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  1. J. Blanchard, Phys. Rev. 11, 11 (1918).
    [Crossref]
  2. P. Moon, J. Opt. Soc. Am. 32, 348 (1942).
    [Crossref]
  3. P. Reeves, Psychol. Rev. 25, 330 (1918); J. Opt. Soc. Am. 4, 35 (1920).
    [Crossref]
  4. B. H. Crawford, Proc. Roy. Soc. B121, 376 (1936).
    [Crossref]
  5. W. S. Stiles, Dept. Sci. Ind. Research, (London), 1929, p. 63.
  6. R. J. Lythgoe, Medical Research Council, Rpt. of Committee upon Physiology of Vision, London, X (1932).
  7. L. L. Holladay, J. Opt. Soc. Am. 12, 310 (1926).
    [Crossref]
  8. J. Couvreux, Comptes rendus 178, 416 and 1388 (1924).
  9. H. Schroeder, Zeits. f. Sinnesphysiol. 57, 219 (1927).
  10. W. S. Stiles and B. H. Crawford, Proc. Roy. Soc. B112, 428 (1933).
    [Crossref]
  11. C. F. Goodeve, Proc. Roy. Soc. A155, 664 (1936).
    [Crossref]
  12. W. D. Wright and J. H. Nelson, Proc. Phys. Soc. London 48, 401 (1936).
    [Crossref]
  13. W. Dziobek, Das Licht 4, 150 (1934). L. J. Collier and W. G. A. Taylor, J. Sci. Inst. 15, 5 (1938).
    [Crossref]
  14. B. H. Crawford, Proc. Roy. Soc. B124, 81 (1937).
    [Crossref]
  15. W. S. Stiles, Proc. Roy. Soc. B127, 64 (1939).
    [Crossref]
  16. W. S. Stiles, Proc. Roy. Soc. B123, 90 (1937); Sci. Prog. 33, 676 (1939).
    [Crossref]
  17. W. E. K. Middleton, J. Opt. Soc. Am. 27, 112 (1937).
    [Crossref]
  18. P. W. Cobb, Am. J. Physiol. 36, 335 (1915).
  19. S. Hecht, J. Gen. Physiol. 18, 767 (1935).
  20. P. Moon and D. E. Spencer, J. Opt. Soc. Am. 33, 444 (1943).
    [Crossref]

1943 (1)

1942 (1)

1939 (1)

W. S. Stiles, Proc. Roy. Soc. B127, 64 (1939).
[Crossref]

1937 (3)

W. S. Stiles, Proc. Roy. Soc. B123, 90 (1937); Sci. Prog. 33, 676 (1939).
[Crossref]

W. E. K. Middleton, J. Opt. Soc. Am. 27, 112 (1937).
[Crossref]

B. H. Crawford, Proc. Roy. Soc. B124, 81 (1937).
[Crossref]

1936 (3)

C. F. Goodeve, Proc. Roy. Soc. A155, 664 (1936).
[Crossref]

W. D. Wright and J. H. Nelson, Proc. Phys. Soc. London 48, 401 (1936).
[Crossref]

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

1935 (1)

S. Hecht, J. Gen. Physiol. 18, 767 (1935).

1934 (1)

W. Dziobek, Das Licht 4, 150 (1934). L. J. Collier and W. G. A. Taylor, J. Sci. Inst. 15, 5 (1938).
[Crossref]

1933 (1)

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

1927 (1)

H. Schroeder, Zeits. f. Sinnesphysiol. 57, 219 (1927).

1926 (1)

L. L. Holladay, J. Opt. Soc. Am. 12, 310 (1926).
[Crossref]

1924 (1)

J. Couvreux, Comptes rendus 178, 416 and 1388 (1924).

1918 (2)

P. Reeves, Psychol. Rev. 25, 330 (1918); J. Opt. Soc. Am. 4, 35 (1920).
[Crossref]

J. Blanchard, Phys. Rev. 11, 11 (1918).
[Crossref]

1915 (1)

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

Blanchard, J.

J. Blanchard, Phys. Rev. 11, 11 (1918).
[Crossref]

Cobb, P. W.

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

Couvreux, J.

J. Couvreux, Comptes rendus 178, 416 and 1388 (1924).

Crawford, B. H.

B. H. Crawford, Proc. Roy. Soc. B124, 81 (1937).
[Crossref]

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

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

Dziobek, W.

W. Dziobek, Das Licht 4, 150 (1934). L. J. Collier and W. G. A. Taylor, J. Sci. Inst. 15, 5 (1938).
[Crossref]

Goodeve, C. F.

C. F. Goodeve, Proc. Roy. Soc. A155, 664 (1936).
[Crossref]

Hecht, S.

S. Hecht, J. Gen. Physiol. 18, 767 (1935).

Holladay, L. L.

L. L. Holladay, J. Opt. Soc. Am. 12, 310 (1926).
[Crossref]

Lythgoe, R. J.

