Abstract

Light from a set of target rings is directed onto a living cornea at near-normal incidence. The reflected real image of the target is photographed simultaneously with a profile of the cornea projected onto a scale that indicates the radius of a reference sphere. The difference of position between any target point on the photograph and the corresponding point on a photograph taken with a spherical reflector in the apparatus is used to calculate the departure of the cornea from the reference sphere. Errors of positioning of the cornea with respect to the apparatus are compensated by calculating the asphericity of the cornea for a reference sphere that most closely matches the corneal surface for the central 3-mm-diam zone. In tests, the standard deviation of calculated asphericity at the edge of the 9-mm-diam region observed on known surfaces was 4.3 μm.

© 1972 Optical Society of America

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References

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  1. J. Stone, Brit. J. Physiol. Opt. 19, 205 (1962).
  2. H. von Helmholtz, Treatise on Physiologicol Optics, English translation by J. C. P. Southall (Opt. Soc. Am., Rochester, N. Y., 1924; Dover, New York, 1962), Vol. 1, pp. 10–14.
  3. A. Gullstrand, Kgl. Svenska Vetenskaps Akad. Handl. 28, 12 (1896), English translation by W. Ludlam, Am. J. Optom. Arch. Am. Acad. Optom. 43, 249 (1966).
    [Crossref]
  4. L. Evershed-Martin, Brit. J. Physiol. Opt. 16, 24 (1959).
  5. R. Bonnet and P. Cochet, Am. J. Optom. Arch. Am. Acad. Optom. 39, 227 (1962).
    [Crossref]
  6. A. G. Bennett, Brit. J. Physiol. Opt. 21, 234 (1964).
  7. M. Uhlig, Ophthalmologica 153, 43 (1967).
    [Crossref]
  8. S. Wittenberg and W. M. Ludlam, J. Opt. Soc. Am. 56, 1612 (1966).
    [Crossref]
  9. B. A. J. Clark, Master’s thesis, University of Melbourne, 1966.
  10. J. H. Prince and W. H. Havener, Am. J. Ophthalmol. 43, 461 (1957).
    [PubMed]
  11. B. A. J. Clark and L. G. Carney, Am. J. Optom. Arch. Am. Acad. Optom. 48, 333 (1971).
    [PubMed]
  12. A. Gullstrand in Appendix II of Ref. 2, p. 314.
  13. B. A. J. Clark, Appl. Opt. 7, 1403 (1968).
    [Crossref]
  14. L. G. Carney, Master’s thesis, University of Melbourne, 1970.
  15. B. A. J. Clark, PhD thesis, University of Melbourne, 1971.

1971 (1)

B. A. J. Clark and L. G. Carney, Am. J. Optom. Arch. Am. Acad. Optom. 48, 333 (1971).
[PubMed]

1968 (1)

1967 (1)

M. Uhlig, Ophthalmologica 153, 43 (1967).
[Crossref]

1966 (1)

1964 (1)

A. G. Bennett, Brit. J. Physiol. Opt. 21, 234 (1964).

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]

1959 (1)

L. Evershed-Martin, Brit. J. Physiol. Opt. 16, 24 (1959).

1957 (1)

J. H. Prince and W. H. Havener, Am. J. Ophthalmol. 43, 461 (1957).
[PubMed]

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, 249 (1966).
[Crossref]

Bennett, A. G.

A. G. Bennett, Brit. J. Physiol. Opt. 21, 234 (1964).

Bonnet, R.

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

Carney, L. G.

B. A. J. Clark and L. G. Carney, Am. J. Optom. Arch. Am. Acad. Optom. 48, 333 (1971).
[PubMed]

L. G. Carney, Master’s thesis, University of Melbourne, 1970.

Clark, B. A. J.

