Abstract

An optical method for measuring the thickness of transparent structures has been developed, and has been used to measure, in vivo, the thickness of the human cornea. The thickness is measured by placing the anterior surface of the cornea at the focus of a beam of coherent laser light and then measuring the spacing between the interference fringes generated by the reflected light. The thickness is then calculated from the fringe spacing. The method has been used to measure corneal thickness in frog and human corneas. These measurements have been correlated with histologic and pachometer measurements of corneal thickness. A significant capability of this technique is to measure the thickness of optically opaque corneas.

© 1975 Optical Society of America

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References

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  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968).
  2. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1964).
  3. N. Ehlers, Acta Ophthalmol. Suppl. 81, 11 (1965).
  4. S. Mishima, Arch. Ophthalmol. 73, 233 (1965).
    [Crossref] [PubMed]
  5. M. S. Norn, Acta Ophthalmol. 44, 212 (1966).
    [Crossref]
  6. D. M. Maurice, Invest. Ophthalmol. 6, 464 (1967).
    [PubMed]
  7. H. Von Helmholtz, Handbuch der physiologischen Optik, 3te Aufl. (edited by Gullstrand, von Kries, Nagel, Hamburg, and Leipzig: Leopold Voss-English trans., with additions, edited by Southall, publ. 1924–5 by The Optical Society of America; 3 vols, 1, pp. 326–329). Reprinted by Dover, New York (1964).
  8. G. von Bahr, Acta Ophthalmol. 26, 247 (1948).
  9. N. Ehlers and F. K. Hansen, Acta Ophthalmol. 49, 65 (1971).
    [Crossref]
  10. H. Goldmann, Ber. Dtsche. Ophthalmol. Ges. 49, 435 (1932).
  11. D. M. Maurice and A. A. Giardini, Br. J. Ophthalmol. 35, 169 (1951).
  12. D. D. Donaldson, Arch. Ophthalmol. 76, 25 (1966).
    [Crossref] [PubMed]
  13. R. F. Lowe, Am. J. Ophthalmol. 62, 7 (1966).
    [PubMed]
  14. S. Mishima and B. O. Hedbys, Arch. Ophthalmol. 80, 710 (1968).
    [Crossref] [PubMed]
  15. Fizeau, C. R. Acad. Sci. (Paris) 54, 1237 (1862).
  16. Schweitzer, Arch. Ophthalmol. 77, 548 (1967).
    [Crossref] [PubMed]
  17. H. Goldmann and W. Lotmar, Klin. MbI. Augenheilk 154, 324 (1969).
  18. D. G. Green, Science 168, 1240 (1970).
    [Crossref] [PubMed]
  19. D. G. Green and M. M. Cohen, Trans. Am. Acad. Ophthalmol. Otolaryngol. 75, 629 (1971).
    [PubMed]
  20. R. J. Gstalder and D. G. Green, Arch. Ophthalmol. 87, 269 (1972).
    [Crossref] [PubMed]

1972 (1)

R. J. Gstalder and D. G. Green, Arch. Ophthalmol. 87, 269 (1972).
[Crossref] [PubMed]

1971 (2)

N. Ehlers and F. K. Hansen, Acta Ophthalmol. 49, 65 (1971).
[Crossref]

D. G. Green and M. M. Cohen, Trans. Am. Acad. Ophthalmol. Otolaryngol. 75, 629 (1971).
[PubMed]

1970 (1)

D. G. Green, Science 168, 1240 (1970).
[Crossref] [PubMed]

1969 (1)

H. Goldmann and W. Lotmar, Klin. MbI. Augenheilk 154, 324 (1969).

1968 (1)

S. Mishima and B. O. Hedbys, Arch. Ophthalmol. 80, 710 (1968).
[Crossref] [PubMed]

1967 (2)

Schweitzer, Arch. Ophthalmol. 77, 548 (1967).
[Crossref] [PubMed]

D. M. Maurice, Invest. Ophthalmol. 6, 464 (1967).
[PubMed]

1966 (3)

M. S. Norn, Acta Ophthalmol. 44, 212 (1966).
[Crossref]

D. D. Donaldson, Arch. Ophthalmol. 76, 25 (1966).
[Crossref] [PubMed]

R. F. Lowe, Am. J. Ophthalmol. 62, 7 (1966).
[PubMed]

1965 (2)

N. Ehlers, Acta Ophthalmol. Suppl. 81, 11 (1965).

S. Mishima, Arch. Ophthalmol. 73, 233 (1965).
[Crossref] [PubMed]

1951 (1)

D. M. Maurice and A. A. Giardini, Br. J. Ophthalmol. 35, 169 (1951).

1948 (1)

G. von Bahr, Acta Ophthalmol. 26, 247 (1948).

1932 (1)

H. Goldmann, Ber. Dtsche. Ophthalmol. Ges. 49, 435 (1932).

1862 (1)

Fizeau, C. R. Acad. Sci. (Paris) 54, 1237 (1862).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1964).

