JP2003035663A - Creation method for working curve of absorption spectrum - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a creation method for the working curve of an absorption spectrum in one substance in a mixed substance. SOLUTION: A noise component amount at each wavelength is calculated on the basis of the absorption spectrum of a single substance, the light receiving spectrum at a concentration of zero of the mixed substance and a plurality of light receiving spectra with a changed composition ratio are sampled, the processed wavelength of each light receiving spectrum is set at a prescribed wavelength as a wavelength setting stage, a noise component amount at the prescribed wavelength selected from the noise component at each wavelength is subtracted from the light receiving spectrum at the concentration of zero and from the light receiving spectrum in each composition ratio, an extinction at the prescribed wavelength in each composition ratio is calculated, the prescribed wavelength is changed to other prescribed wavelengths, a processing procedure is returned to the wavelength setting stage, the same processing operation is repeated, extinctions at the other prescribed wavelengths in each composition ratio are calculated respectively, a multivariate analysis is performed by using the extinction at each wavelength and by using data on each composition ratio, and the working curve of the prescribed substance in the mixed substance is created.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for preparing a calibration curve of absorption spectrum at each wavelength.

[0002]

2. Description of the Related Art Generally, when quantitatively analyzing a substance using an absorption spectrum, the concentration and the absorbance are proportional to each other according to Lambert-Beer's law. Is measured to obtain each absorbance, a calibration curve is created from each predetermined concentration and each absorbance, and in the case of a substance whose concentration is unknown, the absorbance is measured and applied to the calibration curve for quantification.

The wavelength 210 in actual gas absorption analysis
For example, the calibration curve for SO ₂ in nm is shown in FIG.
As shown in, the slope of the calibration curve is saturated in the high-concentration portion in the horizontal direction, and the Lambert-Beer law is not obeyed.

It is considered that one of the causes of not complying with the Lambert-Beer's law is due to a noise component. There is stray light noise in which unwanted stray light enters the detector in the noise component, and as shown in FIG. In the case of a spectroscopic analysis example that does not use a detector, the stray light 1 is generated by the light source 2 such as reflected light from the housing, scattered light, etc., and enters the detector 4 without passing through the sample 3 to affect the measurement. I'm giving. Further, as shown in FIG. 19, when the spectroscope 7 is provided on the rear side of the sample 6, the stray light 8 is generated by scattering in the spectroscope 7 from the light source 9, and the stray light 8 is detected separately from the light of the target wavelength. 10
It gets in and affects the measurement. Here, FIG.
In FIG. 8 and FIG. 19, 5 and 11 are optical paths, and 12 is a diffraction grating.

Therefore, when a calibration curve is used in quantitative analysis, only a narrow portion on a straight line is used or various methods of dividing the calibration curve range are adopted.

[0006]

However, in a mixed substance such as a mixed gas, a noise component is also present, and the absorption spectrum of one substance overlaps with the absorption spectrum of another substance. There is a problem in that it is not possible to measure only the spectrum, and it is not possible to create a calibration curve for a predetermined substance in the mixed substance. or,
It was required to correct the calibration curve saturated at a high concentration to a linear calibration curve.

The present invention has been made in view of the above situation, and an object thereof is to provide a method for preparing a calibration curve of an absorption spectrum of one substance in a mixed substance.

[0008]

According to claim 1 of the present invention, the noise component amount of each wavelength is calculated from the absorption spectrum of a single substance, and the concentration of the mixed substance is zero by the same measuring device measuring the single substance. Collect a plurality of received light spectra with different received light spectra and composition ratios, set the processing wavelength of each received light spectrum to a predetermined wavelength as a wavelength setting step, and set the noise component amount of the predetermined wavelength selected from the noise component amount of each wavelength Calculate the absorbance of a given wavelength at each composition ratio by subtracting from the zero received spectrum and the received spectrum of each composition ratio, and returning the processing procedure to the wavelength setting step by changing the specified wavelength to another specified wavelength. Repeat the same process to calculate the absorbance of each other predetermined wavelength at each composition ratio, and use the data of the absorbance at each wavelength and each composition ratio for multivariate analysis. Ri calibration curve method absorption spectrum, characterized in that a calibration curve of a predetermined substance in the mixed substances are those according to.

According to a first aspect of the present invention, as shown in the second aspect, each received light spectrum from a single substance concentration of zero to each predetermined concentration is sampled, and a processing wavelength of each received light spectrum is set to a predetermined wavelength as a wavelength setting step. In the noise component amount setting step, the noise component is temporarily set to a light-receiving spectrum of zero density or an arbitrary temporary noise component amount smaller than the light-receiving spectrum of a predetermined density, and the temporary noise component amount is a light-receiving spectrum of zero density and Assuming that the absorbance of each given concentration is calculated by subtracting it from the received spectrum of the given concentration, and the relationship between each given concentration and the absorbance follows a straight line.

