JPH0462010B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a method for measuring emissivity. In general, the emissivity of a sample changes depending on the material, temperature, oxidation state, surface roughness, wavelength, etc. of the sample, so a blackbody is placed at the same temperature and in the same condition as the sample, and thermal radiation from the blackbody and thermal radiation from the sample are It is determined by measuring each of these and finding the ratio, but this requires knowing the temperatures of the sample and blackbody in advance, and the blackbody must be installed to have the same temperature, making the measurement complicated. There are drawbacks. For example, if the sample is in an isolated location and contact temperature measurement is not possible, it is particularly difficult to measure emissivity. You can't know by formula.

The purpose of the present invention is to eliminate these drawbacks, and while measuring the spectral thermal radiation of three or more color wavelengths by spectrally dispersing the thermal radiation from the sample, the spectral thermal emissivity at each wavelength is assumed. Find an approximate formula for each spectral thermal emissivity, and then find the temperature that minimizes the error between the approximate spectral thermal radiation of each wavelength in the approximate formula and the corresponding spectral thermal radiation of the measurement. The method is characterized in that the temperature of the sample is taken as the temperature of the sample, and the spectral thermal emissivity of the sample is determined from this temperature and the approximate expression.

An embodiment of the present invention is shown in a vacuum container 1 as shown in the first diagram.
A case will be explained in which the emissivity of the sample 2 contained in the sample 2 is measured. In the figure, reference numeral 4 denotes a spectroscope 5 that separates the thermal radiation of the sample 2 into multiple wavelengths through the vacuum window 3.
and a radiation thermometer equipped with a detector 6 for detecting the amount of spectrothermal radiation, and a calculator such as a microprocessor 7 for calculating the detected value. The radiation is divided into four color wavelengths or more wavelengths, and each spectral thermal radiation is simultaneously measured by a detector 6 having a light-receiving section corresponding to the number of spectral wavelengths, and each measured value is sent to the sample 2 in a microprocessor 7. is used for calculations to determine the emissivity of.

Generally, when measuring the emissivity of a sample using a radiation thermometer, it is necessary to also install a blackbody and measure the thermal radiation from this, but in the present invention, there is no need to provide a blackbody. The emissivity of the sample can be determined accurately.

In the example, it is assumed that the temperature of the sample 2 is T, the thermal emissivity is ε, and the thermal radiation is L. Of these, the temperature T and thermal emissivity ε are unknown quantities, and the thermal radiation L is spectrally divided into three or more color wavelengths λ ₁ , λ ₂ , ... λ _o , and the spectral thermal radiation at each wavelength is L ₁ , L ₂ ...L _o is radiation thermometer 4
It is measured by

On the other hand, the spectral thermal emissivity ε ₁ , ε ₂ ...ε _o at each wavelength λ ₁ , ...λ _o cannot be determined without knowing the thermal radiation to be compared, such as the thermal radiation of a black body. , is known to change along a certain curve, and as shown in the second figure, the spectral thermal emissivity ε ₁ , ε ₂ ...ε _o
The curve of spectral thermal emissivity passing through each point or near each point ε _c
can be assumed. This curve ε _c can be approximately expressed as an m-th order polynomial of wavelength λ as follows. Of course, this curve ε _c can be approximated by other functions such as a trigonometric function or an exponential function, but here we will explain the case where it is approximated by an m-th order polynomial.

ε _c = a _n λ ^m + a _n-1 λ ^m-1 +……+a ₀ …[] If this polynomial approximation is performed using the least square error method, the coefficients of the formula [] a _n , a _n-1 …a ₀ is given by the solution of the following simultaneous linear equations.

｜A｜・｜x｜=｜b｜ …[] ｜A｜=Σλ ^2m _j Σλ ^2m-1 _j …Σλ ^m _j Σλ ^2m-1 _j Σλ ^2m-2 _j …Σλ ^m-1 _j 〓 〓 〓 Σλ ^m _j Σλ ^m-1 _j …Σλ ⁰ _j |x|=a _n a _n-1 〓 a ₀ |b|=Σλ ^m _j・ξj Σλ ^m-1 _j・ξj 〓 Σξj [] On the other hand, thermal emissivity ε If the thermal radiation of a black body is L ^* , then ε=L/L ^* ...[], and L ^* is generally expressed as a function of temperature T from Blank's formula as follows.

