# Airborne Waveform Lidar Simulator Using the Radiative Transfer of a Laser Pulse
## 3 Results
### Boresighting Error Effect  
The boresighting angles are the angular offsets between the SBF and IBF. A sensor optical model defines the 3D Cartesian coordinate system SBF. The coordinate axis of an IMU system is usually printed on the cover as arrows, and the lidar axis is aligned to the IMU axis as close as possible, but the boresighting (fine tuning) is required. The IMU system bridges between the \"subjective\" sensor coordinate to the \"objective\" local real-world coordinate system by telling the (\(R\), \(P\), \(H\)) angles. Thus, if there are any misalignment angles, (\(R\), \(P\), \(H\)) must be corrected by those misalignment (boresighting) angles. Frequently, those misalignment angles are called \"roll, pitch, and heading\". However, they are reserved terms for IMU angles. Strictly speaking boresighting angle means the angular offset between the SBF and IBF coordinates. The three angle sets (\(\omega\), \(\varphi\), \(\kappa\)) are the angular offset defined by rotating x, y, and z axes, respectively. The most commonly used convention is that the x-axis points to the nose of an aircraft, the y-axis points to the right-wing, and the z-axis points downward nadir. Thus, rotating the x-axis (axis that points the nose) results in the net effect such as a body roll, and so forth. Thus, the \(\omega\) boresighting angle will effectively increase the IMU roll (R) angle by \(\omega\), and the IMU (P, H) angle adjustment in the same manner by (\(\varphi\), \(\kappa\)). The data for boresighting correction is obtained by flying multiple swaths in different flight directions. If the perfect boresighting angles are found, the overlapped area by multiple flightsneeds to be aligned. Thus, boresighting angles are iteratively optimized until the relative differences between multiple virtual planes become minimal. The airborne lidar simulator can achieve this via visual demonstration. The net effect of the boresighting error is illustrated in Figure 8. The point cloud in the middle shows perfect boresighting, thus the point cloud from two swaths makes a perfect overlap. Figure 8a and b demonstrate the effect of an incorrect \(\omega,\ \varphi\) angle for two parallel swaths to the same direction, while Figure 8c,d show the effect for two parallel swaths to the opposite direction. Figure 8 shows the overestimation, which means the optimized boresighting angles are greater than the true value. For the overestimated \(\omega\) for parallel same direction swaths, the point cloud from both swaths shifts to the left side, as shown in Figure 8a, while the underestimated \(\omega\) will send both swaths to the right side. For the overestimated \(\omega\) for parallel opposite direction swaths, the point cloud from each swath is shifted to the opposite (one left and the other right) direction, as shown in Figure 8c. If underestimated, each swath will change direction but the end result will be the same, which is to be separated, as shown in Figure 8c. For the overestimated \(\varphi\) for the parallel same direction swaths, the point cloud from both swaths shifts forward, as shown in Figure 8b, while the underestimated \(\varphi\) will send both swaths to the rear. For the overestimated \(\varphi\) for parallel opposite direction swaths, the point cloud from each swath is shifted to the opposite (one forward and the other backward) direction, as shown in Figure 8c. If underestimated each swath will change direction but the end result will be the same, which is to be separated, as shown in Figure 8d. As demonstrated in Figure 8, the net result of boresighting error cannot be explained by the boresighting angle error itself. The flight pattern plays a major role to amplify or lessen the boresighting angle error effect because the relative location of the target from one swath and the other swath is different. This is an example that a airborne lidar simulator can reproduce.