Abstract

Visual acuity for a grating test object was determined as a function of artificial pupil diameter at five luminance levels. In order to eliminate the effect of variation of retinal illuminance with pupil size changes as a factor in acuity, the luminance of the acuity test field as viewed through each artificial pupil was previously adjusted to match a reference field of constant luminance viewed by the other eye through a fixed pupil at five luminance values of the reference field. Selection of maximum artificial pupil size was made on the basis of photographs of the natural pupil taken under conditions similar to those which obtained in the main experiment. As pupil size is increased, acuity improves rapidly at first and then more slowly before reaching a maximum value of acuity. Further increase in pupil size, when possible, results in lowered acuity. The rise in acuity up to the maximum is steeper the higher the luminance level, whereas the drop in acuity which occurs when the pupil is made even larger is steeper the lower the luminance level. The results are interpreted as reflecting the increased importance of aberrations as a factor in acuity as pupil size is increased and the luminance level is lowered. The data are plotted to show the effect of pupil size as a parameter of the acuity-reference luminance function.

© 1952 Optical Society of America

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  1. According to the recommendations of the O.S.A. Colorimetry Committee (J. Opt. Soc. Am. 34, 245 (1944)) retinal illuminance is proportional to the product of the luminous flux emitted or reflected from the test object (specified in units of luminance) and pupil size. The assumption is made in the present study that two fields of the same size and color, each viewed simultaneously by different eyes and imaged on comparable retinal areas, will produce equal retinal illuminance when matched for equality by the subject independent of the sizes of the entrance pupils of two eyes.
  2. S. Shlaer, J. Gen. Physiol. 21, 165 (1937).
  3. Shlaer, Smith, and Chase, J. Gen. Physiol. 25, 553 (1942).
  4. J. Lister, J. Roy. Microscop. Soc., 34 (1913). E. Hummelsheim, Graefe’s Arch. Ophthalmol. 45, 357 (1898); A. Arnulf, Compt. rend. 200, 52 (1935), La Vision dans les Instruments (Editions de la Revue d’Optique, Paris, 1937); G. M. Byram, J. Opt. Soc. Am. 34, 718 (1944); Coleman, Coleman, Fridge, and Harding, J. Opt. Soc. Am. 39, 766 (1949).
    [Crossref] [PubMed]
  5. W. Uthoff, Graefe’s Arch. Ophthalmol. 36, 40 (1890); P. W. Cobb, Am. J. Physiol. 36, 335 (1914–15).
  6. A. Koenig, Gesammelte Abhandlungen (Johann Ambrosius Barth, Leipzig, 1903).
  7. L. T. Troland, J. Exptl. Psychol. 2, 1 (1917).
    [Crossref]
  8. W. S. Stiles and B. W. Crawford, Proc. Roy. Soc. (London) B112, 428 (1933).
    [Crossref]
  9. R. J. Lythgoe, Great Britain Med. Research Council, (1929).
  10. D. McL. Purdy, J. Gen. Psychol. 7, 189 (1932).
    [Crossref]
  11. Ferree, Rand, and Harris, J. Exptl. Psychol. 16, 408 (1933); M. Luckiesch and F. Moss, J. Opt. Soc. Am. 24, 130 (1934); B. H. Crawford, Proc. Roy. Soc. (London),  B121, 376 (1936); H. E. Page, J. Exptl. Psychol. 29, 177 (1941).
    [Crossref]
  12. M. Luckiesch and F. Moss, J. Opt. Soc. Am. 24, 130 (1934); G. A. Fry, Am. J. Optom. 22, 451 (1945); E. Marg and M. W. Morgan, Am. J. Optom. 26, 183 (1949) Am. J. Optom. 27, 217 (1950).
    [Crossref]
  13. Nitsche and Gunther, Mittleilungen 117 (1930); W. S. Duke-Elder, Textbook of Ophthalmology (Mosby, St. Louis, 1934) Vol. 1, p. 542.
  14. P. Reeves, Psychol. Rev. 25, 330 (1918); F. Flamant, Rev. Optique. 27, 751 (1948).
    [Crossref]
  15. J. P. C. Southall, Mirrors, Prisms, and Lenses (MacMillan Company, New York, 1947), third edition, p. 399.
  16. H. S. Gradle and W. Ackerman, J. Am. Med. Assoc. 99, No. 16, 1334 (1932); O. Lowenstein and E. D. Friedman, Arch. Ophthalmol. (Chicago) 27, 969 (1942); W. R. Biersdorf, unpublished thesis, State College of Washington (1951).
    [Crossref]
  17. H. Helmholtz, Physiological Optics. Translated by J. P. C. Southhall (Optical Society of America, New York, 1924), Vol. 2, pp. 34–35.

