Radial and tangential velocity effects of a probed scanning mirror on laser Doppler frequency shift

A laser Doppler vibrometer (LDV) is precise and fast in measuring the translational velocity of a vibrating diffuse surface. However, it could fail to measure the tangential velocity of a rotating mirror. While the specular reflection away from the mirror can be recovered by a retroreflective collector, the recovered LDV reading is found to deviate from the true tangential velocity of the probed scanning mirror. This happens because the probed spot shifts radially along the rotating mirror surface and thus introduces extra Doppler shift, while the laser beam is aimed at a constant height on the scanning mirror. Here, we derive an analytical relationship between the laser Doppler shift and the tangential velocity of the measured spot. With the input of the prescribed scan profile, we recover the true reading of tangential velocity of the scanning mirror even at a large rotational angle. This corrected LDV reading is as precise as the measurement by a high-speed camera.