1. 长春理工大学理学院, 吉林 长春 130022
2. 西安应用光学研究所, 陕西 西安 710000
*通讯联系人 e-mail: lishuang-317@126.com

Inversion Research on the Spectrum Emissivity Based on Slowing Varying Properties of Emissivity
YANG Yi-fan1, CAI Hong-xing1, WANG Zhao-xuan1, LI Yan2, LI Shuang1,*
1. School of Science, Changchun University of Science and Technology, Changchun 130022, China
2. Xi’an Institute of Applied Optics Research, Xi’an 710000, China;
Abstract

Emissivity is an important parameter of radiation thermometry. Based on Planck’s law, in the temperature measurement by radiation , there is an underdetermined problem, N equation containing N+1 unknown number, a new calculation method is put forward with the application of the emissivity of slowly varying characteristics, in order to reduce the number of unknowns, simplify the calculation process, we conducted theoretical and experimental measures to verify the calculation method. The results showed that both theoretical thermal radiation spectrum and the experimental data of the inversion results of emissivity spectrum and temperature were consistent with material emissivity and its real temperature. When T=1 173 K, the maximum difference of the inversion temperature is 13 K, and the maximum absolute error of the emissivity is 0.05,the greater the emissivity of slowly vary, the shorter the wavelength interval , the higher the accuracy of calculation is. Such method can be applied to obtain temperature and emissivity based on multi-spectral data.

Keyword: Spectroscopy; Material emissivity; Slowly varying characteristics; Temperature

1 计算原理

$Mi(λi, Τ)=εi(λi, Τ)2hc2λi5(ehcκλiΤ-1)(i=1, 2, …, n)(1)$

$ε(λ1, Τ)=ε(λ2, Τ)ε(λ3, Τ)=ε(λ4, Τ)…ε(λn-1, Τ)=ε(λn, Τ)(2)$

$M(λi-1, Τ)M(λi, Τ)=λi5ehcκλnΤ-λi5λi-15ehcκλi-1Τ-λi-15i=1, 2, …, n(3)$

$εi(λi, Τ)=Mi(λi, Τ)2hc2λi5(ehcκλiΤ-1)(4)$

2 算法的理论及实验验证

 Figure Option 图1 不同发射率模型在T=1 373 K时的理论热辐射谱Fig.1 Theoretical thermal radiation spectrum of different emissivity models at T=1 373 K

 Figure Option 图2 发射率的计算结果Fig.2 The results of calculated emissivity

 Figure Option 图3 缓变程度对发射率反演结果的影响Fig.3 The effect of slowly varying degree on the emissivity inversion results

 Figure Option 图4 随机扰动.Fig.4 Disturbance variable.

 Figure Option 图5 随机扰动对计算结果的影响Fig.5 The effect of disturbance variable on the emissivity inversion results

 Figure Option 图6 不同波长间隔对计算结果的影响Fig.6 The influence of different wavelength intervals on the calculation results

 Figure Option 图7 黑体腔不同温度的热辐射谱Fig.7 Thermal radiation spectra of the black body cavity at different temperatures

 Figure Option 图8 不同温度黑体腔的发射率及温度反演结果Fig.8 The inversion results of emissivity and temperature for the black body cavity at different temperatures

3 结论

(1)材料发射率的缓变程度对发射率的反演结果有影响, 缓变程度越大, 计算结果与真实温度和发射率的吻合度越高, 温差最小1.4 K, 此时发射率的最大绝对误差为0.000 6。

(2)测量精度对真实温度和发射率的计算结果有影响, 波长间隔越小, 信噪比越小, 温度和发射率计算的精确度越高。

(3)基于黑体的实验热辐射谱数据, 能反演出黑体的真实温度和发射率谱。 计算所得发射率值接近于1, 温差最大13 K。

The authors have declared that no competing interests exist.

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