X-ray fluorescence spectrometer

Abstract

In this X-ray fluorescence spectrometer, a quantification means displays, on a display device, as a theoretical quantitative value standard deviation of analysis components, the difference between a first quantitative value of the analysis components, which is based on the measurement intensity with respect to each component, and a second quantitative value of the analysis components, which is found by varying the measurement intensity in a direction of increase in the change of content of the analysis components in a calibration curve for each component.

Description

X-ray fluorescence analyzer Related Applications

[0001] This application claims priority to Japanese Patent Application No. 2023-027359, filed February 24, 2023, the entire contents of which are incorporated herein by reference.

[0002] The present invention relates to an X-ray fluorescence analyzer that determines the content of components in a sample by irradiating the sample with primary X-rays and determining the content of components in the sample based on the measured intensity of the fluorescent X-rays generated by the calibration curve method, which performs absorption / excitation correction and overlap correction, or the fundamental parameter method, which includes overlap correction.

[0003] Conventionally, X-ray fluorescence analyzers for quantitative analysis are broadly divided into those that use the calibration curve method and those that use the fundamental parameter method (also referred to as the FP method). In quantitative analysis using the calibration curve method, a set of standard samples with known component contents (also referred to as concentration ratios) is used to analyze an unknown sample, and a calibration curve is obtained as a correlation between the component contents and the measured intensity of the fluorescent X-rays (measurement lines) of the measurement elements corresponding to the components. Note that a component is an element or a compound. Furthermore, if the component is an element, the element itself is the measurement element corresponding to the component, and if the component is a compound, an element representative of the compound is the measurement element corresponding to the component (see, for example, paragraph 0002 of Patent Document 1).

[0004] In quantitative analysis using the calibration curve method, in addition to background correction for the background, absorption-excitation correction (also referred to as matrix correction) for absorption-excitation due to coexisting elements and overlap correction for overlap of interference lines may be performed (for example, see paragraph 0003 of Patent Document 1 for absorption-excitation correction).

[0005] On the other hand, in quantitative analysis using the FP method, the theoretical intensity of fluorescent X-rays emitted from each component in a sample is calculated based on the assumed content of each component, and the assumed content of each component is corrected and calculated in an iterative manner so that the theoretical intensity matches the converted measured intensity obtained by converting the measured intensity measured by the detection means to a theoretical intensity scale, thereby calculating the content of the component in the sample. Here, for analysis of an unknown sample, a set of standard samples with known component contents is used to obtain an instrument sensitivity curve as a correlation between the theoretical intensity calculated based on the known content and the measured intensity (see, for example, paragraphs

[0003] and

[0004] , and paragraph

[0009] , of Patent Document 1).

[0006] In quantitative analysis using the FP method, absorption-excitation correction is performed for all components in principle, and if necessary, overlap correction is also performed for some components in the instrument sensitivity curve expressed by, for example, the following formula (a) (for absorption-excitation correction, see, for example, paragraphs 0069-0074 of Patent Document 2):

[0007] I Ｔｉ = aI ｉ ３ + bI ｉ ２ +cI ｉ +d+Σ ｊ b Ｏ ｉｊ I ｊ …(a) I Ｔ : Theoretical intensity I: Measured intensity a, b, c, d: Instrument sensitivity constant i: Analytical component j: Overlap correction component b Ｏ ｉｊ : overlap correction coefficient of j component to i component

[0008] In quantitative analysis using the calibration curve method, when creating a calibration curve, it is necessary to calculate and display the standard deviation of the quantitative value, which is the content of the analyte obtained from the calibration curve, as a criterion for determining whether or not correction should be made. Furthermore, after the analysis, it is necessary to calculate and display the standard deviation of the quantitative value as a measure of the reliability of the quantitative value.

[0009] In quantitative analysis using the FP method, as a criterion for determining whether or not overlap correction should be performed, it is required to calculate and display the standard deviation of the quantitative value obtained by the FP method including the overlap correction, and after the analysis, it is required to calculate and display the standard deviation of the quantitative value as a measure of the reliability of the quantitative value.

[0010] Thus, in quantitative analysis that performs absorption-excitation correction and overlap correction, the calculation of standard deviation must take into account the fact that errors in the analysis of the correction components affect errors in the analysis of the analyte components, i.e., the propagation of errors from the correction components to the analyte components. However, there is no method for calculating the theoretical standard deviation of quantitative values ​​that takes into account the effects of the correction components. Therefore, the current practice is to actually perform repeated analyses of the same sample and calculate the standard deviation based on the multiple quantitative values ​​obtained.

[0011] As a conventional technique for determining analytical accuracy as a measure of the reliability of quantitative values, for example, the fluorescent X-ray analyzer described in Patent Document 3 calculates and displays the measurement time required to obtain a specified analytical accuracy, but this calculation does not take into account the influence of correction components.

[0012] JP 2021-51053 A International Publication No. 2018 / 168939 JP 2000-65765 A

[0013] Currently, in quantitative analysis that performs absorption / excitation correction and overlap correction, in order to calculate the standard deviation of the quantitative value while taking into account the influence of the correction components, it is necessary to actually perform repeated analyses of the same sample, which is time-consuming. Furthermore, in the calibration curve method, there is no indicator for determining whether or not correction should be performed when creating a calibration curve, and in the FP method, there is no indicator for determining whether or not overlap correction should be performed.

[0014] The present invention has been made in view of the above-mentioned problems in the prior art, and has as its object to provide an X-ray fluorescence analyzer that determines the content of a component in a sample by a quantitative means that uses a calibration curve method that performs absorption-excitation correction and overlap correction, or a fundamental parameter method that includes overlap correction, and that can determine and display the standard deviation of a theoretical quantitative value while appropriately incorporating the influence of correction components, within an acceptable time, without actually performing repeated analyses.

