Abstract

Threshold summation indices were determined in a study of interrelations among Stiles π mechanisms. Test wavelengths of 630, 520, 475, and 420 nm were presented upon a 555-nm adapting field. The 630–520-nm test-stimulus combination showed very small summation indices compared to the index derived on the assumption of independence of the π4 and π5 mechanisms. We suggest that π5 is not a single or unitary mechanism, but is comprised of two components, π5r and π5g, that may inhibit or cancel each other’s effects in producing the net response of mechanism π5. The hypothesis also explains fairly well the observed small index for the combination 630–475 nm at low field luminance. The mechanisms π1, π4, and the composite π5 seem to be independent, as shown by good agreement between the calculated and experimental indices at high field luminance for the combination 630–475 nm, and over the entire range of field luminance for the combination 520–475 nm. Complete summation is observed for the combination 475–420 nm at high field luminance, with which mechanism π1 should be almost exclusively involved.

© 1970 Optical Society of America

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References

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  1. M. Ikeda, J. Opt. Soc. Am. 53, 1305 (1963).
    [CrossRef] [PubMed]
  2. M. Ikeda, J. Opt. Soc. Am. 54, 89 (1964).
    [CrossRef] [PubMed]
  3. R. M. Boynton, M. Ikeda, and W. S. Stiles, Vision Res. 4, 87 (1964).
    [CrossRef] [PubMed]
  4. W. S. Stiles, Newton Lecture, J. Colour Group No. 11, 106 (1967).
  5. S. L. Guth, J. Opt. Soc. Am. 55, 718 (1965).
    [CrossRef]
  6. S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, Vision Res. 8, 913 (1968).
    [CrossRef] [PubMed]
  7. M. Alpern and W. A. H. Rushton, J. Physiol. (London) 176, 473 (1965).
  8. R. M. Boynton and S. R. Das, Science 156, 1581 (1966).
    [CrossRef]
  9. R. M. Boynton, S. R. Das, and J. Gardiner, J. Opt. Soc. Am. 56, 1775 (1966).
    [CrossRef]
  10. W. S. Stiles, Proc. Natl. Acad. Sci. (U.S.) 45, 100 (1959).
    [CrossRef]
  11. F. H. C. Marriott in The Eye, H. Davson, Ed. (J. & A. Churchill Ltd., London, 1962), Vol. 2, p. 261.
  12. G. Wyszecki and W. S. Stiles, Color Science (John Wiley & Sons, Inc., New York, 1967), p. 574.
  13. M. Ikeda and M. Urakubo, J. Opt. Soc. Am. 59, 217 (1969).
    [CrossRef] [PubMed]
  14. The characteristics of π5′ are known only in an incomplete and tentative sense. The proposed spectral sensitivity is given on p. 574 of Ref. 12.
  15. G. Wald, Science 145, 1007 (1964).
    [CrossRef]
  16. R. M. Boynton, J. Opt. Soc. Am. 53, 165 (1963).
    [CrossRef] [PubMed]

1969 (1)

1968 (1)

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, Vision Res. 8, 913 (1968).
[CrossRef] [PubMed]

1967 (1)

W. S. Stiles, Newton Lecture, J. Colour Group No. 11, 106 (1967).

1966 (2)

1965 (2)

M. Alpern and W. A. H. Rushton, J. Physiol. (London) 176, 473 (1965).

S. L. Guth, J. Opt. Soc. Am. 55, 718 (1965).
[CrossRef]

1964 (3)

M. Ikeda, J. Opt. Soc. Am. 54, 89 (1964).
[CrossRef] [PubMed]

R. M. Boynton, M. Ikeda, and W. S. Stiles, Vision Res. 4, 87 (1964).
[CrossRef] [PubMed]

G. Wald, Science 145, 1007 (1964).
[CrossRef]

1963 (2)

1959 (1)

W. S. Stiles, Proc. Natl. Acad. Sci. (U.S.) 45, 100 (1959).
[CrossRef]

Alexander, J. V.

