JPH06300684A - Quantitative method for spectrochemical analysis - Google Patents

Abstract

PURPOSE:To accurately quantitatively calculate absorbance against an absorption not proportional to density by obtaining as calibration data relationship between the density and an absorbance sum, estimating the sum of components to be measured, and using the relationship between the density and the sum. CONSTITUTION:As calibration data, an absorption spectrum, density and an absorbance sum regarding a certain component are prepared. Then, the spectrum is calculated with a calibration matrix by a method of main component analysis PCR or partial minimum squaring method PLS by using the sum, and a quantity matrix is formed. On the other hand, relationship between the absorbance sum and the density is obtained by executing a nonlinear curve fitting process, and a relation curve between the sum and the density is obtained. Thereafter, an absorbance sum of a component to be measured is estimated from the quantity matrix and a density unknown spectrum obtained separately. The sum obtained by the estimation is substituted for a quartic equation, and an estimated density at this time is obtained. The absorption in which the absorbance is not proportional to the density is accurately quantitated by using the sum.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a quantification method using an infrared absorption spectrum, and more particularly, to a quantification calculation for absorption that does not follow Lambert-Beer's law, that is, absorption in which absorbance and concentration are not in a proportional relationship. It relates to a method of performing with high accuracy.

[0002]

2. Description of the Related Art A component having a sharp peak shape, such as CO (carbon monoxide), has a non-linear absorption due to the resolution of the device when the resolution of the device is low.
For example, in FIG. 6, the CO absorption spectrum of 2373 ppm is divided into seven concentrations, that is, 339 ppm steps (33
9,678,1356,1695,2034,2373
ppm), but the area is not divided into seven equal parts.

By the way, the applicant of the present application filed “October 13, 1990,“ Multi-component quantification method in spectroscopic analysis ”.
(Japanese Patent Application No. 2-274204 (JP-A-4-148830)). This patent application, in the infrared absorption spectrum obtained when the sample is irradiated with infrared light, for example, the local peak and the frequency point of the local base for the absorption of a plurality of components are determined in advance, Obtain the relative absorbance from the difference in the absorbance of the base, then determine the component spectrum using the sum of the relative absorbance obtained by adding these relative absorbance, based on this component spectrum and the reference spectrum for each component, The plurality of components are individually analyzed. According to this quantification method, accurate quantification can be performed without being affected by noise and interference between the components.

Here, the sum of absorbances is the sum of the absorbances at a plurality of predetermined wave number points when there is an absorption spectrum as shown in FIG. 2, for example. That is, when the value at each point of the spectrum is as shown in the figure, the absorbance in a certain region of this spectrum is
1.89 (= 0.08 + 0.2 + 0.4 + 0.5 + 0.
39 + 0.15 + 0.1 + 0.07).

[0005]

However, the quantification method according to the above-mentioned prior application is based on the assumption that the absorption follows Lambert-Beer's law, that is, the absorbance is proportional to the concentration. When applied to various absorptions, a contradiction may occur, resulting in poor quantification accuracy and interference between components.

In contrast, the conventional principal component analysis (Prin
cipal Component Regression (hereinafter referred to as PCR) or Partial Least Square (hereinafter referred to as PLS)
It is also possible to estimate the concentration by associating the spectrum with the non-linear concentration using an algorithm such as ".

That is, as shown in FIG. 7, the reference spectrum and the equally divided (for example, 7 divided) concentration are expressed as P
The calibration matrix is obtained by the CR or PLS method, and the concentration is estimated by using the calculation result for the sample spectrum of unknown concentration.

However, this conventional quantitative analysis method has a drawback in that there are many errors and noise increases during continuous measurement.

That is, in the conventional quantification method in which the absorbance is not proportional to the concentration and is calibrated using the spectrum and the concentration, interference increases and noise increases as the absorption becomes nonlinear. There was a flaw.

The present invention has been made in view of the above matters, and an object thereof is a quantitative method in a spectroscopic analysis (hereinafter, simply referred to as a quantitative method for quantitatively calculating absorption whose absorbance is not proportional to concentration). Quantitative method).

[0011]

In order to achieve the above object, the quantification method according to the present invention provides a plurality of absorption spectra for a certain component, the corresponding concentrations and the sum of absorbances as calibration data, and While creating a quantification matrix using the absorption spectrum and the absorbance sum, the relationship between the absorbance sum and the concentration is subjected to a non-linear curve fitting process in advance, from the quantification matrix and the concentration unknown spectrum. The sum of the absorbances of the components to be measured is estimated, and the sum of the absorbances obtained by this estimation is used to estimate the concentration of the components to be measured by using the relationship between the sum of the absorbances and the concentration.

[0012]

If the spectrum changes in a similar manner to the change in concentration, the spectrum and its own sum of absorbance (area) are proportional. Therefore, linear information can be input at the PCR or PLS calibration stage. For example, even when there is no similar shape like CO shown in FIG. 6, the linearity is much higher when the sum of absorbance is used than when the concentration value is used. Therefore, according to the present invention, it is possible to accurately perform a quantitative calculation for absorption in which the absorbance and the concentration are not proportional.

