Analytical Formula to Investigate the Modulation of Sloped Targets Using LiDAR Waveform

The relationship between the properties of targets and the features of modulated waveforms is fundamental to remote sensing based on the full-waveform light detection and ranging (LiDAR). Developing a mathematical formula of modulated LiDAR waveforms is of great importance in establishing this relationship. In this study, we derive the mathematical formula of a laser echo waveform modulated by four typical targets: a rectangle, a square, a circle, and an equilateral triangle. By using these formulas, numerical calculations are performed to investigate the relationship between the properties of the targets and the features of the modulated waveform. The results show that, at a rotation angle of 80°, the modulated waveform changes from a Gaussian form to a non-Gaussian form and finally returns to a Gaussian form as the target size increases. When the target center deviates from the laser spot center and the rotation angle increases, the modulated waveform varies from Gaussian to non-Gaussian form, the value of the peak intensity decreases, and the position of the peak intensity shifts. The specific trends of these changes are successfully explained in terms of the geometric characteristics of the target and the spatial intensity distribution of the incident laser. The distinct dependencies of modulated waveforms on geometric shape, size, center position, and rotation angle indicate a convenient method for identity extraction and target recognition in remote sensing using full-waveform LiDAR. This offers exciting implications for applications, such as topological mapping, environment monitoring, and aerial target detection and recognition.