Cohen, M. M.

D. G. Green and M. M. Cohen, Trans. Am. Acad. Ophthalmol. Otolaryngol. 75, 629 (1971).
[PubMed]

Donaldson, D. D.

D. D. Donaldson, Arch. Ophthalmol. 76, 25 (1966).
[Crossref] [PubMed]

Ehlers, N.

N. Ehlers and F. K. Hansen, Acta Ophthalmol. 49, 65 (1971).
[Crossref]

N. Ehlers, Acta Ophthalmol. Suppl. 81, 11 (1965).

Fizeau,

Fizeau, C. R. Acad. Sci. (Paris) 54, 1237 (1862).

Giardini, A. A.

D. M. Maurice and A. A. Giardini, Br. J. Ophthalmol. 35, 169 (1951).

Goldmann, H.

H. Goldmann and W. Lotmar, Klin. MbI. Augenheilk 154, 324 (1969).

H. Goldmann, Ber. Dtsche. Ophthalmol. Ges. 49, 435 (1932).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968).

Green, D. G.

R. J. Gstalder and D. G. Green, Arch. Ophthalmol. 87, 269 (1972).
[Crossref] [PubMed]

D. G. Green and M. M. Cohen, Trans. Am. Acad. Ophthalmol. Otolaryngol. 75, 629 (1971).
[PubMed]

D. G. Green, Science 168, 1240 (1970).
[Crossref] [PubMed]

Gstalder, R. J.

R. J. Gstalder and D. G. Green, Arch. Ophthalmol. 87, 269 (1972).
[Crossref] [PubMed]

Hansen, F. K.

N. Ehlers and F. K. Hansen, Acta Ophthalmol. 49, 65 (1971).
[Crossref]

Hedbys, B. O.

S. Mishima and B. O. Hedbys, Arch. Ophthalmol. 80, 710 (1968).
[Crossref] [PubMed]

Lotmar, W.

H. Goldmann and W. Lotmar, Klin. MbI. Augenheilk 154, 324 (1969).

Lowe, R. F.

R. F. Lowe, Am. J. Ophthalmol. 62, 7 (1966).
[PubMed]

Maurice, D. M.

D. M. Maurice, Invest. Ophthalmol. 6, 464 (1967).
[PubMed]

D. M. Maurice and A. A. Giardini, Br. J. Ophthalmol. 35, 169 (1951).

Mishima, S.

S. Mishima and B. O. Hedbys, Arch. Ophthalmol. 80, 710 (1968).
[Crossref] [PubMed]

S. Mishima, Arch. Ophthalmol. 73, 233 (1965).
[Crossref] [PubMed]

Norn, M. S.

M. S. Norn, Acta Ophthalmol. 44, 212 (1966).
[Crossref]

Schweitzer,

Schweitzer, Arch. Ophthalmol. 77, 548 (1967).
[Crossref] [PubMed]

von Bahr, G.

G. von Bahr, Acta Ophthalmol. 26, 247 (1948).

Von Helmholtz, H.

H. Von Helmholtz, Handbuch der physiologischen Optik, 3te Aufl. (edited by Gullstrand, von Kries, Nagel, Hamburg, and Leipzig: Leopold Voss-English trans., with additions, edited by Southall, publ. 1924–5 by The Optical Society of America; 3 vols, 1, pp. 326–329). Reprinted by Dover, New York (1964).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1964).

