Measuring angular velocity through atmospheric turbulence with rotational Doppler-shifted intervals

Rotational Doppler velocimetry (RDV) plays a vital role in applications ranging from space debris detection to industrial monitoring. However, RDV through atmospheric turbulence remains a significant challenge, particularly for non-cooperative diffuse targets. While the frequency-shifted interval method has demonstrated high stability for RDV in free space, the viability of employing the frequency-shifted interval method itself under atmospheric turbulence has remained unexplored. Herein, we experimentally demonstrate the successful introduction of this method for RDV through turbulent media. Using a two-step verification process, we first established a reliable baseline by measuring an aligned diffuse rotor under turbulence, achieving accurate velocity extraction via Doppler-shifted intervals. We then confirmed the method's robustness by measuring a misaligned, diffuse target under identical turbulent conditions, obtaining a remarkably low maximum relative error of 1.58%. This work establishes the frequency-shifted interval method as a robust and accurate solution for angular velocimetry facing combined challenges of atmospheric turbulence and target misalignment, showcasing significant potential for applications in rotating body detection and object identification.