Fast data processing method for multispectral radiation thermometry based on Euclidean distance optimization

Kaihua Zhang; Yinxin He; Kun Yu; Kun Yu; Yufang Liu; Yufang Liu

doi:10.1364/OE.510084

1. Introduction

Metal materials are indispensable for a wide range of industrial and societal applications due to their unique properties and functions. Among them, steel is the most prevalent and versatile metal, and has a vital role in sectors such as aviation, construction, and machinery, where high strength and durability are required. The temperature of the manufacturing process is a critical factor that affects the quality of steel. Accurate measurement and control of steel temperature is key to testing and analyzing the accuracy of the steel's thermal conductivity and expansion coefficient. The traditional contact pyrometer is known to destroy the temperature field of the measured object, which has led to an increased interest in non-contact thermometry. Multispectral radiation thermometry is an essential branch of non-contact thermometry that plays a vital role in scientific research and engineering applications [1–5].

Multispectral radiation thermometry is a widely used technique for measuring the true temperature and material emissivity of high-temperature objects. It has numerous advantages, such as fast response, high upper-limit, and wide dynamic range [6–11]. However, the surface emissivity of materials is influenced by various factors, such as oxidation state, roughness, temperature, wavelength and so on. Its law cannot be predicted with complete accuracy, which affects the accuracy of radiation temperature measurement. To solve this problem, researchers have proposed an algorithm based on hypothetical emissivity models [12–17]. These models are generally in the form of wavelength-emissivity models [14,15] or temperature-emissivity models [16,17]. These models address the issue of temperature inaccuracies caused by emissivity, but each model is only applicable to a specific material in a specific environment, which limits the widespread application of the algorithm.

Some researchers have attempted to process the data of multispectral radiation thermometry without the hypothetical model and have proposed a series of methods to overcome the deficiency of the hypothetical model method. Xing et al. [18] proposed an algorithm that does not rely on the emissivity model and realizes rapid and accurate temperature measurement for high temperature targets by multi-wavelength pyrometer (MWP) and emissivity range constraints to optimize data. Liang et al. [19] proposed a generalized inverse matrix-exterior penalty function (GIM-EPF) algorithm that efficiently and accurately inverses the temperature and emissivity without limiting the emissivity range in advance. Xing et al. [20] proposed two algorithms: the Gradient Projection (GP) algorithm and Internal Penalty Function (IPF) algorithm, which do not require to fix the emissivity model in advance. All these methods use optimization algorithms to transform the solution of multi-channel temperature and emissivity into a minimum optimization function problem. However, these methods may be significantly affected by the deviation of the emissivity model from the actual emissivity of the measured object. Liu et al. [21] proposed a multi-wavelength radiation thermometry that determines the temperature and emissivity of the measured object according to spectroscopic radiation intensities based on the Rayleigh approximation. Zhao et al. [22] proposed a narrow-band spectral window moving temperature inversion algorithm that does not rely on an assumed emissivity model. However, both these methods need to be used within a range that is sufficiently close to the actual temperature of the object. Therefore, they cannot effectively measure the temperature of objects in real time.

To address the limitations of existing methods, a multispectral radiation temperature data processing method has been proposed that does not require pre-setting of an emissivity model. This method uses the Euclidean distance between the inversion temperature and the true temperature of the object as the objective function, and an unconstrained optimization method is adopted to obtain the minimum Euclidean distance, finally obtaining the true temperature of the object. The simulation experiment is conducted to invert temperature for six different types of emissivity targets using the method presented in this paper. The simulation results indicate that the method has a maximum relative error within 0.229% and response speed of no more than 112.301 ms in the response band of 1.4 ∼ 2.5 µm and temperature range of 873 ∼ 1173 K. At the same time, a temperature inversion device based on a fiber optic spectrometer was established to measure the spectral intensity of the 42CRMO and Q355B in the 1.4 ∼ 2.5 µm band. The experimental results show that the proposed method has excellent effect on temperature measurement of actual objects.