Acta Ophthalmol. (3)

G. von Bahr, Acta Ophthalmol. 26, 247 (1948).

N. Ehlers and F. K. Hansen, Acta Ophthalmol. 49, 65 (1971).
[Crossref]

M. S. Norn, Acta Ophthalmol. 44, 212 (1966).
[Crossref]

Acta Ophthalmol. Suppl. (1)

N. Ehlers, Acta Ophthalmol. Suppl. 81, 11 (1965).

Am. J. Ophthalmol. (1)

R. F. Lowe, Am. J. Ophthalmol. 62, 7 (1966).
[PubMed]

Arch. Ophthalmol. (5)

S. Mishima and B. O. Hedbys, Arch. Ophthalmol. 80, 710 (1968).
[Crossref] [PubMed]

Schweitzer, Arch. Ophthalmol. 77, 548 (1967).
[Crossref] [PubMed]

S. Mishima, Arch. Ophthalmol. 73, 233 (1965).
[Crossref] [PubMed]

D. D. Donaldson, Arch. Ophthalmol. 76, 25 (1966).
[Crossref] [PubMed]

R. J. Gstalder and D. G. Green, Arch. Ophthalmol. 87, 269 (1972).
[Crossref] [PubMed]

Ber. Dtsche. Ophthalmol. Ges. (1)

H. Goldmann, Ber. Dtsche. Ophthalmol. Ges. 49, 435 (1932).

Br. J. Ophthalmol. (1)

D. M. Maurice and A. A. Giardini, Br. J. Ophthalmol. 35, 169 (1951).

C. R. Acad. Sci. (Paris) (1)

Fizeau, C. R. Acad. Sci. (Paris) 54, 1237 (1862).

Invest. Ophthalmol. (1)

D. M. Maurice, Invest. Ophthalmol. 6, 464 (1967).
[PubMed]

Klin. MbI. Augenheilk (1)

H. Goldmann and W. Lotmar, Klin. MbI. Augenheilk 154, 324 (1969).

Science (1)

D. G. Green, Science 168, 1240 (1970).
[Crossref] [PubMed]

Trans. Am. Acad. Ophthalmol. Otolaryngol. (1)

D. G. Green and M. M. Cohen, Trans. Am. Acad. Ophthalmol. Otolaryngol. 75, 629 (1971).
[PubMed]

Other (3)

H. Von Helmholtz, Handbuch der physiologischen Optik, 3te Aufl. (edited by Gullstrand, von Kries, Nagel, Hamburg, and Leipzig: Leopold Voss-English trans., with additions, edited by Southall, publ. 1924–5 by The Optical Society of America; 3 vols, 1, pp. 326–329). Reprinted by Dover, New York (1964).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968).

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1964).

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Figures (8)

FIG. 1
FIG. 1

Interference-fringe formation.

FIG. 2
FIG. 2

Geometric relationships for case of plane transparent plate.

FIG. 3
FIG. 3

Geometric relationships for (a) concentric spherical shell and (b) detail of rays reflected from outer shell.

FIG. 4
FIG. 4

Experimental apparatus.

FIG. 5
FIG. 5

Interference fringes generated by light reflected from (a) normal bullfrog cornea and (b) after injection of air into anterior chamber of the eye.

FIG. 6
FIG. 6

Patterns obtained from normal human cornea. Insert shows fringes from central portion of pattern at 2.4× magnification.

FIG. 7
FIG. 7

Fringes from patient with clinically opaque cornea owing to a lye burn. Insert shows central pattern at 1.6× magnification.

FIG. 8
FIG. 8

Fringes from tear film on human eye.

Equations (17)

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u ( x , y ) = 1 e j k r ¯ 0 / j λ r ¯ 0 + p e j k r ¯ 1 / j λ r ¯ 1 ,
I ( x , y ) = I 0 [ 1 + p 2 + 2 p cos ( k a x / r 0 ) ] .
δ = λ r 0 2 / d a sin θ ,
C N / C M = sin C M N = sin 2 α
C F / C M = sin α .
C F = F D tan β = t tan β ,
C N = t tan β ( sin 2 α ) / sin α .
n sin α = n sin β .
C N = t sin 2 α [ ( n / n ) 2 sin 2 α ] 1 / 2 ,
t = λ r 0 2 f [ ( n / n ) 2 sin 2 α ] 1 / 2 d sin 2 α ,
ϕ 2 sin ϕ 2 = B E R t t tan β R t .
a p = R ϕ cos α ,
a p = t sin 2 α [ ( n / n ) 2 sin 2 α ] 1 / 2 R R t .
t = 1 1 / t 2 + 1 / R ,
λ r 0 2 f / d = λ d f .
λ d f = λ ( d / D ) f D ,
t 2 = λ ( d / D ) f D ( n 2 sin 2 α ) 1 / 2 sin 2 α ,