While the pure Doppler shift is a simple affair, the frequency shift between an emitter of monochromatic light and a receiver becomes a rather complex event if these move at arbitrary speeds through a transmitting medium which is optically heterogeneous and anisotropic. In that case, such phenomena as aberration of light, light drag by flowing matter, the so-called “local-index-effect,” and the bending of the light path due to refraction, combine with the pure Doppler shift in affecting the frequency relation.
Anisotropy of the medium, as resulting from light drag by flowing matter, is inevitable if there does not exist an inertial frame of reference in which the medium is everywhere at rest. An example is the shock front.
The theory of these effects is developed on the basis of the “principle of the invariance of the phase function under Lorentz transformation” and the “principle of the constancy of the frequency in stationary media.”
Formulas are developed for the frequency shift between emitter and receiver if the signal goes from the emitter via one or more reflectors to the receiver, all moving at arbitrary speeds through a medium which may be heterogeneous, anisotropic, and include flow fields, shock fronts, etc.
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