[0013]

Embodiments of the present invention will be described below with reference to the drawings.

FIG. 1 is a flow chart showing an example of the quantification method according to the present invention. Before going into the explanation of FIG.
The data used in the method of the present invention will be described. As a calibration data, a certain component (eg CO) as shown in FIG.
Reference spectrum (absorption spectrum)
Then, the equally divided concentrations shown in Table 1 below and the sum of absorbances shown in Table 2 below are prepared. Here, the sum of absorbance is different from the concentration and is non-linear.

[0015]

[Table 1]

[0016]

[Table 2]

Next, the quantification method according to the present invention will be described based on FIG. 1. As shown in the flow chart of FIG. 1, first, in the calibration stage, step 1: using the absorption spectrum and the sum of absorbances,
Calibration matrix calculation is performed by the PCR or PLS method to create a quantification matrix. Step 2: On the other hand, a nonlinear curve fitting process is performed on the sum of absorbance and the concentration to obtain the relationship between the two, and a relationship curve between the sum of absorbance and the concentration as shown in FIG. 3 is obtained. In this embodiment, this relational curve is expressed by the following quartic equation from the data shown in Tables 1 and 2 above. That is, when the concentration (horizontal axis) is y and the total absorbance is x, y = 1.74 × 10 ⁻⁶ x ⁴ + 2.49 × 10 ² x ³ + 2.786 × 10 ³ x ² + 1.765 × 10 ² x …… (1)

Next, in the estimation step, step 3: the sum of absorbances of the components to be measured is estimated from the quantification matrix and the unknown concentration spectrum obtained separately. In this embodiment, the estimated absorbance sum is, for example, 0.7.
And Step 4: Substituting the sum of absorbances obtained by the above estimation, that is, x = 0.7 into the quartic equation represented by the above equation (1) to obtain the value of y, that is, the estimated concentration at this time. Is 1574 ppm.

When PLS was used as an algorithm in the calibration stage and the concentration estimation ability of the quantification method according to the present invention and the conventional quantification method shown in FIG. 7 were compared, the method of the present invention shown in FIG. 4 (A). The concentration estimation ability of
It was found that they are almost the same as those of the conventional method shown in FIG. 6B, and both have satisfactory density estimation ability.

As to zero noise when 100 N ₂ (nitrogen gas) spectra (absence of absorption at all) were quantified, the quantification method according to the present invention was compared with the conventional method, as shown in FIG. Results were obtained. That is, in this figure, a curve A shows zero noise by the method of the present invention, and a curve B shows zero noise by the conventional method. The RMS (effective value) of zero noise according to the conventional method is 9.95 ppm, respectively, whereas that of the method according to the present invention is greatly reduced to 0.29 ppm, and it can be seen that the deviation is small according to the present invention.

The present invention is not limited to the above-mentioned embodiments, and the association between the sum of the absorbance and the concentration can be expressed by, for example, an exponential function in addition to the polynomial such as the quartic expression.

Further, as a pretreatment of the method of the present invention, the "multi-component quantification method in spectroscopic analysis" (Japanese Patent Application No. 2-274204) described above is carried out to obtain a more accurate relative value of the sum of absorbances. Obtainable.

[0023]

As described above, according to the present invention,
PC if absorption does not follow Lambert-Beer's law
Even if an algorithm such as R or PLS is applied, quantification with a small error can be performed. Moreover, the high interference correction capability of these algorithms is not impaired. In particular, in a spectrum with low resolution, the nonlinearity of absorption increases, and in such a case, a great effect is exhibited.

[Brief description of drawings]

FIG. 1 is a flow chart for explaining an example of a quantification method according to the present invention.

FIG. 2 is a diagram showing an example of an absorption spectrum.

FIG. 3 is a diagram showing a relationship between sum of absorbance and concentration.

FIG. 4 is a diagram showing the concentration estimation ability in the quantification method according to the present invention and the conventional method.

FIG. 5 is a diagram showing the magnitude of zero noise in the quantification method according to the present invention and the conventional method.

FIG. 6 is a diagram showing an example of an absorption spectrum of CO.

FIG. 7 is a flowchart for explaining a conventional quantification method.

Claims (1)

[Claims] 1. As calibration data, a plurality of absorption spectra for a certain component and the corresponding concentrations and absorbance sums are prepared, and a quantification matrix is created using the absorption spectra and the absorbance sums, while the absorbance The sum and the concentration are subjected to a non-linear curve fitting process to obtain the relationship between them, and the sum of the absorbances of the components to be measured is estimated from the quantification matrix and the concentration unknown spectrum, and the sum of the absorbances obtained by this estimation is calculated. A quantitative method in spectroscopic analysis, characterized in that the concentration of the component to be measured is estimated by using the relationship between the sum of the absorbance and the concentration.