1944 (1)

1942 (1)

Shlaer, Smith, and Chase, J. Gen. Physiol. 25, 553 (1942).

1937 (1)

S. Shlaer, J. Gen. Physiol. 21, 165 (1937).

1934 (1)

1933 (2)

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

Ferree, Rand, and Harris, J. Exptl. Psychol. 16, 408 (1933); M. Luckiesch and F. Moss, J. Opt. Soc. Am. 24, 130 (1934); B. H. Crawford, Proc. Roy. Soc. (London),  B121, 376 (1936); H. E. Page, J. Exptl. Psychol. 29, 177 (1941).
[Crossref]

1932 (2)

D. McL. Purdy, J. Gen. Psychol. 7, 189 (1932).
[Crossref]

H. S. Gradle and W. Ackerman, J. Am. Med. Assoc. 99, No. 16, 1334 (1932); O. Lowenstein and E. D. Friedman, Arch. Ophthalmol. (Chicago) 27, 969 (1942); W. R. Biersdorf, unpublished thesis, State College of Washington (1951).
[Crossref]

1930 (1)

Nitsche and Gunther, Mittleilungen 117 (1930); W. S. Duke-Elder, Textbook of Ophthalmology (Mosby, St. Louis, 1934) Vol. 1, p. 542.

1918 (1)

P. Reeves, Psychol. Rev. 25, 330 (1918); F. Flamant, Rev. Optique. 27, 751 (1948).
[Crossref]

1917 (1)

L. T. Troland, J. Exptl. Psychol. 2, 1 (1917).
[Crossref]

1913 (1)

J. Lister, J. Roy. Microscop. Soc., 34 (1913). E. Hummelsheim, Graefe’s Arch. Ophthalmol. 45, 357 (1898); A. Arnulf, Compt. rend. 200, 52 (1935), La Vision dans les Instruments (Editions de la Revue d’Optique, Paris, 1937); G. M. Byram, J. Opt. Soc. Am. 34, 718 (1944); Coleman, Coleman, Fridge, and Harding, J. Opt. Soc. Am. 39, 766 (1949).
[Crossref] [PubMed]

1890 (1)

W. Uthoff, Graefe’s Arch. Ophthalmol. 36, 40 (1890); P. W. Cobb, Am. J. Physiol. 36, 335 (1914–15).

Ackerman, W.

H. S. Gradle and W. Ackerman, J. Am. Med. Assoc. 99, No. 16, 1334 (1932); O. Lowenstein and E. D. Friedman, Arch. Ophthalmol. (Chicago) 27, 969 (1942); W. R. Biersdorf, unpublished thesis, State College of Washington (1951).
[Crossref]

Chase,

Shlaer, Smith, and Chase, J. Gen. Physiol. 25, 553 (1942).

Crawford, B. W.

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

Ferree,

Ferree, Rand, and Harris, J. Exptl. Psychol. 16, 408 (1933); M. Luckiesch and F. Moss, J. Opt. Soc. Am. 24, 130 (1934); B. H. Crawford, Proc. Roy. Soc. (London),  B121, 376 (1936); H. E. Page, J. Exptl. Psychol. 29, 177 (1941).
[Crossref]

Gradle, H. S.

H. S. Gradle and W. Ackerman, J. Am. Med. Assoc. 99, No. 16, 1334 (1932); O. Lowenstein and E. D. Friedman, Arch. Ophthalmol. (Chicago) 27, 969 (1942); W. R. Biersdorf, unpublished thesis, State College of Washington (1951).
[Crossref]

Gunther,

Nitsche and Gunther, Mittleilungen 117 (1930); W. S. Duke-Elder, Textbook of Ophthalmology (Mosby, St. Louis, 1934) Vol. 1, p. 542.

Harris,

Ferree, Rand, and Harris, J. Exptl. Psychol. 16, 408 (1933); M. Luckiesch and F. Moss, J. Opt. Soc. Am. 24, 130 (1934); B. H. Crawford, Proc. Roy. Soc. (London),  B121, 376 (1936); H. E. Page, J. Exptl. Psychol. 29, 177 (1941).
[Crossref]

Helmholtz, H.

