Abstract

It is shown that the absorption of one quantum can excite a rod in the human retina, but that at least two, and probably many more, excited rods are needed to give a sensation of light. It is suggested that noise in the optic pathway limits its sensitivity, and this idea is subjected to an experimental test. The hypothesis is then formulated quantitatively, and shown to be able to account for the above experiment, and also the disagreement in the literature between those who believe that the absorption of two quanta can cause a sensation, and those who believe that 5 or more are required. The formulation of the hypothesis is used to calculate the maximum allowable noise (expressed as a number x of random, independent events confusable with the absorption of a quantum of light) in the optic pathway for the absorption of various fractions of the total number of quanta incident at the cornea.

© 1956 Optical Society of America

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References

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  1. E. J. Denton and J. H. Wyllie, J. Physiol. 127, 81–89 (1955).
  2. W. A. Hagins and W. A. H. Rushton, J. Physiol. 120, 61P (1953).
  3. W. A. H. Rushton, the density of rhodopsin in a human rod is about 0.12; personal communication (1955).
  4. F. D. Collins and R. A. Morton, Biochem J. 47, 3–24 (1950).
  5. Wald, Durell, and St. George, Science 111, 179–181 (1950).
    [Crossref] [PubMed]
  6. W. A. Hagins, J. Physiol. 128, 22–23P (1955).
  7. (a)H. L. de Vries, Physica 10, 553–564 (1943). (b)M. H. Pirenne, “Quantum physics of vision: theoretical discussion,” in Progress in Biophysics, edited by J. A. V. Butler and J. T. Randall (Pergamon Press, 1951, London), Vol. 2, pp. 193–223.
  8. R. A. Weale, Physiol. Rev. 35, 233–246 (1955).
    [PubMed]
  9. F. Crescitelli and H. J. A. Dartnall, Nature 172, 195–197 (1953).
    [Crossref] [PubMed]
  10. F. W. Campbell and W. A. H. Rushton, J. Physiol. 130, 131–147 (1955).
  11. Granit, Holmberg, and Zewi, J. Physiol. 94, 430–440 (1938).
  12. M. H. Pirenne and F. H. C. Marriott, J. Opt. Soc. Am. 45, 909–912 (1955).
    [Crossref] [PubMed]
  13. Hecht, Shlaer, and Pirenne, J. Gen. Physiol. 25, 819–840 (1942).
  14. H. A. van der Velden, Physica 11, 179–189 (1944); Ophthalmologica 111, 321–331 (1946).
    [Crossref]
  15. M. A. Bouman and H. A. van der Velden, J. Opt. Soc. Am. 37, 908–919 (1947).
    [PubMed]
  16. E. J. Denton and M. H. Pirenne, J. Physiol. 123, 417–442 (1954).
  17. H. B. Barlow, J. Physiol. 119, 69–87 (1953).
  18. G. S. Brindley, Proc. Phys. Soc. (London) B67, 673–676 (1954).
  19. (a)S. Hecht, “Energy and vision,” in Science in Progress, (Yale University Press, New Haven, 1945), Ser. 4, pp. 75–97. (b)M. H. Pirenne, Biol. Revs. Cambridge Phil Soc. (to be published).
    [Crossref] [PubMed]
  20. A. Rose, J. Opt. Soc. Am. 38, 196–208 (1948).
  21. R. L. Gregory and V. Cane, Nature (to be published).
  22. W. P. Tanner and J. A. Swets, “Human use of information. I. Signal detection for the case of the signal known exactly,” Trans. Inst. Radio Engrs. PGIT 4, pp. 213–221 (1954).
    [Crossref]
  23. R. Granit, Acta Physiol. Scand. 1, 370–379 (1941).
  24. Barlow, FitzHugh, and Kuffler, J. Physiol. 125, 28–29P (1954).
  25. Barlow, FitzHugh, and Kuffler (to be published).
  26. E. C. Molina, Poisson’s Exponential Binomial Limit (D. Van Nostrand Company, Inc., New York, 1942).
  27. C. H. Graham and R. Margaria, Am. J. Physiol. 113, 299–305 (1935).
  28. R. J. Lythgoe and J. P. Quilliam, J. Physiol. 93, 24–38 (1938).