2. Principle of temperature measurements

2.1 Principle of radiation thermometry

The thermal radiation emitted by a blackbody at a given wavelength λ follows Planck's law of radiation, which can be expressed as:

(1)$${L_b}(\lambda ,T) = \frac{c_1}{\lambda^5}\frac{1}{e^{c_{2}/\lambda T}-1}$$

where T is the temperature of the blackbody; c₁ is the first radiation constant with a value of 3.7418 × 10⁸ W·µm⁴/m²; c₂ is the second radiation constant with a value of 1.4388 × 10⁴ µm·K

The emissivity of an object is defined as the ratio of the radiation emitted by the object at a given temperature (T_s) to the radiation emitted by a blackbody at the same temperature. The spectral radiance of object can be expressed as:

(2)$${L_s}(\lambda ,T) = \varepsilon (\lambda ,{T_s}){L_b}(\lambda ,{T_s})$$

where ε(λ,T_s) is the spectral emissivity of the object at the wavelength λ and the temperature T_s. If the emissivity is given, the temperature of sample can be calculated by substituting Eq. (2) into Eq. (1):

(3)$$T({\varepsilon _x},\lambda ) = \frac{{{c_2}}}{{\lambda \ln (\frac{{\varepsilon (\lambda ,{T_s}){c_1}}}{{{L_s}(\lambda ,{T_s}){\lambda ^5}}} + 1)}}$$

2.2 Method for processing multispectral radiation thermometry

Multispectral radiation thermometry is a technique of using a radiation pyrometer to collect spectral radiation information at three or more wavelengths and then use the relevant data processing algorithm inversion to obtain the measured wavelength of the emissivity value, and finally use the Planck formula to calculate the real temperature of the object [3]. In this paper, the principle that the true temperature calculated from all measured wavelengths should be unique is used [20], and the true temperature of the measured object is obtained by inversion through the data processing algorithm.

For the radiance L_s(λ_i,T_s) at the wavelength λ_i, different emissivity values will result in different temperatures. Estimate the emissivity range of the object being measured, set the upper and lower limits of the range, and calculate the step size. Discretize the estimated emission range into an arithmetic vector [ε₁, ε₂,…, ε_j] of J-dimensions according to the set step size, and ensure that the elements in the discretized vector traverse the entire estimated emission range. By substituting the spectral intensity and the discretized emissivity vector at wavelength λ_i into Eq. (3), a set of temperatures can be obtained. These temperatures are defined as the temperature vector Y_s(λ_i):

(4)$${Y_s}({\lambda _i}) = [{T_s}({\lambda _i},{\varepsilon _1}),{T_s}({\lambda _i},{\varepsilon _2}), \cdots {T_s}({\lambda _i},{\varepsilon _j})]$$

where i = 1,2,…,I represents the spectral channel of the spectrometer, and I is the total number of spectral channels in the spectrometer. j = 1,2,…,J represents the index of each element in the array [ε₁, ε₂,…,ε_j].

Calculate the temperature vector corresponding to each wavelength of the entire spectrometer wavelength response band using Eq. (4) to form an I × J matrix:

(5)$$\left[ {\begin{array}{c} {{Y_s}({\lambda_1})}\\ {{Y_s}({\lambda_2})}\\ \vdots \\ {{Y_s}({\lambda_i})} \end{array}} \right] = \left[ {\begin{array}{cccc} {{T_s}({\lambda_1},{\varepsilon_1})}&{{T_s}({\lambda_1},{\varepsilon_2})}& \cdots &{{T_s}({\lambda_1},{\varepsilon_j})}\\ {{T_s}({\lambda_2},{\varepsilon_1})}&{{T_s}({\lambda_2},{\varepsilon_2})}& \cdots &{{T_s}({\lambda_2},{\varepsilon_j})}\\ \vdots & \vdots & \ddots & \vdots \\ {{T_s}({\lambda_i},{\varepsilon_1})}&{{T_s}({\lambda_i},{\varepsilon_2})}& \cdots &{{T_s}({\lambda_i},{\varepsilon_j})} \end{array}} \right]$$

