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  1. P. Moon and D. E. Spencer, J. Opt. Soc. Am. 34, 605 (1944).
    [Crossref]
  2. P. Moon and D. E. Spencer, J. Opt. Soc. Am. 33, 444 (1943).
    [Crossref]
  3. L. L. Holladay, J. Opt. Soc. Am. 12, 271 (1926).
    [Crossref]
  4. W. Uhthoff, Arch. f. Ophth. 32, 171 (1886); Arch. f. Ophth. 36, 33 (1890); R. Depène, Monats. Augenhlk,  38, 289, 390 (1900).
  5. U. Bordoni, Elettrotecnica,  11, 585 (1924).
  6. W. S. Stiles, Proc. Roy. Soc. B104, 322 (1929).
    [Crossref]
  7. W. S. Stiles and C. Dunbar, Illum. Res. Comm. (Great Britain), , 1935.
  8. P. W. Cobb and F. K. Moss, Trans. I.E.S. 23, 1104 (1928).
  9. R. J. Lythgoe, (1932).
  10. P. G. Nutting, Trans. I.E.S. 11, 939 (1916).
  11. P. S. Millar and S. McK. Gray, Proc. C.I.E., 277 (1928).
  12. E. W. Fowler and C. L. Crouch, Illum. Eng. 36, 897 (1941).
  13. E. E. Potter and P. Meaker, Trans. I.E.S. 26, 1025 (1931). E. E. Potter and W. G. Darley, Trans. I.E.S. 35, 775 (1940). A. B. O’Day and W. Sturrock, Trans. I.E.S. 31, 351 (1936).
  14. Reference 3. The first mention of the Holladay principle seems to have been made in a paper by M. Luckiesh and L. L. Holladay, “Glare and visibility,” presented before the Annual Convention of the Illuminating Engineering Society in October, 1924. This paper was published in the Trans. I.E.S. 20, 221 (1925). It contained no data, however, and the curves showed no experimental points. A more satisfactory presentation was made by Holladay in 1926 (reference 3). Further work of a similar nature is given in L. L. Holladay, J. Opt. Soc. Am. 14, 1 (1927).
    [Crossref]
  15. W. S. Stiles and B. H. Crawford, Proc. Roy. Soc. B116, 55 (1934); Phys. Soc., London, “Discussion on vision,” 194 (1932).
    [Crossref]
  16. B. H. Crawford, Proc. Phys. Soc. London,  48, 35 (1936).
    [Crossref]
  17. B. H. Crawford, Proc. Roy. Soc. B129, 94 (1940).
    [Crossref]
  18. P. W. Cobb, J. Exper. Psychol. 1, 419 (1916).
    [Crossref]
  19. M. Luckiesh and F. K. Moss, Trans. I.E.S. 34, 571 (1939).
  20. Ward Harrison, Trans. I.E.S. 15, 34 (1920).
  21. Ward Harrison, Trans. I.E.S. 32, 208 (1937).
  22. H. Eguchi, C.I.E. Proc., 1932, p. 36; J. Steinhardt, J. Gen. Physiol. 20, 185 (1936); Hecht, Haig, and Chase, J. Gen. Physiol. 20, 831 (1937).
  23. S. Hecht, J. Gen. Physiol. 18, 767 (1935).
  24. P. Moon and D. E. Spencer, J. Opt. Soc. Am. 35, 43 (1945); Visual dark adaptation: a mathematical formulation, to be published.
    [Crossref]
  25. H. K. Hartline and C. H. Graham, J. Cell. and Comp. Physiol. 1, 277 (1932); C. H. Graham, Handbook of General Experimental Psychology (Worcester, 1934), p. 829.
    [Crossref]
  26. P. Moon and D. E. Spencer, J. Opt. Soc. Am. 34, 319 (1944).
    [Crossref]

1945 (1)

1944 (2)

1943 (1)

1941 (1)

E. W. Fowler and C. L. Crouch, Illum. Eng. 36, 897 (1941).

1940 (1)

B. H. Crawford, Proc. Roy. Soc. B129, 94 (1940).
[Crossref]

1939 (1)

M. Luckiesh and F. K. Moss, Trans. I.E.S. 34, 571 (1939).

1937 (1)

Ward Harrison, Trans. I.E.S. 32, 208 (1937).

