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  1. Simon Shlaer, J. Gen. Physiol. 21, 165–188 (1937).
  2. Simon Shlaer, E. L. Smith, and A. M. Chase, J. Gen. Physiol. 25, 553–569 (1942).
  3. P. W. Cobb, Am. J. Physiol. 36, 335–346 (1915).
  4. Matthew Luckiesh and F. K. Moss, The Science of Seeing (D. Van Nostrand Company, Inc., New York, 1937).
  5. Visual Mechanisms, edited by Heinrich Kluver (The Jaques Cattell Press, Lancaster, Pennsylvania, 1942), Chapter VII.
  6. W. H. Stiles and B. H. Crawford, Proc. Roy. Soc. London B112, 428–450 (1933).
    [CrossRef]
  7. H. Hartridge, J. Physiol. 57, 52–67 (1923).
  8. Selig Hecht and Esther U. Mintz, J. Gen. Physiol. 22, 593–612 (1939).
  9. H. K. Hartline, J. Opt. Soc. Am. 30, 239–247 (1940).
    [CrossRef]
  10. S. H. Bartley, Vision (D. Van Nostrand Company, Inc., New York, 1941).
  11. Selig Hecht, Physiol. Rev. 17, 239–290 (1937).
  12. Jacinto Steinhardt, J. Gen. Physiol. 20, 185–209 (1936).
  13. W. W. Wilcox, Proc. Nat. Acad. Sci. 18, 47–56 (1932).
    [CrossRef]
  14. W. W. Wilcox, J. Gen. Psychol. 15, 405–435 (1936).
    [CrossRef]
  15. Gordon L. Walls, J. Opt. Soc. Am. 33, 487–505 (1943).
    [CrossRef]

1943 (1)

1942 (1)

Simon Shlaer, E. L. Smith, and A. M. Chase, J. Gen. Physiol. 25, 553–569 (1942).

1940 (1)

1939 (1)

Selig Hecht and Esther U. Mintz, J. Gen. Physiol. 22, 593–612 (1939).

1937 (2)

Selig Hecht, Physiol. Rev. 17, 239–290 (1937).

Simon Shlaer, J. Gen. Physiol. 21, 165–188 (1937).

1936 (2)

W. W. Wilcox, J. Gen. Psychol. 15, 405–435 (1936).
[CrossRef]

Jacinto Steinhardt, J. Gen. Physiol. 20, 185–209 (1936).

1933 (1)

W. H. Stiles and B. H. Crawford, Proc. Roy. Soc. London B112, 428–450 (1933).
[CrossRef]

1932 (1)

W. W. Wilcox, Proc. Nat. Acad. Sci. 18, 47–56 (1932).
[CrossRef]

1923 (1)

H. Hartridge, J. Physiol. 57, 52–67 (1923).

1915 (1)

P. W. Cobb, Am. J. Physiol. 36, 335–346 (1915).

Bartley, S. H.

S. H. Bartley, Vision (D. Van Nostrand Company, Inc., New York, 1941).

Chase, A. M.

Simon Shlaer, E. L. Smith, and A. M. Chase, J. Gen. Physiol. 25, 553–569 (1942).

Cobb, P. W.

P. W. Cobb, Am. J. Physiol. 36, 335–346 (1915).

Crawford, B. H.

W. H. Stiles and B. H. Crawford, Proc. Roy. Soc. London B112, 428–450 (1933).
[CrossRef]

Hartline, H. K.

Hartridge, H.

H. Hartridge, J. Physiol. 57, 52–67 (1923).

Hecht, Selig

Selig Hecht and Esther U. Mintz, J. Gen. Physiol. 22, 593–612 (1939).

Selig Hecht, Physiol. Rev. 17, 239–290 (1937).

Luckiesh, Matthew

Matthew Luckiesh and F. K. Moss, The Science of Seeing (D. Van Nostrand Company, Inc., New York, 1937).

Mintz, Esther U.

Selig Hecht and Esther U. Mintz, J. Gen. Physiol. 22, 593–612 (1939).

Moss, F. K.

Matthew Luckiesh and F. K. Moss, The Science of Seeing (D. Van Nostrand Company, Inc., New York, 1937).

Shlaer, Simon

Simon Shlaer, E. L. Smith, and A. M. Chase, J. Gen. Physiol. 25, 553–569 (1942).

Simon Shlaer, J. Gen. Physiol. 21, 165–188 (1937).

Smith, E. L.

Simon Shlaer, E. L. Smith, and A. M. Chase, J. Gen. Physiol. 25, 553–569 (1942).

Steinhardt, Jacinto

Jacinto Steinhardt, J. Gen. Physiol. 20, 185–209 (1936).