L ^* = C ₁ /λ ₅・1/exp(C ₂ /λ _T )−1 … [] In this case, C ₁ = 1.19196×10 ^-16 [W・m ² ] C ₂ = 0.014388 [m・K].
From the above formula [] [], the thermal emissivity has the following relationship: ε=L·λ ₅ /C ₁ [exp(C ₂ /λ _T )−1]...[]. Therefore, the thermal emissivity ε _j in the formula [] is also ε _j =L _j・λ ⁵ / _j /C ₁ [exp(C ₂ /λ _j T)−1]...[
] If we set exp(C ₂ /λ _j T)−1=U _j … [], we can further express it as ε _j =L _j・λ ⁵ / _j /C ₁・U _j … [] Ru. If we use this ε _j to express the vector b in the equation [], we get becomes. Column k of |A| in [] equation is |
Letting Δk be the determinant replaced by b|, it is as follows.

Therefore, the solution a _k of the simultaneous equations [] is a _k =Δk/|A| (k=m, m-1,...,0) ...[XII], and the approximation of the equation [] is ε _c = 1/|A |(Δmλ ^m +Δm−1λ ^m−1 + …+Δ ₁ λ+Δ ₀ ) … [ ]. Using this ε _c , approximate spectral thermal radiation L _ci
From the [] [] [] formula, L _ci = ε _ci・L _i ^* = ε _ci・C ₁ / λ ⁵ / _i・1/U _i = C ₁ / |A|・λ ⁵ / _i・U _i (Δmλ ^m _i +Δm _-1 λi ^m-1 +...+Δ ₁ λ _i +Δ ₀ ) ... [XI] In this formula, λ _i is the wavelength of λ ₁ ... λ _1o spectroscopically from the sample 2 is a known number, |A| is a known number as a function of λ _i , C ₁ is a constant, U _i is a function of λ _i and temperature T,
Δk is λ _i , T and the measured value of thermal radiation of sample 2 L ₁ ...
Since it is a function of L _j which corresponds to L _o , this equation is a function of the unknown T after all.

Therefore, by giving an appropriate temperature T, approximate spectral thermal radiation
If L _ci is found and it matches or approximates the spectral heat radiation L _i measured by the radiation thermometer 4, then the temperature T
can be determined to be the temperature of sample 2.
In this case, the approximate spectral thermal radiation L _ci obtained by changing T
are the curves T ₁ , T ₂ , T ₃ in Fig. 3, and if the values of the measured spectral thermal radiation L _i are L ₁ , L ₂ ...L _o , then L _ci and
For example, the temperature that minimizes the sum E of the squared errors of L _i
T ₂ is the temperature of sample 2. Expressing this as a formula, Emin=minΣ(L _ci −L _i ) ² …[].

Such arithmetic processing by changing the temperature T can be easily and quickly performed by the microprocessor 7 within about 0.5 seconds.

In the above method, each spectral thermal radiation ε _c given by assumption is approximated by an m-th order polynomial, but in order to make it simpler and more practical, ε _c is expressed as 1 of the next wavelength λ, as shown in Figure 4. The following equation can also be used as an approximation.

ε _c = a ₁ λ + a ₀ ...[] The coefficients a ₁ and a ₀ are given by the solution of the following equation.

Σλ ² _j Σλ ¹ _j Σλ ¹ _j Σλ ⁰ _j・a ₁ a ₀ =Σλ _j・ε _j Σε _j …[] For simplicity, Zλ ² _j , Z ₁ =Σλ ¹ _j , Z ₀ =Σλ ⁰ _j … [], then ε _c is given by the following formula by finding a ₁ and a ₀ from [] [].

ε _c = 1/Z ₂ Z ₀ −Z ² / ₁ {(Z ₀ λ−Z ₁ )Σλ _j・ε _j +(
−Z ₁ λ ₁ +Z ₂ )Σε _j }…[XI] In this case, ε _j can be given by [], so ε _c = 1/Z ₂ Z ₀ −Z ² / ₁ {(Z ₀ λ−Z ₁ )1/C ₁ ΣL _j・λ
⁶ _j・U _j + (−Z ₁ λ+Z ₂ ) 1/C ₁ ΣL _j・λ ⁵ _j・U _j }…[
_{[ _} ^_ _{_ _ _ _} ^_ _{_ _ _} Z ₁
)×ΣL _j λ ⁶ _j U _j + (−Z ₁ λ _i +Z ₂ )ΣL _j λ ₁ ⁵ _j U _j }…[
XI]. Like [XI], this equation is also a function with the temperature T included in U _i as an unknown quantity, so by giving various values of T, the sum E of the squared errors of the approximate spectral heat radiation L _ci and the measured value L _i is calculated. Find the minimum temperature T,
The point that this is the temperature of the sample 2 is similar to the case where ε _c is given by the approximation of the m-th order polynomial.

