C.

M. H. Pirenne and F. H. C. Marriott, The Quantum Theory of Light and the Psycho-Physiology of Vision in Psychology: A Study of a Science, edited by S. Koch (McGraw-Hill Book Company, Inc., New York, 1959), Study 1, Vol. I.

Matin, L.

L. Matin, “Corresponding Points, Correlated Measurements, and Binocular Summation” (to be published).

Matthews, R.

E. D. Adrian and R. Matthews, J. Physiol. (London) 64, 279 (1927); H. K. Hartline, J. Cell. Comp. Physiol. 5, 222 (1934).
[CrossRef]

Mote, F. A.

C. H. Graham, R. H. Brown, and F. A. Mote, J. Exptl. Psychol. 24, 555 (1939).
[CrossRef]

Ogle, K. H.

K. H. Ogle, Researches in Binocular Vision (W. B. Saunders Company, Philadelphia, 1950).

Piper, H.

H. Piper, Z. f. Psychol. u. Physiol. D. Sinnesorg. 31, 161 (1903); W. Lohmann, Arch. Augenheilk 74, 110 (1915); W. DeW. Abney and W. Watson, Phil. Trans. Roy. Soc. London A216, 91 (1916); E. Muller, Arch. ges. Physiol. Pflüger’s 193, 427 (1921); D. A. Laird, J. Exptl. Psychol. 7, 276 (1924); C. H. Graham, J. Gen. Psychol. 3, 494 (1930) J. Gen. Psychol. 5, 311 (1931); C. B. Hewson, “An Experimental Study of ‘Binocular Stimulus Summation,’” unpublished Master’s thesis, University of Virginia (1931); T. W. Cook, Psychol. Monogr. 45, No. 3 (1934); D. Shaad, J. Exptl. Psychol. 18, 391 (1935); R. J. Lythgoe and L. R. Phillips, J. Physiol. London 91, 427 (1938); N. R. Bartlett and R. M. Gagne, J. Exptl. Psychol. 25, 91 (1939); W. J. Crozier and A. H. Holway, J. Gen. Physiol. 23, 101 (1939); B. H. Crawford, Proc. Roy. Soc. (London) B128, 552 (1940); L. M. Forbes and F. A. Mote, J. Comp. and Physiol. Psychol. 49, 431 (1956).
[CrossRef]

Pirenne, M. H.

M. H. Pirenne, Nature 152, 698 (1943).
[CrossRef]

S. Hecht, S. Shalaer, and M. H. Pirenne, J. Gen. Physiol. 25, 819 (1942).

M. H. Pirenne and F. H. C. Marriott, The Quantum Theory of Light and the Psycho-Physiology of Vision in Psychology: A Study of a Science, edited by S. Koch (McGraw-Hill Book Company, Inc., New York, 1959), Study 1, Vol. I.

Ratliff, F. A.

L. A. Riggs and F. A. Ratliff, Science 114, 17 (1951).
[CrossRef] [PubMed]

Riggs, L. A.

Rosenfalck, A. M.

Roush, R. G.

R. G. Roush and E. T. Urbanski, Electronics 26, 154 (1953).

Schlosberg, H.

R. C. Casperson and H. Schlosberg, J. Exptl. Psychol. 40, 81 (1950).
[CrossRef]

Shalaer, S.

S. Hecht, S. Shalaer, and M. H. Pirenne, J. Gen. Physiol. 25, 819 (1942).

Urbanski, E. T.

R. G. Roush and E. T. Urbanski, Electronics 26, 154 (1953).

Van den Brink, G.

Yule, G. U.

Values of χ2 were computed for each experiment with P′(B) as the theoretical value and P(B) at the different values of ITI as the observed values. They were significant in each experiment beyond the .0001 level of confidence. Since P′(B) is an efficient estimate of its population value and since sufficiently large numbers of measurements were taken the use of P′(B) as a population estimate is reasonable: cf., G. U. Yule and M. G. Kendall, Theory of Statistics (Charles Griffin and Company, London, 1940), p. 428.

Am. J. Physiol. (1)

C. H. Graham and R. Margaria, Am. J. Physiol. 113, 299 (1935).

Am. J. Psychol. (1)

D. B. Judd, Am. J. Psychol. 38, 507 (1927).
[CrossRef]

Arch. ges. Physiol. Pflüger’s (1)

R. Dittler and J. Eisenmeier, Arch. ges. Physiol. Pflüger’s 126, 610 (1909).
[CrossRef]

Electronics (1)

R. G. Roush and E. T. Urbanski, Electronics 26, 154 (1953).

J. Exptl. Psychol. (4)

R. C. Casperson and H. Schlosberg, J. Exptl. Psychol. 40, 81 (1950).
[CrossRef]

G. Collier, J. Exptl. Psychol. 47, 75 (1954).
[CrossRef]

S. H. Bartley, J. Exptl. Psychol. 30, 125 (1942).
[CrossRef]

C. H. Graham, R. H. Brown, and F. A. Mote, J. Exptl. Psychol. 24, 555 (1939).
[CrossRef]

J. Gen. Physiol. (1)

S. Hecht, S. Shalaer, and M. H. Pirenne, J. Gen. Physiol. 25, 819 (1942).

J. Opt. Soc. Am. (3)

J. Physiol. (London) (1)

E. D. Adrian and R. Matthews, J. Physiol. (London) 64, 279 (1927); H. K. Hartline, J. Cell. Comp. Physiol. 5, 222 (1934).
[CrossRef]

J. Psychol. (1)

S. H. Bartley, J. Psychol.,  35, 299 (1953).
[CrossRef]

Nature (1)

M. H. Pirenne, Nature 152, 698 (1943).
[CrossRef]

Science (1)