## EQU3 ## Y = aX + b a: slope b: substitute the concentration into X and the absorbance into Y from the intercept to obtain the correlation coefficient by the linear regression method, and then change the temporary noise component amount to another temporary noise component amount The same procedure is repeated by returning the processing procedure to the noise component amount setting step to obtain another correlation coefficient, and by selecting the largest one from the plurality of correlation coefficients in each temporary noise component amount, the selection is performed. The amount of noise component of a predetermined wavelength corresponding to the determined correlation coefficient is determined, the predetermined wavelength is changed to another predetermined wavelength, and the processing procedure is returned to the wavelength setting step to repeat the same processing and repeat the other predetermined wavelength. The noise component amount of each wavelength contained in the absorption spectrum of a single substance may be calculated by determining the noise component amount of each wavelength and integrating the noise component amount of each wavelength.

According to a first aspect of the present invention, as shown in the third aspect, each received light spectrum from zero concentration of a single substance to each predetermined concentration is sampled, and a processing wavelength of each received light spectrum is set to a predetermined wavelength as a wavelength setting step. In the noise component amount setting step, the noise component is temporarily set to a light-receiving spectrum of zero density or an arbitrary temporary noise component amount smaller than the light-receiving spectrum of a predetermined density, and the temporary noise component amount is a light-receiving spectrum of zero density and Assuming that the absorbance of each given concentration is calculated by subtracting it from the received spectrum of the given concentration, and the relationship between each given concentration and the absorbance follows a straight line.

## EQU00004 ## Y = aX + b a: slope b: the intercept is obtained from the intercept by substituting the concentration in X and the absorbance in Y to obtain the intercept by the linear regression method, and then the temporary noise component amount is changed to another temporary noise component amount and processed. The same processing is repeated by returning the procedure to the noise component amount setting step to obtain another intercept, and by selecting the intercept closest to zero from the plurality of intercepts in each provisional noise component amount, the selected intercept is obtained. The noise component amount of the corresponding predetermined wavelength is determined, and the same process is repeated by changing the predetermined wavelength to another predetermined wavelength and returning the processing procedure to the wavelength setting step to determine the noise component amount of another predetermined wavelength. The noise component amount of each wavelength contained in the absorption spectrum of a single substance may be obtained by determining each and integrating the noise component amount of each wavelength.

As described above, according to the first aspect, the absorbance at each composition ratio is calculated by removing the noise component amount from the mixed substance by using the noise component amount of each wavelength calculated from a single substance, and Since multivariate analysis is performed using each data,
It is possible to calculate data such as the absorbance of a predetermined substance contained in the mixed substance and create a plurality of calibration curves for the predetermined substance at each wavelength. Here, since the measuring devices for measuring the single substance and the mixed substance are the same, the noise component amount of each wavelength contained in the single substance and the noise component amount of each wavelength contained in the mixed substance are substantially the same. The noise component amount of the mixed substance can be removed by the noise component amount of the single substance. Further, since the amount of noise components is removed from the received light spectrum, it is possible to correct a calibration curve saturated at high concentration and create a highly accurate calibration curve with high reproducibility.

According to the second or third aspect, the optimum one is selected from a plurality of correlation coefficients or a plurality of intercepts calculated from the linear regression method via the amount of temporary noise components, and the optimum wavelength of a single substance is selected. Since the noise component amount is obtained and the predetermined wavelength is changed and the same process is performed to obtain the noise component amount of other predetermined wavelengths, the noise component amounts of the respective wavelengths are integrated,
The amount of noise components of each wavelength in a single substance can be accurately obtained.

[0013]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described below with reference to the drawings.

1 and 2 show the flow of an embodiment for carrying out the method for preparing a calibration curve for an absorption spectrum of the present invention, and A shows the connection points of the respective flows.

When carrying out the method for preparing a calibration curve for the absorption spectrum of the present invention, as in the case of preparing a general calibration curve, when the concentration of a single substance (single gas) is zero and the concentration is n1. , N2, n3 ... (At least three or more), the light reception spectrum P (d) (light reception intensity, light reception area) is measured.

Next, after measuring a plurality of received light spectra P (d), the initial wavelength d is set as a single substance wavelength processing step so as to select a wavelength for processing each received light spectrum.

Here, the measured light reception spectrum of each wavelength contains stray light noise of a noise component,

## EQU00005 ## P (d) = Ps (d) + Pm (d) P (d): Measured received light spectrum (measured spectrum) Ps (d): received light spectrum of substance Pm (d): Stray light noise received spectrum Becomes

Therefore, in general, an expression for obtaining the absorbance at each wavelength,

## EQU6 ## A (d) = log (Pz (d) / P (d)) A (d): Absorbance Pz (d): Zero spectrum (reception spectrum when the concentration of the substance is zero) P (d): From the measured received spectrum (measured spectrum), subtract the received spectrum of stray light noise,

## EQU00007 ## As (d) = log ((Pz (d) -nPm
(D)) / (P (d) -nPm (d))) As (d): corrected absorbance Pz (d): zero spectrum (light-receiving spectrum when the concentration of the substance is zero) P (d): measured Light reception spectrum (measurement spectrum) nPm (d): Temporary stray light noise is set as a noise component amount setting step so as to quantify the noise component of stray light noise by transforming it into a light reception spectrum of temporary stray light noise (temporary noise component amount). A noise component amount (temporary stray light) nPm (d) is provisionally set.