Each row of the matrix in Eq. (5) represents the represents the temperature calculated at the same wavelength, and each column represents the temperature calculated at the same emissivity. Select one row from the matrix in Eq. (5) and define it as the reference vector, denoted as:

(6)$${Y_s}({\lambda _y}) = [{{T_s}({\lambda_y},{\varepsilon_1}),{T_s}({\lambda_y},{\varepsilon_2}), \cdots ,{T_s}({\lambda_y},{\varepsilon_j})} ]$$

where y represents the selected channel in the spectral wavelength response band, 1 ≤ y ≤ I. Remove the reference vector Y_S(λ_y) from the matrix in Eq. (5) to form the new matrix:

(7)$$\left[ {\begin{array}{c} {{Y_s}({\lambda_1})}\\ {{Y_s}({\lambda_2})}\\ \vdots \\ {{Y_s}({\lambda_{i - 1}})} \end{array}} \right] = \left[ {\begin{array}{cccc} {{T_s}({\lambda_1},{\varepsilon_1})}&{{T_s}({\lambda_1},{\varepsilon_2})}& \cdots &{{T_s}({\lambda_1},{\varepsilon_j})}\\ {{T_s}({\lambda_2},{\varepsilon_1})}&{{T_s}({\lambda_2},{\varepsilon_2})}& \cdots &{{T_s}({\lambda_2},{\varepsilon_j})}\\ \vdots & \vdots & \ddots & \vdots \\ {{T_s}({\lambda_{i - 1}},{\varepsilon_1})}&{{T_s}({\lambda_{i - 1}},{\varepsilon_2})}& \cdots &{{T_s}({\lambda_{i - 1}},{\varepsilon_j})} \end{array}} \right]$$

where the value in each row can be regarded as points in the J-dimensional space. Replace points in J-dimensional space to form a new vector Y^′_s(λ_n_-1). Each element in the vector is given by:

(8)$$T_s^m({\lambda _{n - 1}}) = \min [{|{{Y_s}({{\lambda_{i - 1}}} )- {T_s}({{\lambda_y},{\varepsilon_j}} )} |} ]$$

where M and N are equal to J and I, respectively. Use Eq. (8) to replace the elements in each row of the Eq. (7) matrix to form a new matrix.

(9)$$\left[ {\begin{array}{c} {Y_s^{\prime}({\lambda_1})}\\ {Y_s^{\prime}({\lambda_2})}\\ \vdots \\ {Y_s^{\prime}({\lambda_{n - 1}})} \end{array}} \right] = \left[ {\begin{array}{cccc} {{T_s}^1({\lambda_1})}&{{T_s}^2({\lambda_1})}& \cdots &{{T_s}^m({\lambda_1})}\\ {{T_s}^1({\lambda_2})}&{{T_s}^2({\lambda_2})}& \cdots &{{T_s}^m({\lambda_2})}\\ \vdots & \vdots & \ddots & \vdots \\ {{T_s}^1({\lambda_{n - 1}})}&{{T_s}^2({\lambda_{n - 1}})}& \cdots &{{T_s}^m({\lambda_{n - 1}})} \end{array}} \right]$$

Figure 1 shows the schematic diagram of the process for replacing each row of elements in a matrix. The purple arrow in Fig. 1(a) represents the calculation process of Eq. (8). Figure 1(b) represents the matrix in Eq. (9).

Fig. 1. Schematic diagram of the process for replacing each row of elements in a matrix.

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Combine the matrix in Eq. (9) with the reference vector Y_s (λ_y) to form a new matrix, and then use the Euclidean distance to calculate the distance between each column of the new matrix and its corresponding column mean.