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, Vision Res. 8, 913 (1968).
[CrossRef] [PubMed]

Alpern, M.

M. Alpern and W. A. H. Rushton, J. Physiol. (London) 176, 473 (1965).

Boynton, R. M.

R. M. Boynton and S. R. Das, Science 156, 1581 (1966).
[CrossRef]

R. M. Boynton, S. R. Das, and J. Gardiner, J. Opt. Soc. Am. 56, 1775 (1966).
[CrossRef]

R. M. Boynton, M. Ikeda, and W. S. Stiles, Vision Res. 4, 87 (1964).
[CrossRef] [PubMed]

R. M. Boynton, J. Opt. Soc. Am. 53, 165 (1963).
[CrossRef] [PubMed]

Chumbly, J. I.

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, Vision Res. 8, 913 (1968).
[CrossRef] [PubMed]

Das, S. R.

Gardiner, J.

Gillman, C. B.

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, Vision Res. 8, 913 (1968).
[CrossRef] [PubMed]

Guth, S. L.

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, Vision Res. 8, 913 (1968).
[CrossRef] [PubMed]

S. L. Guth, J. Opt. Soc. Am. 55, 718 (1965).
[CrossRef]

Ikeda, M.

Marriott, F. H. C.

F. H. C. Marriott in The Eye, H. Davson, Ed. (J. & A. Churchill Ltd., London, 1962), Vol. 2, p. 261.

Patterson, M. M.

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, Vision Res. 8, 913 (1968).
[CrossRef] [PubMed]

Rushton, W. A. H.

M. Alpern and W. A. H. Rushton, J. Physiol. (London) 176, 473 (1965).

Stiles, W. S.

W. S. Stiles, Newton Lecture, J. Colour Group No. 11, 106 (1967).

R. M. Boynton, M. Ikeda, and W. S. Stiles, Vision Res. 4, 87 (1964).
[CrossRef] [PubMed]

W. S. Stiles, Proc. Natl. Acad. Sci. (U.S.) 45, 100 (1959).
[CrossRef]

G. Wyszecki and W. S. Stiles, Color Science (John Wiley & Sons, Inc., New York, 1967), p. 574.

Urakubo, M.

Wald, G.

G. Wald, Science 145, 1007 (1964).
[CrossRef]

Wyszecki, G.

G. Wyszecki and W. S. Stiles, Color Science (John Wiley & Sons, Inc., New York, 1967), p. 574.

J. Opt. Soc. Am. (6)

J. Physiol. (London) (1)

M. Alpern and W. A. H. Rushton, J. Physiol. (London) 176, 473 (1965).

Newton Lecture (1)

W. S. Stiles, Newton Lecture, J. Colour Group No. 11, 106 (1967).

Proc. Natl. Acad. Sci. (U.S.) (1)

W. S. Stiles, Proc. Natl. Acad. Sci. (U.S.) 45, 100 (1959).
[CrossRef]

Science (2)

G. Wald, Science 145, 1007 (1964).
[CrossRef]

R. M. Boynton and S. R. Das, Science 156, 1581 (1966).
[CrossRef]

Vision Res. (2)

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, Vision Res. 8, 913 (1968).
[CrossRef] [PubMed]

R. M. Boynton, M. Ikeda, and W. S. Stiles, Vision Res. 4, 87 (1964).
[CrossRef] [PubMed]

Other (3)

F. H. C. Marriott in The Eye, H. Davson, Ed. (J. & A. Churchill Ltd., London, 1962), Vol. 2, p. 261.

G. Wyszecki and W. S. Stiles, Color Science (John Wiley & Sons, Inc., New York, 1967), p. 574.

The characteristics of π5′ are known only in an incomplete and tentative sense. The proposed spectral sensitivity is given on p. 574 of Ref. 12.

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Figures (11)

Fig. 1
Fig. 1

Threshold-vs-radiance curves for two test wavelengths, (a) λ = 630 nm and (b) λ = 475 nm, with field wavelength μ = 555 nm, according to the Stiles theory. Units are arbitrary.

