Fractional Legendre transformation and its use in Hamilton's formalism

Miguel Angel Alonso; Gregory W. Forbes

doi:10.1117/12.231076

5 February 1996 Fractional Legendre transformation and its use in Hamilton's formalism

Miguel Angel Alonso, Gregory W. Forbes

Proceedings Volume 2730, Second Iberoamerican Meeting on Optics; (1996) https://doi.org/10.1117/12.231076
Event: Second Iberoamerican Meeting on Optics, 1995, Guanajuato, Mexico

Abstract

A generalization of Hamilton's formalism for geometrical optics is given here to provide more convenient descriptions of the optical properties of certain classes of systems. This generalization is made by replacing the usual points and planes that are used as references in the definition of characteristic functions by more general surfaces. In this context, the fractional Legendre transform is used in the semigeometrical estimation of field propagators to eliminate errors introduced by caustics.

Citation Download Citation

Miguel Angel Alonso and Gregory W. Forbes "Fractional Legendre transformation and its use in Hamilton's formalism", Proc. SPIE 2730, Second Iberoamerican Meeting on Optics, (5 February 1996); https://doi.org/10.1117/12.231076

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