(10)$$\left[ {\begin{array}{c} {Y_s^{\prime}({\lambda_1})}\\ {Y_s^{\prime}({\lambda_2})}\\ \vdots \\ \begin{array}{l} Y_s^{\prime}({\lambda_{n - 1}})\\ {Y_s}({\lambda_y}) \end{array} \end{array}} \right] = \left[ {\begin{array}{cccc} {{T_s}^1({\lambda_1})}&{{T_s}^2({\lambda_1})}& \cdots &{{T_s}^m({\lambda_1})}\\ {{T_s}^1({\lambda_2})}&{{T_s}^2({\lambda_2})}& \ldots &{{T_s}^m({\lambda_2})}\\ \vdots & \vdots & \ddots & \vdots \\ \begin{array}{l} {T_s}^1({\lambda_{n - 1}})\\ {T_s}({\lambda_y},{\varepsilon_1}) \end{array}&\begin{array}{l} {T_s}^2({\lambda_{n - 1}})\\ {T_s}({\lambda_y},{\varepsilon_2}) \end{array}&\begin{array}{l} \cdots \\ \cdots \end{array}&\begin{array}{l} {T_s}^m({\lambda_{n - 1}})\\ {T_s}({\lambda_y},{\varepsilon_j}) \end{array} \end{array}} \right]$$

(11)$${\left[ {\begin{array}{c} {{d_1}}\\ {{d_2}}\\ \vdots \\ {{d_m}} \end{array}} \right]^\mathrm{{\rm T}}} = {\left[ {\begin{array}{c} {||{({T_s}^1({\lambda_1}),{T_s}^1({\lambda_2}), \cdots ,{T_s}^1({\lambda_{n - 1}}),{T_s}({\lambda_y},{\varepsilon_1})),Av{e^1}} ||}\\ {||{({T_s}^2({\lambda_1}),{T_s}^2({\lambda_2}), \cdots ,{T_s}^2({\lambda_{n - 1}}),{T_s}({\lambda_y},{\varepsilon_2})),Av{e^2}} ||}\\ \vdots \\ {||{({T_s}^m({\lambda_1}),{T_s}^m({\lambda_2}), \cdots ,{T_s}^m({\lambda_{n - 1}}),{T_s}({\lambda_y},{\varepsilon_j})),Av{e^m}} ||} \end{array}} \right]^\mathrm{{\rm T}}}$$

Equation (11) contains M elements, each element represents the Euclidean distance between the temperature elements represented by each column of the matrix in Eq. (10) and the true temperature of the object. The formula for calculating the Euclidean distance is:

(12)$${d_m} = \sqrt {{{({T_s}^m({\lambda _1}) - Av{e^m})}^2} + {{({T_s}^m({\lambda _2}) - Av{e^m})}^2} + \cdots + {{({T_s}^m({\lambda _{n - 1}}) - Av{e^m})}^2} + {{({T_s}({\lambda _y},{\varepsilon _j}) - Av{e^m})}^2}}$$

within

(13)$$Av{e^m} = \frac{1}{N}\left( {{T_s}({\lambda_y},{\varepsilon_j}) + \sum\limits_{n = 1}^{n = N - 1} {{T_s}^m({\lambda_n})} } \right)$$

As the Euclidean distance, d_m becomes larger, the correlation between the temperature elements represented by each column of the matrix in Eq. (10) and the true temperature of the object becomes weaker. On the other hand, the smaller the distance coefficient, the stronger the correlation. When the distance coefficient represented by the p-th element in Eq. (11) is minimized, the corresponding p-th element in the reference array Y_s(λ_y) represents the true temperature of the object at wavelength λ_y.