Then, it is confirmed that the temporary noise component amount nPm (d) is smaller than the zero-density received light spectrum Pz (d) or the predetermined density received light spectrum P (d),
For Equation 7, a temporary setting value of zero of the temporary noise component amount nPm (d), each predetermined density (n1, n2, n2) at the initial wavelength d.
n3 ...) The measured value of the received spectrum P (d) and the measured value of the zero spectrum (received spectrum) Pz (d) at zero concentration at the initial wavelength d are respectively substituted, and the absorbance As (d) corresponding to each predetermined concentration is substituted. ) Is calculated.

The relationship between each calculated absorbance and each predetermined concentration is given by the Lambert-Beer equation.

(8) A = αn A: Absorbance α: extinction coefficient n: concentration According to, a linear calibration curve is obtained, so

## EQU9 ## Y = aX + b a: slope b: in the equation of intercept, X is a value of each predetermined concentration (n1, n2, n3 ...),
The calculated value of each absorbance As (d) is substituted for Y and processed by a linear regression method such as the least square method to obtain the correlation coefficient r (R ² ), the intercept b, and the slope a.

Here, the processing by the linear regression method is shown in [Table 1].
In the linear regression method, a plurality of sets (at least three sets or more) of the collected and calculated concentration X and absorbance Y are considered as K.

[0022]

[Table 1]

The covariance Sxy of X and Y is

## EQU10 ## Sxy = (1 / k) Σxy−avg_x × a
vg_y At this time,

(11) a = Sxy / Sxx

B = avg_y−Sxy × avg_y / Sxx Further, the square R ² of the correlation coefficient r is

[Mathematical formula-see original document] R ² = Sxy ² / (Sxx · Syy), and when r (R ² ) becomes the maximum (when approaching 1) by this calculated value, a plurality of sets of concentration X and absorbance Y are obtained. Judge that it is located on a straight line. Further, when r (R ² ) becomes the largest, b = 0 (closest to zero), so b may be used as a reference. In the linear regression method, when nPm that minimizes the sum of squares of the errors is obtained, R ² does not always become the maximum, and b = 0 does not hold, so that it cannot be applied.

After obtaining the correlation coefficient r, the intercept b, and the slope a when the provisional noise component amount nPm is zero by such a linear regression method, after the slope a, at least the correlation coefficient r and the intercept b are obtained. One is temporarily stored.

Next, the zero temporary noise component amount nPm (d)
To the noise component amount setting step, the noise component is temporarily set to another temporary noise component amount nPm (d) by adding a predetermined increase amount ΔnPm to It is confirmed that the component amount nPm (d) is smaller than the light-receiving spectrum (zero spectrum) Pz (d) of zero concentration or the light-receiving spectrum (measurement spectrum) P (d) of a predetermined concentration.

After the confirmation, first the absorbance As (d)
In the same manner as the process of obtaining the above, for [Equation 7], a temporary setting value of other temporary noise component amount nPm (d) and a received light spectrum of each predetermined density (n1, n2, n3 ...) At the initial wavelength d. The absorbance As (d) corresponding to each predetermined concentration at the initial wavelength d is calculated by substituting the measured value of P (d) and the measured value of the zero spectrum Pz of zero concentration at the initial wavelength d, respectively, and Similar to the above-described process of calculating the correlation coefficient and the like by the linear regression method, another correlation coefficient r, another intercept b, and another slope a in another temporary noise component amount nPm (d) are obtained, and similarly. Temporarily store.

Next, another temporary noise component amount nPm (d)
To the noise component amount setting step by adding a predetermined increase amount ΔnPm to
Pm (d) is temporarily set and the same process is repeated to obtain another correlation coefficient r, another intercept b, and another slope a for another temporary noise component amount nPm (d), and similarly temporarily store them. .

As described above, in the process of gradually increasing the increase amount ΔnPm to the temporary noise component amount nPm (d), a plurality of slopes a at the initial wavelength d and a plurality of correlation coefficients r and intercepts b at the initial wavelength d are obtained. It seeks and accumulates.

Further, the temporary noise component amount nPm which increases
(D) Receiving spectrum with zero concentration (zero spectrum)
The process is stopped at the time when the light-receiving spectrum (measurement spectrum) P (d) of Pz (d) or a predetermined concentration is exceeded. Here, the processing may be stopped when the accumulated number of the correlation coefficient r or the accumulated number of the intercept b exceeds a predetermined value.

After the processing is stopped, each temporary noise component amount nP
Correlation coefficient r from among a plurality of correlation coefficients r in m (d)
Is selected, the one having the largest (closest to 1) is selected, and the one having the intercept b closest to zero is selected from the plurality of intercepts b in each temporary noise component amount nPm (d). Here, when selecting the correlation coefficient r and the intercept b,
Either the correlation coefficient r or the intercept b may be processed. Further, when the one having the largest correlation coefficient r is selected, the maximum value of R ² is obtained, and it can be obtained by the differential method or the hill climbing method. In addition, ΔnP is set only for the section near the maximum value so that the point that becomes the maximum is searched in detail.
You may make m small. Furthermore, the correlation coefficient r and the intercept b
In the case of selecting, the correlation coefficient r and the intercept b in the predetermined temporary noise component amount nPm (d) are calculated without accumulating a large number of the correlation coefficient r and the intercept b, and are temporarily stored before. It is also possible to compare the correlation coefficient r and the intercept b, and always leave the one having the largest correlation coefficient r and the one having the intercept b closest to zero.