L. A. Riggs and F. A. Ratliff, Science 114, 17 (1951).
[CrossRef] [PubMed]

Z. f. Psychol. u. Physiol. D. Sinnesorg. (1)

H. Piper, Z. f. Psychol. u. Physiol. D. Sinnesorg. 31, 161 (1903); W. Lohmann, Arch. Augenheilk 74, 110 (1915); W. DeW. Abney and W. Watson, Phil. Trans. Roy. Soc. London A216, 91 (1916); E. Muller, Arch. ges. Physiol. Pflüger’s 193, 427 (1921); D. A. Laird, J. Exptl. Psychol. 7, 276 (1924); C. H. Graham, J. Gen. Psychol. 3, 494 (1930) J. Gen. Psychol. 5, 311 (1931); C. B. Hewson, “An Experimental Study of ‘Binocular Stimulus Summation,’” unpublished Master’s thesis, University of Virginia (1931); T. W. Cook, Psychol. Monogr. 45, No. 3 (1934); D. Shaad, J. Exptl. Psychol. 18, 391 (1935); R. J. Lythgoe and L. R. Phillips, J. Physiol. London 91, 427 (1938); N. R. Bartlett and R. M. Gagne, J. Exptl. Psychol. 25, 91 (1939); W. J. Crozier and A. H. Holway, J. Gen. Physiol. 23, 101 (1939); B. H. Crawford, Proc. Roy. Soc. (London) B128, 552 (1940); L. M. Forbes and F. A. Mote, J. Comp. and Physiol. Psychol. 49, 431 (1956).
[CrossRef]

Other (9)

In any system we may talk about Y as the largest barrier between input and output if the following holds: (1) there are signals from the input which reach Y but do not go beyond Y; (2) any signal which does go beyond Y reaches the output. Of course, it should be recognized that the location of the largest barrier may be itself a stochastic variable for fixed conditions of stimulation, or vary as a function of conditions of stimulation. With regard to the latter possibility see reference 7.

M. H. Pirenne and F. H. C. Marriott, The Quantum Theory of Light and the Psycho-Physiology of Vision in Psychology: A Study of a Science, edited by S. Koch (McGraw-Hill Book Company, Inc., New York, 1959), Study 1, Vol. I.

Statistical time lag of the glow modulator tube was reduced to negligible values (i.e., less than 2 µ sec) by continuously irradiating its cathode with ultraviolet radiation derived from a General Electric argon glow lamp AR-3 (U, Fig. 2; see also Fig. 1) whose output was filtered by Corning filter 5860 (T, Fig. 2) so as to pass only wavelengths below 390 mμ. A Kodak No. 4 filter (D, Fig. 2) plus the high-flint component of achromatic lenses B and G prevented the ultraviolet from reaching the subject’s eye.

K. H. Ogle, Researches in Binocular Vision (W. B. Saunders Company, Philadelphia, 1950).

We have called this effect “Binocular Flash Diplopia.” A detailed study of the phenomenon will be reported elsewhere.

For subject 1, this resulted in an intertrial interval which could range from 20 to 40 sec; for subject 2 the intertrial interval could range from 10 to 30 sec. The actual range for all responses, however, was 25 to 35 sec for subject 1 and 15 to 25 sec for subject 2.

Values of χ2 were computed for each experiment with P′(B) as the theoretical value and P(B) at the different values of ITI as the observed values. They were significant in each experiment beyond the .0001 level of confidence. Since P′(B) is an efficient estimate of its population value and since sufficiently large numbers of measurements were taken the use of P′(B) as a population estimate is reasonable: cf., G. U. Yule and M. G. Kendall, Theory of Statistics (Charles Griffin and Company, London, 1940), p. 428.

J. C. R. Licklider, “Basic Correlates of the Auditory Stimulus” in Handbook of Experimental Psychology, edited by S. S. Stevens (John Wiley & Sons, Inc., New York, 1951).

L. Matin, “Corresponding Points, Correlated Measurements, and Binocular Summation” (to be published).

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Figures (6)

Fig. 1
Fig. 1

Photograph of optical unit. See text for description.

Fig. 2
Fig. 2

Side view of optical system for one eye. A, Sylvania glow modulator tube, R1131C; B, condensing lens; C, crossed polaroids; D, neutral-density filters; E, field stop; F, beamsplitter; G, field lens; H, artificial pupil; J, 6-V pilot light bulb; K, diffusing glass; L, fixation target; M,N, lenses; O, microscope cover glass; P, photomultiplier 931A; Q, lens; R, filter; U, AR-3 ultraviolet source; T, Corning filter 5860.

Fig. 3
Fig. 3

Fixation targets: (a) for left eye; (b) for right eye; (c) binocular view as seen by subject.

Fig. 4
Fig. 4

Stimulus sequence on a single trial; symbols are defined in text.

Fig. 5
Fig. 5

Binocular probability of seeing P(B) as a function of interstimulus temporal interval, ITI; monocular probabilities of seeing, P(R) and P(L) are also shown at R and L, respectively. P′(B) was obtained in each case from Eq. (2).

Fig. 6
Fig. 6

Probability of reporting “multiple flashes” and “delayed flashes.” Results are for subject 2. L2 is for left eye with X=291 msec.

Tables (1)

Tables Icon

Table I Values of P(L) and P(B) in experiments B and C at indicated values of X(=ITI+15 msec).

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

P ( B ) = P ( B ) ,
P ( B ) P ( R ) + P ( L ) - P ( R ) · P ( L ) ,
P ( B ) P ( R ) + P ( L ) - P ( R ) · P R ( L ) P ( B ) - r R , L σ R σ L ,
P ( B ) P ( B ) - σ R σ L r R , L ( ITI )
P IV ( B ) P ( B ) - σ R σ L [ r R , L + r R , L ( ITI ) ] .