(14)$${T_{ture}}({\lambda _y}) = {T_s}({\lambda _y},{\varepsilon _p}){|_{p = \arg \min [{{d_1},{d_2}, \cdots ,{d_m}} ]}}$$

where argmin refers to the index of the minimum element in an array [d₁, d₂,…, d_m]. As the true temperature of the object being measured is calculated within a fixed step size in the estimated emissivity range, a solution for the temperature can be obtained at each wavelength within the spectral response band. Thus, the method proposed in this paper solves the problem of the objective function in the minimization optimization theory being unable to converge. Select g different rows from the matrix of Eq. (5) to serve as the reference array for temperature inversion. Then, calculate the inverted temperature for each of these rows and take the average of the g results to obtain the final inverted temperature.

(15)$$T = \frac{1}{g}\sum\limits_{y = 1}^g {{T_{ture}}({\lambda _y})} $$

3. Simulation verification

The simulation experiment is conducted to invert temperature for six different types of emissivity targets using the method presented in this paper (Simulation environment: PyCharm 2022; Windows 7; Intel Core i7-10700 CPU @ 2.90 GHz; 8 G RAM). Six emissivity targets with different distribution trends were obtained by setting the parameters of the two emissivity functions listed in Table 1 to several different values.

Table 1. Emissivity targets and parameters.

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Figure 2 illustrates the spectral intensity curves of the measured object under different emissivity models and temperatures. The emissivity models are based on two functions with different parameters, as shown in Table 1. The temperatures range from 873 K to 1173 K with an interval of 50 K. It can be observed that the curves have small differences when the emissivity model is fixed and the temperature varies, indicating that the temperature has a minor effect on the spectral intensity. However, the curves have larger differences when the temperature is fixed and the emissivity model varies, indicating that the emissivity has a significant effect on the spectral intensity. Based on the proposed method in this paper, which minimizes the Euclidean distance between the measured spectral radiance and a reference vector, a simulation experiment was conducted on six kinds of target materials labeled A-F, which represent different trends of emissivity change.

Fig. 2. Spectral intensity and emissivity distribution of the object under different emissivity targets.

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Figure 3 shows the relative error distribution curves of targets with different emissivity at 1173 K. The relative errors at different wavelengths are unevenly distributed on both sides of the mean relative error, and the curve oscillates greatly. It indicates that it is not sufficient to simply select spectral data at a single wavelength as a reference array to invert the temperature of the measured object. Figure 4 shows the standard deviation and response time of the inversion results for different numbers of wavelengths. It can be seen from this figure that as the number of wavelengths increases, the standard deviation gradually decreases, but the response time increases.

Fig. 3. Relative error distribution curves of different wavelengths at 1173 K.

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Fig. 4. The inversion results for different numbers of wavelengths.

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This study aims to balance response time and accuracy in measuring the temperature of an object using spectral data. To achieve this goal, eight spectral data of different wavelengths were selected as reference arrays to reverse the object’s temperature. In this paper, based on the principle that the true temperature calculated by all measured wavelengths is unique, all values in the temperature array obtained by randomly selecting one wavelength are compared with the values in the temperature array of all other measured wavelengths, and the closest set of temperature values is found and averaged, and the true temperature at this wavelength is finally obtained. Through the relationship between the number of wavelengths and the relative error and time consumption reflected in Fig. 4, eight wavelengths are selected as the number of wavelengths to invert the true temperature of the object in this paper. It can be seen from Fig. 2 that the six emissivity models selected in this paper have six different emissivity trends. In order to highlight that the emissivity obtained by inversion also has six different emissivity trends, eight wavelengths are randomly selected as the wavelengths of inversion temperature. The Euclidean distance between the reference arrays and the measured data was calculated to determine the best match. Figure 5 shows the distribution trend of the Euclidean distance curve for each wavelength. The bottom of the graph shows the projection of the Euclidean distance curve. From the projection, it can be seen that each target can obtain a unique emissivity at different wavelengths, which indicates that the reference arrays are suitable for temperature measurement. To better display the convergence status of the Euclidean distance, Fig. 6 extracts the distribution curve of the Euclidean distance of the emissivity target E at 1.53 µm, which is one of the optimal wavelengths. The figure shows that the Euclidean distance distribution curves in the figure converge smoothly without oscillation near the convergence point. This not only avoids local convergence but also indicates that the method has good stability and reliability.

