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.
G.1985 Symplectically invariant WKB wave functions.Phys
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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.