Modulation of Typical Three-Dimensional Targets on the Echo Waveform Using Analytical Formula

Despite the wide applications of full-waveform light detection and ranging (FW-LiDAR) on target detection and recognizing, topographical mapping, and ecological management, etc., the mapping between the echo waveform and the properties of the targets, even for typical three-dimensional (3D) targets, has not been established. The mechanics of the modulation of targets on the echo waveform is thus ambiguous, constraining the retrieval of target properties in FW-LiDAR. This paper derived the formula of echo waveform modulated by typical 3D targets, namely, a rectangular prism, a regular hexagonal prism, and a cone. The modulation of shape, size, position, and attitude of 3D targets on the echo waveform has been investigated extensively. The results showed that, for prisms, variations in the echo waveforms under various factors essentially arise from changes in the inclination angles of their reflective surfaces and their positions relative to the laser spot. For cones, their echo waveforms can be approximated and analyzed using isosceles triangular micro-facets. The work in this paper is helpful in probing the modulation of 3D targets on echo waveform, as well as extracting the properties of 3D targets in FW-LiDAR domains, which are significant in areas ranging from topographical mapping to space debris monitoring.