A method for calibration and noise analysis of a multi-wavelength area array CCD pyrometer

Abstract

The application discloses a kind of multi-wavelength area array CCD pyrometer's calibration and noise analysis method, constructs temperature measurement calibration model, obtains the parameter that each channel R of CCD camera, G, B needs calibration;Solving the unknown parameter of calibration model, analysis calibration error;Construct noise analysis model, find out the unknown parameter of each channel R of CCD camera in noise analysis model, G, B;Quantitative analysis is carried out to the noise of each channel R of CCD camera, G, B by noise analysis model.The influence caused by each channel R of CCD camera, G, B noise is evaluated.The calibration model of pyrometer in the application is an innovative model, the error of each channel of pyrometer is very small when calibration is carried out under this model;The noise analysis method in the application can quantitatively analyze the noise of pyrometer, the gray value fluctuation caused by each noise can be solved by the method, and the temperature error caused by each noise can be analyzed.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of CCD pyrometer, and particularly relates to a calibration and noise analysis method of a multi-wavelength area array CCD pyrometer. BACKGROUND

[0002] The CCD-based pyrometer is widely used in industry, and its temperature measurement principle is to measure the surface two-dimensional temperature field of a target object by using the spectral response characteristics and photoelectric conversion characteristics of the CCD and the image output of the CCD. This is a radiation temperature measurement technology, which has the characteristics of wide temperature measurement range and real-time measurement of the two-dimensional temperature field of the target object surface, and thus has more advantages than traditional pyrometers. The calibration of the pyrometer before use can ensure the acquisition of the real temperature of the target object. The calibration methods of the pyrometer include effective wavelength calibration method and fixed point calibration method. Since there are dark current noise, readout noise and shot noise in the CCD, these three kinds of noise will cause temperature measurement error of the CCD pyrometer, so noise analysis is also important, and a noise analysis model needs to be introduced for quantitative analysis of the noise.

[0003] Effective wavelength calibration method: when a multispectral pyrometer is used for measurement, since there is no interference filter in the optical path, the effective wavelength of the spectral channel cannot be obtained through the transmittance curve of the filter, and thus the effective wavelength of the corresponding spectral channel needs to be obtained by measurement. The disadvantage of this method is that the effective wavelength is difficult to obtain and the calibration process is also complex. Fixed point calibration method: using a heat source as a standard, the temperature is reproduced and transmitted. The calibration accuracy of the fixed point calibration method is high, and the disadvantage is that the fixed point calibration method is limited by the standard temperature points, at least three fixed point temperatures need to be fitted, and it is difficult to manufacture fixed points in high temperature areas. SUMMARY

[0004] The present application aims to overcome the defects of the prior art and provide a calibration and noise analysis method of a multi-wavelength area array CCD pyrometer, which uses this model for calibration of the pyrometer. This new calibration model can reduce the calibration error, thus improving the measurement accuracy and making the measurement results more accurate.

[0005] The present application is achieved by the following technical solutions:

[0006] A calibration and noise analysis method of a multi-wavelength area array CCD pyrometer, specifically comprising the following steps:

[0007] (1) constructing a temperature measurement calibration model to obtain the parameters of each channel R, G and B of the CCD camera that need to be calibrated;

[0008] (2) solving the unknown parameters of the calibration model and analyzing the calibration error;

[0009] (3) Construct a noise analysis model and determine the unknown parameters of R, G, and B for each channel of the CCD camera in the noise analysis model;

[0010] (4) Quantitative analysis of the noise of R, G, and B in each channel of the CCD camera is performed using a noise analysis model.

[0011] (5) Evaluate the impact of R, G, B noise in each channel of the CCD camera.