Stiles, W. H.

W. H. Stiles and B. H. Crawford, Proc. Roy. Soc. London B112, 428–450 (1933).
[CrossRef]

Walls, Gordon L.

Wilcox, W. W.

W. W. Wilcox, J. Gen. Psychol. 15, 405–435 (1936).
[CrossRef]

W. W. Wilcox, Proc. Nat. Acad. Sci. 18, 47–56 (1932).
[CrossRef]

Am. J. Physiol. (1)

P. W. Cobb, Am. J. Physiol. 36, 335–346 (1915).

J. Gen. Physiol. (4)

Simon Shlaer, J. Gen. Physiol. 21, 165–188 (1937).

Simon Shlaer, E. L. Smith, and A. M. Chase, J. Gen. Physiol. 25, 553–569 (1942).

Selig Hecht and Esther U. Mintz, J. Gen. Physiol. 22, 593–612 (1939).

Jacinto Steinhardt, J. Gen. Physiol. 20, 185–209 (1936).

J. Gen. Psychol. (1)

W. W. Wilcox, J. Gen. Psychol. 15, 405–435 (1936).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Physiol. (1)

H. Hartridge, J. Physiol. 57, 52–67 (1923).

Physiol. Rev. (1)

Selig Hecht, Physiol. Rev. 17, 239–290 (1937).

Proc. Nat. Acad. Sci. (1)

W. W. Wilcox, Proc. Nat. Acad. Sci. 18, 47–56 (1932).
[CrossRef]

Proc. Roy. Soc. London (1)

W. H. Stiles and B. H. Crawford, Proc. Roy. Soc. London B112, 428–450 (1933).
[CrossRef]

Other (3)

S. H. Bartley, Vision (D. Van Nostrand Company, Inc., New York, 1941).

Matthew Luckiesh and F. K. Moss, The Science of Seeing (D. Van Nostrand Company, Inc., New York, 1937).

Visual Mechanisms, edited by Heinrich Kluver (The Jaques Cattell Press, Lancaster, Pennsylvania, 1942), Chapter VII.

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Figures (16)

Fig. 1
Fig. 1

Curves showing 1/αd as a function of the artificial iris aperture at different brightness levels for black parallel bars on a white ground. The brightness Hb of the white background for the different curves was: A—7000 millilamberts, B—700 millilamberts, C—70 millilamberts, D—7 millilamberts, E—0.7 millilambert, F—0.07 millilambert.

Fig. 2
Fig. 2

Curves showing 1/αd as a function of the artificial iris aperture at different brightness levels for white parallel bars on a black ground. The brightness H of the white bars for the different curves was the same as for the backgrounds in Fig. 1.

Fig. 3
Fig. 3

The curves 1/αd, ut, and 1/α for the grating test object are shown on logarithmic scales as a function of the artificial iris aperture d. Values of the curves for apertures greater than 2.5 mm were obtained by observing a bright line source through a double-slit diaphragm. To bring all curves to approximately the same position, the ut curve is multiplied by a factor of 10.

Fig. 4
Fig. 4

The distribution of illumination in the retinal image of a bright line source of light viewed through a double-slit diaphragm for which a=0.3 mm and b=4.5 mm. The dotted line is an envelope representing the single-slit pattern.

Fig. 5
Fig. 5

These drawings show the appearance of the lines in the image of a line source viewed through a double-slit diaphragm for α=0.75, 0.35, and 0.20 minute. When α=0.20, the lines become broken up into discontinuous curved segments.

Fig. 6
Fig. 6

The curves 1/αd, ut, and 1/α for a black line are shown as a function of the artificial iris aperture d. To give all curves approximately the same vertical range, ut is multiplied by a factor of 104.

Fig. 7
Fig. 7

The solid curves show the distribution of illumination in the image of a black line at threshold for d=2.5 mm and d=0.8 mm. The broken curve is a supra-threshold curve (with d=0.8 mm) for which the angular diameter of the line is twice its threshold value.

Fig. 8
Fig. 8

The 1/αd curve for a black disk viewed on a white background with a brightness of 1200 millilamberts.

Fig. 9
Fig. 9

The border between C and D is plainly visible. If one holds the page at a distance of about 14 inches from the eyes and fixates for about 20 seconds on the small black dot at the center of the parallel lines and then fixates on the border, it will be difficult to see for a few seconds. The border between D and E is not appreciably affected. If one fixates on the border between A and B for about 20 seconds and then on the border between C and D, the relative brightness of C and D will appear reversed.

Fig. 10
Fig. 10

The energy rate r for the steady state and the corresponding adaptation β are shown as a function of KI.

