Abstract

A general solution of the eikonal equation is used to derive general expressions for both the wave fronts and the caustic surface associated with an orthotomic system of rays in a homogeneous optical medium. Both wave front and caustic can be expressed as the sum of two vectors, the first being the direction vector of the ray and the second being the gradient of the arbitrary function occurring in the general solution of the eikonal equation. This vector can be determined from a knowledge of the angle characteristic function and is closely related to Herzberger’s diapoint characterization of the geometrical image.

© 1976 Optical Society of America

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References

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  1. John A. Kneisly II, "Local curvatures of wave fronts," J. Opt. Soc. Am. 54, 229–235 (1964).
  2. O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics (Academic, New York, 1972), Chap. X.
  3. Steven C. Parker, "Properties and applications of generalized ray tracing," M. S. thesis, University of Arizona, 1971; also published as Optical Sciences Center Tech. Rept. 71 (1971) (University of Arizona, Tucson).
  4. Reference 2, Chap. IX.
  5. Donald G. Burkhard and David L. Shealy, "Flux density for ray propagation in geometrical optics," J. Opt. Soc. Am. 63, 299–304 (1973).
  6. David L. Shealy and Donald G. Burkhard, "Caustic surfaces and irradiance for reflection and refraction from an ellipsoid, elliptic parabolid and elliptic cone," Appl. Opt. 12, 2955–2959 (1973).
  7. R. K. Luneburg, Mathematical Theory of Optics (University of California, Berkeley, 1966), p. 36 et seq. Luneberg's remarks here provided the motivation for the line of research that led to these results.
  8. Reference 2, Chap. VIII.
  9. See, for example, Max Herzberger, Modern Geometrical Optics (Interscience, New York, 1958), Chap. 16.
  10. Dirk J. Struik, Lectures on Classical Differential Geometry (Addison-Wesley, Reading, Mass., 1961), Chaps. 2 and 3.
  11. Reference 2, Chap. IX.
  12. See Refs. 5 and 6.
  13. Reference 9, p. 174.
  14. Reference 9, Chap. 7.
  15. Max Herzberger, "Symmetry and Asymmetry in Optical Images," in R. K. Luneburg (Ref. 7), pp. 440–448.
  16. Reference 9, pp. 260–263.

1973 (2)

1964 (1)

Burkhard, Donald G.

Herzberger, Max

See, for example, Max Herzberger, Modern Geometrical Optics (Interscience, New York, 1958), Chap. 16.

Max Herzberger, "Symmetry and Asymmetry in Optical Images," in R. K. Luneburg (Ref. 7), pp. 440–448.

Kneisly II, John A.

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (University of California, Berkeley, 1966), p. 36 et seq. Luneberg's remarks here provided the motivation for the line of research that led to these results.

Parker, Steven C.

Steven C. Parker, "Properties and applications of generalized ray tracing," M. S. thesis, University of Arizona, 1971; also published as Optical Sciences Center Tech. Rept. 71 (1971) (University of Arizona, Tucson).

Shealy, David L.

Stavroudis, O. N.

O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics (Academic, New York, 1972), Chap. X.

Struik, Dirk J.

Dirk J. Struik, Lectures on Classical Differential Geometry (Addison-Wesley, Reading, Mass., 1961), Chaps. 2 and 3.

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

Other (13)

R. K. Luneburg, Mathematical Theory of Optics (University of California, Berkeley, 1966), p. 36 et seq. Luneberg's remarks here provided the motivation for the line of research that led to these results.

Reference 2, Chap. VIII.

See, for example, Max Herzberger, Modern Geometrical Optics (Interscience, New York, 1958), Chap. 16.

Dirk J. Struik, Lectures on Classical Differential Geometry (Addison-Wesley, Reading, Mass., 1961), Chaps. 2 and 3.

Reference 2, Chap. IX.

See Refs. 5 and 6.

Reference 9, p. 174.

Reference 9, Chap. 7.

Max Herzberger, "Symmetry and Asymmetry in Optical Images," in R. K. Luneburg (Ref. 7), pp. 440–448.

Reference 9, pp. 260–263.

O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics (Academic, New York, 1972), Chap. X.

Steven C. Parker, "Properties and applications of generalized ray tracing," M. S. thesis, University of Arizona, 1971; also published as Optical Sciences Center Tech. Rept. 71 (1971) (University of Arizona, Tucson).

Reference 2, Chap. IX.

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