[0012] The temperature calibration model constructed in step (1) yields the parameters that need to be calibrated for each channel of the CCD camera (R, G, B), as follows:

[0013] The CCD camera radiation imaging formula is shown in equation (1):

[0014]

[0015] Among them G r (T), G g (T), G b (T) represents the grayscale output of each channel (R, G, B) of the CCD camera, k represents the scaling factor between the charge output of the CCD sensor and its grayscale value; q is the charge of an electron; S0 is the area of ​​a single pixel; t is the camera's exposure time; F is the camera's aperture number (F-number); E b (λ,T) represents Planck's law for a blackbody at wavelength λ and temperature T; S r (λ), S g (λ), S b (λ) represent the spectral sensitivity of each channel of R, G, and B, respectively; R r (λ), R g (λ), R b (λ) represents the spectral response function of the three channels, including the spectral responsivity of the CCD sensor and the total spectral transmittance of the optical system; C1 is Planck's first constant, a fixed value C1 = 3.742 × 10⁻⁶. -16 W·m 2 ;

[0016] The total emission power of a blackbody is given by equation (2):

[0017]

[0018] L bλ This represents the emitted power of a blackbody in a certain wavelength band;

[0019] Equation (2) expresses the total emission power of a blackbody at temperature T as an integral of wavelength. For most spectra of a semi-transparent medium, under the assumption of constant refractive index, the calculation of the total emission power of the blackbody surface is shown in Equation (3):

[0020]

[0021] In equation (3), n is the refractive index of the medium, which is 1 in vacuum, and k is the Boltzmann constant, which is 1.3807 × 10⁻⁶. -23 c0 is the speed of light in a vacuum, where h is the convective heat transfer coefficient; combining formulas (2) and (3), we obtain formula (4):

[0022]

[0023] C2 is Planck's second constant, C2 = 1.4388 × 10 -2 m·K;

[0024] The integral in equation (4) is calculated using complex integrals and retrieved from the integral table, thus yielding equations (5) and (6):

[0025] L b (T)=n 2 σT 4 (5)

[0026]

[0027] Where σ represents the Stefan–Boltzmann constant. W, m, and K represent the units of power, length, and temperature, respectively; the total emission power of the blackbody within the wavelength ranges of λ2 and λ1 is calculated using equation (7):

[0028]

[0029] The integral in equation (7) is usually expressed as the blackbody emission power fraction between 0 and nλT, thus yielding equation (8):

[0030]

[0031] Equation (8) is expanded into an infinite series and then integrated, resulting in equation (9):

[0032]

[0033] By combining equations (7) and (8), we obtain equation (10):

[0034]

[0035] Combining formulas (1) and (10), and considering the noise in actual data acquisition, an offset c is added to each channel based on the approximate calculation formula. i (i = r, g, b), thus obtaining formula (11):

[0036]

[0037] Formula (11) is the temperature measurement calibration model mentioned above. Therefore, the parameter that needs to be calibrated for the R channel is a. r0 a r1 c r The parameter that needs to be calibrated for the G channel is a. g0 a g1 c g The parameter that needs to be calibrated for channel B is a. b0 a b1 c b .

[0038] The specific steps for solving the unknown parameters of the calibration model are as follows:

[0039] Solving for the unknown parameters is equivalent to solving the following system of linear equations:

[0040]

[0041] Where, x r x g x b Let b be the parameter vector. r b g b b It is a vector of grayscale values;

[0042] Since a blackbody furnace is used for calibration experiments, n = 1 in equation (12); therefore, the coefficient matrix A in equation (12) is:

[0043]

[0044] parameter vector x r ,x g ,x b for:

[0045]

[0046] grayscale vector b r ,b g ,b b for:

[0047]

[0048] When calculating f(λT) according to formula (9), the wavelengths of the R, G, and B channels of the CCD camera need to be selected. The wavelengths of the R, G, and B channels of the CCD camera are obtained from the spectral response sensitivity curve of the CCD camera.

