Simultaneous range and velocity measurement with Doppler single-photon lidar

Single-photon lidar (SPL) can accurately measure distances to targets from extremely weak reflections. However, the conventional wisdom holds that pulsed lidar cannot directly measure velocity, unlike other forms of lidar. We present a detection model for SPL that explicitly includes a target’s radial velocity, manifesting as a Doppler shift in the repetition frequency of the received laser pulse train. We propose an approach called Doppler SPL, comprising a pair of methods for jointly estimating range and velocity. Our first method estimates the Doppler shift via Fourier analysis of the detection times. The second method is a maximum likelihood (ML) estimator that can improve the Fourier estimate and enable joint estimation of the flux from signal and background sources. We derive the Cramér–Rao bound for the estimation problem and show via simulations that the ML estimator is statistically efficient across diverse acquisition settings. We also demonstrate simultaneous estimation of range with sub-centimeter accuracy and velocity with 0.1 m/s root mean square error for experimental measurements at 50 frames per second (fps), despite a signal-to-background ratio as low as 0.007. Finally, we present an example of a 3D video reconstruction at 120 fps with per-pixel velocity estimates. With the addition of velocimetry, Doppler SPL has the potential to introduce advanced capabilities in applications such as atmospheric monitoring or autonomous navigation.