Considering flame as graybody, the relation between wavelength of flame radiation light (λ ) and radiation intensity (E_λ )[W· m^-2] is described by Planck’ s law:

Eλ=ε(T)C1λ5[exp(C2/λT)-1](1)

Where, ε is emissivity, which is the function of temperature; C₁, C₂ are the first and second radiation constant, and T[K] is the radiation temperature.

Due to different responses of photoelectric detecting element in different wavelength of light radiation, the spectral response coefficient is defined as the ratio of the measured response (I_λ ) to the real radiation intensity (E_λ )

kλ=EλIλ(2)

As usual, the spectral response coefficients at different wavelength are calibrated by blackbody furnace. The real radiation intensity is calculated by equation (1).

Hence, the relation between wavelength and measured response is described as

Iλi=kλiεC1λi5[exp(C2/λiT)-1](3)

Once the radiation spectrum is measured by spectrometer, the average temperature of field can be obtained by fitting of equation (3). Due to different spectral response coefficients of different wavelength radiation light, the spectral response coefficient has great influence on fitting result.

As shown in Figure 1, the experimental system consisted of the blackbody furnace (Fuyuan Photoelectric, HFY-203B), optical fiber spectrometer, lens, optical fiber probe, computer, etc. The diameter of high temperature blackbody radiation tube arranged in blackbody furnace is 40 mm, and its effective emissivity is 0.98~0.99. The spectrometers used in the experiment are 200~1 100 nm VIS spectrometer (Ocean Optics, HR4000, Toshiba TCD1304AP detector) and 900~1 700 nm NIR spectrometer (Isuzu Optics, NIRez, Sony ILX554B detector).

Fig.1

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	Fig.1 Experiment system of radiation calibration

The blackbody furnace is set to the specified temperature. The radiation light of tube in the blackbody furnace is collected by the probe and transmitted to the optical fiber spectrometer. The measured spectrums are recorded and analyzed by the computer. In this paper the temperature range of blackbody furnace is set to 981~1 053 K. The radiation spectrums of blackbody at different temperatures in this range are alternately measured by NIR and VIS spectrometers. The integral time of VIS spectrometer is 200 ms, and the spectrum width of NIR spectrometer is 10.53 nm.

Due to the spectral response coefficient associates with wavelength, temperature and other parameters, the spectral range selection has a great influence on the fitting results of temperature. In order to improve measurement accuracy, the Signal to Nosie Ratio (SNR) of measured spectrums and temperature stability of spectral response coefficient should be considered.

3.1 Radiation spectrums of blackbody furnace with different spectrometers

The radiation spectrums of blackbody furnace obtained by VIS and NIR spectrometers in the temperature range of 981~1 503 K are shown in Figure 2, in which (a) is the VIS spectrometer, and (b) is NIR spectrometer. Compared with the two wave-band spectrums, the SNR and lower limit of temperature detection response of NIR are better than VIS. There are obvious response in NIR above 1 073 K, but above 1 173 K in VIS.

Fig.2

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	Fig.2 Radiation spectrums of blackbody furnace using VIS and NIR spectrometers

3.2 Spectral response coefficients at different temperatures

According to the VIS and NIR spectrums at different temperature obtained by experiment, the corresponding spectral response coefficients can be calculated by equation (2). Considering SNR of the VIS and NIR spectrums, 600~1 000 and 950~1 050 nm are selected for further analysis. The spectral response coefficients in these two wavebands are shown in Figure 3. Due to stronger radiation intensity at higher temperature, the curves of spectral response coefficients become more stable as temperature increases.

Fig.3

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	Fig.3 Response coefficient of VIS and NIR spectrometer for different temperature blackbody radiation

For VIS waveband, the response coefficients vary greatly in different wavelength. Due to the small value in 600~700 nm, the temperature sensitivity of response coefficients is low, and there is great fluctuation at low temperature. Moreover, the spectral response coefficients is large in 900~1 000 nm. The spectral noise will be amplified by real radiation calculation.

For NIR waveband, the changing characteristics in different temperature ranges are different. The curves have large, fluctuations in 950~1 300 nm waveband below 1 273 K, but these fluctuations are disappeared above 1 273 K.

Considering stability and roughly equivalent value of response coefficients in the selected range, the spectral data in 700~900 nm (VIS) and 1 000~1 600(NIR) ranges are appropriate to determine temperature.

3.4 Spectral range selection influence on Radiation Spectroscopy thermometry

Based on the above analysis, the selecting criterions of response coefficient can be summarized as follows:

(1) For VIS waveband, due to the SNR of the radiation spectrums at different temperature, VIS Radiation Spectroscopy is only suitable for thermometry above 1 173 K. And the recommended fitting range of spectral data is 700~900 nm.

(2) For NIR waveband, the lower limit of temperature measurement can be reach 1 073 K, and 1 000~1 600 nm fitting range is recommended.

Fig.4

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	Fig.4 Response coefficient of VIS and NIR spectrometer for different wavelength blackbody radiation

These criterions are verified by the same experiment system, but at different temperature form calibration. The comparison results are shown in Table 1. Temperature fitting in the optimized selected range can reduce the relative deviation of measurement and improve the accuracy of measurement. Moreover, for high-temperature measurement, the selection of spectral response coefficients at specific temperature has less influence on measurement results.

Table 1

Table 1

Table 1 Comparison of relative deviation of results based on full range and optimized selected range (a) VIS Set Full range fitting Optimized selected temperature range /K Temperature Relative Temperature Relative /K deviation /K deviation /% /% 1 123 1 142.2 2.26 1 117.4 0.66 1 223 1 236.1 1.38 1 235.2 1.28 1 353 1 393.9 3.79 1 381.1 2.6 1 398 1 398.3 0.03 1 397.7 0.03 (b) NIR Set Full range fitting Optimized selected temperature range /K Temperature Relative Temperature Relative /K deviation /K deviation /% /% 1 173 1 130.6 4.71 1 155.9 1.9 1 298 1 282.6 1.5 1 282.0 1.56 1 353 1 329.9 2.14 1 330.1 2.12 1 398 1 395.4 0.23 1 395.6 0.21

Table 1 Comparison of relative deviation of results based on full range and optimized selected range

Furthermore, it is worth pointing out that the spectral response coefficients depend on detector material of different waveband. Therefore, the results have applicability for the spectrometers with the same detector material.

(1) The spectral response coefficients vary with temperatures in different wavelengths. For the visible band, the spectral response coefficients tend to be stable in the range of 700~850 nm which is the suitable spectral range for the temperature fitting. While the near-infrared spectral range selection depends on temperature range. For the temperature below 1 273 K, 1 300~1 600 nm spectral range is more appropriate. But for the temperature above 1 273 K, 1 000~1 600 nm spectral range is better. Compared to the full band spectral data, the accuracy of these measurements can be improved by fitting the spectrums in these selected wavelength ranges.

(2) With temperature rising, visible and near-infrared spectral response coefficients are both stable. For high-temperature measurement, the selection of spectral response coefficients at specific temperature has less influence on measurement results.