Abstract

Available measurements by different investigators on the relationship between pupil diameter and luminance of large adapting fields were compiled and weighted for the number of observers used. The equation for the curve that best fits eight sets of data is logd=0.8558−0.000401 (logB+8.1)3, where d is the diameter of the natural pupil in millimeters and B is the luminance of the adapting field in millilamberts. This is the best estimate that can be made to date of the pupil size—luminance relationship. To make the data of more general use they were corrected for the Stiles-Crawford effect and expressed so that retinal illuminance, adjusted for average pupil size, may be obtained directly from knowledge of the luminance of the stimulus field. The expression for this is logE(trolands)=logB+1.8614–0.000986 (logB+6.5)3, where E is the retinal illuminance in trolands and B is luminance in millilamberts. It is unfortunate that no extensive measurements have been made in this important area.

© 1952 Optical Society of America

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References

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  1. L. T. Troland, Psychol. Rev. 22, 167 (1915); J. Exp. Psychol. 2, 1 (1917).
    [Crossref]
  2. J. Blanchard, Phys. Rev. 11, 81–99 (1918); M. J. Couvreux, Compt. rend. 178, 416 (1924); B. H. Crawford, Proc. Roy. Soc. (London) B121, 376 (1936); L. L. Holladay, J. Opt. Soc. Am. 12, 271 (1926); L. Lythgoe, Med. Research Council, Gt. Britain, Special Rep. Series 173, (1932); P. Reeves, Psychol. Rev. 25, 330 (1918); P. Reeves, J. Opt. Soc. Am. 4, 35 (1920); W. S. Stiles, Proc. Roy. Soc. (London) B105, 131 (1930); I. Wagman and L. Nathanson, Proc. Soc. Exp. Biol. 49, 466 (1942).
    [Crossref]
  3. H. Schroeder, Z. Psychol. Physiol. Sinnesorg. 57, 195 (1926).
  4. C. Ferree and G. Rand, J. Exp. Psychol. 15, 37 (1932).
    [Crossref]
  5. L. Lythgoe, reference 2.
  6. P. Moon and D. Spencer, J. Opt. Soc. Am. 34, 319 (1944).
    [Crossref]
  7. L. R. Phillips, Proc. Roy. Soc. (London) B127, 405 (1939); L. L. Sloan, private communication.
    [Crossref]
  8. W. S. Stiles and B. H. Crawford, Proc. Roy. Soc. (London) B112, 428 (1933).
    [Crossref]
  9. D. H. Jacobs, J. Opt. Soc. Am. 34, 694 (1944).
    [Crossref]
  10. Ferree, Rand, and Harris, J. Exp. Psychol. 16, 408 (1933); M. Luckiesh and F. Moss, J. Opt. Soc. Am. 24, 130 (1934); H. E. Page, J. Exp. Psychol. 29, 177 (1941).
    [Crossref]
  11. W. S. Duke-Elder, Textbook of Ophthalmology IV (Henry Kempton, London, 1932), p. 3744.

1944 (2)

1939 (1)

L. R. Phillips, Proc. Roy. Soc. (London) B127, 405 (1939); L. L. Sloan, private communication.
[Crossref]

1933 (2)

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

Ferree, Rand, and Harris, J. Exp. Psychol. 16, 408 (1933); M. Luckiesh and F. Moss, J. Opt. Soc. Am. 24, 130 (1934); H. E. Page, J. Exp. Psychol. 29, 177 (1941).
[Crossref]

1932 (1)

C. Ferree and G. Rand, J. Exp. Psychol. 15, 37 (1932).
[Crossref]

1926 (1)

H. Schroeder, Z. Psychol. Physiol. Sinnesorg. 57, 195 (1926).

1918 (1)

J. Blanchard, Phys. Rev. 11, 81–99 (1918); M. J. Couvreux, Compt. rend. 178, 416 (1924); B. H. Crawford, Proc. Roy. Soc. (London) B121, 376 (1936); L. L. Holladay, J. Opt. Soc. Am. 12, 271 (1926); L. Lythgoe, Med. Research Council, Gt. Britain, Special Rep. Series 173, (1932); P. Reeves, Psychol. Rev. 25, 330 (1918); P. Reeves, J. Opt. Soc. Am. 4, 35 (1920); W. S. Stiles, Proc. Roy. Soc. (London) B105, 131 (1930); I. Wagman and L. Nathanson, Proc. Soc. Exp. Biol. 49, 466 (1942).
[Crossref]

1915 (1)

L. T. Troland, Psychol. Rev. 22, 167 (1915); J. Exp. Psychol. 2, 1 (1917).
[Crossref]

Blanchard, J.

J. Blanchard, Phys. Rev. 11, 81–99 (1918); M. J. Couvreux, Compt. rend. 178, 416 (1924); B. H. Crawford, Proc. Roy. Soc. (London) B121, 376 (1936); L. L. Holladay, J. Opt. Soc. Am. 12, 271 (1926); L. Lythgoe, Med. Research Council, Gt. Britain, Special Rep. Series 173, (1932); P. Reeves, Psychol. Rev. 25, 330 (1918); P. Reeves, J. Opt. Soc. Am. 4, 35 (1920); W. S. Stiles, Proc. Roy. Soc. (London) B105, 131 (1930); I. Wagman and L. Nathanson, Proc. Soc. Exp. Biol. 49, 466 (1942).
[Crossref]

Crawford, B. H.

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

Duke-Elder, W. S.