Next, the actual noise component amount Pm (d) is calculated from the information of at least one of the selected correlation coefficient r and intercept b.
And the corresponding slope a calculated by the linear regression method is determined, and the determined slope a is used as the absolute absorption coefficient α at the initial wavelength d.

Actual noise component amount Pm at initial wavelength d
After obtaining (d), a predetermined wavelength width Δd is added to the initial wavelength d.
Is set to another predetermined wavelength d, and another predetermined wavelength d is set.
Is within the specified range, and as shown in Fig. 1,
By returning the processing procedure to the single substance wavelength setting stage,
Below, the stray light noise is calculated as the temporary noise component amount (temporary stray light) nPm.
Similar processing such as provisional setting in (d) is performed, and the correlation coefficient r
And the intercept b, the actual noise component amount Pm (d) at another predetermined wavelength d is determined, and the corresponding slope a calculated by the linear regression method is determined, and the determined slope a
Is an absolute absorption coefficient α at another predetermined wavelength d.

In this way, by gradually adding the predetermined wavelength width Δd to the predetermined wavelength d and performing the same processing, the actual noise component amount Pm (d) and the absolute absorption coefficient α at each wavelength are integrated. When the increasing predetermined wavelength d exceeds a predetermined range, the processing is stopped and the absolute absorption coefficient spectrum at each wavelength is obtained.

Actual noise component amount Pm at each wavelength
After determining (d), as shown in FIG. 2, a plurality of received spectra (received light intensity) when the concentration of the mixed substance (mixed gas) is zero and when the composition ratio (concentration ratio) of each component is changed. , Light receiving area). Here, the mixed substance (mixed gas) to be measured may or may not contain a single substance (single gas).

Next, the initial wavelength d is set as a mixed material wavelength processing step so as to select a wavelength for processing each received light spectrum P (d), and it is confirmed that the initial wavelength d is within a predetermined range. Subsequently, the noise component amount Pm (d) in the case of the initial wavelength d is selected and prepared from the actual noise component amount Pm (d) at each wavelength previously obtained, and the initial value is calculated with respect to the following [Equation 14]. The value of the noise component amount Pm (d) at the wavelength d,
Reception spectrum P (d) of each composition ratio at the initial wavelength d
And the measured values of the zero spectrum (light-receiving spectrum) Pz (d) at zero concentration at the initial wavelength d are substituted respectively, and the absorbance As (d) of the mixed substance at each composition ratio (concentration) is substituted.
To calculate.

## EQU14 ## As (d) = log ((Pz (d) -Pm
(D)) / (P (d) -Pm (d))) As (d): modified absorbance Pz (d) of the mixed substance: zero spectrum of the mixed substance (light-receiving spectrum when the concentration of the substance is zero) P (D): Measured light-receiving spectrum of the mixed substance (measurement spectrum) Pm (d): Actual light-receiving spectrum of stray light noise calculated from a single substance (actual noise component amount)

Here, the measurement of a single substance and a mixed substance is
By using the same measuring device, the noise component amount of each wavelength contained in the single substance and the noise component amount of each wavelength contained in the mixed substance are substantially the same. The measurement interval between the measurement of the absorption spectrum of a single substance and the measurement of the absorption spectrum of a mixed substance is the time during which the amount of noise components does not change.

After calculating the absorbance As (d) at the initial wavelength d, a predetermined wavelength width Δd is added to the initial wavelength d to set another predetermined wavelength d, and as shown in FIG. Return to the wavelength setting stage for use, perform the same processing below,
The absorbance As (d) at another predetermined wavelength d at each composition ratio is determined.

In this way, by gradually adding the predetermined wavelength width Δd to the predetermined wavelength d and performing the same processing, the absorbance As (d) of each composition ratio at each wavelength is accumulated, and the increasing predetermined wavelength d is increased. Processing is stopped when the specified range is exceeded,
Multivariate analysis is performed using the data such as the absorbance As (d) and each composition ratio.

The multivariate analysis will be described below.
Multivariate analysis includes multiple regression analysis, principal component regression analysis, PLS,
There are CLS, neural network, etc.
(Partial Least Squares) An example of using the calculation theory of the model will be described.

(PLS model calculation theory) X is an explanatory variable and y is an objective variable.

[0041]

[Equation 15]

In the case of the concentration estimation model by the absorbance spectrum waveform analysis, x (n, d) in the equation [15] is
Absorbance at wavelength d and measurement number n, y (n)
Is the concentration when the measurement number is n. N is the number of measurements (the number of samples), and D is the number of wavelength divisions (the number of explanatory variables).

In the PLS method, the explanatory variable X and the objective variable y are obtained by the two basic equations [Equation 16] and [Equation 17].