Fig. 5. Euclidean distance distribution curves of different emissivity targets at eight wavelengths.

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Fig. 6. Euclidean distance distribution curves of emissivity target E at 1.53 µm.

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Figure 7 shows the comparison of the inversion emissivity and the true emissivity of six objects. It indicates that the developing trend of the inversion emissivity for each target is roughly the same as that of the true emissivity.

Fig. 7. Comparison of the true emissivity and inversion emissivity of six targets.

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For testing the computational speed of the method, 100 times simulation calculations are repeated for each temperature of each emissivity model. Table 2 shows the simulation results of six emissivity models in the temperature range of 873∼1173 K. The experimental results indicate that the mean operation time of the proposed method is not more than 112.301 ms, and the maximum relative error is not more than 0.229%. It means that the proposed method is effective in real-time temperature measurement.

Table 2. Simulation results of different emissivity targets.

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4. Experimental verification

4.1 Experimental samples and processing

This experiment employs two steels, 42CRMO and Q355B, which have good oxidation and heat resistances as well as fatigue and cold stamping characteristics. The measured samples have a circular disc structure with a radius of 25 mm and a thickness of 3 mm. During the experiment, the temperature of the sample surface is measured using a K-type thermocouple that is embedded into a small hole on the side of the sample. In order to ensure consistency between the temperature detected by the thermocouple and the temperature on the surface of the sample, boron nitride material with exceptional thermal conductivity is utilized to fill the holes on the side of the sample. The surfaces of both steel samples are equally treated to the same level of roughness using sandpaper. The sample is placed 100 cm away from the measuring device, ensuring that the center of the sample is at the same horizontal height as the measuring device.

4.2 Experimental platform construction

The experimental device for measuring the spectral radiance of the samples at different temperatures is shown in Fig. 8. The device consists of a fiber optic spectrometer, which can measure both the wavelength and amplitude of the radiation emitted from the samples, and a constant temperature heating furnace, which can control the sample’s temperature precisely. The temperature of the sample is monitored by a K-type thermocouple, which is inserted into the sample and connected to a digital thermometer. The thermocouple measurement is repeated three times for each sample, and the average value of the three readings is taken as the true temperature of the sample. This method ensures the accuracy and reliability of the temperature measurement.

Fig. 8. Structure diagram of the experimental device for the temperature measurements of steel samples.

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As shown in Fig. 9, the spectral radiance of the samples is transmitted to a fiber optic spectrometer by optical system. The fiber optic spectrometer is a NIR25S model, which uses a charged coupled device (CCD) as its core technology. The main components of the spectrometer are a grating, a slit, a CCD, a filter and electronic circuit components. The spectrometer can measure the spectral radiance in the range of 0.9 ∼ 2.5 µm.

Fig. 9. Diagram of the optical system.

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Accurately measuring the radiation signal of the sample is a prerequisite for temperature inversion, thus it is essential to have a precise understanding of the response function [23]. The detected signal S_s(λ,T_s) of the sample surface is given by:

(16)$${S_s}({\lambda ,{T_s}} )= R(\lambda )[\varepsilon (\lambda ,{T_s}){L_b}(\lambda ,{T_s}) + {S_0}(\lambda )]$$

where R(λ) is the response function of the optical fiber spectrometer, it is a function of wavelength λ, independent of temperature. The signal S₀(λ) is composed of background radiation emitted by the instrument's own and surroundings, while L_b(λ,T_s) represents the intensity of blackbody radiation calculated using Planck's law at a given temperature T_s. The spectral radiation curve of the blackbody furnace in Fig. 10(a) was corrected using the response function and background radiation. The measurement curve results of the optical system after corrections are shown in Fig. 10(b).

