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.2022 The Van Vleck formula on Ehrenfest time scales and stationary phase asymptotics for frequency-dependent phases.Commun
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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.