# Long-Range Multispectral Thermal Imager for Simultaneous Measurement of Distance and Temperature
## 1 Introduction  
Multispectral thermal imagers are one of the fastest thermodynamic temperature-measuring instruments available, and are widely used for real-time measurements of high-temperature [1] or transient-temperature fields [2]. Compared with traditional single-band or narrow-spectrum thermal imaging equipment, the multi-spectral thermal imager achieves high-precision measurements of temperature field distribution in complex scenes by acquiring radiation information under multiple spectra [3]. This advantage makes it more applicable in the measurement of high-temperature and high-dynamic environment, especially in the fields of industry, energy, and flame research. Among them, the multispectral thermal imager based on a multi-aperture splitting structure can effectively improve the balance between spectral resolution and imaging efficiency by introducing multi-aperture splitting elements into the optical system. Compared with traditional spectral scanning or filtering array schemes, this structure can acquire multi-spectral information faster and meet the needs of high-speed and high-precision measurements. However, at present, the focus of relevant research is mainly on temperature measurement, while other potential functions have not been fully explored. Flame distance and flame size are two key physical quantities in combustion research, and their measurement is of great significance for the study of heat transfer characteristics, flow field structure, and kinetic behavior of combustion reactions. In high-temperature combustion environments, the accurate measurement of flame distance can provide reliable boundary conditions for subsequent radiation correction and heat transfer models, while avoiding the accumulation of errors due to high-temperature radiation and environmental perturbations. Flame size, especially flame diameter and height, directly affects the chemical reaction rate and heat release distribution in the combustion region, and is an important parameter for evaluating combustion efficiency and flame stability. In the military field, flame size and maximum temperature are important indicators to evaluate the effectiveness of weapons. Therefore, it is essential to accurately measure the diameter of the flame. Multispectral thermal imagers are mainly used to measure the temperature and geometry of large flame sizes at long distances, usually for high-temperature flame sources, such as solid rocket engine plumes and explosion flames; their typical temperature range is about 1000 K to 3000 K. Previous studies have focused on the measurement of flame temperature characteristics rather than flame size. Because of the short duration of the explosion flame, a laser distance measurement [4] based on a phase method is difficult to be applied to flame size measurement. Therefore, the spatial distribution of solid rocket engine plumes and explosion flame is measured by a high-speed camera. Recently, our research has shown that the application of multispectral thermal imagers is not limited to temperature field measurement, but also has the potential to realize distance measurement. This discovery is based on the optical characteristics of the multi-aperture spectroscopic system. By combining the theoretical model, the distance relationship between the measured target and the multispectral thermal imager, and the inherent law of the temperature field are derived. This distance measurement method based on thermal radiation and multispectral analysis provides a new idea for non-contact measurement in complex environments. Thanks to the continuous development of binocular vision theory, distance measurement based on binocular vision has been widely used in mechanical manufacturing [5], medical diagnosis [6], environmental detection [7; 8], industrial production [9; 10] and other fields. Most of the current research focuses on improving the calibration accuracy of binocular cameras.