Once the temperature T is determined in this way, the approximate expression [ ] for the emissivity ε _c becomes a function of spectral thermal radiation and wavelength, so substitute the values of the actually measured wavelength λ ₁ ...λ _o and spectral thermal radiation L ₁ ...L _o By doing this, an approximate value of the spectral thermal emissivity ε ₁ ...ε _o can be obtained.

In a practical example, the thermal radiation from sample 2 is λ ₁ = 1064, λ ₂ = 1570, λ ₃ = 1990, λ ₄ = 2200 (n _n ).
It was measured by spectroscopy at each wavelength.

Under these conditions, the approximate spectral thermal radiation L _ci is calculated at various temperatures from the approximation formula of the m-th order polynomial of the spectral thermal emissivity, and compared with the actually measured spectral thermal radiation L ₁ ...L _o of sample 2. The temperature at which the sum of the squared errors was the minimum was defined as the temperature T of sample 2.

It was confirmed through actual measurement that this temperature T coincided with the temperature of Sample 2. Approximate formula for emissivity ε _c [] includes temperature T, each measured wavelength λ ₁ ...λ _o , and each spectral thermal radiation.
When the spectral thermal emissivity was obtained by substituting L ₁ ...L _o respectively, it almost coincided with the spectral thermal emissivity measured using a blackbody as a comparison object.

Furthermore, when the spectral thermal emissivity is approximated by a linear equation under the above conditions, the sum E of the squares of the errors between the approximate spectral thermal radiation L _ci and the actually measured spectral thermal radiation _{L 1} . Although there were cases where there were two minimum values as shown in the figure, the temperature T _B of the smaller minimum value E _B coincided with the actually measured temperature of sample 2 in all cases.
Therefore, the ratio E _A /E _B between the two minimum values is generally 70 or more, and the selection of the minimum value is easy. In this case, the emissivity ε _c
In the approximate formula [], the temperature T and the actually measured wavelength λ ₁ ...
When the spectral thermal emissivity was determined by substituting λ _o , spectral _thermal radiation L ₁ .

In addition, as a means of comparing the approximate spectral thermal radiation L _ci and _the spectral thermal radiation actually measured from sample 2 L ₁ .

In this way, according to the present invention, the spectral thermal radiation of three or more colors is actually measured, an approximate expression is obtained assuming the spectral thermal radiation, and the sample temperature is calculated based on the approximate spectral thermal radiation of the approximate expression and the actually measured spectral thermal radiation. Since the emissivity of the sample can be calculated from the temperature that minimizes the error in , and then the emissivity of the sample can be calculated from that temperature and the approximation formula, there is no need to install a black body, etc., and the comparison can be made by simply measuring the thermal radiation of the sample. It has the advantage of being able to measure emissivity accurately and easily.

[Brief explanation of the drawing]

Fig. 1 is a diagram of one example of the measuring method of the present invention, Fig. 2 is a diagram of an example of the measuring method of the present invention;
The figure is a diagram showing the relationship between wavelength and the approximation formula of the m-th order polynomial of spectral thermal emissivity. Figure 3 is a diagram showing the relationship between actually measured thermal radiation and approximate thermal radiation. Figure 4 is a diagram showing the relationship between wavelength and the linear Relationship diagram with the approximation formula for spectral thermal emissivity given by the formula, 5th
The figure is a curve diagram for finding the minimum sum of squared errors.

Claims (1)

[Claims] 1 Spectral thermal radiation from a sample is spectrally analyzed to measure the spectral thermal radiation of three or more color wavelengths, while assuming the spectral thermal emissivity at each wavelength, find an approximate formula for each spectral thermal emissivity, and calculate the approximation. The temperature that minimizes the error between the approximate spectral thermal radiation of each wavelength in the formula and the corresponding spectral thermal radiation of the measurement is determined as the temperature of the sample, and from this temperature and the approximate formula, the temperature of the sample is determined. An emissivity measurement method characterized by determining the spectral thermal emissivity of.