[0044]

X = TP ^T + E T: Latent variable P: Loading E: Residual of explanatory variable X Superscript T: Transposed matrix

[0045]

Y = Tq + f q: coefficient f: residual of the objective variable y

Further, the latent variable T, the loading P and the coefficient q are shown as [Equation 18], [Equation 19] and [Equation 20].

[0047]

[Equation 18] t (n, a): a component th measurement number n of latent variables A: Number of component (a range of 1~N selectable) t _a: latent variable vector of a component th latent variables T

[0048]

[Formula 19] p (a, d): Loading of the wavelength d of the a-component A: Number of components (selectable within the range of 1 to N) p _a : Loading vector of the a-component of the loading P

[0049]

## EQU20 ## q = (q (1), q (2), q (3), q
(A), ... q (A)) q _a = q (a) q (a): coefficient of the a-th component

Here, the top 6 represents the characteristics of the model.
It is a component for the second time, and more than that reduces the prediction error. The optimum number of components A is determined by performing cross variation.

Next, in the PLS method, the information of the explanatory variable X is not directly used for modeling the objective variable y, but a part of the information of the explanatory variable X is converted into a latent constant t and the latent constant t.
Is used to model the objective variable y.

[0052] (potential constant t) t _a, if a is a linear combination of the explanatory variables X, represented by [Expression 21].

[0053]

T _a = Xw _a w _a is a weight vector, which is expressed as [Equation 22].

[0054]

[Equation 22] w (d, a): Weighting coefficient of the wavelength d of the a-th component

(Calculation of the First Component) Next, when the case where there is one component (a = 1) is calculated and explained, when there is one component a, [Equation 16] and [Equation 17] become [Equation 23] ], [Equation 2
4].

[0056]

X = t ₁ p ₁ ^T + E

[0057]

Y = t ₁ q ₁ + f From [Equation 21], the latent constant t is transformed into [Equation 25].

[0058]

[Equation 25] When the norm of w is set to be 1, [Equation 26] is obtained.

[0059]

[Equation 26]

Further, the model of PLS is to increase the correlation between the objective variable y and the latent constant t and at the same time increase the variance of t. This is the point where the covariance S of the constant t is maximized.

[0061]

(27) S = y ^T t

Here, the condition that maximizes S under the constraint condition that the norm of w is 1 is obtained by using Lagrange's undetermined multiplier method as shown in [Equation 28].

[0063]

[Equation 28]

Since the function G is a function of the variable w,
Partial differentiation is performed on (d, 1) to obtain [Equation 29] and [Equation 3].
0] is obtained.

[0065]

[Equation 29]

[0066]

[Equation 30] Multiplying both sides of [Equation 30] by w (d, 1), [Equation 3]
1].

[0067]

[Equation 31] Further, the sum of d is obtained as [Equation 32].

[0068]

[Equation 32]

[Mathematical formula-see original document] Here, according to the constraint condition of ‖w ₁ ‖ = 0, [Equation 33] is obtained.

[0070]

[Expression 33]

The left side of [Equation 29] is S = y ^T t of Equation 27.
2 μ is the value of y ^T t. Therefore,
The maximum value of w that maximizes S = y ^T t is given by [Equation 34].

[0072]

[Equation 34] Since the norm of w ₁ is 1, w is [Equation 35].

[0073]

[Equation 35] Here, the latent variable t is obtained by [Equation 36].

[0074]

(36) t ₁ = Xw ₁

The loading vector p of [Equation 23]
₁ is calculated by [Equation 37] so that the sum of squares of the elements of the residual E of the explanatory variable X is minimized.

[0076]

[Equation 37]

The coefficient q _a of [Equation 24] is calculated by [Equation 38] from the condition so that the sum of squares of the elements of the residual vector f of the objective variable y is minimized.

[0078]

[Equation 38]

(Calculation after Second Component) The model formula of the second component is represented by [Formula 39] and [Formula 40].

[0080]

X = t ₁ p ₁ ^T + t ₂ p ₂ ^T + E

[0081]

Y = t ₁ q ₁ + t ₂ q ₂ + f

Here, in modeling with one component, t ₁ p ₁ ^T of [Equation 39] of X is used and t ₁ q _{1 of} y is used.
Was used for the explanation, the remaining information is [Equation 41],
It can be replaced with [Equation 42].

[0083]

[Expression 41] X _new = X−t ₁ p ₁ ^T

[0084]

Y _new = y−t ₁ q ₁

Using X _new and y _new , [Formula 39],
[Formula 40] becomes [Formula 43] and [Formula 44].

[0086]

[Expression 43] X _new = t ₂ p ₂ ^T + E

[0087]

Y _new = t ₂ q ₂ + f

This is except that the component number is increased by one.
This is the same formula as [Formula 23] and [Formula 24].

Therefore, similarly to the first component, t ₂ , p ₂ , q
You can ask for ₂ .

By repeating this loop, the third and subsequent components can be calculated.

