Combustion, as a chemical reaction, widely exists in metallurgy, power stations, aerospace and other industrial production processes.Flame temperature and emissivity can directly reflect the combustion state, then diagnose, predict and optimize the device. Its accurate measurement is significant for establishing a combustion model, optimizing the combustion process and controlling pollutant emissions^{[1, 2, 3]}. With the development of spectroscopy and digital image technology, flame radiation measurement has become one of the research hotspots in combustion diagnosis technology^[4]. Compared with active laser spectroscopy^{[5, 6, 7, 8]}, the passive flame radiation measurement method has the advantages of non-contact, high spatial and temporal resolution, reliable system and no influence of combustion particle scattering, which is more suitable for online measurements of combustion flame parameters in the presence of industry.

The radiation image method is based on the image formed by projecting the radiation intensity emitted by combustion flame onto the image sensor area array. The two-dimensional distribution measurements of flame combustion parameters were realized by the processing of RGB three-band mode digital image. Matsuoka et al. calculated the 2D flame temperature field based on the two-color method through the obtained internal flame image of the diesel engine^[9]. In order to further improve the spatial resolution of radiation image thermometry, Hossain et al. used cameras to obtain flame images from different viewing angles based on the two-color method. Combined with optical tomography, the 3D flame radiation image is reconstructed by Logical Filtered Back Projection (LFBP), Simultaneous iterative reconstruction and Algebraic Reconstruction Techniques (SART). Then, the 3D temperature field of flame is obtained^[10]. Zhou et al devoted to the visualization and online detection technology of 2D and 3D temperature fields of combustion in furnace and proposed a variety of multi-parameter inversion algorithms based on the thermal radiation of the combustion field. Distribution of Ratio of Energy Scattered or Reflected (DRESOR) method based on the improved Tikhonov regularization method is used to invert the temperature field and radiation characteristics of dispersive media from the measured radiation images. Adding a certain random normal distribution error to the calculated radiant energy distribution, the error of the final result is less than 3%^{[11, 12, 13, 14]}. Xu et al. applied light field imaging technology to the inversion of the 3D temperature field of flame and proposed a new method of 3D temperature measurement based on single and multi-light field cameras^{[15, 16]}. Based on light field imaging, Niu et al. used the generalized source multiple flow method (GSMFM) to calculate the corresponding light intensity and optimized the simultaneous reconstruction method of photothermal parameters of dispersed media based on the hybrid optimization algorithm of least-square QR decomposition-particle swarm optimization (LSQR-PSO), which greatly improved the reconstruction accuracy of temperature field and radiation characteristic parameters of media^[17].

Under the rapid development of multispectral imaging technology in recent years^{[18, 19]}, this technique adds a spectral dimension to the traditional two spatial dimensions by multispectral imaging camera to measure the radiation intensity of many continuous bands at each imaging unit. Multispectral imaging techniques can generate spectral images containing spatial and spectral information^[20]. It is helpful to improve the measurement accuracy of flame combustion parameters. Liu et al. applied hyperspectral imaging technology to combustion diagnosis, combined multi-wavelength with radiation characteristics, and proposed a combustion parameter analysis method based on Newton iteration to realize the measurement of flame internal parameter distribution^[21]. Mahfouz et al. used a hyperspectral camera to study the reaction rate intensity in and around a turbulent flame mixed with light diesel, waste cooking oil and light and light diesel fuel. The error between calculated flame temperature and thermocouple measurement data is less than 2%^[22].

To further improve the measurement accuracy of temperature and emissivity, the measurement method of flame temperature and emissivity based on parameter fitting of Planck’ s blackbody radiation law is proposed by obtaining flame multispectral radiation images. The spectral response coefficients of 25 bands of multispectral imaging cameras are obtained by calibrating the response coefficients of high-temperature blackbody radiation multispectral imaging cameras. Therefore, the experimental study on measuring the temperature and emissivity distribution of typical candle flame is carried out.

Unlike color RGB cameras, which have only three bands per pixel, the sensors of multispectral cameras have dozens to hundreds of various bands for each pixel. Multispectral imaging technology can simultaneously obtain information on the spatial distribution of combustion flameand spectral information in multiple bands; this technology has higher spectral resolution and can use the rich radiation spectral information to analyze the emissivity model of combustion flame. The spectral response bandwidth of each band is small, and the integrated response within the band can be equivalent to the single wavelength response, which can reflect the information of combustion flame in the spectral dimension more accurately. As shown in Fig.1, this is the schematic diagram of multispectral imaging. Fig.1(a) shows the schematic diagram of multispectral imaging. When the flame high-temperature radiation source into the front slit of the spectral module is filtered into a line, this line through the prism-grating-prism group after the spectral expansion in the direction perpendicular to this line, and then reflected the microarray sensor assembly, can achieve the same radiation source of multiple different wavelength imaging. The spectral imaging technique uses microarray photoreceptors, as shown in Fig.1(b), where each spatial image element of the microarray sensor of the multispectral camera which used in this paper has a detector with 25 bands ranging from 665 to 960 nm. Thus, the acquired two-dimensional multispectral image can be reconstructed into a three-dimensional image based on the response of each band.

