# Retrieval of Nearshore Bathymetry around Ganquan Island from LiDAR Waveform and QuickBird Image
## 3 Materials and Methods
### Data Processing and Method
#### 3.2.1 QuickBird Image Preprocessing  
1. Radiation calibration  
The ground object signals received by satellite sensors are recorded with a dimensionless Digital Number (DN) value, and the process of converting the DN value into a radiation brightness value with practical physical significance is called radiation calibration. The basic principle of radiometric calibration is to establish the quantitative relationship between the DN value and the radiation brightness value in the corresponding field of view. The calibration formula for the remote sensing image of QuickBird is  
\[L=\frac{DN\times absCalFactor}{effectiveBandwidth}, \tag{1}\]  
where \(L\) is the inputted pupil radiation brightness of the sensor, \(DN\) is the pixel gray value, \(absCalFactor\) is the absolute scaling factor, and \(effectiveBandwidth\) is the effective width of the spectrum. The information on absolute calibration factor and effective spectral width can be found in the calibration file (*.IMD). The details are listed in Table 3.  
After radiometric calibration, the QuickBird remote sensing image is converted from one with the original dimensionless DN into one with a radiance value with \(\mu W/cm^{2}\times nm\times sr\) units. 2. Atmospheric correction  
Satellite sensors are affected by the scattering and absorption of atmospheric particles, aerosols, and molecules in the process of receiving solar photoelectric and electromagnetic radiation. The effects of scattering attenuate the signals received by the sensors. Meanwhile, some of the scattered light from the sky directly penetrates the satellite sensor without interacting with ground objects. This part of the signal does not contain any ground object information; we call this phenomenon atmospheric path radiation. Therefore, the atmospheric effects need to be eliminated to obtain highly realistic ground radiation or reflectance. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Band** & \(absCalFactor\) & \(effectiveBandwidth\) \\ \hline
1 & \(1.604120\times 10^{-2}\) & \(6.80\times 10^{-2}\) \\
2 & \(1.438470\times 10^{-2}\) & \(9.90\times 10^{-2}\) \\
3 & \(1.267350\times 10^{-2}\) & \(7.10\times 10^{-2}\) \\
4 & \(1.542420\times 10^{-2}\) & \(1.14\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Radiation scaling transformation parameters of QuickBird. The atmospheric correction method used in this study was the 6S model method. The 6S model, which is the abbreviation of second simulation of the satellite signal in the solar spectrum, was developed by adding a new scattering algorithm based on the 5S model and, thus, can better reflect the real situation than the LOW resolution atmospheric TRANsmission (LOWTRAN) and MODerate resolution atmospheric TRANsmission (MODTRAN) models. Figure 3 shows the technical route of the 6S atmospheric correction that consists of three parts: Parametric setting of the atmospheric correction model, radiation calibration, and atmospheric correction [27]. The parameters of the 6S atmospheric correction model were set as follows: Ground elevation, solar observation geometry, satellite observation geometry, and other parameters obtained directly from the *IMD file corresponding to the metadata of the remote sensing image; the spectral response function obtained from the data disclosed by the sensor; the atmospheric model parameters with default values obtained according to the remote sensing image data, mainly in the aerosol mode, atmospheric mode, and solar spectrum function; and a customization of the actual situation. We selected marine aerosol and tropical atmospheric mode in accordance with the needs of the study area. After radiation calibration, the DN value of the remote sensing image is converted into an apparent radiation brightness value, followed by a conversion into an apparent reflectance value by Equations (2) and (3).