# Temperature Estimation Adaptive to Variables over Distance Using Infrared-LiDAR
## 1 Introduction  
Temperature measurement and heat sensing are widely used in various fields, such as military and industrial applications and medical health [1, 2, 3, 4, 5, 6, 7, 8]. For temperature measurement, there are two main methods. One is a non-contact thermometer that measures temperature without contact, so it is mainly used for industrial high temperature measurement. The other is a contact thermometer that is primarily used when accurate temperature measurements are required, such as body temperature measurements. However, due to the risk of infection, it is increasingly preferred to use a non-contact thermometers to measure body temperature [9]. In particular, due to the recent spread of the COVID-19 epidemic [10, 11, 12, 13], body temperature measurements using infrared cameras, a non-contact thermometer, is essential in crowded places such as airports and event venues. Therefore, accurate temperature measurement using infrared cameras has become an important challenge. In long wave infrared cameras, the digital count is obtained through radiation. Therefore, the temperature is estimated through the obtained digital count. In fact, the model for measuring the radiation of an object with a long-wave infrared camera is shown in Equation (1). \[L_{obs}(\lambda)=\tau(\lambda)\Big{[}\varepsilon(\lambda)L_{obj}(\lambda,T_{ obj})+(1-\varepsilon(\lambda))(L_{t}^{\downarrow}+L_{s}^{\downarrow})\Big{]}+ \hat{L_{s}}(\lambda)+\hat{L_{t}}(\lambda) \tag{1}\]  
\(L_{obs}(\lambda)\) is the observed at-sensor object radiation; \(\lambda\) is wavelength; \(\varepsilon(\lambda)\) is spectral emissivity of object; \(L_{obj}(\lambda,T_{obj})\) is the spectral radiation of the object, assuming a blackbody in the Planck function with the object temperature (\(T_{obj}\)); \(\tau(\lambda)\) is the spectral atmospheric transmittance, and \(\hat{L_{s}}(\lambda)\) and \(\hat{L_{t}}(\lambda)\) are the diffuse solar and thermal path radiation, respectively, reaching the sensor. Figure 1 intuitively shows Equation (1). Radiation actually measured is affected by atmospheric and solar noise and atmospheric transmittance according to distance. In fact, according to [14], visible radiation from the sun can be neglected from the mid-wave infrared band (4.2-5.6 \(\upmu\)m). Likewise, the 8-14 \(\upmu\)m band range in which the long wave infrared camera works, thermal radiation is important and visible radiation from the sun is negligible. Furthermore, emissivity is a very important factor in temperature estimation. Emissivity is the ratio of radiation emitted from a blackbody at the same temperature as the radiation emitted from the surface of an object. The emissivity of an ideal blackbody is 1, and human skin is mainly calculated as 0.98. In previous studies, temperature measurements attempted to estimate the temperature by calibrating for various variables. In [15], a method for estimating temperature by compensating for the size-of-source effect is proposed. In [16], the effect of the angle of view on the temperature measurement was analyzed using an infrared camera and an infrared radiator. In [17], it attempts to estimate precise temperature based on the nonlinear response of individual pixels. Ref. [18] proposes a method to reduce the influence of atmospheric dust in temperature measurement. In [19], analyzes the effect on atmospheric transmittance, and based on this, [20] proposes a method to reduce the influence of atmospheric transmittance in infrared cameras. In [21], the temperature is estimated as compensation for each effect by analyzing the object temperature, environmental temperature, and atmospheric transmittance according to the distance. Figure 1: Principle of the radiation measured by a long-wave infrared camera that intuitively shows Equation (1).