[0049] Step (3) involves constructing a noise analysis model and determining the unknown parameters R, G, and B for each channel of the CCD camera in the noise analysis model, as detailed below:

[0050] The noise analysis model consists of quadratic and linear functions. By fitting these two functions, the parameter values ​​in the model are obtained. These parameter values ​​can characterize the three types of noise signals. The noise analysis model is as follows:

[0051]

[0052] μ(I) represents the mean image of multiple consecutive frames; σ 2 (I) represents the variance image composed of the variance of each pixel in multiple consecutive frames; m(ρ) is a constant related to non-uniformity, m(ρ) = Var(ρ) / E 2 (ρ); Var() refers to the variance in the spatial domain; E() refers to the mean in the temporal domain. The formulas for calculating Var(μ(I)) and E(μ(I)) are shown in (17):

[0053]

[0054] In equation (16), m(ρ) and E(N) D ), Var(N D ), σ 2 (G RQ The parameters K can characterize the three types of noise. The parameters of each channel of R, G, and B in a CCD camera are different; m×n represents the width and height of the selected image region pixels, and I(i,j) represents the gray value of the pixel with coordinates (i,j) in the image.

[0055] Through noise separation experiments, two sets of data points for each channel of the CCD camera (R, G, B) at nine temperature points in the blackbody furnace were obtained. The data points of each channel were then substituted into the noise analysis model (16) for data fitting to solve for the unknown parameters of the model. In the model, Var(μ(I)) and E(μ(I)) are quadratic functions, and E(σ) is a quadratic function. 2 (I)) and E(μ(I)) are linear functions in one variable;

[0056]

[0057] Where I t (i,j) represents the t-th image out of 100 consecutive images.

[0058] Step (4) involves quantitatively analyzing the noise of each channel (R, G, B) of the CCD camera using a noise analysis model, as detailed below:

[0059] The relationship between the gray value fluctuations caused by the three types of noise in the R channel and the calculated model parameter values ​​is shown in formula (19):

[0060]

[0061] Equation (19) shows that the grayscale fluctuation caused by dark current noise and readout noise in the R channel is a constant, while the grayscale fluctuation caused by shot noise is variable and needs to be determined based on the R channel image I. R The grayscale value is calculated;

[0062] The relationship between the gray value fluctuations caused by the three types of noise in the G channel and the calculated model parameter values ​​is shown in formula (20):

[0063]

[0064] Equation (20) shows that the grayscale fluctuation caused by dark current noise and readout noise in the G channel is a constant, while the grayscale fluctuation caused by shot noise is variable and needs to be determined based on the G channel image I. G The grayscale value is calculated;

[0065] The relationship between the gray value fluctuations caused by the three types of noise in channel B and the calculated model parameter values ​​is shown in formula (21):

[0066]

[0067] Equation (21) shows that the grayscale fluctuation caused by dark current noise and readout noise in channel B is a constant, while the grayscale fluctuation caused by shot noise is variable and needs to be determined based on the B channel image I. B The grayscale value is calculated.

[0068] The evaluation of the impact of R, G, and B noise in each channel of the CCD camera described in step (5) is as follows:

[0069] The principle of measuring the temperature measurement error of a pyrometer is shown in formula (22):

[0070]

[0071] In equation (22), ΔT / ΔG represents the slope, which is given by the calibrated model for each channel, and ΔG... N The grayscale value fluctuations caused by each type of noise are used to calculate the temperature measurement error caused by different types of noise in each channel.

[0072] The advantages of this invention are: 1. The calibration model of the pyrometer in this invention is an innovative model, and the error of each channel of the pyrometer is very small when calibrated under this model;

[0073] 2. The noise analysis method in this invention can quantitatively analyze the noise of the pyrometer. This method can determine the gray value fluctuation caused by each type of noise and analyze the temperature error caused by each type of noise. Attached Figure Description

[0074] Figure 1 The color CCD spectral response sensitivity curve;

[0075] Figure 2 This refers to the calibration error of the R channel of the pyrometer.

[0076] Figure 3 This refers to the calibration error of the G channel of the pyrometer.

[0077] Figure 4 This refers to the calibration error of channel B of the pyrometer.