Fig.1

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	Fig.1 Schematic of multispectral imaging (a) and Microarray sensor (b) (a): Multispectral imaging schematic; (b): Microarray sensors

Planck’ s blackbody radiation law^{[23, 24]} describes the change of spectral radiation force of an actual object with wavelength at a specific temperature

Eλ=ελC1λ-5exp-C2λT-1(1)

where E_λ is spectral radiation force, W· m^-3; ε _λ is the actual emissivity of the object; T is thermodynamic temperature, K; λ is wavelength, μ m; C₁=3.741 9× 10^-16 W· m² and C₂=1.438 8× 10^-2 m· K are the first and second Planck radiation constants, respectively. When the temperature and wavelength follow λ T≤ 3 000 μ m· K, plank’ s law can be simplified to Wien’ s law

Eλ=ελC1λ-5exp-C2λT(2)

In measuring temperature and emissivity parameters based on radiation spectroscopy, it is necessary to use multispectral imaging system to measure radiation signals at different wavelengths of radiation objects. Because the measured radiation image signal is the electrical signal after photoelectric conversion, it is the relative intensity related to the response characteristics of multispectral camera. Therefore, it is necessary to calibrate the absolute intensity of multispectral imaging system by using a standard blackbody furnace, and the radiation intensity detected by the spectrometer can be expressed as:

Emλ=a0+a1Rλt+a2Rλt2+a3Rλt3+a4Rλt4(3)

In the equation, the absolute radiation intensity of E_mλ multispectral imaging camera calibrated by standard high-temperature radiation source in λ band, R_λ is the response value of multispectral imaging camera in this band, t is the exposure time, and a_i(i=1~4) is the coefficients of each order of assumed polynomial relationship, which is obtained by blackbody furnace calibration experiment. Based on the nonlinear least square algorithm, the measured radiation intensity is selected and combined with Equation (2) to establish an objective function, as shown in Equation (4)

$\text{minf}\left( \text{ }\!\!\varepsilon\!\!\text{ }, \text{T} \right)=\text{min}\overset{n}{\mathop{\underset{\lambda =1}{\mathop \sum }\, }}\, {{(\text{ln}{{E}_{\lambda }}-\text{ln}{{E}_{m\lambda }})}^{2}}=\text{ }\!\!~\!\!\text{ min}\overset{n}{\mathop{\underset{\lambda =1}{\mathop \sum }\, }}\, {{\left( \text{ln}\varepsilon +\text{ln}{{C}_{1}}-5\text{ln}\lambda -\frac{{{C}_{2}}}{\lambda T}-\text{ln}{{E}_{m\lambda }} \right)}^{2}}$(4)

where C₁ and C₂ are known constants, and n is a number of the wavelengths when wavelength is λ . When the objective function f(ε , T) gets the minimum value, ε and T are the emissivity and temperature of pixels obtained by fitting. According to ε and T, the binding force E of flame in the range of high temperature can be calculated based on Stefan-Boltzmann’ s law.

E=εc0T1004(5)

The experimental system of standard high-temperature blackbody radiation multispectral imaging, as shown in Fig.2 is built. The calibration system consists of a blackbody furnace (Shanghai Fuyuan Photoelectric Technology Co., Ltd., HFY-203B), multispectral camera(XIMEA, VIS-NIR, IMEC), zoom lens and computer. The blackbody furnace is used as the standard blackbody radiation source, and the blackbody radiation objects at different temperatures are obtained by setting different temperature values. The 25 bands response law of standard high-temperature blackbody radiation spectral image is studied, and the inversion algorithm of temperature and emissivity parameter distribution of multispectral image is established. The zoom lens is used to accurately focus on the radiation cavity’ s target surface. The lens transmits the blackbody radiation optical signal to a multi-spectral camera sensor array for photoelectric conversion to obtain the multispectral radiation image of the target surface of the blackbody furnace. The range of multispectral cameras is 665~960 nm, and each spatial pixel unit corresponds to 25 spectral bands. The sampling frame rate of the multispectral camera is 80 fps, and the total pixel arrangement is 2 045× 1 088 pixels. The spectral bandwidth of each band is within 15 nm.