B. A. J. Clark and L. G. Carney, Am. J. Optom. Arch. Am. Acad. Optom. 48, 333 (1971).
[PubMed]

B. A. J. Clark, Appl. Opt. 7, 1403 (1968).
[Crossref]

B. A. J. Clark, Master’s thesis, University of Melbourne, 1966.

B. A. J. Clark, PhD thesis, University of Melbourne, 1971.

Cochet, P.

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

Evershed-Martin, L.

L. Evershed-Martin, Brit. J. Physiol. Opt. 16, 24 (1959).

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, 249 (1966).
[Crossref]

A. Gullstrand in Appendix II of Ref. 2, p. 314.

Havener, W. H.

J. H. Prince and W. H. Havener, Am. J. Ophthalmol. 43, 461 (1957).
[PubMed]

Ludlam, W. M.

Prince, J. H.

J. H. Prince and W. H. Havener, Am. J. Ophthalmol. 43, 461 (1957).
[PubMed]

Stone, J.

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

Uhlig, M.

M. Uhlig, Ophthalmologica 153, 43 (1967).
[Crossref]

von Helmholtz, H.

H. von Helmholtz, Treatise on Physiologicol Optics, English translation by J. C. P. Southall (Opt. Soc. Am., Rochester, N. Y., 1924; Dover, New York, 1962), Vol. 1, pp. 10–14.

Wittenberg, S.

Am. J. Ophthalmol. (1)

J. H. Prince and W. H. Havener, Am. J. Ophthalmol. 43, 461 (1957).
[PubMed]

Am. J. Optom. Arch. Am. Acad. Optom. (2)

B. A. J. Clark and L. G. Carney, Am. J. Optom. Arch. Am. Acad. Optom. 48, 333 (1971).
[PubMed]

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

Appl. Opt. (1)

Brit. J. Physiol. Opt. (3)

A. G. Bennett, Brit. J. Physiol. Opt. 21, 234 (1964).

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

L. Evershed-Martin, Brit. J. Physiol. Opt. 16, 24 (1959).

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, 249 (1966).
[Crossref]

Ophthalmologica (1)

M. Uhlig, Ophthalmologica 153, 43 (1967).
[Crossref]

Other (5)

B. A. J. Clark, Master’s thesis, University of Melbourne, 1966.

H. von Helmholtz, Treatise on Physiologicol Optics, English translation by J. C. P. Southall (Opt. Soc. Am., Rochester, N. Y., 1924; Dover, New York, 1962), Vol. 1, pp. 10–14.

L. G. Carney, Master’s thesis, University of Melbourne, 1970.

B. A. J. Clark, PhD thesis, University of Melbourne, 1971.

A. Gullstrand in Appendix II of Ref. 2, p. 314.

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Figures (14)

Fig. 1
Fig. 1

The autocollimating photokeratoscope. The topographic system begins with lamp a and the profile system with lamp a′.

Fig. 2
Fig. 2

Ray paths in the topographic system. Virtual images are shown by dashed lines.

Fig. 3
Fig. 3

Calibration keratogram of 7.225-mm-radius glass hyperhemisphere. (i) Topographic-system image, (ii) profile-system scale, (iii) T indicates test surface, (iv) accommodation stimulus scale, (v) subject, time, and date indicator, (vi) seconds clock.

Fig. 4
Fig. 4

Central and general ray paths before and after reflection from the cornea. Calculation of Sjm.

Fig. 5
Fig. 5

Keratogram of the cornea of a living human right eye. The topographic-system image (reversed right-to-left) is vignetted by the subject’s upper eyelid and lashes. The decreased diameter of the outer rings compared with the calibration image (Fig. 3) indicates positive values of asphericity, i.e., the cornea shows the usual “flattening” towards the periphery. The photographed area is about 10 mm in diameter at the cornea.

Fig. 6
Fig. 6

Elevation showing the corneal profile that is projected by the profile system, and the relationship between this profile, the axes, and the profile and vertical section of the second reference sphere. IA is the instrument axis, OA is the first approximation to the ophthalmometric axis, A is the section of the second reference sphere in the vertical plane containing the IA, B is the profile of the second reference sphere of radius K2, C is the profile of the cornea, o′ is the point at which the profile scale is read, and z′ is the center of the second reference sphere.

