Generalized Doppler effect for high-accuracy frequency shift measurement

(1 + ℓ/|m|), compared with conventional DS and DPS schemes. Furthermore, directional ambiguity inherent to these shifts can be resolved via phase analysis of either initial polarization offset or analyzer angle difference. Our generalized framework not merely unifies previous Doppler formulations but offers a potential pathway to substantially improved Doppler metrology, enabling unprecedented accuracy in high-resolution fluid vorticity mapping, quantitative hemodynamic monitoring, and next-generation LiDAR systems.