Abstract

A system is derived which permits evaluation of the corneal curvature. It relates the instrumental conditions of the photokeratoscope, the first derivative, instantaneous radius of the point on the surface forming the reflected image, and the position of the surface as determined by focusing upon this image. The experimental data obtained from a photograph of the reflected image can be used to test the validity of any hypothesized expression for the corneal contour. For the first time a proposed analytic form can be used directly in the evaluation, thus minimizing recourse to simplifying, but distorting, assumptions. The system is nonspecific and may be applied to the analysis of other aspheric surfaces. Its application to a nonphotographic technique of corneal measurement is presented.

© 1966 Optical Society of America

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References

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  1. Christopher Scheiner, Oculusive fundamenium Oplicum, Innsbruck, 1619.
  2. Hermann Helmholtz, Treatise on Physiological Optics, English transl. (Optical Society of America, 1924, Dover Publications, Inc., New York, 1965), Vol. I, Chap. 2, p. 9.
  3. L. Matthiessen, Pfluegers Arch. Ges. Physiol. 91, 295 (1902).
    [Crossref]
  4. J. W. Nordenson, Graefes Arch. Ophtholmol. 157, 528 (1956).
    [Crossref]
  5. Robert B. Mandell, Contact Lens Practice: Basic and Advanced (Charles C Thomas, Springfield, Ill., 1965), Chap. 3, p. 36.
  6. F. Berg, Acta Ophthalmol. 7, 225 (1929).
    [Crossref]
  7. H. Aubert, Pfluegers Arch. Ges Physiol. 35, 597 (1885).
    [Crossref]
  8. R. Bonnet and P. Cochet, Am. J. Optom. Arch. Am. Acad. Optom. 39, 227 (1962).
    [Crossref]
  9. A. Gullstrand in Treatise on Physiological Optics by H. von Helmholtz, English transl. (Optical Society of America, 1924, Dover Publications, Inc., New York, 1965), Vol. I, Appendix 314.
  10. W. Ludlam and S. Wittenberg, Am. J. Optom. Arch. Am. Acad. Optom. 43, 249 (1966).
    [Crossref]
  11. A. Gullstrand, Kgl. Svenska Vetenskaps akad. Handl. 28, 12 (1896). English translation by W. Ludlam, Am. J. Optom. Arch. Am. Acad. Optom. 43, 143 (1966).
    [Crossref]
  12. S. Wittenberg, Am. J. Optom. Arch. Am. Acad. Optom. 43, 198 (1966).
  13. F. Berg, Acta Ophthalmol. 7, 386 (1929).
    [Crossref]
  14. M. Amsler, Opthalmologica 96, 77 (1938).
    [Crossref]
  15. E. Streiff, Ophthalmologica 96, 84 (1938).
    [Crossref]
  16. H. Knoll, J. Opt. Soc. Am. 47, 221 (1957).
    [Crossref] [PubMed]
  17. E. Fincham, Med. Biol. Illust. 3, 87 (1953).
  18. J. Stone, Brit. J. Physiol. Opt. 19, 205 (1962).
  19. A. Reynolds and H. Kratt, Contacto 3, 53 (1959).
  20. H. Dekking, Graefes Arch. Ophthalmol. 124, 708 (1930).
    [Crossref]
  21. H. Knoll, Am. J. Optom. Arch. Am. Acad. Optom. 38, 389 (1961).
    [Crossref] [PubMed]
  22. All have been larger than 0.4 mm.
  23. G. Westheimer, Am. J. Optom Arch. Am. Acad. Optom. 42, 315 (1965).
    [Crossref] [PubMed]

1966 (2)

W. Ludlam and S. Wittenberg, Am. J. Optom. Arch. Am. Acad. Optom. 43, 249 (1966).
[Crossref]

S. Wittenberg, Am. J. Optom. Arch. Am. Acad. Optom. 43, 198 (1966).

1965 (1)

G. Westheimer, Am. J. Optom Arch. Am. Acad. Optom. 42, 315 (1965).
[Crossref] [PubMed]

1962 (2)

J. Stone, Brit. J. Physiol. Opt. 19, 205 (1962).

R. Bonnet and P. Cochet, Am. J. Optom. Arch. Am. Acad. Optom. 39, 227 (1962).
[Crossref]

1961 (1)

H. Knoll, Am. J. Optom. Arch. Am. Acad. Optom. 38, 389 (1961).
[Crossref] [PubMed]

1959 (1)

A. Reynolds and H. Kratt, Contacto 3, 53 (1959).

1957 (1)

1956 (1)

J. W. Nordenson, Graefes Arch. Ophtholmol. 157, 528 (1956).
[Crossref]

1953 (1)