(Calculation of Regression Vector) The model formula in which the required number of components is repeatedly calculated A times is [Equation 45], [Equation 46]
Can be written as

[0092]

X = TP ^T = t ₁ p ₁ ^T + ... + t _a p _a ^T + ... + t _A p _A ^T

[0093]

Y = Tq = t ₁ q ₁ + ... + t _a q _a + ... + t _a q _a

The latent variable t in [Equation 46] is t in [Equation 21].
Substituting ₁ = Xw ₁ , the model equation estimated is
7].

[0095]

Y = Xw ₁ q ₁ + (X−t ₁ p ₁ ^T ) w ₂ q ₂ +.

Y = Xw ₁ q ₁ + Xw ₂ q ₂ −t ₁ p ₁ ^T w ₂ q ₂ + ...

In this [Equation 48], t ₁ = Xw of [Equation 21]
Substituting ₁ and putting together in X gives [Equation 49].

[0097]

Y = X (w ₁ q ₁ + w ₂ q ₂ −w ₁ p ₁ ^T w ₂ q ₂ ...

Here, a vector to be explained, as in [Equation 50]

[Outer 1] For the objective variable

[Outside 2] Is converted into a model formula for estimating.

[0099]

[Equation 50]

In [Equation 50], b is called a regression vector and is represented by [Equation 51].

[0101]

[Equation 51]

The regression vector b is calculated from [Formula 49] to [Formula 5].
2] is required.

[0103]

B = W (P ^T W) ⁻¹ q

The above PLS algorithm is summarized in FIG.

First, from the start of the calculation by the PLS method, the component is set to a = 1 to obtain the first component, and then the weight vector w _a of the first component described in Equation 35 is calculated to obtain w _a . Based on the above, the latent variable t of the equation 35 is calculated, the loading vector P _a of the equation 37 is calculated, and the coefficient q _a of the equation 38 is calculated.
Formula 4 from the obtained loading vector P _a and coefficient q _a
Set the model of the second component described in 1, 42, and set the component a
Is incremented to a = a + 1, and in step 1, it is determined whether or not the calculation of the next component is necessary.
es), that is, after returning to the calculation of the weight vector w _a of the second component and repeating the same calculation, the next component is set and incremented, and in step 1, the necessary number of component calculations are performed (No), the regression vector b described in [Equation 52] is calculated, and the process ends.

When the multivariate analysis is completed, data such as the absorbance and composition ratio (concentration) of the predetermined substance contained in the mixed substance can be calculated, and a plurality of calibration curves can be created for each wavelength of the predetermined substance. .

In the following, various processes in the process of creating the calibration curve are actually shown, and in the example in which the temporary noise component amount nPm (d), the correlation coefficient R ² , the intercept b, etc. are obtained, the predetermined wavelength d is set to 2
By setting the thickness to 10 nm, the temporary noise component amount nPm
(D) is nPm, and the noise component amount Pm (d) is Pm,
The zero spectrum Pz (d) is shown as Pz, and the received light spectrum (measurement spectrum) P (d) is shown as P.

(Embodiment 1) The case of changing the temporary noise component amount nPm of stray light in SO ₂ will be described with reference to a calibration curve. As shown in FIG. 4, when the temporary noise component amount nPm is changed, the calibration curve is changed. It is clear that the slope of rises and the calibration curve becomes substantially linear with a certain value of the temporary noise component amount nPm. Further, the relationship between the temporary noise component amount nPm and the square of the correlation coefficient R ² when the temporary noise component amount nPm at this time is changed is shown in FIGS. 5 and 6. nPm has a maximum at a predetermined position (near 1560). Here, FIG. 6 is an enlarged view of the vicinity of the maximum value of FIG. Furthermore,
Intercept b when the temporary noise component amount nPm at this time is changed
As shown in FIG. 7, b is a predetermined position and b =
It becomes 0. Therefore, when the correlation coefficient R ² is the maximum value and b is zero, the provisional noise component amount nPm becomes the actual noise component amount Pm (actual stray light), and the actual noise component amount P
It is assumed that m is 1560 to 1570, and the slope a corresponding to the extinction coefficient α is 0.0149 at 210 nm. Furthermore, as to how much the measured received light spectrum P includes the noise component amount Pm, as shown in FIG. 8, a predetermined amount of noise component amount Pm is provided below the zero spectrum Pz and the received light spectrum P at each wavelength. It is clear that there exists.

(Embodiment 2) The noise component amount Pm of the actual stray light is adjusted by intentionally adjusting the optical system in the same device.
When an example in which the noise component amount Pm is changed is shown in FIG. 9, the calibration curve including the noise component amount Pm is a noise component amount Pm of stray light.
The curvature increases and the inclination changes with the magnitude of the. Further, when each noise component amount Pm is removed from the calibration curve of FIG. 9, the stray light is large (noise component is large) in FIG. 10, the stray light is in medium (noise component) in FIG. 11, and the stray light is small (noise component is small) in FIG. As shown, it is apparent that the calibration curve becomes a substantially straight line and the slope becomes substantially constant regardless of the size of the stray light (the size of the noise component amount).

