黑体红外波段辐射亮度响应的通用公式

doi:10.3964/j.issn.1000-0593(2020)05-1329-05

Abstract
References
Related Citation (15)

Download: PDF (2108 KB)
Export: BibTeX | EndNote (RIS)

Abstract Based on the infrared temperature measurement technology, this paper focuses on the model f(T)＝∫^λ₂_λ₁R_λL_bλ(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^-8T⁴, 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: $\100dpi \inline \bar{\varepsilon }$ ₀＝0.92 is the reference value of true target emissivity, $\100dpi \inline \bar{\varepsilon }$ ₀＝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.

Key words：Infrared temperature measurement; Blackbody waveband radiation brightness response; f(T)≈CTⁿ; Value of n

Received: 2019-04-08 Accepted: 2019-08-29

ZTFLH:

TN219

Corresponding Authors: SUN Xiao-gang E-mail: sxg@hit.edu.cn

Cite this article:

URL:

https://www.gpxygpfx.com/EN/10.3964/j.issn.1000-0593(2020)05-1329-05 OR https://www.gpxygpfx.com/EN/Y2020/V40/I05/1329