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References

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  1. P. Moon and D. E. Spencer, J. Opt. Soc. Am. 34, 319 (1944).
    [Crossref]
  2. P. Reeves, J. Opt. Soc. Am. 4, 35 (1920); Psychol. Rev. 25, 330 (1918).
    [Crossref]
  3. B. H. Crawford, Proc. Roy. Soc. London B121, 376 (1936).
    [Crossref]
  4. W. S. Stiles and B. H. Crawford, Proc. Roy. Soc. B112, 428 (1933).
    [Crossref]
  5. Reference 3, Fig. 9, p. 393.
  6. P. Moon and D. E. Spencer, “Visual dark adaptation: a mathematical formulation,” to be published.
  7. Hecht, Haig, and Chase, J. Gen. Physiol. 20, 831 (1927).
    [Crossref]

1944 (1)

1936 (1)

B. H. Crawford, Proc. Roy. Soc. London B121, 376 (1936).
[Crossref]

1933 (1)

W. S. Stiles and B. H. Crawford, Proc. Roy. Soc. B112, 428 (1933).
[Crossref]

1927 (1)

Hecht, Haig, and Chase, J. Gen. Physiol. 20, 831 (1927).
[Crossref]

1920 (1)

Chase,

Hecht, Haig, and Chase, J. Gen. Physiol. 20, 831 (1927).
[Crossref]

Crawford, B. H.

B. H. Crawford, Proc. Roy. Soc. London B121, 376 (1936).
[Crossref]

W. S. Stiles and B. H. Crawford, Proc. Roy. Soc. B112, 428 (1933).
[Crossref]

Haig,

Hecht, Haig, and Chase, J. Gen. Physiol. 20, 831 (1927).
[Crossref]

Hecht,

Hecht, Haig, and Chase, J. Gen. Physiol. 20, 831 (1927).
[Crossref]

Moon, P.

P. Moon and D. E. Spencer, J. Opt. Soc. Am. 34, 319 (1944).
[Crossref]

P. Moon and D. E. Spencer, “Visual dark adaptation: a mathematical formulation,” to be published.

Reeves, P.

Spencer, D. E.

P. Moon and D. E. Spencer, J. Opt. Soc. Am. 34, 319 (1944).
[Crossref]

P. Moon and D. E. Spencer, “Visual dark adaptation: a mathematical formulation,” to be published.

Stiles, W. S.

W. S. Stiles and B. H. Crawford, Proc. Roy. Soc. B112, 428 (1933).
[Crossref]

J. Gen. Physiol. (1)

Hecht, Haig, and Chase, J. Gen. Physiol. 20, 831 (1927).
[Crossref]

J. Opt. Soc. Am. (2)

Proc. Roy. Soc. (1)

W. S. Stiles and B. H. Crawford, Proc. Roy. Soc. B112, 428 (1933).
[Crossref]

Proc. Roy. Soc. London (1)

B. H. Crawford, Proc. Roy. Soc. London B121, 376 (1936).
[Crossref]

Other (2)

Reference 3, Fig. 9, p. 393.

P. Moon and D. E. Spencer, “Visual dark adaptation: a mathematical formulation,” to be published.

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Figures (8)

Fig. 1
Fig. 1

Closing of the pupil. The vertical scale is logarithmic and thus the straight line represents an exponential function of time, Eq. (1). The black circles represent the Reeves data (Av. of 6 subjects) while the open circles are for individual subjects.

Fig. 2
Fig. 2

Opening of pupil. ● Reeves (Av. of 6). ○ Reeves (individual subjects). × Crawford (Av. of 12).—Eq. (2).

Fig. 3
Fig. 3

Calculated curves of pupil diameter δ (mm) as a function of time (sec.). The eye was initially dark-adapted with the pupil at its maximum diameter. At t=0, a uniform field of helios HA (blondel) was suddenly exposed. The pupil remains at its original diameter until t=0.10 sec., at which time it begins to decrease in size as shown by the curves.

Fig. 4
Fig. 4

Calculated curves of pupil diameter as a function of time. The eye was initially adapted to a large surface of helios HA. At t=0, this helios was suddenly reduced to zero. Pupil size remains constant for 0.20 sec., after which it changes according to the curves. The final pupil diameter reached in all cases is indicated by the dotted line.

Fig. 5
Fig. 5

The Stiles factor as a function of time (closing pupil). Pupil initially at maximum size. Cone vision.

Fig. 6
Fig. 6

The Stiles factor as a function of time (opening pupil). Eye initially adapted to helios HA. Cone vision.

Fig. 7
Fig. 7

Calculated dark-adaptation curves showing the effect of an artificial pupil. Threshold helios (blondels) is plotted against time (sec.). Rod vision.—2-mm artificial pupil. – – natural pupil.

Fig. 8
Fig. 8

Calculated dark-adaptation curves. Cone vision.—2-mm artificial pupil. – – natural pupil.

Tables (2)

Tables Icon

Table I Pupil diameter (closing), Reeves (Av. of 6).

Tables Icon

Table II Pupil diameter (opening).

Equations (21)

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δ - δ min δ max - δ min = 1.10 exp ( - t ) ,
δ max - δ δ max - δ min = 0.880 exp ( - 0.228 t ) + 0.160 exp ( - 0.0125 t ) .
1.040 / 2.718 = 0.880 ( exp ( - 0.228 t ) + 0.160 exp ( - 0.125 t ) ,
ζ ( δ , β ) = 0 δ / 2 η ( x ) x d x 0 β / 2 η ( x ) x d x .
η ( x ) = F ( 0 ) / F ( x ) .
ζ ( δ , β ) = ( δ / β ) 2 .
ζ ( δ , β ) = ( δ β ) 2 [ 1 - A δ 2 / 8 + B δ 4 / 48 ] [ 1 - A β 2 / 8 + B β 4 / 48 ] ,
ζ ( δ , 2 ) = 0.2620 δ 2 [ 1 - 1.06 × 10 - 2 δ 2 + 4.17 × 10 - 5 δ 4 ] .
H β ( t ) = ζ ( δ , β ; t ) H δ ( t ) ,
x = x 0 [ exp ( 3 k 2 t ) - k 4 x 0 3 [ exp ( 3 k 2 t ) - 1 ] / k 2 ] - 1 3 ,
H A = ( k 2 - k 4 x 0 3 ) a x 0 a k 1 [ exp ( - a x 0 ) - exp ( - a ) ] ,
( H T / H T ) 2 = [ exp ( - a x ) - exp ( - a ) ] - 1 .
H T n = H T 2 / ζ .
( H T / H T ) n = ( H T H T ) 2 ( 15.3 ζ ) .
log ( H T ) 2 = log ( H T / H T ) 2 + 6.184 - 10 , log ( H T ) n = log ( H T / H T ) 2 + log ( 15.3 / ζ ) + 5.00 - 10.
x = x 0 exp ( k 2 t ) .
H A = ( k 2 / a k 1 ) ( a x 0 ) exp ( a x 0 ) ,
( H T / H T ) 2 = exp ( a x ) .
a k 1 = 3 × 10 - 5 ,             k 2 = 0.0110 ,             a = 30.
( H T / H T ) n = ( H T / H T ) 2 ( 8.17 / ζ ) .
log ( H T ) 2 = log ( H T / H T ) 2 + 8.389 - 10 , log ( H T ) n = log ( H T / H T ) 2 + log ( 8.17 / ζ ) + 7.477 - 10.