# A Thermopile-Based Colorimetric Temperature Measurement Method for Arbitrary Bandwidth
## 1 Introduction  
Temperature is a crucial parameter that reflects the state of matter, playing a vital role in daily life, industrial production, national defense, military applications, and scientific research. There are two primary categories of temperature measurement methods based on different principles: contact and non-contact. Contact temperature measurement commonly utilizes thermocouples or resistance thermometers [1]. This method is easy to operate and yields results closer to the actual temperature. However, sensors require direct contact with the object, which may disrupt the temperature field of the object and result in slower response time, thereby restricting its applicability to high-temperature or corrosive objects. Non-contact temperature measurement, employing radiation-sensitive sensors, offers advantages such as high accuracy, rapid response time, a wide temperature measurement range, and minimal interference with the object's temperature field [2]. Non-contact temperature measurement currently relies primarily on radiation thermometry. According to [PERSON]'s radiation law, which calculates radiative temperature, the infrared energy emitted by the object itself reliably assesses the surface temperature of the object [3]. Radiation thermometry techniques mainly include total radiation thermometry, single-wavelength thermometry (brightness thermometry), dual-wavelength thermometry (colorimetric thermometry), and multi-wavelength thermometry. The application of radiation thermometrynecessitates considering emissivity, which is influenced by material properties, surface conditions, temperature, and radiation wavelength. Therefore, accurately determining emissivity values presents a significant challenge. Moreover, when measuring the radiative temperature of targets in the atmosphere, atmospheric molecules and aerosol particles impact the absorption and scattering attenuation of target radiation. In addition, the atmosphere emits background radiation, which affects measurement accuracy [4, 5, 6]. Total radiation thermometry simplifies optical designs, reduces size, and lowers costs. However, this method calculates temperature by measuring the entire band of radiation energy, making it difficult to obtain the total emissivity of different objects across the full spectrum and, consequently, challenging to achieve high accuracy [7]. Single-wavelength thermometry provides a straightforward system structure by detecting radiation within a narrow band. However, it requires the selected bandwidth to be as narrow as possible, which reduces the energy received by the detector and thereby affects measurement accuracy. Additionally, this method is susceptible to factors such as object emissivity and atmospheric attenuation, leading to lower accuracy [8]. Multi-wavelength thermometry provides rich signal information and achieves high measurement accuracy but involves complex processes and higher costs. In addition, strict wavelength selection is necessary, which limits its widespread adoption in radiation thermometry [9, 10]. Dual-wavelength thermometry determines temperature by comparing the ratio of radiation energies in two narrow-band wavelength ranges [11]. When these bands are close in wavelength, the degree of radiation energy attenuation is similar, enhancing its immunity to interference compared to total radiation thermometry and single-wavelength thermometry. This method reduces the impact of environmental factors like smoke, dust, vapor, and particles during transmission, while also effectively mitigating the effect of emissivity [12]. As a result, the measured result closely approximates the actual temperature of the object, making it more accurate than brightness temperature and radiance temperature. Especially when the object being measured approaches a grey body, the measured temperature can be considered equivalent to the true temperature. Dual-wavelength thermometry finds widespread application across various temperature measurement fields.