The Orthogonal Polynomial Regression Method of Multi-Wavelength Radiation Thermometry
LI Qi-nan1, XU Xiao-xuan1, WU Zhong-chen1, SONG Ning1, ZHANG Cun-zhou1, YU Gang2
1. The Photonics Center of the Physics Institute, Nankai University, Tianjin 300071, China 2. Visiting Professor of Nankai University (Dupont Display, California), Tianjin 300071, China
Abstract：For the problem of multi-wavelength radiation thermometry, the traditional data processing methods are the least squares techniques, the multiple linear regression fitting, and the stepwise regression fitting. There are some shortages in these methods, resulting in a certain error between the fitting result and the true temperature of the object surface. A new data processing method of multi-wavelength radiation thermometry——the orthogonal polynomial regression method was brought forward in this article on the base of variable emissivity. The mathematic principle of orthogonal polynomial regression method was expounded and according to the surface emissivities of tungsten, the true temperature of tungsten surface was simulated by the stepwise regression method and the orthogonal polynomial regression method. By comparing the fitting results, the authors found that the orthogonal polynomial regression method has the merit of simple principle and small operation, and the relative error between the fitting result and the surface true temperature is smaller. So the authors can draw the conclusion that using the orthogonal polynomial regression method to process the data of the multi-wavelength radiation thermometry, the fitting result has smaller error, it can fit the true temperature of object faster, and the result is more accurate than the traditional data processing methods.
[1] MENG Jian-ping，YANG Jing-guo，TAN Hua，et al(蒙建平，杨经国，谭 华，等). Spectroscopy and Spectral Analysis(光谱学与光谱分析)，2002，22(5)：721. [2] ZHAN Chun-lian，LI Yan-mei，LIU Jian-ping，et al(占春连，李燕梅，刘建平，等). Journal of Applied Optics(应用光学)，2002，23(6)：39. [3] SUN Xiao-gang，DAI Jing-min，CONG Da-cheng，et al(孙晓刚，戴景民，丛大成，等). Journal of Infrared and Millimeter Waves(红外与毫米波学报)，1998，17(3)：221. [4] DAI Jing-min, SUN Xiao-gang(戴景民, 孙晓刚).Theory and Practice of Multi-spectral Thermometry(多光谱辐射测温理论与应用). Beijing： Higher Education Press(北京：高等教育出版社)，2002. 11. [5] ZHOU Ji-xiang(周纪芗). Practical Regression Analysis Method(实用回归分析方法). Shanghai：Shanghai Scientific and Technical Publishers(上海：上海科学技术出版社)，1990. 77. [6] GE Shao-yan，NA Hong-yue(葛绍岩，那鸿悦). The Character and Measurement of Heat Radiation(热辐射性质及其测量). Beijing：Science Press(北京：科学出版社)，1989. 243.