1955 (5)

E. J. Denton and J. H. Wyllie, J. Physiol. 127, 81–89 (1955).

W. A. Hagins, J. Physiol. 128, 22–23P (1955).

R. A. Weale, Physiol. Rev. 35, 233–246 (1955).
[PubMed]

F. W. Campbell and W. A. H. Rushton, J. Physiol. 130, 131–147 (1955).

M. H. Pirenne and F. H. C. Marriott, J. Opt. Soc. Am. 45, 909–912 (1955).
[Crossref] [PubMed]

1954 (4)

E. J. Denton and M. H. Pirenne, J. Physiol. 123, 417–442 (1954).

G. S. Brindley, Proc. Phys. Soc. (London) B67, 673–676 (1954).

W. P. Tanner and J. A. Swets, “Human use of information. I. Signal detection for the case of the signal known exactly,” Trans. Inst. Radio Engrs. PGIT 4, pp. 213–221 (1954).
[Crossref]

Barlow, FitzHugh, and Kuffler, J. Physiol. 125, 28–29P (1954).

1953 (3)

H. B. Barlow, J. Physiol. 119, 69–87 (1953).

F. Crescitelli and H. J. A. Dartnall, Nature 172, 195–197 (1953).
[Crossref] [PubMed]

W. A. Hagins and W. A. H. Rushton, J. Physiol. 120, 61P (1953).

1950 (2)

F. D. Collins and R. A. Morton, Biochem J. 47, 3–24 (1950).

Wald, Durell, and St. George, Science 111, 179–181 (1950).
[Crossref] [PubMed]

1948 (1)

1947 (1)

1944 (1)

H. A. van der Velden, Physica 11, 179–189 (1944); Ophthalmologica 111, 321–331 (1946).
[Crossref]

1943 (1)

(a)H. L. de Vries, Physica 10, 553–564 (1943). (b)M. H. Pirenne, “Quantum physics of vision: theoretical discussion,” in Progress in Biophysics, edited by J. A. V. Butler and J. T. Randall (Pergamon Press, 1951, London), Vol. 2, pp. 193–223.

1942 (1)

Hecht, Shlaer, and Pirenne, J. Gen. Physiol. 25, 819–840 (1942).

1941 (1)

R. Granit, Acta Physiol. Scand. 1, 370–379 (1941).

1938 (2)

R. J. Lythgoe and J. P. Quilliam, J. Physiol. 93, 24–38 (1938).

Granit, Holmberg, and Zewi, J. Physiol. 94, 430–440 (1938).

1935 (1)

C. H. Graham and R. Margaria, Am. J. Physiol. 113, 299–305 (1935).

Barlow,

Barlow, FitzHugh, and Kuffler, J. Physiol. 125, 28–29P (1954).

Barlow, FitzHugh, and Kuffler (to be published).

Barlow, H. B.

H. B. Barlow, J. Physiol. 119, 69–87 (1953).

Bouman, M. A.

Brindley, G. S.

G. S. Brindley, Proc. Phys. Soc. (London) B67, 673–676 (1954).

Campbell, F. W.

F. W. Campbell and W. A. H. Rushton, J. Physiol. 130, 131–147 (1955).

Cane, V.

R. L. Gregory and V. Cane, Nature (to be published).

Collins, F. D.

F. D. Collins and R. A. Morton, Biochem J. 47, 3–24 (1950).

Crescitelli, F.

F. Crescitelli and H. J. A. Dartnall, Nature 172, 195–197 (1953).
[Crossref] [PubMed]

Dartnall, H. J. A.

F. Crescitelli and H. J. A. Dartnall, Nature 172, 195–197 (1953).
[Crossref] [PubMed]

de Vries, H. L.

(a)H. L. de Vries, Physica 10, 553–564 (1943). (b)M. H. Pirenne, “Quantum physics of vision: theoretical discussion,” in Progress in Biophysics, edited by J. A. V. Butler and J. T. Randall (Pergamon Press, 1951, London), Vol. 2, pp. 193–223.

Denton, E. J.

E. J. Denton and J. H. Wyllie, J. Physiol. 127, 81–89 (1955).

E. J. Denton and M. H. Pirenne, J. Physiol. 123, 417–442 (1954).

Durell,

Wald, Durell, and St. George, Science 111, 179–181 (1950).
[Crossref] [PubMed]

FitzHugh,

Barlow, FitzHugh, and Kuffler, J. Physiol. 125, 28–29P (1954).

Barlow, FitzHugh, and Kuffler (to be published).

Graham, C. H.