[0078] Figure 5 The temperature measurement error in the R channel caused by different types of noise;

[0079] Figure 6 The temperature measurement error in the G channel caused by different types of noise;

[0080] Figure 7 The temperature measurement error in channel B is caused by different types of noise. Detailed Implementation

[0081] A calibration and noise analysis method for a multi-wavelength area array CCD pyrometer is presented. The calibration model construction process is as follows: The relevant formulas for color CCD radiation imaging are shown in equation (1):

[0082]

[0083] Among them G r (T), G g (T), G b (T) represents the grayscale output of each channel (R, G, B) of the CCD camera. This camera has a 12-bit output, and the grayscale value range is 0-4095; k represents the scaling factor between the charge output of the CCD sensor and its grayscale value; q is the charge of an electron; S0 is the area of ​​a single pixel; t is the camera's exposure time; F is the camera's aperture number (F-number); E b (λ,T) represents Planck's law for a blackbody at wavelength λ and temperature T; S r (λ), S g (λ), S b (λ) represent the spectral sensitivity of each channel of R, G, and B, respectively; R r (λ), R g (λ), R b(λ) represents the spectral response function of each of the three channels, including the spectral responsivity of the CCD sensor and the total spectral transmittance of the optical system. The specific spectral response characteristics of the R, G, and B channels are shown in [reference needed]. Figure 1 As shown, the spectral response functions of the R, G, and B channels are also different; C1 is Planck's first constant, a fixed value C1 = 3.742 × 10⁻⁶. -16 W·m 2

[0084] The total emission power of a blackbody is given by equation (2):

[0085]

[0086] L bλ This represents the emitted power of a blackbody in a certain wavelength band;

[0087] Equation (2) expresses the total emitted power of a blackbody at temperature T as an integral of wavelength across all wavelengths. For most spectra of some semi-transparent media, under the assumption of a constant refractive index, the total emitted power of the blackbody surface is calculated as shown in Equation (3):

[0088]

[0089] In equation (3), n is the refractive index of the medium, which is 1 in vacuum, and k is the Boltzmann constant, which is 1.3807 × 10⁻⁶. -23 c0 is the speed of light in a vacuum, and h is the convective heat transfer coefficient. Combining equations (2) and (3), we can obtain equation (4):

[0090]

[0091] C2 is Planck's second constant, C2 = 1.4388 × 10 -2 m·K;

[0092] The integral in equation (4) can be calculated using complex integrals and can be looked up in the integral table, thus yielding equations (5) and (6):

[0093] L b (T)=n 2 σT 4 (5)

[0094]

[0095] Where σ represents the Stefan–Boltzmann constant. W, m, and K represent the units of power, length, and temperature, respectively. The total emitted power of the blackbody within the wavelength ranges of λ2 and λ1 is calculated using equation (7):

[0096]

[0097] The integral in equation (7) is usually expressed as the blackbody emission power fraction between 0 and nλT, thus yielding equation (8):

[0098]

[0099] Equation (8) can be integrated by expanding the denominator into an infinite series, resulting in equation (9):

[0100]

[0101] By combining equations (7) and (8), we can obtain equation (10):

[0102]

[0103] Combining formulas (1) and (10), and considering the noise in actual data acquisition, an offset c is added to each channel based on the approximate calculation formula. i (i = r, g, b), thus obtaining formula (11):

[0104]

[0105] Formula (11) is the temperature measurement calibration model mentioned above. Therefore, the parameter that needs to be calibrated for the R channel is a. r0 a r1 c r The parameter that needs to be calibrated for the G channel is a. g0 a g1 c g The parameter that needs to be calibrated for channel B is a. b0 a b1 c b .

