A flame temperature measurement method based on Taylor approximation guided exponential model

Abstract

A Taylor approximation-guided exponential model method for flame temperature measurement, which improves the accuracy and stability of temperature measurement results, is proposed. The method involves acquiring flame radiation signals in the visible-near-infrared band, converting them into dimensional spectral radiance to obtain the continuous spectral radiance of the flame; calculating the colorimetric temperature corresponding to each wavelength pair under the Wien approximation to obtain the relationship between the colorimetric temperature and the true temperature; applying a first-order Taylor approximation to the reciprocal of the wavelength term to obtain the constraint relationship between the colorimetric temperature and the true temperature for each wavelength pair; when the colorimetric temperatures of wavelength pairs are equal, the emissivity and wavelength satisfy an exponential relationship; determining that the colorimetric temperatures are approximately equal under tolerance conditions indicates that the corresponding emissivity and wavelength satisfy an exponential relationship; for the full spectrum in the visible-near-infrared range, the emissivity and wavelength satisfy an exponential relationship; and limiting the range of the true temperature to construct an objective function containing a curvature regularization term (logarithmic emissivity-wavelength linear function) and a logarithmic consistency term for the full-spectrum radiance.

Description

Technical Field

[0001] This invention belongs to the field of visible-near infrared measurement of combustion furnace flame radiation temperature technology, specifically relating to a flame temperature measurement method based on an exponential model guided by Taylor approximation. Background Technology

[0002] Flame temperature is a key parameter affecting combustion efficiency, pollutant emissions, and operational safety issues such as slagging and corrosion. Low temperatures can lead to incomplete combustion, increasing emissions of pollutants like CO and soot; excessively high temperatures promote the volatilization and deposition of alkali metals such as sodium and potassium, resulting in slagging and high-temperature corrosion. Existing flame temperature measurement methods include contact and non-contact methods. Contact methods mostly use different types of thermocouples to measure flame temperature. This method has advantages such as simple principle, convenient operation, and low cost, but it requires the thermocouple to be in contact with the target, causing heat conduction and transferring some heat from the target to the measuring element, disrupting the target's temperature field. Simultaneously, prolonged exposure of the thermocouple to the flame can lead to high-temperature oxidation and corrosion, resulting in decreased thermocouple sensitivity and measurement temperature drift, making stable and accurate flame measurement impossible. Non-contact temperature measurement methods mainly rely on dual-color and multispectral temperature measurement. The core of dual-color temperature measurement is selecting two wavelengths / bands with equal emissivity. Accurate flame temperature measurement is achieved by assuming equal emissivity for two wavelengths / bands. However, this assumption is often difficult to satisfy when there is enhanced absorption and scattering of smoke and dust, superposition of spectral radiation, and complex changes in emissivity, leading to significant errors. Multispectral thermometry mainly uses three typical flame emissivity methods—Hottel-Broughton, polynomial, and Rayleigh approximation—to measure flame temperature. During combustion, the flame is affected by factors such as the concentration of combustion components, air flow, and combustion rate, resulting in large temperature fluctuations and real-time changes in emissivity. It is impossible to cover all situations with one or a few emissivity models, leading to unstable temperature solutions or non-unique results.

[0003] Therefore, there is a need for a visible-near-infrared flame radiation temperature measurement method that does not require an emissivity assumption model. This method identifies and constructs an emissivity model that conforms to the flame radiation characteristics based on the flame radiation signal, reducing reliance on empirical models and thus improving the stability and accuracy of flame temperature measurement. Summary of the Invention

[0004] This invention addresses the problems of existing flame radiation temperature measurement methods that rely on two-color methods with approximately equal emissivity and multispectral radiometric methods with emissivity and wavelength models. It provides a flame temperature measurement method based on an exponential model guided by the Taylor approximation, which is suitable for non-contact temperature measurement of flame radiation in the visible-near-infrared band.