E. Fincham, Med. Biol. Illust. 3, 87 (1953).

1938 (2)

M. Amsler, Opthalmologica 96, 77 (1938).
[Crossref]

E. Streiff, Ophthalmologica 96, 84 (1938).
[Crossref]

1930 (1)

H. Dekking, Graefes Arch. Ophthalmol. 124, 708 (1930).
[Crossref]

1929 (2)

F. Berg, Acta Ophthalmol. 7, 225 (1929).
[Crossref]

F. Berg, Acta Ophthalmol. 7, 386 (1929).
[Crossref]

1902 (1)

L. Matthiessen, Pfluegers Arch. Ges. Physiol. 91, 295 (1902).
[Crossref]

1896 (1)

A. Gullstrand, Kgl. Svenska Vetenskaps akad. Handl. 28, 12 (1896). English translation by W. Ludlam, Am. J. Optom. Arch. Am. Acad. Optom. 43, 143 (1966).
[Crossref]

1885 (1)

H. Aubert, Pfluegers Arch. Ges Physiol. 35, 597 (1885).
[Crossref]

Amsler, M.

M. Amsler, Opthalmologica 96, 77 (1938).
[Crossref]

Aubert, H.

H. Aubert, Pfluegers Arch. Ges Physiol. 35, 597 (1885).
[Crossref]

Berg, F.

F. Berg, Acta Ophthalmol. 7, 225 (1929).
[Crossref]

F. Berg, Acta Ophthalmol. 7, 386 (1929).
[Crossref]

Bonnet, R.

R. Bonnet and P. Cochet, Am. J. Optom. Arch. Am. Acad. Optom. 39, 227 (1962).
[Crossref]

Cochet, P.

R. Bonnet and P. Cochet, Am. J. Optom. Arch. Am. Acad. Optom. 39, 227 (1962).
[Crossref]

Dekking, H.

H. Dekking, Graefes Arch. Ophthalmol. 124, 708 (1930).
[Crossref]

Fincham, E.

E. Fincham, Med. Biol. Illust. 3, 87 (1953).

Gullstrand, A.

A. Gullstrand, Kgl. Svenska Vetenskaps akad. Handl. 28, 12 (1896). English translation by W. Ludlam, Am. J. Optom. Arch. Am. Acad. Optom. 43, 143 (1966).
[Crossref]

A. Gullstrand in Treatise on Physiological Optics by H. von Helmholtz, English transl. (Optical Society of America, 1924, Dover Publications, Inc., New York, 1965), Vol. I, Appendix 314.

Helmholtz, Hermann

Hermann Helmholtz, Treatise on Physiological Optics, English transl. (Optical Society of America, 1924, Dover Publications, Inc., New York, 1965), Vol. I, Chap. 2, p. 9.

Knoll, H.

H. Knoll, Am. J. Optom. Arch. Am. Acad. Optom. 38, 389 (1961).
[Crossref] [PubMed]

H. Knoll, J. Opt. Soc. Am. 47, 221 (1957).
[Crossref] [PubMed]

Kratt, H.

A. Reynolds and H. Kratt, Contacto 3, 53 (1959).

Ludlam, W.

W. Ludlam and S. Wittenberg, Am. J. Optom. Arch. Am. Acad. Optom. 43, 249 (1966).
[Crossref]

Mandell, Robert B.

Robert B. Mandell, Contact Lens Practice: Basic and Advanced (Charles C Thomas, Springfield, Ill., 1965), Chap. 3, p. 36.

Matthiessen, L.

L. Matthiessen, Pfluegers Arch. Ges. Physiol. 91, 295 (1902).
[Crossref]

Nordenson, J. W.

J. W. Nordenson, Graefes Arch. Ophtholmol. 157, 528 (1956).
[Crossref]

Reynolds, A.

A. Reynolds and H. Kratt, Contacto 3, 53 (1959).

Scheiner, Christopher

Christopher Scheiner, Oculusive fundamenium Oplicum, Innsbruck, 1619.

Stone, J.

J. Stone, Brit. J. Physiol. Opt. 19, 205 (1962).

Streiff, E.

E. Streiff, Ophthalmologica 96, 84 (1938).
[Crossref]

Westheimer, G.

G. Westheimer, Am. J. Optom Arch. Am. Acad. Optom. 42, 315 (1965).
[Crossref] [PubMed]

Wittenberg, S.