Fig. 11
Fig. 11

Curve A shows the form of the retinal image of the border of a bipartite field for which the ratio I1/I2 is 0.6. Curve B gives the corresponding energy rates in the photochemical image when I1 and I2 are 0.15 and 0.25 lumen per square meter, respectively; C is a similar curve for which I1 and I2 are 150 and 250 lumens per square meter.

Fig. 12
Fig. 12

Area A is obviously brighter than area B. If one places this figure in bright light and covers up the lower half of the figure and fixates on the black line, it is difficult to judge which area is brighter. The line drawn on the border blots out the energy rate gradient shown in Fig. 11 between−Δϕ and +Δϕ. If the eyes are now rapidly shifted from one area to the other, the brightness difference once more becomes noticeable.

Fig. 13
Fig. 13

Possible relation between the visual sensation s and the energy rate r if the adaptation β is constant.

Fig. 14
Fig. 14

Possible relation between the visual sensation s and the energy rate r for the photochemical steady state. The adaptation β varies from 0 to 1.

Fig. 15
Fig. 15

The photochemical image of a black line viewed on a bright white background. The broken line shows the probable effect of the retinal mosaic on the energy rate. It is assumed that at threshold only the A and B cones are involved in the process of discrimination.

Fig. 16
Fig. 16

Curve A is the subjective or apparent width of a white line on a dark background plotted as a function of the brightness of the line; B is a similar curve for a black line on a white background plotted as a function of the background brightness. The actual width of both lines was about 2 minutes.

Tables (2)

Tables Icon

Table I Visual acuity data for different values of the background brightness Hb and different artificial iris apertures d. All data are for the Luckiesh-Moss test object.

Tables Icon

Table II Visual acuity data for different values of the test object brightness H and different artificial iris apertures d. Data are for a test object complementary to that used for the data in Table I.

Equations (45)

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α = 1.22 λ / d ,
u t = f ( z a ) .
z a = π d α / λ ,
1 / α d = k / λ ,
I = I 0 ( sin z 1 / z 1 ) 2 cos 2 z 2 ,
z 1 = π a ϕ / λ ,             z 2 = π b ϕ / λ ,
d = 2.36 b .
α = λ / 2 b .
( d x d t ) 1 = k 1 I ( a - x - y ) m ,
d y d t = - k 3 y l ,
( d x d t ) 2 = - k 2 x n ,
d x d t = k 1 I ( a - x ) m - k 2 x n .
K I = x n / ( a - x ) m ,
r = C K I ( a - x ) m ,
K I = p n / ( 1 - p ) m
r = r a K I ( 1 - p ) m ,
K ( I 1 + I 2 ) / 2 = p n / ( 1 - p ) m .
r 1 = r a K I 1 ( 1 - p ) m = 2 r a p n I 1 / ( I 1 + I 2 ) ,
r 2 = r a K I 2 ( 1 - p ) m = 2 r a p n I 2 / ( I 1 + I 2 ) .
( r 1 - r 2 ) t = A + B ( r 1 + r 2 ) 1 2 ,
2 u t / ( 2 - u t ) = c 1 / p n + c 2 / p n / 2 ,
u t = c 2 / p n / 2 ,
K I 1 = p 1 2 / ( 1 - p 1 ) ,
r 1 = r a K I ( 1 - p 1 ) .
r = r a K I ( 1 - p ) ,
K I = p 2 / ( 1 - p ) .
r 1 = r a K I ( 1 - p ) .
I = ( I 2 / I 1 ) ( p 1 / p ) 2 .
I / I = ( I 2 / I 1 ) ( p 1 / p 2 ) 2 .
r = r a K I β .
I = ρ ( a / F ) 2 ( 10 H ) ,
K ( I 1 + I 2 ) / 2 = p 2 / ( 1 - p ) .
r 1 = r a K I 1 ( 1 - p )
r 2 = r a K I 2 ( 1 - p ) .
Δ r / r = Δ I / I = u t ,
r 1 / r 2 = I 1 ( 1 - p 1 ) / I 2 ( 1 - p 2 ) .
u = v f ( α ) ,
f ( α ) = A α - C α 3 + E α 5 - G α 7 + ,
f ( α ) = B α 2 - D α 4 + F α 6 - H α 8 + ,
1 / f ( α ) = v p n / 2 / c 2 ,
1 / α = ( 1 / α 0 ) v p n / 2 ,
1 / α = ( 1 / α 0 ) v 1 2 p n / 4 ,
1 / τ = ( 1 / τ 0 ) v p n / 2 ,
2 p = [ ( K I ) 2 + 4 K I ] 1 2 - K I .
d = ( R - 2 x ) / 4 ,