W. S. Duke-Elder, Textbook of Ophthalmology IV (Henry Kempton, London, 1932), p. 3744.

Ferree,

Ferree, Rand, and Harris, J. Exp. Psychol. 16, 408 (1933); M. Luckiesh and F. Moss, J. Opt. Soc. Am. 24, 130 (1934); H. E. Page, J. Exp. Psychol. 29, 177 (1941).
[Crossref]

Ferree, C.

C. Ferree and G. Rand, J. Exp. Psychol. 15, 37 (1932).
[Crossref]

Harris,

Ferree, Rand, and Harris, J. Exp. Psychol. 16, 408 (1933); M. Luckiesh and F. Moss, J. Opt. Soc. Am. 24, 130 (1934); H. E. Page, J. Exp. Psychol. 29, 177 (1941).
[Crossref]

Jacobs, D. H.

Lythgoe, L.

L. Lythgoe, reference 2.

Moon, P.

Phillips, L. R.

L. R. Phillips, Proc. Roy. Soc. (London) B127, 405 (1939); L. L. Sloan, private communication.
[Crossref]

Rand,

Ferree, Rand, and Harris, J. Exp. Psychol. 16, 408 (1933); M. Luckiesh and F. Moss, J. Opt. Soc. Am. 24, 130 (1934); H. E. Page, J. Exp. Psychol. 29, 177 (1941).
[Crossref]

Rand, G.

C. Ferree and G. Rand, J. Exp. Psychol. 15, 37 (1932).
[Crossref]

Schroeder, H.

H. Schroeder, Z. Psychol. Physiol. Sinnesorg. 57, 195 (1926).

Spencer, D.

Stiles, W. S.

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

Troland, L. T.

L. T. Troland, Psychol. Rev. 22, 167 (1915); J. Exp. Psychol. 2, 1 (1917).
[Crossref]

J. Exp. Psychol. (2)

C. Ferree and G. Rand, J. Exp. Psychol. 15, 37 (1932).
[Crossref]

Ferree, Rand, and Harris, J. Exp. Psychol. 16, 408 (1933); M. Luckiesh and F. Moss, J. Opt. Soc. Am. 24, 130 (1934); H. E. Page, J. Exp. Psychol. 29, 177 (1941).
[Crossref]

J. Opt. Soc. Am. (2)

Phys. Rev. (1)

J. Blanchard, Phys. Rev. 11, 81–99 (1918); M. J. Couvreux, Compt. rend. 178, 416 (1924); B. H. Crawford, Proc. Roy. Soc. (London) B121, 376 (1936); L. L. Holladay, J. Opt. Soc. Am. 12, 271 (1926); L. Lythgoe, Med. Research Council, Gt. Britain, Special Rep. Series 173, (1932); P. Reeves, Psychol. Rev. 25, 330 (1918); P. Reeves, J. Opt. Soc. Am. 4, 35 (1920); W. S. Stiles, Proc. Roy. Soc. (London) B105, 131 (1930); I. Wagman and L. Nathanson, Proc. Soc. Exp. Biol. 49, 466 (1942).
[Crossref]

Proc. Roy. Soc. (London) (2)

L. R. Phillips, Proc. Roy. Soc. (London) B127, 405 (1939); L. L. Sloan, private communication.
[Crossref]

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

Psychol. Rev. (1)

L. T. Troland, Psychol. Rev. 22, 167 (1915); J. Exp. Psychol. 2, 1 (1917).
[Crossref]

Z. Psychol. Physiol. Sinnesorg. (1)

H. Schroeder, Z. Psychol. Physiol. Sinnesorg. 57, 195 (1926).

Other (2)

L. Lythgoe, reference 2.

W. S. Duke-Elder, Textbook of Ophthalmology IV (Henry Kempton, London, 1932), p. 3744.

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Figures (3)

Fig. 1
Fig. 1

Diameter of the natural pupil due to the luminance of large adapting fields. Separate measurements from eight studies.

Fig. 2
Fig. 2

Diameter of the natural pupil due to the luminance of large adapting fields. Combined measurements from eight studies.

Fig. 3
Fig. 3

Estimated retinal illuminance due to the luminance of large adapting fields using mean diameters of the natural pupil.

Tables (3)

Tables Icon

Table I Comparison of experimentally determined diameters with those predicted by two equations.

Tables Icon

Table II Retinal illuminance E in Trolands adjusted for mean pupil size adjusted for the Stiles-Crawford effect.

Tables Icon

Table III Retinal illuminance E in Trolands adjusted for mean pupil size unadjusted for the Stiles-Crawford effect.

Equations (9)

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d = 4.9 - 3.0 tanh [ 0.4 ( log B + 0.5 ) ] ,
d = 4.6 - 2.8 tanh [ 0.3 ( log B + 0.3 ) ] ,
log d = 0.8558 - 0.000401 ( log B + 8.1 ) 3 .
Fe = π D r 2 - 0.0425 π D r 4 + 0.00067 π D r 6 ,
Fe = π D r 2 ( 1 - 0.0425 r 2 + 0.00067 r 4 ) ,
E ( trolands ) = 10 r 2 B ,
E ( trolands ) = 10 r 2 B ( 1 - 0.0425 r 2 + 0.00067 r 4 ) .
log E ( trolands ) = log B + 1.8614 - 0.000986 ( log B + 6.5 ) , 3
log E ( trolands ) = log B + 2.1095 - 0.000766 ( log B + 8.2 ) . 3