Abstract：Multi-spectral radiation thermometry is a method for obtaining true temperature inversion by Planck formula by measuring a number of spectral radiant intensity information of a point to be measured. However, the multi-spectral radiation thermometry equations obtained by the Planck formula are the underdetermined equations, that is, N equations, and N+1 unknown (N unknown spectral emissivity ελi and a waiting true temperature T). At present, a set of emissivity models (emissivity-wavelength or emissivity-temperature model) are often assumed. If the assumed model is consistent with the actual situation, then the inversion results can meet the requirements, and if the assumed model does not match with the actual situation, the inversion result will have very large errors. The emissivity model is affected by many factors, including temperature, surface state, wavelength and so on. It is difficult to determine the emissivity model in advance. Therefore, the restriction of unknown spectral emissivity has been the major obstacle to the theory of multi-spectral radiation thermometry. The direct inversion of true temperature and spectral emissivity without any assumption of spectral emissivity has always been a hot and difficult issue in the theory of multi-spectral radiation t thermometry. Through the analysis of reference temperature model, the essence of multispectral radiation thermometry inversion is to find a set of spectral emissivity, so that the true temperature of each channel equation is the same, if different, we’ll continue to find the appropriate spectral emissivity, until the true temperature of each channel is equal. Therefore, it is proposed to convert the solving process of the multi-spectral radiation thermometry reference temperature model into a constrained optimization problem. That is, under the constraint of spectral emissivity 0≤ελi≤1, the spectral emissivity is constantly searched through the gradient projection algorithm. After taking the emissivity into the multi-spectral radiation thermometry reference temperature model equations, the variance of the temperature inversion values is calculated until the temperature values obtained for each of the spectral channel equations should be approximately equal. In this case, the variance of the temperature inversion value of each spectral channel is the smallest, so that the inversion problem of true temperature and emissivity of multi-spectral radiation is converted into a constrained optimization problem. The gradient projection method is the main method to solve this kind of problem. However, in order to satisfy the constraints of Ax≥b, we decompose 0≤ελi≤1 into two constraints of ελi≥0 and -ελi≥-1, so as to satisfy constraints optimization problem of Ax≥b. In this way, the true temperature and spectral emissivity can be directly solved by the gradient projection algorithm without any spectral emissivity assumption. Six kinds of materials with different spectral emissivity distribution modes (increasing, decreasing, convex wave, concave wave, “M” wave and “W” wave) were selected as the research objects, to verify the adaptability of the new algorithm to the inversion of the spectral emissivity distribution of different materials. Using the minRosen function of Matlab, the initial values of the spectral emissivity are all chosen to be 0.5 (taking the middle value to improve the computational efficiency). The simulation results of six different spectral emissivity models showed that the new algorithm does not require any prior knowledge of the emissivity and the inversion of different emissivity models by the new algorithm is better. The absolute error is less than 20 K and the relative error is less than 1.2% when the true temperature is 1 800 K. The new algorithm has the advantage that there is no need to consider any prior knowledge of spectral emissivity, high inversion precision and suitable for various emissivity models. It further improves the theory of multi-spectral radiation thermometry and has a good prospect in the field of high temperature measurement.
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