Example 3 A mixed substance (mixed gas) containing SO ₂ was actually processed from 200 nm to 350 nm by adding a predetermined wavelength width Δd to a predetermined wavelength d, and a multivariate analysis of SO ₂ was performed. S in mixed substances
Data such as the absorbance of O ₂ can be calculated. [Table 2]
Is 3 out of each composition ratio (concentration 20 ppm, 6
0 ppm, 100 ppm), and each composition ratio has three wavelengths (200.52 nm, 200.77 n).
m, 201.02 nm).

[Table 2]

As a result, FIG. 13 shows the zero spectrum Pz, the noise component amount Pm, and the received light spectrum (measurement spectrum) P at each wavelength, and FIG. 14 shows the absolute absorption coefficient spectrum at each wavelength. Further, the calibration curve of the predetermined substance created by the multivariate analysis exists for each wavelength, and the absorbance spectrum before correction shown in FIG. 15 is corrected to the absorbance spectrum after correction shown in FIG.

Thus, by using the noise component amount of each wavelength calculated from a single substance, the absorbance at each composition ratio is calculated by removing the noise component amount from the mixed substance, and the multivariate is calculated using each data. Since the analysis is performed, it is possible to calculate the data such as the absorbance of the predetermined substance contained in the mixed substance, and to create a plurality of calibration curves at the respective wavelengths of the predetermined substance.
Also, since the amount of noise components is removed from the received spectrum,
The calibration curve saturated at high concentration can be corrected to create a highly accurate calibration curve with high reproducibility.

The optimum one is selected from a plurality of correlation coefficients or a plurality of intercepts calculated from the linear regression method via the temporary noise component amount to obtain the noise component amount of a predetermined wavelength in a single substance, and the predetermined wavelength. By changing the value and performing the same processing, the noise component amount of another predetermined wavelength is obtained and the noise component amount of each wavelength is integrated, so that the noise component amount of each wavelength in a single substance can be accurately obtained.

The method for preparing the calibration curve of the absorption spectrum of the present invention is not limited to the above-mentioned embodiments, and it goes without saying that various modifications can be made without departing from the scope of the present invention.

[0115]

As described above, according to the method for preparing the calibration curve of the absorption spectrum of the present invention, various excellent effects as described below can be obtained.

I) According to claim 1, the noise component amount of each wavelength calculated from a single substance is used to remove the noise component amount from the mixed substance, and the absorbance at each composition ratio is calculated, and each data is calculated. Since a multivariate analysis is performed using, it is possible to calculate data such as the absorbance of a predetermined substance in a mixed substance and to create a plurality of calibration curves for the predetermined substance at each wavelength. Further, since the noise component amount is removed from the received light spectrum, it is possible to correct the calibration curve saturated at high concentration and create a highly accurate calibration curve with high reproducibility.

II) According to claim 2 or 3, the optimum one is selected from a plurality of correlation coefficients or a plurality of intercepts calculated from the linear regression method via the amount of temporary noise components, and a predetermined value in a single substance is selected. The noise component amount of each wavelength is obtained by calculating the noise component amount of the wavelength and performing the same process by changing the predetermined wavelength to obtain the noise component amount of the other predetermined wavelength. It is possible to accurately determine the component amounts.

[Brief description of drawings]

FIG. 1 is a flow chart showing an example of an embodiment for carrying out a method for preparing a calibration curve for an absorption spectrum of the present invention.

FIG. 2 is a continuous flow from FIG.

FIG. 3 is a diagram showing an algorithm based on multivariate analysis (PLS method).

FIG. 4 is a diagram showing a calibration curve when the amount of temporary noise component of stray light is changed in SO ₂ .

5 is a diagram showing the relationship between the amount of temporary noise components and the square value of a correlation coefficient when the amount of temporary noise components is changed in FIG.

FIG. 6 is an enlarged view showing the vicinity of the maximum value in FIG.

7 is a diagram showing a relation of intercepts when the amount of temporary noise components is changed in FIG.

FIG. 8 is a diagram showing to what extent a measured light reception spectrum includes a noise component amount.

FIG. 9 is a diagram showing an example of a calibration curve when the optical system is intentionally adjusted in the same device to change the actual noise component amount of stray light.

10 is a diagram showing a calibration curve obtained by removing each noise component amount from the stray light large (noise component large) calibration curve of FIG. 9;

11 is a diagram showing a calibration curve when each noise component amount is removed from the calibration curve in stray light (in noise component) of FIG. 9;

FIG. 12 is a diagram showing a calibration curve when each noise component amount is removed from the calibration curve for small stray light (small noise component) in FIG. 9;

FIG. 13 is a diagram showing a zero spectrum, a noise component amount, and a light reception spectrum (measurement spectrum) at each wavelength.

FIG. 14 is a diagram showing an absolute extinction coefficient spectrum at each wavelength.

FIG. 15 is a diagram showing an absorbance spectrum before correction at each wavelength.

FIG. 16 is a diagram showing a corrected absorbance spectrum at each wavelength.

FIG. 17 is a diagram showing a conventional calibration curve of SO _{2 having} a wavelength of 210 nm.

FIG. 18 is a schematic diagram showing stray light in the case of non-dispersive spectroscopic analysis.

FIG. 19 is a schematic diagram showing stray light in the case of spectroscopic analysis using a spectroscope.

