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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 57, Iss. 4 — Apr. 1, 1967
  • pp: 452–456

Lambert Diffuse Reflection from General Quadric Surfaces

KOLMAN W. BRAND and FRANK A. SPAGNOLO  »View Author Affiliations

JOSA, Vol. 57, Issue 4, pp. 452-456 (1967)

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Employing geometrical optics and assuming Lambert reflection, a general method is developed for calculating the diffusely reflected light from a class of surfaces known as quadrics. The analysis is applied to several well-known nondegenerate as well as degenerate quadric surfaces for cases which are considered to be convex or concave with respect to the directions of incident light and observer vectors. For several examples from the convex category, the results are exact and agree with those previously obtained with other methods of development. The effects of shadowing are included for a few concave-surface geometries, but to the extent that diffraction around edges and multiple reflections are omitted, the results are approximate.

KOLMAN W. BRAND and FRANK A. SPAGNOLO, "Lambert Diffuse Reflection from General Quadric Surfaces," J. Opt. Soc. Am. 57, 452-456 (1967)

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  1. M. Sussman, J. Opt. Soc. Am. 48, 275 (1958).
  2. W. Rambauske and R. G. Gruenzel, J. Opt. Soc. Am. 55, 315 (1965).
  3. D. C. Look, Jr., J. Opt. Soc. Am. 55, 462 (1965).
  4. H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).
  5. In Eq. (3) and the ensuing derivation, the usual vector notation (→) is dropped and the quantity k is set equal to one.
  6. The symbol T, in vector-calculus notation, denotes the transpose of a matrix or vector.
  7. K. W. Brand and F. A. Spagnolo, Lambert Diffuse Reflection front General Quadric Surfaces, Grumman Research Department Report RE-278J, January, 1967.
  8. D. J. Struik, Differential Geomnetry (Addison-Wesley Company, Reading, Massachusetts, 1950).

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