C. H. Graham and R. Margaria, Am. J. Physiol. 113, 299–305 (1935).

Granit,

Granit, Holmberg, and Zewi, J. Physiol. 94, 430–440 (1938).

Granit, R.

R. Granit, Acta Physiol. Scand. 1, 370–379 (1941).

Gregory, R. L.

R. L. Gregory and V. Cane, Nature (to be published).

Hagins, W. A.

W. A. Hagins, J. Physiol. 128, 22–23P (1955).

W. A. Hagins and W. A. H. Rushton, J. Physiol. 120, 61P (1953).

Hecht,

Hecht, Shlaer, and Pirenne, J. Gen. Physiol. 25, 819–840 (1942).

Hecht, S.

(a)S. Hecht, “Energy and vision,” in Science in Progress, (Yale University Press, New Haven, 1945), Ser. 4, pp. 75–97. (b)M. H. Pirenne, Biol. Revs. Cambridge Phil Soc. (to be published).
[Crossref] [PubMed]

Holmberg,

Granit, Holmberg, and Zewi, J. Physiol. 94, 430–440 (1938).

Kuffler,

Barlow, FitzHugh, and Kuffler, J. Physiol. 125, 28–29P (1954).

Barlow, FitzHugh, and Kuffler (to be published).

Lythgoe, R. J.

R. J. Lythgoe and J. P. Quilliam, J. Physiol. 93, 24–38 (1938).

Margaria, R.

C. H. Graham and R. Margaria, Am. J. Physiol. 113, 299–305 (1935).

Marriott, F. H. C.

Molina, E. C.

E. C. Molina, Poisson’s Exponential Binomial Limit (D. Van Nostrand Company, Inc., New York, 1942).

Morton, R. A.

F. D. Collins and R. A. Morton, Biochem J. 47, 3–24 (1950).

Pirenne,

Hecht, Shlaer, and Pirenne, J. Gen. Physiol. 25, 819–840 (1942).

Pirenne, M. H.

M. H. Pirenne and F. H. C. Marriott, J. Opt. Soc. Am. 45, 909–912 (1955).
[Crossref] [PubMed]

E. J. Denton and M. H. Pirenne, J. Physiol. 123, 417–442 (1954).

Quilliam, J. P.

R. J. Lythgoe and J. P. Quilliam, J. Physiol. 93, 24–38 (1938).

Rose, A.

Rushton, W. A. H.

F. W. Campbell and W. A. H. Rushton, J. Physiol. 130, 131–147 (1955).

W. A. Hagins and W. A. H. Rushton, J. Physiol. 120, 61P (1953).

W. A. H. Rushton, the density of rhodopsin in a human rod is about 0.12; personal communication (1955).

Shlaer,

Hecht, Shlaer, and Pirenne, J. Gen. Physiol. 25, 819–840 (1942).

St. George,

Wald, Durell, and St. George, Science 111, 179–181 (1950).
[Crossref] [PubMed]

Swets, J. A.

W. P. Tanner and J. A. Swets, “Human use of information. I. Signal detection for the case of the signal known exactly,” Trans. Inst. Radio Engrs. PGIT 4, pp. 213–221 (1954).
[Crossref]

Tanner, W. P.

W. P. Tanner and J. A. Swets, “Human use of information. I. Signal detection for the case of the signal known exactly,” Trans. Inst. Radio Engrs. PGIT 4, pp. 213–221 (1954).
[Crossref]

van der Velden, H. A.

M. A. Bouman and H. A. van der Velden, J. Opt. Soc. Am. 37, 908–919 (1947).
[PubMed]

H. A. van der Velden, Physica 11, 179–189 (1944); Ophthalmologica 111, 321–331 (1946).
[Crossref]

Wald,

Wald, Durell, and St. George, Science 111, 179–181 (1950).
[Crossref] [PubMed]

Weale, R. A.

R. A. Weale, Physiol. Rev. 35, 233–246 (1955).
[PubMed]

Wyllie, J. H.

E. J. Denton and J. H. Wyllie, J. Physiol. 127, 81–89 (1955).

Zewi,

Granit, Holmberg, and Zewi, J. Physiol. 94, 430–440 (1938).

Acta Physiol. Scand. (1)

R. Granit, Acta Physiol. Scand. 1, 370–379 (1941).

Am. J. Physiol. (1)

C. H. Graham and R. Margaria, Am. J. Physiol. 113, 299–305 (1935).

Biochem J. (1)

F. D. Collins and R. A. Morton, Biochem J. 47, 3–24 (1950).

J. Gen. Physiol. (1)

Hecht, Shlaer, and Pirenne, J. Gen. Physiol. 25, 819–840 (1942).

