On expression of Doppler frequency shift in material medium and related theories

In practice of fluid velocity measurement by using laser Doppler velocimetry (LDV), the applied expression of Doppler frequency shift (EDFS) abruptly relates to an unusual coordinate transformation matrix (CTM) instead of a Lorentz transformation matrix. Here we shall demonstrate that, drawing lessons from general relativity and Fermat’s principle, modifying the interval by adopting optical path to replace space distance, the unusual CTM and practicable EDFS mentioned above can be obtained rationally, and other related electromagnetic topics arising in media may be addressed from a new angle. This work indicates that fluid velocity measurement by using LDV can be applied to examine applicability of EDFSs and related theories, which may be helpful to deepen the understanding of foundations of relativity.