The Lorentz transformation changes the photon four-momentum and therefore its frequency, producing the displayed formula for a boost along the first axis. Here the primed ray angle is measured in the emitting frame and . The angle and frequency transforms must be used together: aberration of light changes the direction, and a photon-number angular fraction need not equal the corresponding radiant-energy fraction.
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The relativistic Doppler effect refers to the change in frequency (and corresponding wavelength) of light or other waves emitted by a source that is moving relative to an observer, taking into account the principles of Einstein's theory of relativity. This effect becomes significant at speeds that are a substantial fraction of the speed of light.