[0106] A calibration experiment for a blackbody furnace was conducted using a color camera based on a calibration model. The experimental procedure is as follows: First, the parameters of the color CCD camera need to be initialized. The exposure time t of the color CCD pyrometer is set to 15ms, the focal length f is set to 75mm, the camera aperture F-number is set to 4, the electronic gain g is set to 13, and the initial target temperature T of the blackbody furnace is set to 800℃. Second, the blackbody furnace is heated to the target temperature T and maintained for at least 30 minutes to ensure temperature stability. Third, a rectangular pixel area with a radius of 30 is specified in the camera image, and the average gray value of each channel (R, G, B) in this area is used to output the target temperature. Fourth, the target temperature T is increased by 50℃, and the previous steps are repeated until the target temperature T of the blackbody furnace reaches 1200℃. Based on the above steps, 9 data points [T] of the R channel are obtained. i G ri ], 9 data points in channel G [Ti G gi ] and 9 data points in channel B [T i G bi ].

[0107] By fitting data from the blackbody furnace calibration experiment, the unknown parameters of the calibration model were solved, and finally, the calibration error was analyzed. Solving for the unknown parameters is equivalent to solving the following system of linear equations:

[0108]

[0109] Since a blackbody furnace is used for calibration experiments, n = 1 in equation (12); therefore, the coefficient matrix A in equation (12) is:

[0110]

[0111] parameter vector x r ,x g ,x b for:

[0112]

[0113] grayscale vector b r ,b g ,b b for:

[0114]

[0115] When calculating f(λT) according to formula (9), the wavelengths of the R, G, and B channels of the CCD camera need to be selected. Based on the spectral response sensitivity curve of the color CCD camera, as shown in... Figure 1 As shown:

[0116] Depend on Figure 1 It is known that the wavelength range of the camera's R channel is 370nm-760nm; the wavelength range of the G channel is 370nm-640nm; and the wavelength range of the B channel is 370nm-580nm. Finally, the wavelengths selected are: R channel wavelength λ2 = 730nm, λ1 = 490nm; G channel wavelength λ2 = 630nm, λ1 = 370nm; and B channel wavelength λ2 = 580nm, λ1 = 370nm.

[0117] The experimental data for the camera's R, G, and B channels are shown in Tables 1, 3, and 5, and the calibrated unknown parameters are shown in Tables 2, 4, and 6.

[0118] Table 1 Gray values ​​of the R channel

[0119]

[0120] Table 2 R Channel Calibration Parameter Values

[0121]

[0122] Table 3G channel grayscale values

[0123]

[0124] Table 4G channel calibration parameter values

[0125]

[0126] Table 5 Gray values ​​of channel B

[0127]

[0128] Table 6B Channel Calibration Parameter Values

[0129]

[0130] The calibration error of the model is as follows Figure 2 , Figure 3 , Figure 4 As shown, the maximum error of the R-channel calibration model is close to 1.5, and the total error is 5.52; the maximum error of the G-channel calibration model is close to 7, and the total error is 27.15, which is larger than the error of the R-channel; the maximum error of the B-channel calibration model does not exceed 8, and the total error is 32.84, which is larger than the errors of the R-channel and G-channel. The calibration errors of all three channels are very small; therefore, the calibration model of this invention can improve calibration accuracy and reduce measurement error.

[0131] A noise analysis model is introduced, consisting of quadratic and linear functions. By fitting these two functions, the parameter values ​​in the model are obtained, and these parameter values ​​can characterize the three types of noise signals. The noise analysis model is as follows:

[0132]

[0133] μ(I) represents the mean image of multiple consecutive frames; σ 2 (I) represents the variance image composed of the variance of each pixel in multiple consecutive frames; m(ρ) is a constant related to non-uniformity, m(ρ) = Var(ρ) / E 2 (ρ); Var() refers to the variance in the spatial domain; E() refers to the mean in the temporal domain. The formulas for calculating Var(μ(I)) and E(μ(I)) are shown in (17):

[0134]

[0135] In equation (16), m(ρ) and E(N) D ), Var(N D ), σ2 (G RQ The parameters K and others can characterize the three types of noise. It should be noted that the parameters of each channel of R, G, and B are different in a color CCD camera; m×n represents the width and height of the selected image region pixels, and I(i,j) represents the gray value of the pixel with coordinates (i,j) in the image.

