Vectorial Doppler metrology exploits spatially varying polarization structures to enable direction-sensitive angular velocimetry, offering capabilities beyond those of scalar Doppler schemes. However, applying such vectorial strategies within nonlinear detection frameworks remains challenging, as conventional frequency-conversion processes are inherently polarization-dependent and tend to distort the vectorial topology that encodes directional Doppler information. In this work, we overcome this fundamental limitation by introducing a spatial-polarization-independent upconversion scheme that preserves the full vectorial structure of rotational Doppler signals. This allows for infrared Doppler polarization signals to be conformally translated into the visible domain while retaining their directional sensitivity. Within this preserved vectorial framework, we realize direction-resolved rotational velocimetry through two complementary detection approaches: a commonly employed polarization differential detection method and a newly proposed polarization heterodyne detection scheme that provides a compact and robust time–frequency route to retrieving the rotation direction. These results establish a practical pathway for vectorial Doppler sensing under nonlinear frequency conversion and highlight the broader utility of multidimensional optical degrees of freedom for robust, high-fidelity multiparameter measurement.
Gao et al. (Mon,) studied this question.