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.

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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).
  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).
  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.

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.

P. Moon and D. E. Spencer, J. Opt. Soc. Am. 34, 319 (1944).

Nelson, J. H.

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

Polyak, S.

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

Spencer, D. E.

P. Moon and D. E. Spencer, J. Opt. Soc. Am. 34, 319 (1944).

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

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

Wright, W. D.

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

Other

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

P. Moon and D. E. Spencer, J. Opt. Soc. Am. 34, 319 (1944).

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

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.

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

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

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.

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).

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

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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