H. Helmholtz, Physiological Optics. Translated by J. P. C. Southhall (Optical Society of America, New York, 1924), Vol. 2, pp. 34–35.

Koenig, A.

A. Koenig, Gesammelte Abhandlungen (Johann Ambrosius Barth, Leipzig, 1903).

Lister, J.

J. Lister, J. Roy. Microscop. Soc., 34 (1913). E. Hummelsheim, Graefe’s Arch. Ophthalmol. 45, 357 (1898); A. Arnulf, Compt. rend. 200, 52 (1935), La Vision dans les Instruments (Editions de la Revue d’Optique, Paris, 1937); G. M. Byram, J. Opt. Soc. Am. 34, 718 (1944); Coleman, Coleman, Fridge, and Harding, J. Opt. Soc. Am. 39, 766 (1949).
[Crossref] [PubMed]

Luckiesch, M.

Lythgoe, R. J.

R. J. Lythgoe, Great Britain Med. Research Council, (1929).

Moss, F.

Nitsche,

Nitsche and Gunther, Mittleilungen 117 (1930); W. S. Duke-Elder, Textbook of Ophthalmology (Mosby, St. Louis, 1934) Vol. 1, p. 542.

Purdy, D. McL.

D. McL. Purdy, J. Gen. Psychol. 7, 189 (1932).
[Crossref]

Rand,

Ferree, Rand, and Harris, J. Exptl. Psychol. 16, 408 (1933); M. Luckiesch and F. Moss, J. Opt. Soc. Am. 24, 130 (1934); B. H. Crawford, Proc. Roy. Soc. (London),  B121, 376 (1936); H. E. Page, J. Exptl. Psychol. 29, 177 (1941).
[Crossref]

Reeves, P.

P. Reeves, Psychol. Rev. 25, 330 (1918); F. Flamant, Rev. Optique. 27, 751 (1948).
[Crossref]

Shlaer,

Shlaer, Smith, and Chase, J. Gen. Physiol. 25, 553 (1942).

Shlaer, S.

S. Shlaer, J. Gen. Physiol. 21, 165 (1937).

Smith,

Shlaer, Smith, and Chase, J. Gen. Physiol. 25, 553 (1942).

Southall, J. P. C.

J. P. C. Southall, Mirrors, Prisms, and Lenses (MacMillan Company, New York, 1947), third edition, p. 399.

Stiles, W. S.

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

Troland, L. T.

L. T. Troland, J. Exptl. Psychol. 2, 1 (1917).
[Crossref]

Uthoff, W.

W. Uthoff, Graefe’s Arch. Ophthalmol. 36, 40 (1890); P. W. Cobb, Am. J. Physiol. 36, 335 (1914–15).

Graefe’s Arch. Ophthalmol. (1)

W. Uthoff, Graefe’s Arch. Ophthalmol. 36, 40 (1890); P. W. Cobb, Am. J. Physiol. 36, 335 (1914–15).

J. Am. Med. Assoc. (1)

H. S. Gradle and W. Ackerman, J. Am. Med. Assoc. 99, No. 16, 1334 (1932); O. Lowenstein and E. D. Friedman, Arch. Ophthalmol. (Chicago) 27, 969 (1942); W. R. Biersdorf, unpublished thesis, State College of Washington (1951).
[Crossref]

J. Exptl. Psychol. (2)

Ferree, Rand, and Harris, J. Exptl. Psychol. 16, 408 (1933); M. Luckiesch and F. Moss, J. Opt. Soc. Am. 24, 130 (1934); B. H. Crawford, Proc. Roy. Soc. (London),  B121, 376 (1936); H. E. Page, J. Exptl. Psychol. 29, 177 (1941).
[Crossref]

L. T. Troland, J. Exptl. Psychol. 2, 1 (1917).
[Crossref]

J. Gen. Physiol. (2)

S. Shlaer, J. Gen. Physiol. 21, 165 (1937).

Shlaer, Smith, and Chase, J. Gen. Physiol. 25, 553 (1942).

