以红外测温技术为背景, 着重研究了f(T)=∫λ1λ2RλLbλ(T)dλ≈CTn模型, 即某段波长范围内, 黑体辐射在探测器上引起的响应, 称其为黑体波段辐射亮度响应。 对于不同的探测器, 不同的波长区间, 不同的温度范围, 有不同的 C及 n。 n值难以准确获取, 多数研究者试验时使用Inagaki及Okamoto在1996年提出的三个固定波段模型, 不能很好的扩展到任意波段的探测器。 通过使用“维恩近似公式”代替普朗克公式, 从理论上推导出 f( T)的解析式, 得到了黑体波段辐射亮度响应的通用公式, 从而能够通过理论计算的方式, 求取任意波段内黑体波段辐射亮度响应 f( T)。 使用黑体波段辐射亮度响应的通用公式进行了两项仿真工作。 一是将通用公式在全波段内进行积分, 得到解析式 M_bb=5.238 5×10^-8 T⁴, 并与斯蒂芬玻尔兹曼定律对比。 通用公式求得的系数 σ'=5.238 5×10^-8与斯蒂芬玻尔兹曼常数 σ=5.667 9×10^-8差值为0.429 4×10^-8。 二是使用通用公式计算出8~13 μm波段内黑体波段辐射亮度响应 f( T), 并绘图与Inagaki及Okamoto文章中的拟合结果 f( T)≈0.136 σT^{4 .09}进行对比, 结果曲线基本一致。 两项仿真说明了通用公式的正确性, 在此基础上, 进一步进行实验验证。 以实验室内面源辐射体为目标, 根据所提出的通用公式, 计算被测目标的发射率 ε, 并将之与目标发射率参考值 ε₀对比。 面源辐射体实验结果:ε̅0=0.92为参考值,ε̅=0.93为测量值, 发射率误差为0.01。 实验误差较小, 说明所提出的通用公式可用于红外测温的工程实践中。 通用公式与原模型 f( T)≈ CTⁿ相比, 最大的优势在于可以在任意波段内, 不需考虑温度分区, 通过理论计算的方式, 求取黑体波段辐射亮度响应 f( T), 具有通用性。 黑体波段辐射亮度响应的通用公式进一步完善了红外测温技术的基础理论。

Based on the infrared temperature measurement technology, this paper focuses on the modelf(T)=∫λ1λ2RλLbλ(T)dλ≈CTn. This model represents the response of blackbody radiation brightness on the detector in a certain wavelength range, which is called the blackbody waveband radiation brightness response in this paper. For different detectors, different wavelength ranges, different temperature ranges, there are different C and n. The value of n is difficult to obtain accurately. Most researchers used the three fitting results of C and n proposed by Inagaki T and Okamoto Y in 1996, and the results could not be well extended to any waveband detectors. In this paper, by using the Wien Approximation Formula to replace Planck’s formula, the analytical formula of f( T) is theoretically derived which is a universal formula of f( T), so that we can obtain the blackbody waveband radiation brightness response f( T) in any waveband through theoretical calculations. The universal formula is applied in simulations. Simulation 1: Integrate the universal formula in the whole waveband to obtain an analytical formula M_bb=5.238 5×10^-8 T⁴, and compare it with Stephen Boltzmann’s law. The difference between the coefficient σ'=5.238 5×10^-8 obtained by the universal formula and the Stefan Boltzmann constant σ=5.667 9×10^-8 is 0.429 4×10^-8. Simulation 2: Acquire the spectral responsivity of the HgCdTe detector with an effective wavelength of 8~13 μm from reference [2], calculate the blackbody waveband radiation brightness response f( T) of the detector in the 8~13 μm band, plot the result to compared with f( T)≈0.136× σT^{4. 09} shown in reference [2], and the results are basically the same. Two simulations illustrate the correctness of the analytical formula. On this basis, further experimental verification is performed. A surface source radiator in the laboratory was applied as the target. Through the universal formula, the emissivity of target ε can be calculated and compared with the reference value of true emissivity of target ε₀. Experimental results of the surface source radiator:ε̅0=0.92 is the reference value of true target emissivity,ε̅0=0.93 is measured value, the error of emissivity is 0.01. The small error indicates that the model proposed in this paper can be used in the engineering practice of infrared temperature measurement technology. In this paper, a universal formula that can replace the model f( T)≈ CTⁿ is proposed. Compared with the original model, the greatest advantage of the universal formula is that it can be applied in any waveband without considering the temperature partition and it is a universality to calculate the blackbody waveband radiation brightness response by theoretical calculation. The universal formula further perfects the basic theory of infrared temperature measurement technology.