[0005] A method for measuring flame temperature using an exponential model guided by Taylor approximation includes the following steps: S1. A spectral acquisition system is used to acquire flame radiation signals in the visible-near-infrared band, and the spectral acquisition system is radiometrically calibrated to obtain the system's spectral responsivity. The acquired flame radiation signals are then converted into dimensional spectral radiance. S2. Preprocess the spectral radiance to remove background radiation and noise effects, and obtain the continuous spectral radiance of the flame. S3. Calculate the colorimetric temperature corresponding to each wavelength pair under the Wien approximation to obtain the relationship between the colorimetric temperature and the true temperature:

[0006] in Indicates the second radiation constant; Represents any three wavelengths within the visible-near-infrared range, where ; and Indicates wavelength pair and Colorimetric temperature calculated based on the colorimetric thermometry method; Indicates the actual temperature of the flame; Indicates wavelength Corresponding emissivity; Based on the formula relating the obtained colorimetric temperature to the true temperature, a first-order Taylor approximation is performed on the reciprocal term of the wavelength to obtain the constraint relationship between the wavelength and the corresponding colorimetric temperature and the true temperature: in Indicated by wavelength The x-axis is... When the vertical axis is used, corresponding and corresponding The slope of the line connecting two points; express corresponding and corresponding The slope of the line connecting two points; When the colorimetric temperatures of the wavelength pairs are equal, i.e. At that time, the emissivity With wavelength Satisfies an exponential relationship; The above derivation The conditions are relaxed to tolerance. , and define the colorimetric temperature. Temperature difference: ; when When the colorimetric temperatures are approximately equal under tolerance conditions, the corresponding emissivity is determined to be... With wavelength It satisfies an exponential relationship; for the full spectrum (n wavelengths) in the visible-near-infrared range, there exists an arbitrary reference wavelength. and Of the calculated (ni) colorimetric temperatures, m temperatures are less than or equal to the tolerance. Then the emissivity With wavelength Satisfies the exponential relationship: in Indicates the slope. Indicates the intercept; S4. Based on the emissivity obtained in the full spectrum With wavelength By satisfying the exponential relationship and using the monochromatic temperature measurement principle, the relationship between the monochromatic color temperature and the true temperature is obtained, and the range of the true temperature is limited by combining the colorimetric temperature. S5. Within the range of the true temperature, construct an objective function containing a curvature regularization term of the logarithmic emissivity-wavelength linear function and a logarithmic consistency term of the full-spectrum radiance. Minimize this objective function point-by-point to achieve the inversion of the true flame temperature. The objective function is: in The weighting coefficient has a range of values. ; The neighborhood segment of the reference wavelength; For the first The number of wavelengths used to calculate curvature in each band; For the first The wavelengths used to calculate curvature in each band; This represents the second derivative with respect to wavelength, i.e., the curvature regularization term; , This represents the wavelength used to calculate the brightness term across the entire band. For brightness consistency, To measure the actual radiance, For different temperatures Radiance.

[0007] Furthermore, in S5, limiting the range of the true temperature means that: when the emissivity decreases monotonically with wavelength, the true temperature is greater than the monochromatic temperature calculated by the monochromatic method, while all colorimetric temperatures obtained by the colorimetric method are greater than the true temperature; when the emissivity increases monotonically with wavelength, the true temperature is greater than the monochromatic temperature calculated by the monochromatic method, while all colorimetric temperatures obtained by the colorimetric method are also less than the true temperature. Combining this with the physical upper limit of the flame temperature, the range of values ​​for the true temperature is obtained.

[0008] Furthermore, if the emissivity monotonically increases with wavelength, i.e. , If the colorimetric method is used, the color temperature of all combinations will be lower than the actual temperature. , can be represented as When emissivity monotonically increases with wavelength, the color temperature calculated by both monochromatic thermometry and colorimetric thermometry is lower than the actual temperature. and The maximum value is the minimum temperature, while the flame temperature is generally below 3000 K, so the true temperature is obtained. scope: .

[0009] Furthermore, the spectral radiance preprocessing involves separating the continuous spectrum and characteristic spectral lines using the AirPLS algorithm; the Wien approximation is performed within the visible-near-infrared range of the acquisition band. ,but .

[0010] Furthermore, hourly emissivity With wavelength Satisfying the exponential relationship means that the wavelength The x-axis is... When the vertical axis is used, the wavelength Corresponding emissivity They lie on a straight line.

[0011] Furthermore, the tolerance This refers to the threshold value of the difference between the calculated colorimetric temperatures. When the calculated colorimetric temperature is less than the tolerance, the colorimetric temperatures are considered to be approximately equal under the tolerance conditions.

