Abstract

The retinal directional effect of several subjects was measured. Flicker brightness matches were made using monochromatic lights. The experiment was performed in two parts. The first measured the Stiles–Crawford effect across only the central 6 mm of the pupil. Objective statistical methods were used to derive the best-fitting parabolas by least-squares criteria. Variances of the data were calculated from the replications and indices of goodness of fit were derived. On these grounds, the parabola was found to be unacceptable. The second part of the experiment included replicate matches made at points across the entire width of the dilated pupil. Similar methods were again used to derive the best-fitting gaussian and parabolic functions. The gaussian proved to be statistically acceptable as a description of the change of brightness with position of pupil entry while the parabola did not. The consequences of accepting the gaussian function are far-reaching. It is argued that the shape of the Stiles–Crawford-effect curve as measured across the pupil is the result of the normal distribution of cone angulations, each cone having inherent directional sensitivity. It follows from this that the directional sensitivity of individual cones cannot be as broad as the observed Stiles–Crawford-effect curve. It is probable that the individual cone will accept energy incident upon it within only a very small angle from its long axis.

© 1969 Optical Society of America

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References

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  1. W. S. Stiles, Proc. Roy. Soc. (London) B123, 90 (1937).
  2. P. Moon and D. E. Spencer, J. Opt. Soc. Am. 34, 319 (1944).
    [Crossref]
  3. B. H. Crawford, Proc. Roy. Soc. (London) B124, 81 (1937).
  4. J. M. Enoch, Summated Response of the Retina to Light Entering Different Parts of the Pupil, doctoral dissertation, Ohio State Univ. (1956). University Microfilms 18, 789, Ann Arbor, Michigan.
  5. W. S. Stiles and B. H. Crawford, Proc. Roy. Soc. (London) B112, 428 (1933).
  6. W. D. Wright and J. H. Nelson, Proc. Phys. Soc. (London) 48, 401 (1936).
    [Crossref]
  7. This method of positioning the subject was mentioned in a paper by W. S. Stiles, Proc. Royal Soc. (London) 27, 74 (1939). He credits the suggestion to Professor Hartridge.
  8. Since the computer program we used for these calculations allowed us to use only points with equal numbers of replications, we were forced to omit two peripheral points.
  9. S. Polyak, The Retina (University of Chicago Press, Chicago, 1941).
  10. R. W. Ditchburn and B. L. Ginsborg, J. Physiol. (London) 119, 1 (1953).
  11. f(x) = [sech2(x/d)]÷2d, − ∞ x∞
  12. f(x)=(1+cosx)÷2π,-π<x<π =0,elsewhere
  13. f(x)=abxb-1e-axb,x>0 =0,elsewhere.

1953 (1)

R. W. Ditchburn and B. L. Ginsborg, J. Physiol. (London) 119, 1 (1953).

1944 (1)

1939 (1)

This method of positioning the subject was mentioned in a paper by W. S. Stiles, Proc. Royal Soc. (London) 27, 74 (1939). He credits the suggestion to Professor Hartridge.

1937 (2)

B. H. Crawford, Proc. Roy. Soc. (London) B124, 81 (1937).

W. S. Stiles, Proc. Roy. Soc. (London) B123, 90 (1937).

1936 (1)

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

1933 (1)

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

Crawford, B. H.

B. H. Crawford, Proc. Roy. Soc. (London) B124, 81 (1937).

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

Ditchburn, R. W.

R. W. Ditchburn and B. L. Ginsborg, J. Physiol. (London) 119, 1 (1953).

Enoch, J. M.

J. M. Enoch, Summated Response of the Retina to Light Entering Different Parts of the Pupil, doctoral dissertation, Ohio State Univ. (1956). University Microfilms 18, 789, Ann Arbor, Michigan.

Ginsborg, B. L.

R. W. Ditchburn and B. L. Ginsborg, J. Physiol. (London) 119, 1 (1953).

Moon, P.

Nelson, J. H.

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

Polyak, S.

S. Polyak, The Retina (University of Chicago Press, Chicago, 1941).

Spencer, D. E.

Stiles, W. S.

This method of positioning the subject was mentioned in a paper by W. S. Stiles, Proc. Royal Soc. (London) 27, 74 (1939). He credits the suggestion to Professor Hartridge.

