Abstract

The Stiles–Crawford effect is treated as an apodization in the plane of the entrance pupil of the eye by computing the pupil function from measured values of the line spread function. The resulting apodized spread function is shown to be different from the measured spread function. The differences are in the order of 10% to 20%, but may be quite significant in the light of certain neurological phenomena.

© 1965 Optical Society of America

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References

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  1. G. Westheimer and F. W. Campbell, J. Opt. Soc. Am. 52, 1040 (1962).
    [Crossref] [PubMed]
  2. J. Krauskopf, J. Opt. Soc. Am. 52, 1046 (1962).
    [Crossref]
  3. Apodization is defined as the occlusion of a pupil by a partially transmitting mask which may have varying transmittance over its surface. In this particular case, the apodization has radial symmetry. An aperture stop is another example of an apodization.
  4. E. O’Neill, Introduction to Statistical Optics (Addison Wesley Publishing Company, Inc., Reading, Massachusetts, 1963), p. 77.
  5. J. M. Enoch, J. Opt. Soc. Am. 48, 392 (1958).
    [Crossref] [PubMed]

1962 (2)

1958 (1)

Campbell, F. W.

Enoch, J. M.

Krauskopf, J.

O’Neill, E.

E. O’Neill, Introduction to Statistical Optics (Addison Wesley Publishing Company, Inc., Reading, Massachusetts, 1963), p. 77.

Westheimer, G.

J. Opt. Soc. Am. (3)

Other (2)

Apodization is defined as the occlusion of a pupil by a partially transmitting mask which may have varying transmittance over its surface. In this particular case, the apodization has radial symmetry. An aperture stop is another example of an apodization.

E. O’Neill, Introduction to Statistical Optics (Addison Wesley Publishing Company, Inc., Reading, Massachusetts, 1963), p. 77.

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Figures (2)

Fig. 1
Fig. 1

Comparison of the exponential fitted to the data by the author of Ref. 1 (dashed) to the function suggested in the present work (solid). Note that the present function has zero slope at the origin and that it lies below the exponential in the region near the origin just as in the original data.

Fig. 2
Fig. 2

Comparison of the apodized spread function (solid) with the present fit to the spread function (dashed). Note that the slope of the former is always less than the slope of the latter.

Equations (6)

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A ( x ) = ( const ) F ( β ) e - i β x d β ,
η = 0.25 ( 1.0 + cos 9.5 θ ) 2 ,
I ( x ) = | C η 1 2 F ( β ) e - i β x d β | 2 .
η = 0.25 [ 1.0 + 1.0 - 1 2 ( 9.5 θ ) 2 ] 2 .
or             FT [ A ( x ) ] = - β 2 FT [ A ( x ) ] , FT { β 2 FT [ A ( x ) ] } = - A ( x ) ,
I ( x ) = A ( x ) + c A ( x ) 2 .