[0012] Furthermore, the de-curvature regularization term is used to constrain the smoothness of the logarithmic emissivity and wavelength function, and the brightness consistency refers to the consistency between the theoretical radiance and the actual measured radiance. The two are weighted and combined through weighting coefficients to form the objective function.

[0013] Furthermore, the collected flame radiation signals Converted to dimensional spectral radiance : in This is the background radiation signal. The system spectral responsivity.

[0014] Furthermore, the spectral acquisition system includes a collimator, optical fiber, spectrometer, and computer; the system spectral responsivity is obtained by calibration using a standard blackbody radiation source.

[0015] The advantages of this invention are: 1. This invention uses a Taylor first-order approximation based on a reference wavelength to form a criterion for identifying exponential spectral bands. It can automatically select effective bands from measured spectra that satisfy the exponential relationship between emissivity and wavelength, thereby reducing dependence on gray body assumptions, iso-emissivity assumptions, or preset emissivity model forms and improving the universality of the method.

[0016] 2. This invention constructs an objective function that simultaneously includes a "curvature regularization term" and a "brightness uniformity term". By optimizing the solution, temperature inversion is achieved. This can effectively suppress fluctuations caused by noise and local spectral interference, improve the accuracy and stability of temperature measurement results, and has real-time or near-real-time inversion capability. Attached Figure Description

[0017] Figure 1 This is a design diagram of the flame radiation signal spectrum acquisition system of the present invention.

[0018] Figure 2 This is a flowchart of the temperature inversion process of the present invention.

[0019] Figure 3 This is a schematic diagram of the heat map of Model 1 at four temperature points.

[0020] Figure 4 This is a schematic diagram of the heat map of the Model 2 model at four temperature points.

[0021] Figure 5 This is a schematic diagram of the heat map of the Model 3 model at four temperature points. Detailed Implementation

[0022] The embodiments of the technical solution of the present invention will now be described in detail with reference to the accompanying drawings. Unless otherwise stated, the technical or scientific terms used in this application should have the ordinary meaning understood by those skilled in the art.

[0023] A method for measuring flame temperature using an exponential model guided by Taylor approximation, such as... Figure 2 As shown, it includes the following steps: (S1-1) The target flame is observed using a spectral acquisition system in the visible-near-infrared range. The acquisition of radiation signals (0.38-0.9 μm) of the target flame involves collimating the radiation through a collimator and transmitting it via optical fiber to a spectrometer to obtain the original spectral radiation signal of the flame. ,in For wavelength, Indicates flame temperature The radiance at that time. For example, Figure 1 As shown, the spectral acquisition system includes a collimator, optical fiber, spectrometer, and computer; and is calibrated using a standard blackbody radiation source to obtain the system's spectral responsivity.

[0024] (S1-2) The spectral acquisition system is radiometrically calibrated using a standard blackbody radiation source to obtain the system's spectral responsivity. The collected flame radiation signals Converted to dimensional spectral radiance Standard blackbody radiation sources at temperature and Theoretical spectral radiance under the following conditions and Recording optical acquisition system at temperature and Acquired raw output signal and The relationship between the two is in This indicates the background radiation signal caused by the combined noise of the surrounding environment and the instrument itself.

[0025] By subtracting the two equations above, the system spectral responsivity can be obtained. Thus, the flame temperature is obtained. Radiance at time : in Indicates temperature At that time, the radiation signal collected by the spectral acquisition system; This is the background radiation signal.

[0026] (S2) The transformed flame radiance based on the AirPLS (Adaptive Iterative Penalized Least Squares) algorithm Separating the continuous spectrum and characteristic spectral lines, the flame spectral radiance, which is dominated by continuous radiation, is obtained. The Wien approximation is based on the acquisition band in the visible-near-infrared range. ,but .

[0027] (S3-1) Target spectral radiance in the wavelength range of 0.38-0.5 μm The relatively low signal-to-noise ratio results in a lower signal-to-noise ratio, making measurements more susceptible to dark current noise and environmental interference. Since each wavelength in the visible-near-infrared full spectrum can be combined with other wavelengths to calculate the colorimetric temperature, if there are n points in the full spectrum, then N colorimetric temperatures can be calculated: Table 1. Colorimetric temperature calculated for different wavelength combinations

[0028] As shown in Table 1, to reduce the computational burden of traversing the entire spectrum for every wavelength, eight reference wavelengths were selected in the 0.5–0.9 μm wavelength range. And for each reference wavelength, its colorimetric temperature relative to other wavelengths in the full spectrum is calculated.

