## 1 Introduction  
Temperature, one of the seven fundamental physical quantities in the International System of Units, holds significant importance for both industrial production [1, 2, 3] and the frontiers of scientific research [4, 5, 6]. Current temperature measurement technologies are primarily categorized into two types: contact measurement and non-contact measurement. Contact temperature measurement technologies, such as thermocouples [7, 8], are generally well established for typical applications. However, the intrusion of sensors into the temperature field can disrupt the surrounding flow field, and their relatively slow response times can adversely affect measurement accuracy. In contrast, non-contact temperature measurement technologies, particularly those based on radiation measurement [9, 10, 11], do not disturb the measured temperature field. These technologies are characterized by rapid response times and a wide measurement range, and they are currently experiencing rapid development. Experts and scholars have studied the measurement methods of flame temperature. Flame temperature measurement methods include planar laser-induced fluorescence (PLIF) [12], coherent anti-Stokes Raman scattering spectroscopy (CARS) [13], and Rayleigh scattering imaging [14]; however, these methods require expensive equipment and complex optical systems. Infrared thermography [15; 16] can determine the temperature of the object to be measured by measuring the infrared radiation of the object itself. Infrared temperature measurement does not affect the temperature field, has high sensitivity and responsivity, is convenient to realize the dynamic observation of flames, has a wide range of temperature measurements, and can be used for night vision operations; however, the infrared temperature measurement method mainly depends on the emissivity, but the actual emissivity value is unknown in many cases. The working bands of the infrared thermal imaging cameras are divided into three bands: short wave (\(1-2.5\)\(\upmu\)m), medium wave (\(2-5\)\(\upmu\)m), and long wave (\(8-14\)\(\upmu\)m). The wavelength bands of \(2-5\)\(\upmu\)m and \(8-14\)\(\upmu\)m are the two atmospheric windows commonly used by infrared thermal imaging cameras. In this range, the atmospheric transmittance is large, and the attenuation of infrared radiation is small, which is commonly used to measure temperature. Many scholars have combined digital image processing technology with the well-developed principle of single-wavelength radiation thermometry of visible light [17; 18] to measure the two-dimensional temperature field of the flame through the temperature calibration of the camera; however, the emissivity of the measured object still needs to be obtained. Multispectral temperature measurement technology [19; 20] requires the selection of an appropriate emissivity model. This model establishes a hypothetical relationship between spectral emissivity and temperature or wavelength to simplify the unknowns. It combines data from multiple spectral channels to establish a temperature measurement model through the optimization of multi-order equations. However, the relationship assumptions of different analytes vary greatly, leading to low universality of the hypothetical relationship. Two-color pyrometry technology has been widely used in temperature measurement, compared with the above-mentioned thermometric method, which needs to consider how to accurately measure emissivity. The two-color pyrometry method can usually ignore the influence of emissivity and optical noise in the process of acquiring images on the temperature measurement accuracy when the selected working band is approximate, and the accuracy is greatly improved. [PERSON] [21] was the first to propose this idea and used the two-color pyrometry developed by it to measure the temperature. [PERSON] [22; 23] calculated the three-dimensional distribution field of flame temperature and emissivity using two-color pyrometry thermometry. [PERSON] et al.