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35, 3422–3426 (1996). McLeod, J. , ‘‘The Axicon: A New Type of Optical Element,’’ J. Opt. Soc. , 44, 592–597 (1954). McLeod, J. , ‘‘Axicons and Their Uses,’’ J. Opt. Soc. , 50, 166–169 (1960). Menchaca, C. , ‘‘Directional Curvatures in a Conic Surface,’’ Appl. , 23, 3258–3260 (1984). Menchaca, C. , ‘‘Toroidal and Sphero-Cylindrical Surfaces,’’ Appl. , 25, 3008–3009 (1986). , ‘‘Geometrical Design for Aspheric Reflecting Systems,’’ Appl. , 18, 4182–4186 (1979a). © 2004 by Marcel Dekker, Inc. , ‘‘Aspheric Potpourri,’’ Appl.

1 WAVE NATURE OF LIGHT AND FERMAT’S PRINCIPLE The nature of light is one of the most difficult concepts in modern physics. Due to its quantum nature, light has to be considered in some experiments as an electromagnetic wave, and in some others it has to be considered as a particle. However, in ordinary optical instruments we may just think of the light as an electromagnetic wave with an electric field and a magnetic field, mutually perpendicular, and both perpendicular to the path of propagation.

Cornejo-Rodrı´ guez, A. , ‘‘Graphical Ray Tracing for Conic Surfaces,’’ Appl. , 18, 3075 (1979). Feder, D. , ‘‘Differentiation of Ray Tracing Equations with Respect to Construction Parameters of Rotationally Symmetric Optics,’’ J. Opt. Soc. , 58, 1494 (1968). Herzberger, M. ‘‘Some Remarks on Ray Tracing,’’ J. Opt. Soc. , 41, 805–807 (1951). Herzberger, M. ‘‘Automatic Ray Tracing,’’ J. Opt. Soc. , 47, 736–739 (1957). Herzberger, M. and Hoadley, H. , ‘‘The Calculation of Aspherical Correcting Surfaces,’’ J.

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