Fig. 2
Fig. 2

Resultant probability-of-seeing curve (solid) from underlying probability-of-seeing curves (dotted) of mechanisms, based upon probability summation. See text for notations.

Fig. 3
Fig. 3

Resultant probability-of-seeing curve (solid) from two superimposed probability-of-seeing curves (dotted), based upon probability summation.

Fig. 4
Fig. 4

Calculated summation index (thick solid curve) for the case of λ1 = 630, λ2 = 475, and μ = 555 nm from subject MI. Dotted curves: responses of underlying mechanisms when they are stimulated with test stimuli shown on curves. Thin solid curves: responses after linear summation takes place within the individual mechanisms.

Fig. 5
Fig. 5

Most-sensitive π mechanisms for various test wavelengths at various field radiances of μ = 555 nm, according to the Stiles theory.

Fig. 6
Fig. 6

Tvr curves for test wavelength 630 nm (circles), 520 nm (triangles), and 475 nm (squares) with field wavelength 555 nm. Abscissa is logarithm of trolands. Subject TU.

Fig. 7
Fig. 7

Summation index σ0 for three test-wavelength combinations, (a) 630–520 nm, (b) 630–475 nm, (c) 520–475 nm with field wavelength 555 nm. Circles: experimental σ0′. Solid curves: calculated σ0. Dotted curves: responses of π1, π4, and π5 after linear summation. Subject TU.

Fig. 8
Fig. 8

Summation index σ0. Small circles are from earlier work. Other notations are the same as in Fig. 7. Subject MI.

Fig. 9
Fig. 9

Calculated summation index σ0 for (a) 630–520-nm, (b) 630–475-nm combination. Solid curves: simple probability summation. Dashed: π5rπ5g inhibitory relation. Dotted: π5rπ5g canceling relation. Hatched: π5rπ5g canceling relation but with increased ω5. Circles: experimental σ0′. Subject TU.

Fig. 10
Fig. 10

Calculated summation index σ0. Notations are same as Fig. 9. Subject MI.

Fig. 11
Fig. 11

(a) Tvr curves for test wavelength 475 (squares) and 420 nm (circles) with field wavelength 555 nm. (b) Summation index σ0 for 475–420-nm combination. Notations are same as Fig. 7. Subject MI.

Equations (38)

