Abstract

A quantitative statistical evaluation of peripheral astigmatism in the horizontal meridian of emmetropic human eyes has been made, using the measurements of Rempt et al. on 363 subjects. A hypothesis of Ferree, Rand, and Hardy, according to which human eyes fall into two distinct classes with respect to Sturm’s interval, is not supported by the present material. The mean values of Sturm’s interval at 20°, 40°, and 60° eccentricity can be well approximated by a symmetrical curve whose axis forms an angle of 4° with the fixation axis and therefore is close to the optical axis of the eye as derived from the Purkinje images. Theoretical values for Sturm’s interval calculated from a relatively simple eye model with aspherics, based on Gullstrand’s model, though lying within the range of experimental findings, do not fit well Rempt’s average values.

© 1974 Optical Society of America

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References

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  1. F. Rempt, J. Hoogerheide, and W. P. H. Hoogenboom, Ophthalmologica 162, 1 (1971).
    [Crossref]
  2. C. E. Ferree, G. Rand, and C. Hardy, Arch. Ophthalmol. 5, 717 (1931).
    [Crossref]
  3. W. Lotmar, J. Opt. Soc. Am. 61, 1522 (1971).
    [Crossref]
  4. Y. Le Grand, in Optique physiologique I (Ed. Revue d’Optique, Paris, 1952), p. 43.
  5. R. Bonnet and P. Cochet, Bull. Mém. Soc. Fr. d’Ophtalmol. 73, 688 (1960).
  6. O. Pomerantzeff, H. Fish, J. Govignon, and C. L. Schepens, Ann. Ophthalmol. 3, 815 (1971).
    [PubMed]

1971 (3)

F. Rempt, J. Hoogerheide, and W. P. H. Hoogenboom, Ophthalmologica 162, 1 (1971).
[Crossref]

W. Lotmar, J. Opt. Soc. Am. 61, 1522 (1971).
[Crossref]

O. Pomerantzeff, H. Fish, J. Govignon, and C. L. Schepens, Ann. Ophthalmol. 3, 815 (1971).
[PubMed]

1960 (1)

R. Bonnet and P. Cochet, Bull. Mém. Soc. Fr. d’Ophtalmol. 73, 688 (1960).

1931 (1)

C. E. Ferree, G. Rand, and C. Hardy, Arch. Ophthalmol. 5, 717 (1931).
[Crossref]

Bonnet, R.

R. Bonnet and P. Cochet, Bull. Mém. Soc. Fr. d’Ophtalmol. 73, 688 (1960).

Cochet, P.

R. Bonnet and P. Cochet, Bull. Mém. Soc. Fr. d’Ophtalmol. 73, 688 (1960).

Ferree, C. E.

C. E. Ferree, G. Rand, and C. Hardy, Arch. Ophthalmol. 5, 717 (1931).
[Crossref]

Fish, H.

O. Pomerantzeff, H. Fish, J. Govignon, and C. L. Schepens, Ann. Ophthalmol. 3, 815 (1971).
[PubMed]

Govignon, J.

O. Pomerantzeff, H. Fish, J. Govignon, and C. L. Schepens, Ann. Ophthalmol. 3, 815 (1971).
[PubMed]

Hardy, C.

C. E. Ferree, G. Rand, and C. Hardy, Arch. Ophthalmol. 5, 717 (1931).
[Crossref]

Hoogenboom, W. P. H.

F. Rempt, J. Hoogerheide, and W. P. H. Hoogenboom, Ophthalmologica 162, 1 (1971).
[Crossref]

Hoogerheide, J.

F. Rempt, J. Hoogerheide, and W. P. H. Hoogenboom, Ophthalmologica 162, 1 (1971).
[Crossref]

Le Grand, Y.

Y. Le Grand, in Optique physiologique I (Ed. Revue d’Optique, Paris, 1952), p. 43.

Lotmar, W.

Pomerantzeff, O.

O. Pomerantzeff, H. Fish, J. Govignon, and C. L. Schepens, Ann. Ophthalmol. 3, 815 (1971).
[PubMed]

Rand, G.

C. E. Ferree, G. Rand, and C. Hardy, Arch. Ophthalmol. 5, 717 (1931).
[Crossref]

Rempt, F.

F. Rempt, J. Hoogerheide, and W. P. H. Hoogenboom, Ophthalmologica 162, 1 (1971).
[Crossref]

Schepens, C. L.

O. Pomerantzeff, H. Fish, J. Govignon, and C. L. Schepens, Ann. Ophthalmol. 3, 815 (1971).
[PubMed]

Ann. Ophthalmol. (1)

O. Pomerantzeff, H. Fish, J. Govignon, and C. L. Schepens, Ann. Ophthalmol. 3, 815 (1971).
[PubMed]

Arch. Ophthalmol. (1)

C. E. Ferree, G. Rand, and C. Hardy, Arch. Ophthalmol. 5, 717 (1931).
[Crossref]

Bull. Mém. Soc. Fr. d’Ophtalmol. (1)

R. Bonnet and P. Cochet, Bull. Mém. Soc. Fr. d’Ophtalmol. 73, 688 (1960).

J. Opt. Soc. Am. (1)

Ophthalmologica (1)

F. Rempt, J. Hoogerheide, and W. P. H. Hoogenboom, Ophthalmologica 162, 1 (1971).
[Crossref]

Other (1)

Y. Le Grand, in Optique physiologique I (Ed. Revue d’Optique, Paris, 1952), p. 43.

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Figures (6)

Fig. 1
Fig. 1

Histograms of Sturm’s interval at 20° visual angle in the horizontal meridian of 363 near-emmetropic adult subject.

Fig. 2
Fig. 2

Same as Fig. 1 but at 40° visual angle.

Fig. 3
Fig. 3

Same as Fig. 1 but at 60° visual angle.

Fig. 4
Fig. 4

Histograms of four subgroups of 90 subjects each, using the same material as for Fig. 3a.

Fig. 5
Fig. 5

Mean values of Sturm’s interval of 726 eyes approximated by curve from Eq. (1). Zero point of eccentricity is displaced by 4° in respect to fixation axis as used for experimental determinations. Broken line: values calculated from theoretical eye model (Ref. 3).

Fig. 6
Fig. 6

Histograms of differences of Sturm’s interval for the right and left eye of individual subjects; 363 cases.

Tables (2)

Tables Icon

Table I Mean values of Sturm’s interval for 726 near-emmetropic eyes, in diopters.

Tables Icon

Table II Fractions of cases for which the difference of Sturm’s interval between the right and left eye, Δ, is not more than ±1 diopter. Mean values are also shown.

Equations (2)

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Δ = α 1.5 × 10 - 2 ,
k = 1000 n Δ s f ( f Δ s ) ,