[Explanation of symbols]

As (d) Absorbance P (d) Light receiving spectrum (measurement spectrum) Pm (d) Actual noise component amount nPm (d) Temporary noise component amount Pz (d) Zero spectrum R ² Correlation coefficient r Correlation coefficient a Slope b Intercept d predetermined wavelength (initial wavelength) n concentration

   ─────────────────────────────────────────────────── ─── Continued front page    (72) Inventor Ken Kobayashi             3-15 Toyosu, Koto-ku, Tokyo Ishikawajima             Harima Heavy Industries Tokyo Engineering Co., Ltd.             In the center (72) Inventor Takehito Yagi             3-15 Toyosu, Koto-ku, Tokyo Ishikawajima             Harima Heavy Industries Tokyo Engineering Co., Ltd.             In the center (72) Inventor Masataka Ohara             2-2-1 Otemachi, Chiyoda-ku, Tokyo Stone             Kawashima Harima Heavy Industries Co., Ltd. F term (reference) 2G059 AA01 BB01 CC06 EE01 EE12                       HH03 JJ05 KK01 MM01 MM04                       MM12 MM15 NN01 NN06

Claims (3)

[Claims] 1. A light receiving spectrum of a zero concentration of a mixed substance and a plurality of light receiving spectra in which the composition ratio is changed by the same measuring device that measures the amount of noise components of each wavelength from the absorption spectrum of a single substance. As a mixed substance wavelength setting step, the processing wavelength of each light-receiving spectrum is set to a predetermined wavelength, and the noise component amount of the predetermined wavelength selected from the noise component amount of each wavelength is set to the zero-concentration light-receiving spectrum and each composition ratio. Repeat the same process by subtracting each from the received spectrum to calculate the absorbance at a predetermined wavelength at each composition ratio, changing the predetermined wavelength to another predetermined wavelength and returning the processing procedure to the wavelength setting step for the mixed substance. Then, calculate the absorbance at each other predetermined wavelength at each composition ratio, and perform multivariate analysis using the data at each wavelength and the absorbance at each wavelength to analyze the A method for preparing a calibration curve for an absorption spectrum, which comprises preparing a calibration curve for a predetermined substance. 2. A step of setting a noise component amount by collecting each received spectrum from zero concentration of a single substance to each predetermined concentration and setting a processing wavelength of each received spectrum to a predetermined wavelength as a wavelength setting step for a single substance. As the noise component is temporarily set to a light-receiving spectrum of zero density or an arbitrary temporary noise component amount smaller than the light-receiving spectrum of a predetermined density, and the temporary noise component amount is subtracted from the light-receiving spectrum of zero density and the light-receiving spectrum of a predetermined density, respectively. The absorbance at each predetermined concentration is calculated, and assuming that the relationship between each predetermined concentration and the absorbance follows a straight line, Y = aX + b a: slope b: the concentration is substituted for X from the intercept, and the absorbance is substituted for Y to obtain a linear regression method. The similar process is repeated by obtaining the relation number, then changing the temporary noise component amount to another temporary noise component amount, and returning the processing procedure to the noise component amount setting step. Of the temporary noise component amount, and by selecting the largest one from the plurality of correlation coefficients in each temporary noise component amount, to determine the noise component amount of a predetermined wavelength corresponding to the selected correlation coefficient, further the predetermined By changing the wavelength to another predetermined wavelength and returning the processing procedure to the single substance wavelength setting step, the same processing is repeated to determine the noise component amounts of other predetermined wavelengths respectively, and the noise component amount of each wavelength is calculated. The method for preparing a calibration curve for an absorption spectrum according to claim 1, wherein the amount of noise components of each wavelength contained in the absorption spectrum of a single substance is obtained by integrating. 3. A light reception spectrum from zero concentration of a single substance to each predetermined concentration is collected, and a processing wavelength of each light reception spectrum is set to a predetermined wavelength as a wavelength setting step for a single substance, and a noise component amount setting step As the noise component is temporarily set to a light-receiving spectrum of zero density or an arbitrary temporary noise component amount smaller than the light-receiving spectrum of a predetermined density, and the temporary noise component amount is subtracted from the light-receiving spectrum of zero density and the light-receiving spectrum of a predetermined density, respectively. Calculate the absorbance at each predetermined concentration, and assume that the relationship between each predetermined concentration and the absorbance follows a straight line. Then, the temporary noise component amount is changed to another temporary noise component amount, and the processing procedure is returned to the noise component amount setting step to repeat the same processing, A piece is obtained, and the one closest to zero is selected from the plurality of intercepts in each temporary noise component amount to determine the noise component amount of the predetermined wavelength corresponding to the selected intercept, and further, the predetermined wavelength is set to another predetermined value. By changing the wavelength and returning the processing procedure to the single substance wavelength setting step, the same processing is repeated to determine the noise component amounts of other predetermined wavelengths respectively, and by integrating the noise component amounts of the respective wavelengths, The method for preparing a calibration curve for an absorption spectrum according to claim 1, wherein the amount of noise components at each wavelength contained in the absorption spectrum of a single substance is obtained.