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p = 1 - ( 1 - p π 1 ) ( 1 - p π 2 ) ( 1 - p π 3 ) ( 1 - p π 4 ) ( 1 - p π 5 ) .
p = 1 - ( 1 - p π 5 ) ( 1 - p π 1 ) .
p = 1 - ( 1 - p π 5 ) 2 = 1 - ( 1 - p π 1 ) 2 .
S 11 = T R 1 / T 11 , S 41 = T R 1 / T 41 , S 51 = T R 1 / T 51 ,
S 12 = T R 2 / T 12 , S 42 = T R 2 / T 42 , S 52 = T R 2 / T 52 .
T 1 ρ 1 of λ 1 and T 1 ρ 2 = ρ T 1 ρ 1 of λ 2 when only π 1 is in action , T 4 ρ 1 of λ 1 and T 4 ρ 2 = ρ T 4 ρ 1 of λ 2 when only π 4 is in action , T 5 ρ 1 of λ 1 and T 5 ρ 2 = ρ T 5 ρ 1 of λ 2 when only π 5 is in action , and T R ρ 1 of λ 1 and T R ρ 2 = ρ T R ρ 1 of λ 2 when all three mechanisms are in action together .
Σ 1 = T R ρ 1 T 11 + T R ρ 2 T 12 = T R ρ 1 ( 1 T 11 + ρ T 12 ) ,
Σ 4 = T R ρ 1 T 41 + T R ρ 2 T 42 = T R ρ 1 ( 1 T 41 + ρ T 42 ) ,
Σ 5 = T R ρ 1 T 51 + T R ρ 2 T 52 = T R ρ 1 ( 1 T 51 + ρ T 52 ) ,
T R ρ 1 / T R 1 = S ρ 1 , T R ρ 2 / T R 2 = S ρ 2 ,
σ = 0.3 - log ( S ρ 1 + S ρ 2 ) .
σ = 0.3 - log ( T R ρ 1 / T R 1 + T R ρ 2 / T R 2 ) .
T R ρ 1 / T R 1 = T R ρ 2 / T R 2 ,
ρ ρ 0 = T R ρ 2 / T R ρ 1 = T R 2 / T R 1 .
σ σ 0 = log ( T R 1 / T R ρ 1 ) = log ( T R 2 / T R ρ 2 ) .
σ σ 0 = log ( T R 1 / T R ρ 1 ) = log ( T R 2 / T R ρ 2 ) .
Σ 1 = ( T R ρ 1 T R 1 ) ( T R 1 T 11 + T R 2 T 1 )
σ 0 = - log Σ 1 + log ( T R 1 T 11 + T R 2 T 12 ) = - log Σ 1 + log ( S 11 + S 12 ) ,
σ 0 = - log Σ 4 + log ( T R 1 T 41 + T R 2 T 42 ) = - log Σ 4 + log ( S 41 + S 42 ) ,
σ 0 = - log Σ 5 + log ( T R 1 T 51 + T R 2 T 52 ) = - log Σ 5 + log ( S 51 + S 52 ) .
σ 0 = log ( S 41 + S 42 ) ,
Σ 4 = 1.
Σ 1 = Σ 5 = 0.
T R ρ 1 [ ( 1 / T 41 ) + ( ρ / T 42 ) ] = 1.
T 11 = T 12 = T 51 = T 52 = .
S 11 = S 12 = S 51 = S 52 = 0 ,
T R 1 / T 41 = T R 2 / T 42 = 1.
σ 0 = 0 + log 2 = 0.30.
T 51 = { T 5 r 1 , if T 5 r 1 - T 5 g 1 0 , T 5 g 1 , if T 5 r 1 - T 5 g 1 > 0.
T 52 = { T 5 r 2 , if T 5 r 2 - T 5 g 2 0 , T 5 g 2 , if T 5 r 2 - T 5 g 2 > 0.
Σ 5 = { T R ρ 1 T R 1 ( T R 1 T 5 r 1 + T R 2 T 5 r 2 ) A r 0 , if A r 0 - A g 0 0 , T R ρ 1 T R 1 ( T R 1 T 5 g 1 + T R 2 T 5 g 2 ) A g 0 , if A r 0 - A g 0 < 0.
σ 0 = - log Σ 5 + log ( T R 1 T 5 r 1 + T R 2 T 5 r 2 ) - log Σ 5 + log ( S 5 r 1 + S 5 r 2 ) , if             ( S 5 r 1 + S 5 r 2 ) - ( S 5 g 1 + S 5 g 2 ) 0 ,
σ 0 = - log Σ 5 + log ( T R 1 T 5 g 1 + T R 2 T 5 g 2 ) - log Σ 5 + log ( S 5 g 1 + S 5 g 2 ) , if             ( S 5 r 1 + S 5 r 2 ) - ( S 5 g 1 + S 5 g 2 ) < 0.
T 51 = T 5 r 1             and             T 52 = T 5 g 2 ,
σ 0 = - log Σ 5 + log S 51 , if S 51 - S 52 0 , σ 0 = - log Σ 5 + log S 52 , if S 51 - S 52 < 0.
1 / T 51 = 1 / T 5 r 1 - 1 / T 5 g 1 , 1 / T 52 = 1 / T 5 r 2 - 1 / T 5 g 2 ,
T 51 = ( T 5 r 1 · T 5 g 1 ) / ( T 5 g 1 - T 5 r 1 ) , T 52 = ( T 5 r 2 · T 5 g 2 ) / ( T 5 g 2 - T 5 r 2 ) .
σ 0 = - log Σ 5 + log | T R 1 T 51 + T R 2 T 52 | = - log Σ 5 + log S 51 + S 52 .