1936 (1)

B. H. Crawford, Proc. Phys. Soc. London,  48, 35 (1936).
[Crossref]

1935 (1)

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

1934 (1)

W. S. Stiles and B. H. Crawford, Proc. Roy. Soc. B116, 55 (1934); Phys. Soc., London, “Discussion on vision,” 194 (1932).
[Crossref]

1932 (2)

H. K. Hartline and C. H. Graham, J. Cell. and Comp. Physiol. 1, 277 (1932); C. H. Graham, Handbook of General Experimental Psychology (Worcester, 1934), p. 829.
[Crossref]

H. Eguchi, C.I.E. Proc., 1932, p. 36; J. Steinhardt, J. Gen. Physiol. 20, 185 (1936); Hecht, Haig, and Chase, J. Gen. Physiol. 20, 831 (1937).

1931 (1)

E. E. Potter and P. Meaker, Trans. I.E.S. 26, 1025 (1931). E. E. Potter and W. G. Darley, Trans. I.E.S. 35, 775 (1940). A. B. O’Day and W. Sturrock, Trans. I.E.S. 31, 351 (1936).

1929 (1)

W. S. Stiles, Proc. Roy. Soc. B104, 322 (1929).
[Crossref]

1928 (2)

P. W. Cobb and F. K. Moss, Trans. I.E.S. 23, 1104 (1928).

P. S. Millar and S. McK. Gray, Proc. C.I.E., 277 (1928).

1926 (1)

1924 (1)

U. Bordoni, Elettrotecnica,  11, 585 (1924).

1920 (1)

Ward Harrison, Trans. I.E.S. 15, 34 (1920).

1916 (2)

P. W. Cobb, J. Exper. Psychol. 1, 419 (1916).
[Crossref]

P. G. Nutting, Trans. I.E.S. 11, 939 (1916).

1886 (1)

W. Uhthoff, Arch. f. Ophth. 32, 171 (1886); Arch. f. Ophth. 36, 33 (1890); R. Depène, Monats. Augenhlk,  38, 289, 390 (1900).

Bordoni, U.

U. Bordoni, Elettrotecnica,  11, 585 (1924).

Cobb, P. W.

P. W. Cobb and F. K. Moss, Trans. I.E.S. 23, 1104 (1928).

P. W. Cobb, J. Exper. Psychol. 1, 419 (1916).
[Crossref]

Crawford, B. H.

B. H. Crawford, Proc. Roy. Soc. B129, 94 (1940).
[Crossref]

B. H. Crawford, Proc. Phys. Soc. London,  48, 35 (1936).
[Crossref]

W. S. Stiles and B. H. Crawford, Proc. Roy. Soc. B116, 55 (1934); Phys. Soc., London, “Discussion on vision,” 194 (1932).
[Crossref]

Crouch, C. L.

E. W. Fowler and C. L. Crouch, Illum. Eng. 36, 897 (1941).

Dunbar, C.

W. S. Stiles and C. Dunbar, Illum. Res. Comm. (Great Britain), , 1935.

Eguchi, H.

H. Eguchi, C.I.E. Proc., 1932, p. 36; J. Steinhardt, J. Gen. Physiol. 20, 185 (1936); Hecht, Haig, and Chase, J. Gen. Physiol. 20, 831 (1937).

Fowler, E. W.

E. W. Fowler and C. L. Crouch, Illum. Eng. 36, 897 (1941).

Graham, C. H.

H. K. Hartline and C. H. Graham, J. Cell. and Comp. Physiol. 1, 277 (1932); C. H. Graham, Handbook of General Experimental Psychology (Worcester, 1934), p. 829.
[Crossref]

Gray, S. McK.

P. S. Millar and S. McK. Gray, Proc. C.I.E., 277 (1928).

Harrison, Ward

Ward Harrison, Trans. I.E.S. 32, 208 (1937).

Ward Harrison, Trans. I.E.S. 15, 34 (1920).

Hartline, H. K.