Fig. 7
Fig. 7

Perspective view showing the two-dimensional separation of the instrument and ophthalmometric axes. Line oz′ is the normal to the cornea at o. K2 is the radius of the second reference sphere. The plane oo’z is horizontal so that m′ = 1 and m = 3. IA is the instrument axis, OA is the first approximation to the ophthalmometric axis, C is the profile of the cornea, D represents the light from the topographic system, and E, light from the profile system. The intersection point of the corneal surface and the IA is approximately at o, and z′ is the center of the second reference sphere.

Fig. 8
Fig. 8

A meridional plane passing through the instrument axis, the projection of the ophthalmometric axis on the plane, and the circle indicating the intersection of the second reference sphere with the plane. Calculation of Sqm′ and θqm′.

Fig. 9
Fig. 9

The separation of the two axes in the meridional plane is increased by Cm. Recalculation of Sqm′ and θqm′.

Fig. 10
Fig. 10

Determination of Em.

Fig. 11
Fig. 11

Calculation of the radius Kqm′ of a circle that passes through P and p, with center on the ophthalmometric axis.

Fig. 12
Fig. 12

Calculation of Sqm″, θqm″, and Em′.

Fig. 13
Fig. 13

Comparison of the cornea with a known reference sphere centered on the ophthalmometric axis. Calculation of Sqm‴ and θqm‴.

Fig. 14
Fig. 14

Computer-plotted perspective diagram showing asphericity Sqm″ of a living human cornea (right eye) exhibiting keratoconus (marked conical shape). K4, the optic-cap radius of curvature, is 7.203 mm.

Equations (14)

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α j m = 1 2 arctan [ ( R sin β ) / ( R cos β - K 1 - S j m ) ] .
δ S j m = ( K 1 + S j - 1 , m ) ( θ j m - θ j - 1 , m ) ( α j m + α j - 1 , m ) / 2.
m = 1 2 arctan { [ R sin ( T m / R ) ] / [ R cos ( T m / R ) - K 1 ] } .
tan θ q m = ( H j m - K 1 tan m ) / [ ( K 1 + S j m ) cos θ j m ] , S q m = [ ( K 1 + S j m ) cos θ j m / cos θ j m ] - K 1 / cos m , H q m = H j m - K 1 tan m .
U = [ m = 1 8 ( sign m ) ω m K 1 / cos m ] / ( m = 1 8 tan m ) .
tan θ q m = ( H j m - K 1 tan m - C m ) / [ ( K 1 + S j m ) cos θ j m + C m / tan m ] , S q m = { [ ( K 1 + S j m ) cos θ j m + C m / tan m ] / cos θ j m } - K 1 / cos m + C m / sin m ,
H q m = H j m - K 1 tan m - C m .
ρ m = arcsin [ ( K 1 tan m + C m ) / ( K 1 + S o m ) ]
E m = ( K 1 + S o m ) cos ρ m + C m / tan m - K 1 / cos m - C m / sin m .
ϕ q m = 2 arctan ( K 1 / cos m + E m + C m / sin m - ( K 1 / cos m + C m / sin m + S q m ) cos θ q m ( K 1 / cos m + C m / sin m + S q m ) sin θ q m )
E m = D ¯ + K 1 / cos m + C m / sin m + E m - K 4 m ,
K 4 m = [ K 4 2 - ( K 1 tan m + C m ) 2 ] 1 2 .
θ q m = arctan { H q m / [ ( K 1 / cos m + C m / sin m + S q m ) cos θ q m + D ¯ ] }
θ q m = arctan { H q m / [ ( K 1 / cos m + C m / sin m + S q m ) cos θ q m + D ¯ + K c - K 3 ] }