Fig.2

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	Fig.2 The experimental system of standard high-temperature blackbody radiation multispectral imaging

The radiation image of the blackbody radiation target surface was collected by multispectral camera. The temperature resolution of the blackbody furnace is 1 ℃. The temperature sensor is a double platinum-rhodium thermocouple, and the range of temperature measurement accuracy of this thermocouple is ± 0.4%× t. The temperature range is 500~1 450 ℃, and the effective emissivity range is 0.98~0.99. Traditional industrial cameras display images through RGB color industrial mode, represented by the response values of R, G and B color channels, whose representative wavelengths are 700.0, 546.1 and 435.8 nm, respectively. Since the spectral range of the multispectral imaging camera is in the near-infrared band of 665~960 nm, the response values of the 18th, 12th and 6th bands (the central wavelengths are 877.54, 803.03 and 728.57 nm) were selected to establish the pseudo-color radiation image according to the RGB color industrial standard. Therefore, a blackbody furnace was used to calibrate the response intensity of the multispectral camera in the temperature range of 1 073~1 533 K, and the pseudo-color radiation image obtained is shown in Fig.3.

Fig.3

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	Fig.3 The pseudo-color images of blackbody radiation at different temperatures

The blackbody furnace provides radiation reference values of the blackbody radiation intensity at different temperatures to obtain the response coefficient between the 25 band camera response value and the theoretical blackbody radiation intensity. According to Equation (3), the fourth-order polynomial is used to characterize the relationship between the instrument response value and the absolute radiation intensity at each wavelength of unit exposure time, as shown in Fig.4.

Fig.4

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	Fig.4 Polynomial fitting results of 25 bands response of multispectral camera (a): 669.62~712.40 nm band; (b): 728.57~780.96 nm band; (c): 787.48~841.37 nm band; (d): 852.25~898.14 nm band; (e): 913.34~949.92 nm band

In order to verify the accuracy of the spectral images’ temperature and emissivity measurement results, six different sets of blackbody furnace temperatures were set in the temperature range of 1 100~1 600 K. The temperature and emissivity measurements were analyzed and compared with the blackbody furnace set temperature to calculate the measurement error. The results of the temperature and emissivity measurements are shown in Table 1. The corrected radiation spectra in the 670~950 nm band were analyzed using the parameter fitting method to obtain the corresponding temperature T_m and emissivity ε . Compared with the experimental blackbody furnace set temperature T_b and emissivity 0.99, it can be seen that the relative deviation of the temperature and reference value of the radiation spectrometry method is less than 1%. The measurement deviation of the emissivity is less than 3%, thus verifying the accuracy of the radiation spectrometry method for high temperature flame radiation parameters.

Table 1

Table 1

Table 1 Measurement results of the verification experiment Blackbody temperature /K Blackbody emissivity Measurement results Calculated temperature/K Relative Deviation/% Calculated emissivity Relative Deviation/% 1 153.15 0.99 1 143.14 0.87 0.96 3.03 1 233.15 0.99 1 239.06 0.48 0.96 3.03 1 333.15 0.99 1 334.09 0.07 0.99 0.00 1 393.15 0.99 1 390.89 0.16 1.02 3.03 1 493.15 0.99 1 492.53 0.04 1.01 2.02 1 538.15 0.99 1 537.61 0.04 0.99 0.00

Table 1 Measurement results of the verification experiment

In this paper, the characterization of candle flame spectra by multispectral imaging techniques is mainly studied, and the following findings are obtained:

(1) A method for measuring the temperature and emissivity of multispectral imaging based on Planck’ s law parameter fitting is investigated. The spectral response coefficients for each band of the multispectral imaging device are obtained utilizing a standard high-temperature blackbody radiation experimental measurement system, and the relative deviations of temperature and emissivity measurements are verified to is less than 1% and 3% respectively.

(2) The temperature and emissivity measurements of multispectral imaging were applied to the measurement of candle flame. The results show that the temperature and emissivity in the vertical plane of the central area of candle flame are higher than those of the upper and lower parts in the vertical plane of flame; the range of flame temperature is about 1 350~2 050 K. The highest temperature of the vertical flame central area is about 2 050 K. The range of candle flame emissivity is about 0.04~0.36, and the highest emissivity in the vertical plane of the central area of flame is about 0.36. The results are consistent with the combustion process of the candle flame and the distribution of radiation characteristics.