Photon counting lidar has emerged as a strong candidate technology for active detection applications because of its advantages of single photon sensitivity and high-ranging accuracy. The timing histogram of a single pixel for photon counting lidar contains the target’s range information, while the laser echo of full-waveform lidar contains abundant structure and reflection information of the target. Based on the previous work of full waveform correction for stationary targets, we propose a new method of full waveform recovery for moving targets, aiming at the issue of obtaining the characteristics of ultra-long-range moving targets under high-flux conditions. Our method achieves full-waveform recovery by means of data preprocessing, motion compensation, and photon waveform correction. Through simulation calculations, we analyze and compare the effectiveness of each step of the method. Compared with the raw histogram, the normalized root mean square error (NRMSE) of the recovery full waveform and the ideal waveform is reduced from 0.137 to 0.032. Furthermore, we validate the algorithm’s robustness. As the speed increases from 5 to 340 m/s, the NRMSE is always less than 0.04. The results indicate that the recovery waveform of targets hardly varies with changes in velocity. For an accumulation of 200 pulses, when the signal photons are 0.019–3 and the signal-to-noise ratio is below 0.033, the algorithm consistently exhibits excellent performance. Besides, we have demonstrated that for single-layer moving targets, multilayer moving targets, and round-trip moving targets, the algorithm has good performance on the recovery of the targets’ full-waveform, and the NRMSE is less than 0.0054. This provides a new idea for obtaining the shape of targets with variable speeds at a single pixel and provides exciting news for applications such as the detection and recognition of ultra-long-range aerial targets and the detection of space debris.

Photon counting lidar has revolutionized the field of lidar technology with its exceptional single-photon sensitivity and picosecond-level time resolution. It is particularly effective for detecting ultra-long-range targets and measuring global ecosystems. Timing histograms and waveforms play vital roles in these applications, as they contain rich structural information about the targets. To systematically explore the performance boundary model for full-waveform applications in photon counting lidar, we have developed a model based on underlying theory and feasibility, which overcomes the limitation of detecting fewer than 5% of illumination cycles. By using the cumulative emission pulse number as the objective function, we establish the performance boundary model for full-waveform in photon counting lidar, revealing the relationship between the accuracy of the full-waveform and system parameters. The model’s accuracy is verified through theoretical analysis and experimental validation. Subsequently, we utilize Pareto Optimality to determine the optimal parameters for the full-waveform performance boundary model. Experimental data indicates that, to ensure a normalized root mean square error (nRMSE) of less than 0.03 between full-waveform and ideal waveform, the performance boundaries are as follows: the optimal time bin width is 256ps, the signal intensity falls within [0.8, 1.6], the tolerable noise is [0, 0.63M]Hz, and the minimum cumulative pulses required is between [282, 319], given that the echo width is 5ns. Finally, we discuss the practical application of the full-waveform performance boundary in photon counting lidar for complex target detection scenarios. Under the optimal parameter configuration, the R-Square (R2) between the full-waveform and the ideal waveform consistently exceeds 90%. This work not only expands the range of applications for photon counting lidar in the field of full-waveform, but also establishes a strong connection with full-waveform processing algorithms.

In remote sensing domains, it is difficult to evaluate the lateral structures using the current remote sensing techniques. The mathematical peak intensity formula of the echo waveform modulated by the lateral structures establishes a quantitative yet concise relationship between the peak intensity and the lateral structures, enabling the retrieval of lateral structural details in terms of inverting the formula. The process of the retrieval includes: 1) mathematical formula derivation; 2) target shape discrimination; and 3) mathematical formula inversion. Using the sizes estimated from the simulated echo waveforms, this study demonstrates how the estimated lateral structures are affected by the number of lateral structural parameters to be solved, instrument noise, movement direction, target shape, and target size. The results reveal that for unknown target size and lateral structures, the averaged size errors are 0.56% and 4.30%, respectively. When the instrument noise is absent and only the target size is unknown, the size error averaged over four shapes is 0.3%, and the size error averaged over the square, circle, and triangle is 0.04%. When only the size is unknown, the size errors of the rectangle, square, circle, and triangle estimated by fitting the experimental peak intensity with the formula are 2.41%, 3.47%, 0.89%, and 1.42%, respectively. The small size errors prove the possibility of retrieving the lateral sizes at a centimeter-level resolution and a distance of hundreds of kilometers, which is of great practical significance in precisely mapping the lateral structures of 3-D targets using full-waveform light detection and ranging (FW-LiDAR).

Waveform decomposition is needed as a first step in the extraction of various types of geometric and spectral information from hyperspectral full-waveform LiDAR echoes. We present a new approach to deal with the ”Pseudo-monopulse” waveform formed by the overlapped waveforms from multi-targets when they are very close. We use one single skew-normal distribution (SND) model to fit waveforms of all spectral channels first and count the geometric center position distribution of the echoes to decide whether it contains multi-targets. The geometric center position distribution of the ”Pseudo-monopulse” presents aggregation and asymmetry with the change of wavelength, while such an asymmetric phenomenon cannot be found from the echoes of the single target. Both theoretical and experimental data verify the point. Based on such observation, we further propose a hyperspectral waveform decomposition method utilizing the SND mixture model with: 1) initializing new waveform component parameters and their ranges based on the distinction of the three characteristics (geometric center position, pulse width, and skew-coefficient) between the echo and fitted SND waveform and 2) conducting single-channel waveform decomposition for all channels and 3) setting thresholds to find outlier channels based on statistical parameters of all single-channel decomposition results (the standard deviation and the means of geometric center position) and 4) re-conducting single-channel waveform decomposition for these outlier channels. The proposed method significantly improves the range resolution from 60cm to 5cm at most for a 4ns width laser pulse and represents the state-of-the-art in ”Pseudo-monopulse” waveform decomposition.

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.