H. K. Hartline and C. H. Graham, J. Cell. and Comp. Physiol. 1, 277 (1932); C. H. Graham, Handbook of General Experimental Psychology (Worcester, 1934), p. 829.
[Crossref]

Hecht, S.

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

Holladay, L. L.

L. L. Holladay, J. Opt. Soc. Am. 12, 271 (1926).
[Crossref]

Reference 3. The first mention of the Holladay principle seems to have been made in a paper by M. Luckiesh and L. L. Holladay, “Glare and visibility,” presented before the Annual Convention of the Illuminating Engineering Society in October, 1924. This paper was published in the Trans. I.E.S. 20, 221 (1925). It contained no data, however, and the curves showed no experimental points. A more satisfactory presentation was made by Holladay in 1926 (reference 3). Further work of a similar nature is given in L. L. Holladay, J. Opt. Soc. Am. 14, 1 (1927).
[Crossref]

Luckiesh, M.

M. Luckiesh and F. K. Moss, Trans. I.E.S. 34, 571 (1939).

Reference 3. The first mention of the Holladay principle seems to have been made in a paper by M. Luckiesh and L. L. Holladay, “Glare and visibility,” presented before the Annual Convention of the Illuminating Engineering Society in October, 1924. This paper was published in the Trans. I.E.S. 20, 221 (1925). It contained no data, however, and the curves showed no experimental points. A more satisfactory presentation was made by Holladay in 1926 (reference 3). Further work of a similar nature is given in L. L. Holladay, J. Opt. Soc. Am. 14, 1 (1927).
[Crossref]

Lythgoe, R. J.

R. J. Lythgoe, (1932).

Meaker, P.

E. E. Potter and P. Meaker, Trans. I.E.S. 26, 1025 (1931). E. E. Potter and W. G. Darley, Trans. I.E.S. 35, 775 (1940). A. B. O’Day and W. Sturrock, Trans. I.E.S. 31, 351 (1936).

Millar, P. S.

P. S. Millar and S. McK. Gray, Proc. C.I.E., 277 (1928).

Moon, P.

Moss, F. K.

M. Luckiesh and F. K. Moss, Trans. I.E.S. 34, 571 (1939).

P. W. Cobb and F. K. Moss, Trans. I.E.S. 23, 1104 (1928).

Nutting, P. G.

P. G. Nutting, Trans. I.E.S. 11, 939 (1916).

Potter, E. E.

E. E. Potter and P. Meaker, Trans. I.E.S. 26, 1025 (1931). E. E. Potter and W. G. Darley, Trans. I.E.S. 35, 775 (1940). A. B. O’Day and W. Sturrock, Trans. I.E.S. 31, 351 (1936).

Spencer, D. E.

Stiles, W. S.

W. S. Stiles and B. H. Crawford, Proc. Roy. Soc. B116, 55 (1934); Phys. Soc., London, “Discussion on vision,” 194 (1932).
[Crossref]

W. S. Stiles, Proc. Roy. Soc. B104, 322 (1929).
[Crossref]

W. S. Stiles and C. Dunbar, Illum. Res. Comm. (Great Britain), , 1935.

Uhthoff, W.

W. Uhthoff, Arch. f. Ophth. 32, 171 (1886); Arch. f. Ophth. 36, 33 (1890); R. Depène, Monats. Augenhlk,  38, 289, 390 (1900).

Arch. f. Ophth. (1)

W. Uhthoff, Arch. f. Ophth. 32, 171 (1886); Arch. f. Ophth. 36, 33 (1890); R. Depène, Monats. Augenhlk,  38, 289, 390 (1900).

C.I.E. Proc. (1)

H. Eguchi, C.I.E. Proc., 1932, p. 36; J. Steinhardt, J. Gen. Physiol. 20, 185 (1936); Hecht, Haig, and Chase, J. Gen. Physiol. 20, 831 (1937).