[0029] (S3-2) Calculate the colorimetric temperature for each of the eight reference wavelengths and the other wavelengths, and further calculate the difference between these colorimetric temperatures. , in It is any one of the eight reference wavelengths, i.e. ; and This refers to two wavelengths that are different from the reference wavelength within the wavelength range of 0.5-0.9 μm.

[0030] And this difference with the tolerance When comparing, When the conditions for the Taylor approximation guiding criterion are met, it is assumed that the logarithm of the emissivity has a linear relationship with the wavelength, thus allowing the selection of wavelength combinations that can be used for exponential spectrum identification.

[0031] (S3-3) If each reference wavelength exists separately indivual The colorimetric temperature corresponds to the reference wavelength. and Each wavelength and its corresponding emissivity With wavelength Constituting an exponential relationship: in Indicates at the reference wavelength The slope, Indicates at the reference wavelength The intercept.

[0032] (S4-1) Calculate the monochromatic temperature of the wavelength in the above exponential spectrum using the monochromatic thermometry method. Based on the relationship between the monochromatic temperature and the true temperature, derive the monotonicity of emissivity with wavelength: (S4-2) When the monochromatic temperature At that time, emission rate With wavelength Monotonically increasing; when the monochromatic temperature At that time, emission rate With wavelength Monotonically decreasing, that is: (S4-3) When the emissivity With wavelength When the temperature decreases monotonically, using colorimetry, we find that the colorimetric temperature for all combinations is greater than the true temperature, while the temperature for each single color is less than the true temperature. This gives us the range of the true temperature. When the emission rate With wavelength When the temperature increases monotonically, the color temperature calculated by both monochromatic thermometry and colorimetric thermometry is lower than the true temperature. Since flame temperature is generally below 3000 K, the true temperature range is obtained as follows: (S5) After obtaining the exponential spectrum, construct an objective function that includes the curvature regularization term of the log emissivity-wavelength linear function and the logarithmic consistency term of the full-spectrum radiance. : The objective function is optimized within a given temperature range to achieve the inversion of the true flame temperature.

[0033] This example selects three representative emissivity-wavelength models (polynomial model, Hottel–Broughton model, and Rayleigh approximation model) to characterize the emissivity characteristics of the flame, and performs spectral radiance simulation calculations at four temperature points (a: 1273 K, b: 1473 K, c: 1673 K, and d: 1873 K) for each model:

[0034] The corresponding model parameters are listed in Table 2.

[0035] Table 2. Parameters of three representative emissivity-wavelength models

[0036] Example 1: Based on the spectral radiance calculated by Model 1 at four temperature points of 1273 K, 1473 K, 1673 K and 1873 K, the above method is used to perform temperature inversion. Figure 3 The following thermograms of Model 1 are provided at four temperature points. The horizontal axis represents eight reference wavelengths (excluding 0.9 μm) in the 0.5–0.9 μm band, spaced at 0.05 μm intervals. The vertical axis represents the tolerance. The value in each cell represents the number of wavelengths that, given a reference wavelength and tolerance, satisfy the condition of approximately equal colorimetric temperature. From Figure 3 It can be seen from this that the tolerance at that time When the values ​​corresponding to the eight reference wavelengths are relatively large, it indicates that each reference wavelength can satisfy the collinearity condition, thus obtaining the bands suitable for the emissivity exponential model at each reference wavelength. At the four temperature points of 1273 K, 1473 K, 1673 K, and 1873 K, the sums of wavelengths that satisfy the exponential relationship between wavelength and emissivity are 69, 44, 50, and 45, respectively.

[0037] In tolerance Under these conditions, this invention utilizes the spectral band where the identified wavelength and emissivity have an exponential relationship, and optimizes the solution using an objective function constructed with a "curvature regularization term" and a "brightness consistency term" to achieve temperature inversion. Table 3 presents the error analysis results between the inverted temperature and the true temperature, where the maximum absolute error is 9 K and the maximum relative error is 0.481%, indicating that this invention has high inversion accuracy within the temperature range described in Model 1.