R. J. Lythgoe, Medical Research Council, Rpt. of Committee upon Physiology of Vision, London, X (1932).

Middleton, W. E. K.

Moon, P.

Nelson, J. H.

W. D. Wright and J. H. Nelson, Proc. Phys. Soc. London 48, 401 (1936).
[Crossref]

Reeves, P.

P. Reeves, Psychol. Rev. 25, 330 (1918); J. Opt. Soc. Am. 4, 35 (1920).
[Crossref]

Schroeder, H.

H. Schroeder, Zeits. f. Sinnesphysiol. 57, 219 (1927).

Spencer, D. E.

Stiles, W. S.

W. S. Stiles, Proc. Roy. Soc. B127, 64 (1939).
[Crossref]

W. S. Stiles, Proc. Roy. Soc. B123, 90 (1937); Sci. Prog. 33, 676 (1939).
[Crossref]

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

W. S. Stiles, Dept. Sci. Ind. Research, (London), 1929, p. 63.

Wright, W. D.

W. D. Wright and J. H. Nelson, Proc. Phys. Soc. London 48, 401 (1936).
[Crossref]

Am. J. Physiol. (1)

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

Comptes rendus (1)

J. Couvreux, Comptes rendus 178, 416 and 1388 (1924).

Das Licht (1)

W. Dziobek, Das Licht 4, 150 (1934). L. J. Collier and W. G. A. Taylor, J. Sci. Inst. 15, 5 (1938).
[Crossref]

J. Gen. Physiol. (1)

S. Hecht, J. Gen. Physiol. 18, 767 (1935).

J. Opt. Soc. Am. (4)

Phys. Rev. (1)

J. Blanchard, Phys. Rev. 11, 11 (1918).
[Crossref]

Proc. Phys. Soc. London (1)

W. D. Wright and J. H. Nelson, Proc. Phys. Soc. London 48, 401 (1936).
[Crossref]

Proc. Roy. Soc. (6)

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

C. F. Goodeve, Proc. Roy. Soc. A155, 664 (1936).
[Crossref]

B. H. Crawford, Proc. Roy. Soc. B124, 81 (1937).
[Crossref]

W. S. Stiles, Proc. Roy. Soc. B127, 64 (1939).
[Crossref]

W. S. Stiles, Proc. Roy. Soc. B123, 90 (1937); Sci. Prog. 33, 676 (1939).
[Crossref]

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

Psychol. Rev. (1)

P. Reeves, Psychol. Rev. 25, 330 (1918); J. Opt. Soc. Am. 4, 35 (1920).
[Crossref]

Zeits. f. Sinnesphysiol. (1)

H. Schroeder, Zeits. f. Sinnesphysiol. 57, 219 (1927).

Other (2)

W. S. Stiles, Dept. Sci. Ind. Research, (London), 1929, p. 63.

R. J. Lythgoe, Medical Research Council, Rpt. of Committee upon Physiology of Vision, London, X (1932).

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Figures (9)

Fig. 1
Fig. 1

Experimental data on pupil diameter as a function of helios. Equilibrium conditions, large uniform field illuminated by incandescent lamps, binocular vision. ◯ Blanchard; ○ Reeves; ● Crawford; □ Stiles; × Couvreux—Eq. (3).

Fig. 2
Fig. 2

Pupil diameters. Average results of the most reliable investigations. ◯ Blanchard; ○ Reeves, average of 7 subjects; ● Crawford, average of 8 subjects; □ Crawford, subject B.H.C.—Eq. (3).

Fig. 3
Fig. 3

The Stiles-Crawford effect. The points represent experimental values of η, the relative effectiveness of rays entering the pupil at various distances x from the center of the pupil. ○ B.H.C. (1933, horizontal traverse); ● B.H.C. (1933, vertical traverse); □ W.S.S. (1933, horizontal traverse); ▽ W.S.S. (1933, vertical traverse); — calculated, Eq. (6a); — — calculated, Eq. (5a).

Fig. 4
Fig. 4

The Stiles-Crawford effect. ○ B.H.C. (1933, flicker-photometer method); ● B.H.C. (1937, threshold method); —calculated, Eq. (6a).

Fig. 5
Fig. 5

The Stiles factor for a 2-mm artificial pupil. Comparison of calculated values for three equations. — power function, Eq. (16); - - - - cosine function, Eq. (17); – – probability function, Eq. (15).

Fig. 6
Fig. 6

Minimum perceptible contrast as a function of helios, showing the effect of changing from natural to artificial pupil.

Fig. 7
Fig. 7

Correction for changing from natural pupil to 2-mm artificial pupil.

Fig. 8
Fig. 8

Effect of varying the size of an artificial pupil. ○ Experimental values of minimum visual angle (Cobb, Av. of results for 3 observers); — calculated.

Fig. 9
Fig. 9

Experimental check of the method. ○ Experimental values of visual angle (Lythgoe, observer J.M., natural pupil); ● Experimental values (J.M., artificial pupil); — natural pupil; – – artificial pupil, calculated curve.