S. Wittenberg, Am. J. Optom. Arch. Am. Acad. Optom. 43, 198 (1966).

W. Ludlam and S. Wittenberg, Am. J. Optom. Arch. Am. Acad. Optom. 43, 249 (1966).
[Crossref]

Acta Ophthalmol. (2)

F. Berg, Acta Ophthalmol. 7, 225 (1929).
[Crossref]

F. Berg, Acta Ophthalmol. 7, 386 (1929).
[Crossref]

Am. J. Optom Arch. Am. Acad. Optom. (1)

G. Westheimer, Am. J. Optom Arch. Am. Acad. Optom. 42, 315 (1965).
[Crossref] [PubMed]

Am. J. Optom. Arch. Am. Acad. Optom. (4)

H. Knoll, Am. J. Optom. Arch. Am. Acad. Optom. 38, 389 (1961).
[Crossref] [PubMed]

W. Ludlam and S. Wittenberg, Am. J. Optom. Arch. Am. Acad. Optom. 43, 249 (1966).
[Crossref]

S. Wittenberg, Am. J. Optom. Arch. Am. Acad. Optom. 43, 198 (1966).

R. Bonnet and P. Cochet, Am. J. Optom. Arch. Am. Acad. Optom. 39, 227 (1962).
[Crossref]

Brit. J. Physiol. Opt. (1)

J. Stone, Brit. J. Physiol. Opt. 19, 205 (1962).

Contacto (1)

A. Reynolds and H. Kratt, Contacto 3, 53 (1959).

Graefes Arch. Ophthalmol. (1)

H. Dekking, Graefes Arch. Ophthalmol. 124, 708 (1930).
[Crossref]

Graefes Arch. Ophtholmol. (1)

J. W. Nordenson, Graefes Arch. Ophtholmol. 157, 528 (1956).
[Crossref]

J. Opt. Soc. Am. (1)

Kgl. Svenska Vetenskaps akad. Handl. (1)

A. Gullstrand, Kgl. Svenska Vetenskaps akad. Handl. 28, 12 (1896). English translation by W. Ludlam, Am. J. Optom. Arch. Am. Acad. Optom. 43, 143 (1966).
[Crossref]

Med. Biol. Illust. (1)

E. Fincham, Med. Biol. Illust. 3, 87 (1953).

Ophthalmologica (1)

E. Streiff, Ophthalmologica 96, 84 (1938).
[Crossref]

Opthalmologica (1)

M. Amsler, Opthalmologica 96, 77 (1938).
[Crossref]

Pfluegers Arch. Ges Physiol. (1)

H. Aubert, Pfluegers Arch. Ges Physiol. 35, 597 (1885).
[Crossref]

Pfluegers Arch. Ges. Physiol. (1)

L. Matthiessen, Pfluegers Arch. Ges. Physiol. 91, 295 (1902).
[Crossref]

Other (5)

A. Gullstrand in Treatise on Physiological Optics by H. von Helmholtz, English transl. (Optical Society of America, 1924, Dover Publications, Inc., New York, 1965), Vol. I, Appendix 314.

Robert B. Mandell, Contact Lens Practice: Basic and Advanced (Charles C Thomas, Springfield, Ill., 1965), Chap. 3, p. 36.

Christopher Scheiner, Oculusive fundamenium Oplicum, Innsbruck, 1619.

Hermann Helmholtz, Treatise on Physiological Optics, English transl. (Optical Society of America, 1924, Dover Publications, Inc., New York, 1965), Vol. I, Chap. 2, p. 9.

All have been larger than 0.4 mm.

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Figures (2)

Fig. 1
Fig. 1

The path of a ray traced from a point target, reflected from a surface, passing through the center of the coordinate system to intersect an image plane.

Fig. 2
Fig. 2

The defined points of the imagery established in photokeratoscopy

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

2 B = A + C .
A = tan 1 [ ( b y ) / ( a x ) ]
C = tan 1 ( y / x ) ,
B = 1 2 { tan 1 [ ( b y ) / ( a x ) ] + tan 1 ( y / x ) } .
B = tan 1 ( d x / d y ) ,
2 tan 1 ( d x d y ) = tan 1 ( b y a x ) + tan 1 ( y x ) .
2 d x / d y 1 ( d x / d y ) 2 = y / x + ( b y ) / ( a x ) 1 y / x · ( b y ) / ( a x ) .
x i a = K .
1 / u + 1 / u = 2 / r cos β .
u = [ ( a x ) 2 + ( b y ) 2 ] 1 / 2 , u = ( x i x ) / cos θ , β = θ + α ,
x = x 0 d 2 [ exp ( y x 0 d ) + exp ( y x 0 d ) ] + d ,
2 d x / d y / [ 1 ( d x / d y ) 2 ] = ( b y ) / ( a x ) .