Velocity measurement of an arbitrary three-dimensional moving object by using a novel modulated field

The rotational Doppler effect caused by vortex beam carrying orbital angular momentum is recently used to estimate the rotational velocity of the object. However, the vortex beam only has the spiral phase distribution in one dimension, which means that only the rotational movement of the object would introduce the frequency shift. Also, the vortex beam has a spatial amplitude distribution of doughnut-shaped, which is not suitable for many application scenarios. To simultaneously measure the velocity of an arbitrary three-dimensional moving object, we propose theoretically and demonstrate experimentally an effective method by constructing a novel modulated field. Different from the plane wave and the vortex beam, the modulated field has linear phase distribution in azimuth and elevation directions. In addition, the modulated field has the maximal radiation intensity in the center, which avoids the beam divergence of the vortex beam. By decomposing the frequency shift caused by the radial, azimuth and elevation movements, we realize the velocity measurement in three dimensions. Experiments in a microwave system show that the estimated velocity errors are lower than 6.0%.