Fig. 10. (a) Measured spectrum radiation curve of the blackbody furnace from 873∼1173 K and (b) measured radiation intensity curve at different temperatures after multi-temperature method corrections.

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4.3 Temperature measurement of steel samples

Figure 11 shows the spectral emissivity of 42CRMO and Q355B at 873 K and 1073 K. The figures show that the two steels have very similar wavelength-dependent emissivity curves, with a small changing trend in the band of 1.4 ∼ 2.5 µm, and a changing range of about 0.1. However, there are peaks and troughs near 1.9 µm due to the absorption of infrared radiation by water vapor, which is consistent with the findings of Huang [24,25]. As the sample temperature increases, the emissivity of Q355B changes greatly, while that of 42CRMO changes little. Additionally, the emissivity of both samples increases with the increase in temperature, which can be attributed to the oxidation state of the samples gradually deepening with the increase in heating time.

Fig. 11. Curves of emissivity versus wavelength for (a) Q355B-873 K, (b) Q355B-1073 K, (c) 42CRMO-873 K and (d) 42CRMO-1073 K.

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Figure 12 shows the comparison of the true emissivity and inversion emissivity of two samples at wavelengths unaffected by water absorption. The steps of the temperature inversion data processing algorithm in this paper are as follows: First, the possible emissivity range of all measured wavelengths of the object is set, and then the emissivity range is divided into an array of emissivity values. In the array, there is always an emissivity value close to the true emissivity at the current measured wavelength. Based on the principle that the true temperature calculated by all measured wavelengths is unique, all values in the temperature array obtained by randomly selecting one wavelength are compared with the values in the temperature array of all other measured wavelengths to find the closest temperature value set and calculate the average value. Finally, the true temperature at the measured wavelength is obtained. Setting the possible emissivity range of all the measured wavelengths of the object is the most critical. If the range is set incorrectly, it will definitely lead to a low accuracy of the inversion temperature. Since the largest true emissivity in Fig. 12(c) is too close to the upper limit of the set emissivity range, 1, and its emissivity curve varies greatly compared with other samples, the deviation between the retrieved emissivity and the true emissivity is large, but the accuracy of the retrieved temperature is not affected. Figure 13 shows the comparison of the true emissivity and inversion emissivity of two samples at wavelengths affected by water absorption. It indicates that for the two samples, the emissivity calculated by the proposed method can correctly reflect the developing trend of the true emissivity, and the values are very close to the true value. In the wavelength band affected by water absorption, the method presented in this paper was able to accurately reflect the true emissivity for both samples, with values that closely match their actual emissivity values. It indicates that the proposed multispectral radiation thermometry is effective in calculating spectral emissivity.

Fig. 12. Comparison of the true emissivity and inversion emissivity of two samples at wavelengths unaffected by water absorption. (a) Q355B-873 K, (b) Q355B-1073 K, (c) 42CRMO-873 K and (d) 42CRMO-1073 K.

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Fig. 13. Comparison of true emissivity and inversion emissivity of two samples at wavelengths affected by water absorption. (a) Q355B-873 K, (b) Q355B-1073 K, (c) 42CRMO-873 K and (d) 42CRMO-1073 K.

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Figure 14 illustrates the inversion temperature and the relative error of two steel samples measured at wavelengths that are unaffected and affected by water absorption, respectively. The results show that the proposed method can accurately estimate the temperature of the two samples in the range of 873 K to 1173 K with a maximum relative error of 0.81%. In the actual measurement experiment, there are three steps from spectral data measurement to inversion to obtain temperature, which are spectral data acquisition, spectral data transmission and spectral data processing, each of which consumes time. The optical fiber spectrometer used in this experiment can complete the acquisition of spectral data within 1 ms, and the transmission of spectral data can also be transmitted to the data processing equipment within 1 ms by means of wire transmission. Among these three steps, the step of data processing takes the longest time. Through repeated experiments, the average time from spectral data measurement to temperature inversion is less than 150 ms. This indicates that the emissivity calculated by the proposed method can correctly reflect the true temperature of the samples and is very close to the actual value.

