# Temperature Estimation Adaptive to Variables over Distance Using Infrared-LiDAR
## 3 Proposed Method
### Offline: Data Acquisition and Interpolation  
An offline process is required before the process of estimating the temperature. In this process, digital counts for each distance obtained through an infrared camera-LiDAR and radiation according to [PERSON]'s law are used to make radiation-digital count mapping function adaptable to a variable according to distance. Offline process consists of \"STEP 1: Data Acquisition\" and \"STEP 2: Digital Count Interpolation\" processes.  
The \"STEP 1: Data Acquisition\" process involves obtaining a digital count for each distance and calculating the radiation through [PERSON]'s law. As shown in Figure 6, the digital count obtains the highest temperature digital count (\(G_{max}\)) and the lowest temperature digital count (\(G_{min}\)) for a specific distance in LiDAR over a range of temperatures to be measured with a blackbody and infrared camera. The reason why it is important to obtain a digital count for each distance is that it is possible to obtain a digital count value that is adapted to the influence of variables such as atmospheric transmittance according to the distance. Figure 7 shows the digital count value that decreases due to the influence of the atmosphere at the same temperature over distance. \(G_{max}\) and \(G_{min}\) measured by this process are used in the interpolation of STEP 2. Furthermore, the radiation calculation process obtains the radiation of each temperature through [PERSON]'s law in the temperature range to  
Figure 5: Overall process flow of the proposed method.  
be measured. The calculated radiation (\(L(T)\)) is then used to obtain the Radiation-Digital Count mapping function for temperature estimation in STEP 3.  
However, it is not possible to measure the digital count for all distances in advance. In order to solve this problem, the \"STEP 2: Digital Count Interpolation\" process obtains \(G_{min}(x)\) and \(G_{max}(x)\) for the distance by linear interpolation of \(G_{min}\) and \(G_{max}\) acquired by distance, as shown in Figure 8. As such, the linear interpolation of the digital count according to the distance is equivalent to the following Equations (9)-(11).  
\[D=\{d_{0},  
Figure 8: [STEP 2: Digital Count Interpolation] Interpolation function is obtained through \(G_{min}\) and \(G_{max}\) by distance.  
Figure 7: Dependence on distance of 16-bit digital count.  
The sets of Equation (9) mean the distance obtained in STEP 1 and the corresponding \(G_{min}\) and \(G_{max}\). For example, the minimum and maximum digital counts measured at distance \(d_{0}\) are \(G_{min}^{0}\) and \(G_{max}^{0}\). Equations (10) and (11) are interpolation equations used to obtain the digital count at an unmeasured distance. Through this, when measuring an object in STEP 3, as shown in Figure 9, the mapping function according to the distance can be newly defined by newly setting the \(G_{min}\) and \(G_{max}\) values according to the distance obtained from LiDAR. The Radiation-Digital count mapping function according to the distance is shown in Figure 10. Therefore, precise temperature estimation is possible through a mapping function that adapts to various variables according to distance.  
Figure 9: Redefined process the Radiation-Digital count mapping function according to distance through the proposed method.