# LESS LiDAR: A Full-Waveform and Discrete-Return Multispectral LiDAR Simulator Based on Ray Tracing Algorithm

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Data

#### 2.1. Abstract Scenes

#### 2.2. Realistic Scene

## 3. Method

#### 3.1. Principles of LiDAR

#### 3.2. LiDAR Simulation Based on Ray Tracing Algorithm

#### 3.2.1. Generating a LiDAR Pulse

#### 3.2.2. Pulse Propagation

#### 3.2.3. Signal Recording

#### 3.2.4. Pulse Post-Processing

#### 3.3. LESS LiDAR Simulator

## 4. Results

#### 4.1. Waveforms

#### 4.1.1. Abstract Scenes

#### 4.1.2. Realistic Scene

#### 4.2. Point Clouds

#### 4.2.1. Airborne Laser Scanning Point Cloud

#### 4.2.2. Terrestrial Laser Scanning Point Cloud

## 5. Discussion

#### 5.1. Multispectral LiDAR vs. Multispectral Imaging

#### 5.2. Performance

#### 5.3. Multi-Ray Point Cloud vs. Single-Ray Point Cloud

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Illustrations of test scenes. (

**a**) Pad/slope (by rotation). (

**b**) Small steps/big steps (changing height difference). (

**c**) Heterogeneous cylinder and pad.

**Figure 2.**Illustration of the example scene generated using the data from the radiative transfer model intercomparison (RAMI). It can be seen that some tree crowns are beneath others in the image. (

**a**) The example scene generated using data from RAMI is shown in the the large-scale remote sensing data and image simulation framework (LESS) three-dimensional (3D) viewer. Colors are used to distinguish different elements, not to reflect the radiometric properties. (

**b**) An orthographic false color image generated by LESS. The near infrared band is shown as red. Red bands are shown in green. Green bands are shown in blue.

**Figure 4.**Illustration of the light detection and ranging (LiDAR) simulation procedure. A virtual laser is supposed to emit virtual laser beams in 3D space. To simulate the divergence of a laser beam, multiple ray casting queries are used to approximate a cone (not all sample rays but rather the representative rays are shown). If an intersection point can be “seen” in the field of view of the sensor, scattered energy is received by the receiver.

**Figure 6.**Illustration of pulse propagation scheme. If a ray k intersects a scene element ${V}_{n}$, a new ray is cast towards the receiver firstly, and the contribution is calculated. Then, another ray is generated to sample the next scattering order. Here, the ray escapes the field of view after the interaction at ${V}_{n+1}$. Note that in reality, the receiver and the emitter are at the same location in the LiDAR sensor.

**Figure 7.**The process of the generation of the waveform. The received weights are binned into several bins according to their travel distances. The width of each bin is defined by the input acquisition rate $\Delta t$, which is related to the device specification. Then, the accumulation of these weights, denoted ${P}_{\mathrm{lidar}}\left(t\right)$, is the estimation of the target profile. The waveform ${\tilde{P}}_{\mathrm{lidar}}\left(t\right)$ is obtained by convolving ${P}_{\mathrm{lidar}}\left(t\right)$ with the emitted pulse ${W}_{\mathrm{t}}\left(t\right)$.

**Figure 8.**Comparison of the full waveforms simulated by LESS and DART LiDAR modules. (

**a**) Waveforms of the pad with different parameters; (

**b**) waveform of the small steps; (

**c**) waveform of the large steps; (

**d**) waveforms of the slope and horizonal pad; (

**e**) waveforms of the cylinder and ground; (

**f**) waveforms of the cylinder and ground (zoomed in).

**Figure 10.**Comparison of point cloud data calculated based on the decomposition of full waveform. Comparison in terms of the layered number of points with the tree height in the realistic scene (Figure 2).

**Figure 11.**Comparison of LESS and DART point clouds. (

**a**) DART (blue) and LESS (red) point clouds. (

**b**) Comparison in terms of the layered number of points with the tree height. (

**c**) The top view for the comparison of LESS and DART points. (

**d**) The relative difference ((LESS-DART)/DART) of the number of points with horizontal cell size $5\mathrm{m}\times 5\mathrm{m}$. (

**e**) Comparison of the number of LESS and DART points based on voxels ($2\mathrm{m}\times 2\mathrm{m}\times 2\mathrm{m}$).

