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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 63, Iss. 3 — Mar. 1, 1973
  • pp: 299–304

Flux density for ray propagation in geometrical optics

Donald G. Burkhard and David L. Shealy  »View Author Affiliations


JOSA, Vol. 63, Issue 3, pp. 299-304 (1973)
http://dx.doi.org/10.1364/JOSA.63.000299


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Abstract

A general formula is derived that specifies the illumination (flux density) over an arbitrary receiver surface when light rays are reflected by or refracted through a curved surface. The direction of the deflected ray and its intersection with the receiving surface, used with the equation for the surfaces, lead to a transformation that maps an element of deflecting area onto the receiving area, by means of the jacobian determinant. A formula for the flux density along a ray path follows as a special case. An equation for the caustic surface is obtained from the latter. As an example radiation flux-density contours are calculated for a plane wave reflected from a sphere. Flux density and the caustic surface are calculated for a plane wave reflected onto a plane from a concave spherical lens and also for a plane wave refracted onto a plane through a hemisphere.

Citation
Donald G. Burkhard and David L. Shealy, "Flux density for ray propagation in geometrical optics," J. Opt. Soc. Am. 63, 299-304 (1973)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-63-3-299


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References

  1. Max Herzberger, Modern Geometrical Optics (Wiley-Interscience, New York, 1958).
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  6. Joseph B. Keller and William Streifer, J. Opt. Soc. Am. 61, 40 (1971).
  7. V. A. Fock, Electromagnetic Diffraction and Propagation Problems (Pergamon, New York, 1965).
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  11. M. M. Lipschutz, Differential Geometry (Schaum's Outline Series) (McGraw-Hill, New York, 1969).

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