Elettrotecnica (1)

U. Bordoni, Elettrotecnica,  11, 585 (1924).

Illum. Eng. (1)

E. W. Fowler and C. L. Crouch, Illum. Eng. 36, 897 (1941).

J. Cell. and Comp. Physiol. (1)

H. K. Hartline and C. H. Graham, J. Cell. and Comp. Physiol. 1, 277 (1932); C. H. Graham, Handbook of General Experimental Psychology (Worcester, 1934), p. 829.
[Crossref]

J. Exper. Psychol. (1)

P. W. Cobb, J. Exper. Psychol. 1, 419 (1916).
[Crossref]

J. Gen. Physiol. (1)

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

J. Opt. Soc. Am. (5)

Proc. C.I.E. (1)

P. S. Millar and S. McK. Gray, Proc. C.I.E., 277 (1928).

Proc. Phys. Soc. London (1)

B. H. Crawford, Proc. Phys. Soc. London,  48, 35 (1936).
[Crossref]

Proc. Roy. Soc. (3)

B. H. Crawford, Proc. Roy. Soc. B129, 94 (1940).
[Crossref]

W. S. Stiles and B. H. Crawford, Proc. Roy. Soc. B116, 55 (1934); Phys. Soc., London, “Discussion on vision,” 194 (1932).
[Crossref]

W. S. Stiles, Proc. Roy. Soc. B104, 322 (1929).
[Crossref]

Trans. I.E.S. (6)

P. W. Cobb and F. K. Moss, Trans. I.E.S. 23, 1104 (1928).

P. G. Nutting, Trans. I.E.S. 11, 939 (1916).

E. E. Potter and P. Meaker, Trans. I.E.S. 26, 1025 (1931). E. E. Potter and W. G. Darley, Trans. I.E.S. 35, 775 (1940). A. B. O’Day and W. Sturrock, Trans. I.E.S. 31, 351 (1936).

M. Luckiesh and F. K. Moss, Trans. I.E.S. 34, 571 (1939).

Ward Harrison, Trans. I.E.S. 15, 34 (1920).

Ward Harrison, Trans. I.E.S. 32, 208 (1937).

Other (3)

Reference 3. The first mention of the Holladay principle seems to have been made in a paper by M. Luckiesh and L. L. Holladay, “Glare and visibility,” presented before the Annual Convention of the Illuminating Engineering Society in October, 1924. This paper was published in the Trans. I.E.S. 20, 221 (1925). It contained no data, however, and the curves showed no experimental points. A more satisfactory presentation was made by Holladay in 1926 (reference 3). Further work of a similar nature is given in L. L. Holladay, J. Opt. Soc. Am. 14, 1 (1927).
[Crossref]

R. J. Lythgoe, (1932).

W. S. Stiles and C. Dunbar, Illum. Res. Comm. (Great Britain), , 1935.

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Figures (12)

Fig. 1
Fig. 1

The helios threshold (HBH0) as a function of helios. Adaptation to a uniform field of helios HB gives the threshold T1. A glare source introduced into this uniform field raises the adaptation helios to HA and increases the threshold to T2.

Fig. 2
Fig. 2

Contribution of the surround. A large uniform surround of helios Hs is varied in size by changing the angle Θ1 subtended by the internal radius. As Θ1 approaches 0, the adaptation helios would approach ∞ according to Eq. (2). For the recommended value of Θ1=0.0131 radian, however, the entire surround contributes only 7.74 percent of the total adaptation helios.

Fig. 3
Fig. 3

Delos (ϒc=cB/cA) as a function of background helios HB and adaptation helios HA.

Fig. 4
Fig. 4

Delos (ϒα=αB/αA) as a function of HB and HA.

Fig. 5
Fig. 5

Delos for a uniform surround of helios Hs. The curves show how the relative visual acuity is reduced as the helios of the surround is raised above the helios of the background. Θ1=0.0131 radian, Θ2=1.00 radian.

Fig. 6
Fig. 6

Delos for a uniform surround of helios Hs. Here HB=100 blondels, Θ1=0.0131 radian. Curve is same as the middle curve of Fig. 5 but is extended to ratios Hs/HB less than 1.0.

Fig. 7
Fig. 7

Delos for a concentrated glare source in an otherwise uniform field. HB=Hs=100 blondels. The glare source is at an angle θ from the line of sight and has a helios H and solid angle ω.