[0136] A noise separation experiment was conducted. The experiment used a spherical blackbody furnace as the uniform surface light source, adjusting the intensity of the light source by changing the target temperature inside the furnace. The experimental procedure was as follows: First, the CCD camera parameters were set (exposure time t = 15ms, focal length f = 75mm, camera aperture F = 4, electronic gain g = 13), and the initial target temperature T of the blackbody furnace was set to 800℃. Second, the blackbody furnace was heated to the target temperature T and maintained for at least 30 minutes. Third, 100 images of the blackbody furnace outlet were continuously captured using a color CCD camera. Fourth, the time-averaged image μ(I) and variance image σ of the 100 consecutive images were calculated. 2 (I), time-averaged image μ(I) and variance image σ 2 (I) Defined as shown in Equation (15); the fifth step is to calculate the spatial mean E(μ(I)) and variance Var(μ(I)) of the average image μ(I), and to calculate the variance image σ. 2 (I) Spatial variance E(σ) 2 (I)); Step 6, increase the target temperature T by 50℃; Step 7, repeat steps 2 to 6 until T = 1200℃. Based on the above steps, two sets of data points for each channel (R, G, B) of the color CCD camera at 9 temperature points in the blackbody furnace are obtained. Substituting the data points of each channel into the noise analysis model for data fitting can solve for the unknown parameters of the model. In the model, Var(μ(I)) and E(μ(I)) are quadratic functions, and E(σ) is a quadratic function. 2 (I)) and E(μ(I)) are linear functions in one variable.

[0137]

[0138] Where I t (i,j) represents the t-th image out of 100 consecutive images.

[0139] Quantitative analysis of noise is performed using a noise analysis model. (1) Noise analysis of the R channel: The parameter estimation results of the R channel noise analysis model are shown in Table 7.

[0140] Table 7 Parameters of the R-channel noise analysis model

[0141]

[0142] The relationship between the gray value fluctuations caused by the three types of noise in the R channel and the calculated model parameter values ​​is shown in formula (19):

[0143]

[0144] Equation (19) shows that the grayscale fluctuation caused by dark current noise and readout noise in the R channel is a constant, while the grayscale fluctuation caused by shot noise is variable and needs to be determined based on the R channel image I. R The grayscale value is calculated. Combined with Table 7, the specific grayscale value fluctuations caused by the three types of noise in the R channel can be calculated.

[0145] (2) Noise analysis of the G channel. The parameter estimation results of the noise analysis model for the G channel are shown in Table 8:

[0146] Table 8 Parameters of the G-channel noise analysis model

[0147]

[0148] The relationship between the gray value fluctuations caused by the three types of noise in the G channel and the calculated model parameter values ​​is shown in formula (20):

[0149]

[0150] Equation (20) shows that the grayscale fluctuation caused by dark current noise and readout noise in the G channel is a constant, while the grayscale fluctuation caused by shot noise is variable and needs to be determined based on the G channel image I. G The grayscale value is calculated. Combined with Table 8, the specific values ​​of grayscale fluctuation caused by the three types of noise in the G channel can be calculated.

[0151] (3) Noise analysis of channel B. The parameter estimation results of the noise analysis model for channel B are shown in Table 9:

[0152] Table 9 Parameters of the B-channel noise analysis model

[0153]

[0154]

[0155] The relationship between the gray value fluctuations caused by the three types of noise in channel B and the calculated model parameter values ​​is shown in formula (21):

[0156]

[0157] Equation (21) shows that the grayscale fluctuation caused by dark current noise and readout noise in channel B is a constant, while the grayscale fluctuation caused by shot noise is variable and needs to be determined based on the B channel image I. BThe grayscale values ​​are calculated. Combined with Table 9, the specific grayscale value fluctuations caused by the three types of noise in channel B can be calculated.

[0158] Assess the impact of noise on each channel. The principle for measuring the temperature measurement error of the pyrometer is shown in formula (22):

[0159]

[0160] In equation (22), ΔT / ΔG represents the slope, which is given by the calibrated model for each channel, and ΔG... N The grayscale value fluctuations caused by each type of noise can be calculated, thus allowing us to calculate the temperature measurement error caused by different types of noise in each channel.

