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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 60, Iss. 7 — Jul. 1, 1970
  • pp: 981–985

Planar Reflected Imagery in Photokeratoscopy

SIDNEY WITTENBERG and WILLIAM M. LUDLAM  »View Author Affiliations


JOSA, Vol. 60, Issue 7, pp. 981-985 (1970)
http://dx.doi.org/10.1364/JOSA.60.000981


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Abstract

The locus of photokeratoscope target points that yield images lying in a plane perpendicular to the camera axis was evaluated for a 15.8-mm radius spherical convex reflector. The linear transform of an ellipse was fitted to sets of theoretical and experimental points by the method of least squares. The semimajor and semiminor axes for the theoretical and experimental points were 103.1, 40.0, 95.0, and 42.9 mm, respectively. The theoretical points conformed to the linear transform of the ellipse with a coefficient of correlation departing from unity by less than 4 parts in 10 000. For the combined experimental points, the coefficient of correlation was 0.998. The theoretical locus was also calculated for an elliptical reflector simulating the gross dimensions of the cornea and found to be essentially elliptical, closely approximating that for the spherical reflector.

Citation
SIDNEY WITTENBERG and WILLIAM M. LUDLAM, "Planar Reflected Imagery in Photokeratoscopy," J. Opt. Soc. Am. 60, 981-985 (1970)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-60-7-981


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References

  1. S. Wittenberg and W. Ludlam, J. Opt. Soc. Am. 56, 1612 (1966).
  2. W. Ludlam and S. Wittenberg, Am. J. Optom., Arch. Am. Acad. Optom. 43, 249 (1966).
  3. H. Dekking, Graefes Arch. Ophthalmol. 124, 708 (1930).
  4. 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).
  5. F. Berg, Acta Ophthalmol. 7, 386 (1929).
  6. E. Fincham, Med. Biol. Illust. 3, 87 (1953).
  7. H. Knoll, R. Stimson, and C. Weeks, J. Opt. Soc. Am. 47, 221 (1957).
  8. H. Knoll, Am. J. Optom., Arch. Am. Acad. Optom. 38, 399 (1961).
  9. J. Stone, Brit. J. Physiological Opt. 19, 205 (1962).
  10. Primed variables are employed here because position was measured with respect to the center of the steel ball, and not with respect to the principal plane, for which the coordinate axes of the theoretical construct is defined.
  11. The goodness of fit of the ellipse to the experimentally or theoretically determined points, as indicated by the correlation coefficient, is somewhat exaggerated by the linear transformation applied.
  12. H. von Helmholtz, Treatise on Physiological Optics, edited by J. P. C. Southall (Optical Society of America, 1924; Dover, New York, 1965), Vol. I, Ch. 2, p. 9.

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