Tables (5)

Tables Icon

Table I Reeves’ data on pupil size.

Tables Icon

Table II The Stiles-Crawford effect. Relative visual effectiveness η. Flicker method, incandescent lamps, Tc=2300°K.

Tables Icon

Table III The Stiles factor ζ(δ, 2). Comparison of values computed by means of three different equations.

Tables Icon

Table V The Stiles factor. Comparison of values computed for average pupil data and for Reeves’ pupil data.

Equations (42)

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δ = 4.90 - 3.20 tanh [ 0.471 ( log H - 1.30 ) ] ,
δ = 5.0 - 2.2 tanh [ 0.447 ( log H + 0.87 ) ] .
δ = 4.90 - 3.00 tanh [ 0.400 ( log H - 0.50 ) ] ,
δ = 4.90 - 3.00 tanh [ 0.400 ( log B ¯ + 0.50 ) ] ,
η = F ( 0 ) / F ( x ) ,
η = 1.025 exp [ - 0.105 ( x + 0.47 ) 2 ] .
η = 1 - A x 2 + B x 4 .
η = exp ( - 0.105 x 2 ) ,
η = ( 1 - a ) + a cos b x .
( 1 - a ) + a cos b x = ( 1 - a ) + a [ 1 - b 2 x 2 / 2 ! + b 4 x 4 / 4 ! - ] = 1 - ( a b 2 / 2 ) x 2 + ( a b 4 / 24 ) x 4 - .
η = 1 - 0.0850 x 2 + 0.0020 x 4
η = 0.379 + 0.621 cos 0.515 x .
d F = 2 π D x d x .
F = 2 π D 0 δ / 2 x d x = π D δ 2 / 4.
d F e = 2 π D η ( x ) x d x
F e = 2 π D 0 δ / 2 η ( x ) x d x .
D = k H
F e = 2 π k H δ 0 δ / 2 η ( x ) x d x .
F e = 2 π k H β 0 β / 2 η ( x ) x d x .
H β H δ = 0 δ / 2 η ( x ) x d x 0 β / 2 η ( x ) x d x
H β = H δ ζ ( δ , β ) .
ζ ( δ , β ) = 0 δ / 2 η ( x ) x d x 0 β / 2 η ( x ) x d x
ζ = 1 - exp [ - p ( δ / 2 ) 2 ] 1 - exp [ - p ( β / 2 ) 2 ] .
ζ = ( δ β ) 2 [ 1 - A δ 2 / 8 + B δ 4 / 48 ] [ 1 - A β 2 / 8 + B β 4 / 48 ]
ζ = ( 1 - a ) b 2 δ 2 / 8 + a [ cos ( b δ / 2 ) - 1 + ( b δ / 2 ) sin ( b δ / 2 ) ] ( 1 - a ) b 2 β 2 / 8 + a [ cos ( b β / 2 ) - 1 + ( b β / 2 ) sin ( b β / 2 ) ] .
ζ ( δ , β ) = ( δ β ) 2 × 1 - 1.06 × 10 - 2 δ 2 + 4.17 × 10 - 5 δ 4 1 - 1.06 × 10 - 2 β 2 + 4.17 × 10 - 5 β 4
ζ ( δ , 2 ) = 0.2620 δ 2 [ 1 - 1.06 × 10 - 2 δ 2 + 4.17 × 10 - 5 δ 4 ] .
ζ ( δ , β ) = ζ ( δ , 2 ) / ζ ( β , 2 ) .
H β = H δ ζ ( δ , β ) ,
ζ ( δ , β ) = ( δ / β ) 2 .
log ζ ( δ , 2 ) = 0.460 [ 1 - tanh 0.450 ( log H - 1.70 ) ]
log ζ ( δ , 2 ) = 0.600 [ 1 - tanh 0.388 ( log H - 1.25 ) ]
δ = 4.90 - 3.00 tanh [ 0.400 ( log H - 0.50 ) ] .
η = 1 - 0.0850 x 2 + 0.0020 x 4 .
F e = 2 π k H δ 0 δ / 2 η ( x ) x d x
ζ = H β / H δ
ζ ( δ , β ) = ( δ β ) 2 × 1 - 1.06 × 10 - 2 δ 2 + 4.17 × 10 - 5 δ 4 1 - 1.06 × 10 - 2 β 2 + 4.17 × 10 - 5 β 4
ζ ( δ , 2 ) = 0.2620 δ 2 [ 1 - 1.06 × 10 - 2 δ 2 + 4.17 × 10 - 5 δ 4 ] .
ζ ( δ , β ) = ( δ / β ) 2 .
log ζ ( δ , 2 ) = 0.460 [ 1 - tanh 0.450 ( log H - 1.70 ) ]
log ζ ( δ , 2 ) = 0.600 [ 1 - tanh 0.388 ( log H - 1.25 ) ]
ζ = ( δ / β ) 2 .