Fig. 8
Fig. 8

Allowable helios ratio is a function of the adaptation helios HA1 for the work. ϒ = 1 3.

Fig. 9
Fig. 9

Allowable helios H of a glare source subtending a solid angle of ω steradians. ϒ = 1 3.

Fig. 10
Fig. 10

Allowable helios ratio. ○ Experimental points of Nutting. ● Experimental points of Holladay, ω=5.5 × 10−2 steradian, sensation “just not unpleasant.” – – Calculated curve of Nutting, Eq. (27).---- Calculated curve of Holladay, Eq. (28), b=2000, boundary between “objectionable and intolerable.” —·— Holladay, b=400, “comfort-discomfort.” —· ·— Holladay, b=80, “limit of pleasure.” —— Theoretical curves, Eq. (38), based on photochemical theory. Very large glare source, cone vision.

Fig. 11
Fig. 11

Effect of size of glare source. ○ Experimental points of Holladay, HA=100, sensation “perceptibly uncomfortable.” – – Calculated curve of Holladay, Eq. (28). — Theoretical curve, Eq. (40), based on. photochemical theory.

Fig. 12
Fig. 12

Recommended helios ratio. HA is the adaptation helios (blondel) and H is the helios of a bright spot subtending the solid angle ω (steradian). – – Steady-state, very large spot, Eq. (20a). —— Transient state, Eqs. (38) and (40), M=0.1032.

Tables (6)

Tables Icon

Table I Investigations of the Holladay principle.

Tables Icon

Table II Effect of changing Θ1. Θ2=1.0, Ci(2Θ2)=0.4230

Tables Icon

Table III Lythgoe’s experimental results on the effect of a dark surround.

Tables Icon

Table IV Allowable helios range for a spot in an otherwise uniform visual field. Calculated by means of Eq. (26).

Tables Icon

Table V Helios ratios to give sensation of shock. (Nutting, Trans. I.E.S. 11, 939, 1916.)

Tables Icon

Table VI Constants in Holladay’s equation.

Equations (66)