J. Gen. Psychol. (1)

D. McL. Purdy, J. Gen. Psychol. 7, 189 (1932).
[Crossref]

J. Opt. Soc. Am. (2)

J. Roy. Microscop. Soc. (1)

J. Lister, J. Roy. Microscop. Soc., 34 (1913). E. Hummelsheim, Graefe’s Arch. Ophthalmol. 45, 357 (1898); A. Arnulf, Compt. rend. 200, 52 (1935), La Vision dans les Instruments (Editions de la Revue d’Optique, Paris, 1937); G. M. Byram, J. Opt. Soc. Am. 34, 718 (1944); Coleman, Coleman, Fridge, and Harding, J. Opt. Soc. Am. 39, 766 (1949).
[Crossref] [PubMed]

Mittleilungen (1)

Nitsche and Gunther, Mittleilungen 117 (1930); W. S. Duke-Elder, Textbook of Ophthalmology (Mosby, St. Louis, 1934) Vol. 1, p. 542.

Proc. Roy. Soc. (London) (1)

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

Psychol. Rev. (1)

P. Reeves, Psychol. Rev. 25, 330 (1918); F. Flamant, Rev. Optique. 27, 751 (1948).
[Crossref]

Other (4)

J. P. C. Southall, Mirrors, Prisms, and Lenses (MacMillan Company, New York, 1947), third edition, p. 399.

H. Helmholtz, Physiological Optics. Translated by J. P. C. Southhall (Optical Society of America, New York, 1924), Vol. 2, pp. 34–35.

R. J. Lythgoe, Great Britain Med. Research Council, (1929).

A. Koenig, Gesammelte Abhandlungen (Johann Ambrosius Barth, Leipzig, 1903).

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Figures (5)

Fig. 1
Fig. 1

Examples of photographs of the eye taken while it views a centrally fixated circular test field of indicated luminance subtending a visual angle of four degrees at a viewing distance of one meter.

Fig. 2
Fig. 2

Average luminance values of a test field viewed through various sized artificial pupils which matched a reference field of constant luminance values viewed by the other eye through a 2-mm pupil. Luminance values of the reference field in millilamberts are indicated at the right of the curves. The curves for the 10, 1, 0.1, and 0.01 luminance levels have been shifted upwards 0.6, 1.2, 1.8, and 2.4 log units, respectively, on the ordinate axis. Filled circles are the data of A.S.; unfilled circles, H.L. The curves are empirical.

Fig. 3
Fig. 3

Log visual acuity as a function of log pupil diameter for photometrically equated test fields. The luminance of the acuity test field was previously adjusted to match a reference field of constant luminance viewed by the other eye through a 2-mm pupil. The luminance values of the reference field, in millilamberts, are indicated at the right of the curves. The data represented by the open circles are the average data of A.S. and H.L.; half-filled circles are the data of H.L. See footnote†† for explanation of the data represented by the filled circles. The curves are empirical.

Fig. 4
Fig. 4

Log (visual acuity/pupil diameter) as a function of log pupil diameter for photometrically equated test fields. The luminance of the acuity test field was previously adjusted to match a reference field of constant luminance viewed by the other eye through a fixed 2-mm pupil. Luminance values of the reference field are indicated at the right of the curves. The curves for the 1, 0.1, and 0.01 luminance levels have been shifted upwards 0.03, 0.06 and 0.17 log unit, respectively, on the ordinate axis. The curves are empirical.

Fig. 5
Fig. 5

Visual acuity as a function of log reference luminance for various pupil diameters. The reference luminance values indicated are those of a reference field viewed by the other eye through a 2-mm pupil with which the acuity test field was previously matched for each pupil diameter. The pupil diameters in millimeters are indicated at the right of the curves. The curves are empirical.

Tables (5)

Tables Icon

Table I Average pupil diameter as a function of luminance for three conditions of observation.

Tables Icon

Table II Average pupil diameter for H.L. under three conditions of observation of a field of constant luminance. Data obtained from photographs taken with the aid of an infrared projector and infrared photoflash bulbs.

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Table III Pupil diameter as a function of luminance for a four degree circular test field at a viewing distance of one meter. Photographs were taken with the aid of infrared radiation.

Tables Icon

Table IV The luminance of a test field viewed monocularly through various sized artificial pupils necessary to match a reference field of constant luminance values viewed by the other eye through a 2.0-mm pupil.

Tables Icon

Table V Log visual acuity for a grating test object as a function of pupil diameter for photometrically equated test fields. The luminance of the test field for a given pupil diameter was previously adjusted to match a reference field of constant luminance values viewed by the other eye through a 2-mm pupil.