[0038] Table 3 Error Analysis Between Actual Temperature and Inverted Temperature

[0039] Example 2: Based on the spectral radiance calculated at four temperature points of 1273 K, 1473 K, 1673 K and 1873 K using the Model 2 model, temperature inversion is performed using the method described above. Figure 4 Provide the heatmaps of Model 2 at four temperature points. Figure 4 It can be seen from this that the tolerance at that time When the values ​​corresponding to the eight reference wavelengths are relatively large, it indicates that each reference wavelength can satisfy the collinearity condition, thus obtaining the bands suitable for the emissivity exponential model at each reference wavelength. At the four temperature points of 1273 K, 1473 K, 1673 K, and 1873 K, the sums of wavelengths that satisfy the exponential relationship between wavelength and emissivity are 83, 59, 53, and 41, respectively.

[0040] In tolerance Under these conditions, this invention utilizes the spectral band where the identified wavelength and emissivity have an exponential relationship, and optimizes the solution using an objective function constructed with a "curvature regularization term" and a "brightness consistency term" to achieve temperature inversion. Table 4 presents the error analysis results between the inverted temperature and the true temperature, where the maximum absolute error is 15 K and the maximum relative error is 0.801%, indicating that this invention has high inversion accuracy within the temperature range described in Model 2.

[0041] Table 4 Error Analysis Between Actual Temperature and Inverted Temperature

[0042] Example 3: Based on the spectral radiance calculated at four temperature points of 1273 K, 1473 K, 1673 K and 1873 K using the Model 3 model, temperature inversion is performed using the method described above. Figure 5 Provide the heatmaps of Model 2 at four temperature points. Figure 5 It can be seen from this that the tolerance at that time When the values ​​corresponding to the eight reference wavelengths are relatively large, it indicates that each reference wavelength can satisfy the collinearity condition, thus obtaining the bands suitable for the emissivity exponential model at each reference wavelength. At the four temperature points of 1273 K, 1473 K, 1673 K, and 1873 K, the sums of wavelengths that satisfy the exponential relationship between wavelength and emissivity are 96, 74, 57, and 57, respectively.

[0043] In tolerance Under these conditions, this invention utilizes the spectral band where the identified wavelength and emissivity have an exponential relationship, and optimizes the solution using an objective function constructed with a "curvature regularization term" and a "brightness consistency term" to achieve temperature inversion. Table 5 presents the error analysis results between the inverted temperature and the true temperature, where the maximum absolute error is 5 K and the maximum relative error is 0.339%, indicating that this invention has high inversion accuracy within the temperature range described in Model 3.

[0044] Table 5 Error Analysis Between Actual Temperature and Inverted Temperature

[0045] The above are merely specific embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention can have various modifications and variations. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for measuring flame temperature using an exponential model guided by Taylor approximation, characterized by: S1. A spectral acquisition system is used to acquire flame radiation signals in the visible-near-infrared band, and the spectral acquisition system is radiometrically calibrated to obtain the system's spectral responsivity. The acquired flame radiation signals are then converted into dimensional spectral radiance. S2. Preprocess the spectral radiance to remove background radiation and noise effects, and obtain the continuous spectral radiance of the flame. S3. Calculate the colorimetric temperature corresponding to each wavelength pair under the Wien approximation to obtain the relationship between the colorimetric temperature and the true temperature: in Indicates the second radiation constant; Represents any three wavelengths within the visible-near-infrared range, where ; and Indicates wavelength pair and Colorimetric temperature calculated based on the colorimetric thermometry method; Indicates the actual temperature of the flame; Indicates wavelength Corresponding emissivity; Based on the formula relating the obtained colorimetric temperature to the true temperature, a first-order Taylor approximation is performed on the reciprocal term of the wavelength to obtain the constraint relationship between the wavelength and the corresponding colorimetric temperature and the true temperature: in Indicated by wavelength The x-axis is... When the vertical axis is used, corresponding and corresponding The slope of the line connecting two points; express corresponding and corresponding The slope of the line connecting two points; When the colorimetric temperatures of the wavelength pairs are equal, i.e. At that time, the emissivity With wavelength Satisfies the exponential relationship: The above derivation The conditions are relaxed to tolerance. , and define the colorimetric temperature. , Temperature difference: ； when When the colorimetric temperatures are approximately equal under tolerance conditions, the corresponding emissivity is determined to be... With wavelength It satisfies an exponential relationship; for the full spectrum in the visible-near-infrared range, there exists an arbitrary reference wavelength. and If m out of the calculated (ni) colorimetric temperatures are less than or equal to the tolerance, then the emissivity... With wavelength Satisfies the exponential relationship: in Indicates the slope. Indicates the intercept; S4. Based on the emissivity obtained in the full spectrum With wavelength By satisfying the exponential relationship and using the monochromatic temperature measurement principle, the relationship between the monochromatic color temperature and the true temperature is obtained, and the range of the true temperature is limited by combining the colorimetric temperature. S5. Within the range of the true temperature, construct an objective function containing a curvature regularization term of the logarithmic emissivity-wavelength linear function and a logarithmic consistency term of the full-spectrum radiance. Minimize this objective function point-by-point to achieve the inversion of the true flame temperature. The objective function is: in The weighting coefficient has a range of values. ; The neighborhood segment of the reference wavelength; For the first The number of wavelengths used to calculate curvature in each band; For the first The wavelengths used to calculate curvature in each band; This represents the second derivative with respect to wavelength, i.e., the curvature regularization term; This represents the wavelength used to calculate the brightness term across the entire band. For brightness consistency, To measure the actual radiance, For different temperatures Radiance.