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H A = H S + k H G ,
H A = H S + K H G π θ 2 cos θ Δ ω ,
H A = H S + K π i = 1 n ( H G ) i θ i 2 cos θ i · Δ ω i .
H A = K π i = 1 n ( H G ) i θ i - 2 cos θ i · Δ ω i .
H A = K π ω H ( θ , φ ) · θ - 2 cos θ d ω = K π Φ 1 Φ 2 d φ Θ 1 Θ 2 H ( θ , φ ) · θ - 2 sin θ cos θ d θ ,
H A / H S = 0.0192 [ 1 - sin 2 Θ 2 2 Θ 2 - C i ( 2 Θ 1 ) + C i ( 2 Θ 2 ) ] ,
H A = 0.923 H B + K π Φ 1 Φ 2 d φ Θ 1 Θ 2 H s ( θ , φ ) · θ - 2 sin θ cos θ d θ .
H A = 0.923 H B + 0.0192 0.0131 1 H S ( θ ) · θ - 2 sin θ cos θ d θ .
( H B - H 0 ) min = c [ A 1 + H A 1 2 ] 2 ,
c = 0.0123 ,             A 1 = 0.808.
c = ( H B - H 0 ) / H B .
c B = ( H B - H 0 ) / H B = c H B [ A 1 + H B 1 2 ] 2 .
c A = c H B [ A 1 + H A 1 2 ] 2 .
c B c A = ( A 1 + H B 1 2 A 1 + H A 1 2 ) 2 = [ K 1 + 1 K 1 + ( H A / H B ) 1 2 ] 2 ,             H A H B ,
ϒ c = 1 / ( H A / H B ) ,             H A H B .
α B = 1 H B f ( H B ) ,
α A = 1 H B f ( H A ) ,
f ( H A ) = α [ A 2 + H A 1 2 ] 3 ,
α A = 118.3 × 10 - 6 H B [ 0.412 + H A 1 3 ] 3 ,             H A H B .
ϒ α = α B α A = [ K 2 + 1 K 2 + ( H A / H B ) 1 3 ] 3 ,             H A H B ,
ϒ α = ϒ c = 1 / ( H A / H B ) ,             H A H B .
ϒ c = [ K 1 + 1 K 1 + ( H B / H A ) 1 2 ] 2 ,             H A H B ,
ϒ c = 1 / ( H B / H A ) ,             H A H B .
ϒ α = [ K 2 + 1 K 2 + ( H B / H A ) 1 3 ] 3 ,             H A H B ,
ϒ = 1 / ( H B / H A ) ,             H A H B .
H A = 0.927 H B ;
ϒ = 0.927.
H A = H B + K cos θ π θ 2 ( H ω ) .
α 1 = α H B 1 [ A 2 + H A 1 1 3 ] 3 ,
α 2 = α H B 1 [ A 2 + H A 2 1 3 ] 3 .
ϒ = [ A 2 + H A 1 1 3 A 2 + H A 2 1 3 ] 3 .
H A 2 1 ϒ [ ( 1 - ϒ 1 3 ) A 2 + H A 1 1 3 ] 3 .
H A 2 3 [ 0.126 + H A 1 1 3 ] 3 .
H A 2 / H A 1 3.
H A 2 = 0.923 Θ 1 2 [ H Θ 3 2 + H A 1 ( Θ 1 2 - Θ 3 2 ) ] + 0.0192 H A 1 [ 1 - sin 2 2 - C i ( 2 Θ 1 ) + C i ( 2 ) ] .
H A 2 = 5380 [ H Θ 3 2 + H A 1 ( 1.715 × 10 - 4 - Θ 3 2 ) ] + 7.72 × 10 - 2 H A 1 = 5380 Θ 3 2 ( H - H A 1 ) + H A 1 .
H H A 1 = 1 Θ 3 2 [ 1.86 × 10 - 4 ( H A 2 H A 1 - 1 ) + Θ 3 2 ] ,
H / H A 1 ( 3.72 × 10 - 4 + Θ 3 2 ) / Θ 3 2 .
ω π Θ 3 2 .
H H A 1 1.17 × 10 - 3 ω + 1
D H A 1 3.72 × 10 - 4 + ω / π ,
H / H A 1 1.17 × 10 - 3 / ω .
D / H A 1 3.72 × 10 - 4 .
1 3 H A 2 / H A 1 3.
H H A 1 ω 1.17 × 10 - 3 + ω .
ω 1.17 × 10 - 3 + ω H H A 1 1.17 × 10 - 3 ω + 1.
H / H A = 8100 H A - 0.68 .
H = b H A 0.30 ( 1 / ω ) 0.25
H / H A = b H A - 0.70 ( 1 / ω ) 0.25 ,
S + h ν = A + B .
( d x d t ) 1 = H · Φ 1 ( x ) .
d x d t = ( d x d t ) 1 + ( d x d t ) 2 .
H A = K x A / Φ 1 ( x A ) ,
f = k 3 ( d x d t ) 1 = k 3 H Φ 1 ( x ) .
f - f A = k 3 ( H - H A ) Φ 1 ( x A ) .
f N - f A N = k 3 ( H N - H A N ) Φ 1 ( x A N ) .
f - f A = f N - f A N , ( H - H A ) Φ 1 ( x A ) = ( H N - H A N ) Φ 1 ( x A N )
( H / H A - 1 ) = H N / H A N - 1 H A / H A N Φ 1 ( x A N ) Φ 1 ( x A ) .
H A = K x A / Φ 1 ( x A ) ,             H A N = K x A N / Φ 1 ( x A N ) ,
1 H A / H A N Φ 1 ( x A N ) Φ 1 ( x A ) = x A N x A .
( H / H A - 1 ) = ( x A N / x A ) ( H N / H A N - 1 ) .
f - f A = k 3 ζ ( δ A , 2 ) [ H - H A ] Φ 1 ( x A ) , f N - f A N = k 3 ζ ( δ A N , 2 ) [ H N - H A N ] Φ 1 ( x A N ) .
H H A = 1 + M ζ A x A ,
M = ζ A N x A N ( H N / H A N - 1 ) .
H H A = ( H / H A ) ω [ A 3 + ω 1 2 ] 2 ,
A 3 = 0.00874 for cone vision .