A reformulation of geometrical optics using ray time and ray energy as canonical coordinates, with an Airy transform connecting the two phase spaces, yields nonsingular envelope equations near reflection points.
D.1973 Group velocity and nonlinear dispersive wave propagation.Proc
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Geometrical optics in phase space
A reformulation of geometrical optics using ray time and ray energy as canonical coordinates, with an Airy transform connecting the two phase spaces, yields nonsingular envelope equations near reflection points.