2. The flame temperature measurement method based on a Taylor approximation-guided exponential model according to claim 1, characterized in that: in S5, limiting the range of the true temperature means that: when the emissivity decreases monotonically with wavelength, the true temperature is greater than the monochromatic temperature calculated by the monochromatic method, while all colorimetric temperatures obtained by the colorimetric method are greater than the true temperature; when the emissivity increases monotonically with wavelength, the true temperature is greater than the monochromatic temperature calculated by the monochromatic method, while all colorimetric temperatures obtained by the colorimetric method are also less than the true temperature, and the range of the true temperature is obtained by combining the physical upper limit of the flame temperature.

3. The flame temperature measurement method based on a Taylor approximation-guided exponential model according to claim 2, characterized in that: If the emissivity increases monotonically with wavelength, then... , If the colorimetric method is used, the color temperature of all combinations will be lower than the actual temperature. , can be represented as When emissivity monotonically increases with wavelength, the color temperature calculated by both monochromatic thermometry and colorimetric thermometry is lower than the actual temperature. and The maximum value is the minimum temperature, while the flame temperature is generally below 3000 K, so the true temperature is obtained. scope: 。 4. The flame temperature measurement method based on a Taylor approximation-guided exponential model according to claim 1, characterized in that: The spectral radiance preprocessing involves separating the continuous spectrum and characteristic spectral lines using the AirPLS algorithm; the Wien approximation is applied within the visible-near-infrared range of the acquisition band. ,but .

5. The flame temperature measurement method based on a Taylor approximation-guided exponential model according to claim 1, characterized in that: hourly emissivity With wavelength Satisfying the exponential relationship means that the wavelength The x-axis is... When the vertical axis is used, the wavelength Corresponding emissivity They lie on a straight line.

6. The flame temperature measurement method based on a Taylor approximation-guided exponential model according to claim 1, characterized in that: The tolerance This refers to the threshold value of the difference between the calculated colorimetric temperatures. When the calculated colorimetric temperature is less than the tolerance, the colorimetric temperatures are considered to be approximately equal under the tolerance conditions.

7. The flame temperature measurement method based on a Taylor approximation-guided exponential model according to claim 1, characterized in that: The de-curvature regularization term is used to constrain the smoothness of the logarithmic emissivity and wavelength function, and the brightness consistency refers to the consistency between the theoretical radiance and the actual measured radiance. The two are weighted and combined by weighting coefficients to form the objective function.

8. The flame temperature measurement method based on a Taylor approximation-guided exponential model according to claim 1, characterized in that: Collected flame radiation signals Converted to dimensional spectral radiance : in This is the background radiation signal. The system spectral responsivity.

9. The flame temperature measurement method based on a Taylor approximation-guided exponential model according to claim 1, characterized in that: The spectral acquisition system includes a collimator, optical fiber, spectrometer, and computer; the system spectral responsivity is obtained by calibration using a standard blackbody radiation source.

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