J. Opt. Soc. Am. (3)

J. Physiol. (9)

R. J. Lythgoe and J. P. Quilliam, J. Physiol. 93, 24–38 (1938).

Barlow, FitzHugh, and Kuffler, J. Physiol. 125, 28–29P (1954).

E. J. Denton and M. H. Pirenne, J. Physiol. 123, 417–442 (1954).

H. B. Barlow, J. Physiol. 119, 69–87 (1953).

E. J. Denton and J. H. Wyllie, J. Physiol. 127, 81–89 (1955).

W. A. Hagins and W. A. H. Rushton, J. Physiol. 120, 61P (1953).

W. A. Hagins, J. Physiol. 128, 22–23P (1955).

F. W. Campbell and W. A. H. Rushton, J. Physiol. 130, 131–147 (1955).

Granit, Holmberg, and Zewi, J. Physiol. 94, 430–440 (1938).

Nature (1)

F. Crescitelli and H. J. A. Dartnall, Nature 172, 195–197 (1953).
[Crossref] [PubMed]

Physica (2)

H. A. van der Velden, Physica 11, 179–189 (1944); Ophthalmologica 111, 321–331 (1946).
[Crossref]

(a)H. L. de Vries, Physica 10, 553–564 (1943). (b)M. H. Pirenne, “Quantum physics of vision: theoretical discussion,” in Progress in Biophysics, edited by J. A. V. Butler and J. T. Randall (Pergamon Press, 1951, London), Vol. 2, pp. 193–223.

Physiol. Rev. (1)

R. A. Weale, Physiol. Rev. 35, 233–246 (1955).
[PubMed]

Proc. Phys. Soc. (London) (1)

G. S. Brindley, Proc. Phys. Soc. (London) B67, 673–676 (1954).

Science (1)

Wald, Durell, and St. George, Science 111, 179–181 (1950).
[Crossref] [PubMed]

Trans. Inst. Radio Engrs. PGIT 4 (1)

W. P. Tanner and J. A. Swets, “Human use of information. I. Signal detection for the case of the signal known exactly,” Trans. Inst. Radio Engrs. PGIT 4, pp. 213–221 (1954).
[Crossref]

Other (5)

Barlow, FitzHugh, and Kuffler (to be published).

E. C. Molina, Poisson’s Exponential Binomial Limit (D. Van Nostrand Company, Inc., New York, 1942).

R. L. Gregory and V. Cane, Nature (to be published).

W. A. H. Rushton, the density of rhodopsin in a human rod is about 0.12; personal communication (1955).

(a)S. Hecht, “Energy and vision,” in Science in Progress, (Yale University Press, New Haven, 1945), Ser. 4, pp. 75–97. (b)M. H. Pirenne, Biol. Revs. Cambridge Phil Soc. (to be published).
[Crossref] [PubMed]

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Figures (2)

Fig. 1
Fig. 1

Frequency of “seen” (dots) and “possible or seen” (crosses) responses of one subject plotted against log (number of quanta at the cornea). Theoretical curves are from Molina’s tabulation of Eq. (1) with a=n+x=0.13N+8.9 for both curves, c=19 for “seen,” c=17 for “possible or seen.”

Fig. 2
Fig. 2

Data from Hecht et al. (dots) and van der Velden (crosses) fitted by theoretical curves obtained from Molina’s tables with a=n+x=0.13N+8.9, c=21 (Hecht et al.); a=0.9N+8.9, c=15 (van der Velden).

Tables (2)

Tables Icon

Table I Best fitting parameters for fitting “possible or seen” response of Fig. 1, with upper and lower limits (see text).

Tables Icon

Table II Allowable noise levels for various fractions of quanta at the cornea exciting rods.a

Equations (5)

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

P a ( c ) = y = c a y e - a y ! .
log N = log ( a - x ) - log ( n / N )
d P a ( c ) d a = e - a a c - 1 ( c - 1 ) ! ,
d P a ( c ) d ( log N ) = d P a ( c ) d ( log n ) = d P a ( c ) d a × d a d ( log n ) = e - a a c - 1 ( c - 1 ) ! × n log e .
d P a ( c ) d ( log N ) × ( 2 π ) 1 2 log e = c - x ( c ) 1 2 .