[0161] The temperature measurement error caused by the three types of noise in each of the R, G, and B channels is as follows: Figure 5 , 6 As shown in Figures 7 and 8, the maximum temperature deviations caused by dark current noise, shot noise, and readout quantization noise in the R channel are 14.18℃, 20.19℃, and 53.98℃, respectively, with average deviations of 2.88℃, 6.36℃, and 10.96℃, respectively; the maximum temperature deviations caused by dark current noise, shot noise, and readout quantization noise in the G channel are 14.54℃, 32.49℃, and 58.58℃, respectively, with average deviations of 2.94℃, 8.77℃, and 11.84℃, respectively; and the maximum temperature deviations caused by dark current noise, shot noise, and readout quantization noise in the B channel are 13.11℃, 26.56℃, and 84.65℃, respectively, with average deviations of 2.67℃, 6.10℃, and 17.24℃, respectively.

Claims

1. A calibration and noise analysis method for a multi-wavelength area array CCD pyrometer, characterized in that: Specifically, the steps include the following: (1) Construct a temperature measurement calibration model and obtain the parameters that need to be calibrated for each channel of the CCD camera (R, G, B); (2) Solve for the unknown parameters of the calibration model and analyze the calibration error; (3) Construct a noise analysis model and determine the unknown parameters of R, G, and B for each channel of the CCD camera in the noise analysis model; (4) Quantitatively analyze the noise of R, G, and B in each channel of the CCD camera using a noise analysis model; (5) Evaluate the impact of R, G, and B noise in each channel of the CCD camera; The temperature calibration model constructed in step (1) yields the parameters that need to be calibrated for each channel of the CCD camera (R, G, B), as follows: The CCD camera radiation imaging formula is shown in equation (1): （1） in , , These represent the grayscale output values ​​of R, G, and B for each channel of the CCD camera, respectively; k represents the scaling factor between the charge output of the CCD sensor and its grayscale value; and q is the charge of an electron. t is the area of ​​a single pixel; t is the camera's exposure time. F is the F-number of the camera aperture; This indicates the wavelength of the blackbody. and Planck's law at temperature T; , , These represent the spectral response functions of the three channels, including the spectral responsivity of the CCD sensor and the total spectral transmittance of the optical system; It is Planck's first constant, a constant value. ; The total emission power of the blackbody is given by equation (2): (2) This represents the emitted power of a blackbody in a certain wavelength band; Equation (2) expresses the total emission power of a blackbody at temperature T as an integral of wavelength. For most spectra of a semi-transparent medium, under the assumption of constant refractive index of the medium, the calculation of the total emission power of the blackbody surface is shown in equation (3): (3) In equation (3), n is the refractive index of the medium, which is 1 in vacuum, and k is the Boltzmann constant, which is 1.3807. , Let h be the speed of light in a vacuum, where h is the convective heat transfer coefficient; combining formulas (2) and (3), we obtain formula (4): (4) It is Planck's second constant. ; The integral in equation (4) is calculated using complex integrals and retrieved from the integral table, thus yielding equations (5) and (6): (5) (6) in This represents the Stefan–Boltzmann constant. ; W, m, and K represent units of power, length, and temperature, respectively. and The total emission power of a blackbody within the wavelength range is calculated using equation (7): (7) The integral in equation (7) is usually expressed as the blackbody emission power fraction between 0 and nλT, thus yielding equation (8): (8) Equation (8) is expanded into an infinite series and then integrated, resulting in equation (9): (9) By combining equations (7) and (8), we obtain equation (10): (10) Combining formulas (1) and (10), and considering the noise in actual data acquisition, an offset c is added to each channel based on the approximate calculation formula. i (i = r, g, b), thus obtaining formula (11): （11） Formula (11) is the temperature measurement calibration model mentioned above. Therefore, the parameters that need to be calibrated for the R channel are: , , The parameters that need to be calibrated for the G channel are: , , The parameters that need to be calibrated for channel B are: , , .