Fig. 14. Inversion temperature and relative error of two samples. (a) 42CRMO unaffected by water absorption, (b) Q355B unaffected by water absorption, (c) 42CRMO affected by water absorption and (d) Q355B unaffected by water absorption.

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5. Conclusion

This study proposes a multispectral radiation thermometry inversion method that does not rely on a predefined emissivity model. The method generates a temperature matrix by inputting emissivity values at different wavelengths, selects a row in the temperature matrix as the reference vector, and rearranges the temperature matrices at other wavelengths accordingly. The objective function is the Euclidean distance between each column element of the rearranged temperature matrix and the reference vector, and an unconstrained optimization method is used to minimize the Euclidean distance and obtain the true temperature of the object. The simulation results show that the method has a maximum relative error of less than 0.229% and a response speed of less than 112.301 ms in the response band of 1.4 ∼ 2.5µm and temperature range of 873 ∼ 1173 K. To validate the method in practical applications, the paper uses a self-built temperature measuring device to measure the spectral intensity of 42CRMO and Q355B in the 1.4 ∼ 2.5µm band. The method performs temperature inversion on the experimental spectral curves of these two samples, with and without water absorption effect, and achieves a maximum relative error of less than 0.813% compared with the measurement of K-type thermocouples. This demonstrates the feasibility of real-time temperature measurement of steel materials.

Funding

Henan Provincial Joint Fund for Science and Technology Research and Development Program (225200810077); Program for Innovative Research Team (in Science and Technology) in University of Henan Province (23IRTSTHN013); Natural Science Foundation of Henan Province (222300420011, 222300420209); Innovation Scientists and Technicians Troop Construction Projects of Henan Province (224000510007); National Natural Science Foundation of China (62075058, U23A20377).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Parameters (λ/nm)	A	B	C	D	E	F
Parameters (λ/nm)	$ε (λ) = exp (a_{0} + a_{1} λ)$		$ε (λ) = a_{0} + a_{1} sin (a_{2} + a_{3} λ)$
$a_{0}$	1.03	-2.47	0.55	0.55	0.55	0.55
$a_{1}$	-0.0009	0.0009	0.25	0.25	0.25	0.25
$a_{2}$	/	/	-5.4	-8	-4.68	-7.7
$a_{3}$	/	/	5	5	5.75178	5.75178

Emissivity target	Maximum relative error /%	Average operation time /ms
A	0.122	103.752
B	0.02	105.194
C	0.027	105.386
D	0.229	102.277
E	0.018	107.881
F	0.05	112.301

Parameters (λ/nm)	A	B	C	D	E	F
Parameters (λ/nm)	$ε (λ) = exp (a_{0} + a_{1} λ)$		$ε (λ) = a_{0} + a_{1} sin (a_{2} + a_{3} λ)$
$a_{0}$	1.03	-2.47	0.55	0.55	0.55	0.55
$a_{1}$	-0.0009	0.0009	0.25	0.25	0.25	0.25
$a_{2}$	/	/	-5.4	-8	-4.68	-7.7
$a_{3}$	/	/	5	5	5.75178	5.75178

Emissivity target	Maximum relative error /%	Average operation time /ms
A	0.122	103.752
B	0.02	105.194
C	0.027	105.386
D	0.229	102.277
E	0.018	107.881
F	0.05	112.301

Fast data processing method for multispectral radiation thermometry based on Euclidean distance optimization

Abstract

1. Introduction

2. Principle of temperature measurements

2.1 Principle of radiation thermometry

2.2 Method for processing multispectral radiation thermometry

3. Simulation verification

4. Experimental verification

4.1 Experimental samples and processing

4.2 Experimental platform construction

4.3 Temperature measurement of steel samples

5. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (14)

Tables (2)

Equations (16)

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