W. S. Stiles, Proc. Roy. Soc. (London) B123, 90 (1937).

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

Wright, W. D.

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

J. Opt. Soc. Am. (1)

J. Physiol. (London) (1)

R. W. Ditchburn and B. L. Ginsborg, J. Physiol. (London) 119, 1 (1953).

Proc. Phys. Soc. (London) (1)

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

Proc. Roy. Soc. (London) (3)

B. H. Crawford, Proc. Roy. Soc. (London) B124, 81 (1937).

W. S. Stiles, Proc. Roy. Soc. (London) B123, 90 (1937).

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

Proc. Royal Soc. (London) (1)

This method of positioning the subject was mentioned in a paper by W. S. Stiles, Proc. Royal Soc. (London) 27, 74 (1939). He credits the suggestion to Professor Hartridge.

Other (6)

Since the computer program we used for these calculations allowed us to use only points with equal numbers of replications, we were forced to omit two peripheral points.

S. Polyak, The Retina (University of Chicago Press, Chicago, 1941).

J. M. Enoch, Summated Response of the Retina to Light Entering Different Parts of the Pupil, doctoral dissertation, Ohio State Univ. (1956). University Microfilms 18, 789, Ann Arbor, Michigan.

f(x) = [sech2(x/d)]÷2d, − ∞ x∞

f(x)=(1+cosx)÷2π,-π<x<π =0,elsewhere

f(x)=abxb-1e-axb,x>0 =0,elsewhere.

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Figures (9)

Fig. 1
Fig. 1

Drawing of the experimental apparatus.

Fig. 2
Fig. 2

Results of a spectral run restricted to 6 mm of pupil entry, right eye. The subject is a protanomalous 40-year-old male, 4.00 diopters myopic, with normal visual acuity. The points for 620 nm are acceptably fitted with a parabola. The others are not.

Fig. 3
Fig. 3

Results of a spectral run restricted to 6 mm of pupil entry, right eye. The subject is a color-normal 21 year old female, 1.00 diopter myopic, with normal visual acuity. The points for 440, 460, 640, and 660 nm are acceptably fitted with parabolas. The others are not.

Fig. 4
Fig. 4

Subject A.S. (same subject as in Fig. 2). Solid dot-represent means of 10 brightness matches. Horizontal lines represent extremes. Data taken on day 1 of 3-day experiment, right eye.

Fig. 5
Fig. 5

Subject A.S. Data from day 2 of 3-day experiment. Solid dots represent the means of 10 brightness matches. The solid line is the best-fitting gaussian.

Fig. 6
Fig. 6

Subject A.S. Combined data from AM and PM of all 3 days of 3-day experiment. Each solid dot represents the mean of 30 observations.

Fig. 7
Fig. 7

Subject A.S. Combined data from all 3 days of 3-day experiment (same as Figure 6). Solid line (——) best-fitting gaussian, dashed line (– – –) best-fitting parabola. Functions fitted using all data points.

Fig. 8
Fig. 8

Subject A. S. Combined data from3 days (same as Fig. 6) Functions fitted using only points data included between solid vertical lines. Solid line (——) best-fitting gaussian, dashed line (– – –) best-fitting parabola.

Fig. 9
Fig. 9

Subject A.S. Combined data from 3 days (same as Fig. 6). Solid line (——) best-fitting gaussian derived using all points shown. A = 0.9040, B = 0.0670, C = 1.4832, K = 0.0130.

Tables (1)

Tables Icon

Table I Brightness matches of two typical trials.

Equations (5)

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η = 1 - 0.0850 x 2 + 0.0020 x 4 ( x = mm ) η = 0.379 + 0.621     cos 0.515 x ( x = rad ) .
η r = 0.25 ( 1 + cos     9.5 θ ) 2 .
Y = log 10 η - K 1 = K 2 + A e - B ( X - C ) 2
F ( obs ) = j = 1 k n j [ y ¯ j - f ( X ) ] 2 ÷ ( k - p ) j = 1 k i = 1 V n [ y ¯ i j - y ¯ j ] 2 ÷ ( N - k ) ;
Y = K 2 + A e - B ( X - C ) 2 ,