2. The calibration and noise analysis method for a multi-wavelength area array CCD pyrometer according to claim 1, characterized in that: The specific steps for solving the unknown parameters of the calibration model are as follows: Solving for the unknown parameters is equivalent to solving the following system of linear equations: （12） in, , , For parameter vectors, , , It is a vector of grayscale values; Since a blackbody furnace is used for calibration experiments, n=1 in equation (12); therefore, the coefficient matrix A in equation (12) is: （13） parameter vector , , for: (14) Gray value vector , , for: （15） Calculate according to formula (9) It is necessary to select the wavelengths of the R, G, and B channels of the CCD camera, and obtain the wavelengths of the R, G, and B channels of the CCD camera based on the spectral response sensitivity curve of the CCD camera.

3. The calibration and noise analysis method for a multi-wavelength area array CCD pyrometer according to claim 2, characterized in that: Step (3) involves constructing a noise analysis model and determining the unknown parameters R, G, and B for each channel of the CCD camera in the noise analysis model, as detailed below: The noise analysis model consists of quadratic and linear functions. By fitting these two functions, the parameter values ​​in the model are obtained. These parameter values ​​can characterize the three types of noise signals. The noise analysis model is as follows: (16) A mean image representing multiple consecutive frames; A variance image representing the variance of each pixel in multiple consecutive frames of images; It is a constant related to non-uniformity. = / ; This refers to the variance in the spatial domain; This refers to the mean at the time domain level. and The calculation formula is shown in (17): (17) In equation (16) E( ), ( ), ( These parameters, K, etc., can characterize the three types of noise. The parameters for each channel of the CCD camera, R, G, and B, are different. This represents the width and height of the selected image region's pixels. The coordinates in the image are The grayscale value of a pixel; Through noise separation experiments, two sets of data points for each channel (R, G, B) of the CCD camera were obtained at nine temperature points in the blackbody furnace. These data points were then used in the noise analysis model (16) for data fitting to solve for the unknown parameters of the model. and It is a quadratic function relationship. and It is a linear function relationship in one variable; (18) in This represents the t-th image out of 100 consecutive images.

4. The calibration and noise analysis method for a multi-wavelength area array CCD pyrometer according to claim 3, characterized in that: Step (4) involves quantitatively analyzing the noise of each channel (R, G, B) of the CCD camera using a noise analysis model, as detailed below: The relationship between the gray value fluctuations caused by the three types of noise in the R channel and the calculated model parameter values ​​is shown in formula (19): (19) Equation (19) shows that the grayscale fluctuation caused by dark current noise and readout noise in the R channel is a constant, while the grayscale fluctuation caused by shot noise is variable and needs to be determined based on the R channel image. The grayscale value is calculated; The relationship between the gray value fluctuations caused by the three types of noise in the G channel and the calculated model parameter values ​​is shown in formula (20): (20) Equation (20) shows that the grayscale fluctuation caused by dark current noise and readout noise in the G channel is a constant, while the grayscale fluctuation caused by shot noise is variable and needs to be determined based on the G channel image. The grayscale value is calculated; The relationship between the grayscale value fluctuations caused by the three types of noise in channel B and the calculated model parameter values ​​is shown in the formula. （21）： (21) Equation (21) shows that the grayscale fluctuation caused by dark current noise and readout noise in channel B is a constant, while the grayscale fluctuation caused by shot noise is variable and needs to be determined based on the image of channel B. The grayscale value is calculated.

5. The calibration and noise analysis method for a multi-wavelength area array CCD pyrometer according to claim 4, characterized in that: The evaluation of the impact of R, G, and B noise in each channel of the CCD camera described in step (5) is as follows: The principle of measuring the temperature measurement error of a pyrometer is shown in formula (22): (22) In equation (22) / This represents the slope, which is given by the calibrated model for each channel. The grayscale value fluctuations caused by each type of noise are used to calculate the temperature measurement error caused by different types of noise in each channel.

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