## Geometrical optics and the field at a caustic with applications to radio wave propagation between aircraft |

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air-to-air propagation altitude antenna aperture plane approximation calculation Chapter constant Contour cusp DATA ON PROPAGATION decibels derivative term discontinuity distance elevated layers evaluated expansion exponential profile expression feet field pattern field strength field strength curves free space field Fresnel zone function geometrical optics height h height zero Hence homogeneous atmosphere initial angle interference region k(Cr linear profile meteorological data method Miles db multilinear profile obtained occur phase integral waves plane wave plot propagation between aircraft PROPAGATION FLIGHTS radio hole radio propagation radio wave propagation radiosonde ratio ray family ray path ray theory result ray tracing receiver heights refractive index gradient refractive index profile second caustic second derivative Shoran shown in Fig slope Snell's Law solution spectrum of plane square root profile square root section stationary phase stationary points substandard superstandard Taylor expansion Taylor series tion transmitter and receiver trilinear profile whence yields