**Figure 12.**An example of multispectral waveforms and the normalized difference vegetation index (NDVI) profile. The NDVI of the background is close to that of the foliage. Therefore, it is difficult to directly separate trees and background in the NDVI image. However, it is clear from the multispectral LiDAR result that there are trees (upper) and a background (lower) with a similar NDVI.

**Figure 13.**Normalized difference vegetation indexes derived from integrated waveform energy ($NDV{I}_{\mathrm{integrated}}$) versus image ($NDV{I}_{\mathrm{image}}$). $NDV{I}_{\mathrm{image}}$ with different solar zenith angles (SZA) in each row and with multiple (left column) and single (right column) scattering (only first order) are calculated and compared with $NDV{I}_{\mathrm{integrated}}$, separately. SZAs, RMSEs, and R${}^{2}$ values are (

**a**) SZA = 0${}^{\circ}$, RMSE = 0.016, R${}^{2}$ = 0.86, (

**b**) SZA = 0${}^{\circ}$, RMSE = 0.013, R${}^{2}$ = 0.96, (

**c**) SZA = 30${}^{\circ}$, RMSE = 0.038, R${}^{2}$ = 0.36, (

**d**) SZA = 30${}^{\circ}$, RMSE = 0.041, R${}^{2}$ = 0.58, (

**e**) SZA = 60${}^{\circ}$, RMSE = 0.035, R${}^{2}$ = 0.15, and (

**f**) SZA = 60${}^{\circ}$, RMSE = 0.032, R${}^{2}$ = 0.76.

Object | Description |
---|---|

Pad | Horizontally placed square 2 m above the ground with a side length of 40 m |

Slope | An inclined pad with a rise of 3 units for every 50 units of run and a center that is 2 m above the ground |

Small steps | Steps with a height difference of 0.9 m. The lowest step is 0.5 m above the ground |

Big steps | Steps with a height difference of 2 m. The lowest step is 0.5 m above the ground |

Heterogeneous cylinder | A cylindrical object placed upright with a height of 12 m and a radius of 3 m that contains 17,999 discs of negligible thickness with a radius of 0.05 m, the bottom-most of which is 2 m above the ground |

Parameter | Symbol | Meaning |
---|---|---|

Sensor area | ${A}_{\mathrm{t}}$ | Aperture area of the telescope |

Footprint half angle | $\beta $ | - |

FOV half angle | ${\beta}_{\mathrm{FOV}}$ | - |

Pulse energy | P | Energy of each pulse |

Acquisition rate (period) | $\Delta t$ | Duration of each measurement. A 1 ns duration corresponds to a path of 30 cm, which, at the nadir and for scattering order 1, corresponds to a 15 cm altitude difference |

Half duration (number of sigma) | ${n}_{\mathrm{t}}$ | - |

Half pulse duration at half peak | ${t}_{\mathrm{half}}$ | This half pulse duration is used to compute the Gaussian pulse standard deviation (sigma) |

Fraction at radius | - | Used to compute the standard deviation of the LiDAR energy Gaussian spatial distribution |

Axial division | ${N}_{\mathrm{s}}$ | The axial subcenter division of illumination |

Max scattering order | - | If a ray reaches the maximum order of scattering + 1, it is considered lost |

Device position (m) | ${V}_{\mathrm{l}}(x,y,z)$ | For example, the terrestrial laser scanning (TLS) Position X, TLS Position Y, and TLS Position Z in TLS mode |

Pulse direction (m) | $\overrightarrow{l}({x}_{\mathrm{d}},{y}_{\mathrm{d}},{z}_{\mathrm{d}})$ | - |

Minimum range (m) | - | Stored minimum waveform distance range from LiDAR |

Maximum range (m) | - | Stored maximum waveform distance range from LiDAR |

**Table 3.**Configurations of the test cases and comparisons for the simple scenes between the LESS and the discrete anisotropic radiative transfer (DART).

Index | Object | Reflectance | Altitude of Device/km | LESS Energy/${10}^{-13}$ J | DART Energy/${10}^{-13}$ J | Relative Error |
---|---|---|---|---|---|---|

1 | Pad | 1.0 | 10 | 3.1844 | 3.1844 | 0 |

2 | Pad | 0.5 | 10 | 1.5922 | 1.5922 | 0 |

3 | Pad | 0.5 | 5 | 6.3713 | 6.3713 | 0 |

4 | Slope | 0.5 | 5 | 6.3686 | 6.3686 | 0 |

5 | Small steps | 0.5 | 5 | 6.3700 | 6.3700 | 0 |

6 | Big steps | 0.5 | 5 | 6.3599 | 6.3599 | 0 |

7 | Cylinder | 0.5 | 3 | - | - | - |

Pad | 1.0 |

Energy/${10}^{-12}$ J | DART Energy/${10}^{-12}$ J | Relative Error | Root Mean Square Error (RMSE)/${10}^{-12}$ J | |
---|---|---|---|---|

First-order scattering waveform | 1.8153 | 1.8154 | 0.006% | 0.0005 |

Full waveform | 1.8618 | 1.8580 | −0.205% | 0.0005 |

Parameter/Unit | Value |
---|---|

Wavelength/nm | 1550 |

Waveform sampling interval/ns | 1 |

Laser beam divergence (half angle)/rad | 0.0012 |

Altitude/m | 1000 |

**Table 6.**Configuration of the multispectral image for computing the normalized difference vegetation index (NDVI) of the simulation.

Parameter | Value |
---|---|

Sensor type | orthographic |

Pixel size | 2 m × 2 m |

View zenith angle/${}^{\circ}$ | 0 |

View azimuth angle/${}^{\circ}$ | 180 |

Solar zenith angle/${}^{\circ}$ | 0, 30, 60 |

Solar azimuth angle/${}^{\circ}$ | 90 |

Parameter | Value |
---|---|

Waveform sampling interval/ns | 1 |

Laser beam divergence (half angle)/rad | 0.0012 |

Altitude/m | 833 |

DART LiDAR | HELIOS ++ | LESS LiDAR | |
---|---|---|---|

Configuration time/min | - | - | 4 |

Loading scene time/min | 6 | 37 | 4 × (2 times) |

Simulation time/min | 135 | 100 | 28 |

Total time/min | 141 | 137 | 40 |

Point number/${10}^{6}$ | 6.4 | 7.6 | 6.6 |

Ground point number/${10}^{6}$ | 3.6 | 3.3 | 3.6 |

Non-ground point number/${10}^{6}$ | 2.8 | 4.3 | 3.0 |

Single-Ray Point Cloud | Multi-Ray Point Cloud | |
---|---|---|

Simulation time/min | less than 1 | 28 |

Point number/${10}^{6}$ | 6.2 | 6.6 |

Ground point number/${10}^{6}$ | 3.5 | 3.6 |

Non-ground point number/${10}^{6}$ | 2.7 | 3.0 |

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**MDPI and ACS Style**

Luo, Y.; Xie, D.; Qi, J.; Zhou, K.; Yan, G.; Mu, X.
LESS LiDAR: A Full-Waveform and Discrete-Return Multispectral LiDAR Simulator Based on Ray Tracing Algorithm. *Remote Sens.* **2023**, *15*, 4529.
https://doi.org/10.3390/rs15184529

**AMA Style**

Luo Y, Xie D, Qi J, Zhou K, Yan G, Mu X.
LESS LiDAR: A Full-Waveform and Discrete-Return Multispectral LiDAR Simulator Based on Ray Tracing Algorithm. *Remote Sensing*. 2023; 15(18):4529.
https://doi.org/10.3390/rs15184529

**Chicago/Turabian Style**

Luo, Yaotao, Donghui Xie, Jianbo Qi, Kun Zhou, Guangjian Yan, and Xihan Mu.
2023. "LESS LiDAR: A Full-Waveform and Discrete-Return Multispectral LiDAR Simulator Based on Ray Tracing Algorithm" *Remote Sensing* 15, no. 18: 4529.
https://doi.org/10.3390/rs15184529