[0015] To achieve the above object, a first aspect of the present invention is an X-ray fluorescence analyzer that first irradiates a sample with primary X-rays, and determines the content of a component in the sample using a quantitative means that employs a calibration curve method that performs absorption-excitation correction and overlap correction based on the measured intensity of the generated fluorescent X-rays. The quantitative means then determines the content of the analyte from the calibration curve equations for the analyte and correction components based on the measured intensities of the analyte and correction components, and sets this as a first quantitative value.

[0016] Furthermore, the quantification means varies the measured intensity of the analytical component by a predetermined amount in a direction in which the content of the analytical component increases or decreases in the calibration curve equation for the analytical component, and also varies the measured intensity of the correction component by a predetermined amount in the same direction as the direction in which the measured intensity of the analytical component is varied in the calibration curve equation for the correction component.

[0017] Furthermore, the quantitative means determines the content of the analytical component from a calibration curve equation for the analytical component and the correction component based on the measured intensities for the analytical component and the correction component and the varied measured intensities for the analytical component and the correction component, and sets this as a second quantitative value, and displays the difference between the first quantitative value and the second quantitative value as the standard deviation of the theoretical quantitative value on a display.

[0018] In the X-ray fluorescence analyzer of the first configuration, the quantification means displays on the display as the standard deviation of the theoretical quantitative values ​​of the analyte, the difference between a first quantitative value of the analyte based on the measured intensity of each component and a second quantitative value of the analyte obtained by varying the measured intensity in the calibration curve equation for each component in a direction that increases the change in the content of the analyte. Here, when varying the measured intensity, further changes in the content of the correction component in the calibration curve equation for the correction component are not taken into consideration. Therefore, the standard deviation of the theoretical quantitative values ​​of the analyte can be determined and displayed within an acceptable time, without actually performing repeated analyses and while appropriately incorporating the influence of the correction component.

[0019] In a second aspect of the present invention, a fluorescent X-ray analyzer is provided that first irradiates a sample with primary X-rays, and determines the content of components in the sample based on the measured intensity of the generated fluorescent X-rays using a quantification means that employs a fundamental parameter method including overlap correction. The quantification means then determines the content of each component from a theoretical intensity formula for each component based on the measured intensity of each component, and sets this as a first quantitative value.

[0020] Furthermore, the quantification means increases the content of components other than the analytical component by a predetermined amount one by one in the theoretical intensity formula for each component, and when the theoretical intensity for the analytical component increases above a predetermined threshold, the measured intensity for the component other than the analytical component is decreased by a predetermined amount to vary it, and when the theoretical intensity for the analytical component decreases below the predetermined threshold, the measured intensity for the component other than the analytical component is increased by a predetermined amount to vary it.

[0021] Furthermore, the quantitative means calculates the content of each component from a theoretical intensity formula for each component based on the measured intensity for each component and the varied measured intensity for each component, and sets this as a second quantitative value, and displays the difference between the first quantitative value and the second quantitative value for each component on a display as the standard deviation of the theoretical quantitative value.

[0022] According to the X-ray fluorescence analyzer of the second configuration, the quantification means displays on the display as the standard deviation of the theoretical quantitative values ​​the difference between the first quantitative value based on the measured intensity for each component and the second quantitative value obtained by varying the measured intensity that has the greatest influence on the theoretical intensity for the analyzed component in the theoretical intensity formula for each component in the direction of increasing the content of the analyzed component. Therefore, the standard deviation of the theoretical quantitative values ​​can be obtained and displayed within an acceptable time, without actually performing repeated analyses, while appropriately incorporating the influence of the correction component.

[0023] Any combination of at least two features disclosed in the claims and / or the specification and / or the drawings is included in the present invention. In particular, any combination of two or more of the claims is included in the present invention.

[0024] The present invention will be more clearly understood from the following description of preferred embodiments with reference to the accompanying drawings. However, the embodiments and drawings are merely for illustration and explanation purposes and should not be used to define the scope of the present invention. The scope of the present invention is defined by the appended claims. In the accompanying drawings, the same part numbers in multiple drawings indicate the same parts.

[0023] Figure 1 is a schematic diagram showing an X-ray fluorescence analysis apparatus according to one embodiment of the present invention.

[0025] An X-ray fluorescence analyzer according to one embodiment of the present invention will now be described. As shown in Fig. 1, the X-ray fluorescence analyzer according to this embodiment is a scanning X-ray fluorescence analyzer that measures the intensity of secondary X-rays 5 generated by irradiating primary X-rays 3 onto a sample 1, 14 (including both an unknown sample 1 and a standard sample 14). The X-ray fluorescence analyzer includes a sample stage 2 on which the sample 1, 14 is placed, an X-ray source 4 such as an X-ray tube that irradiates the sample 1, 14 with the primary X-rays 3, a spectroscopic element 6 that disperses secondary X-rays 5, such as fluorescent X-rays, generated from the sample 1, 14, and a detector 8 that receives secondary X-rays 7 dispersed by the spectroscopic element 6 and detects their intensity. The output of the detector 8 is input to control means 11, such as a computer, which controls the entire apparatus, via an amplifier, a pulse-height analyzer, a counting means, and other means (not shown).

[0026] The X-ray fluorescence analyzer of this embodiment is a wavelength-dispersive scanning X-ray fluorescence analyzer and includes an interlocking means 10, i.e., a so-called goniometer, that interlocks the spectroscopic element 6 and the detector 8 so as to change the wavelength of the secondary X-rays 7 incident on the detector 8. When secondary X-rays 5 are incident on the spectroscopic element 6 at a certain incident angle θ, an extension line 9 of the secondary X-rays 5 and the secondary X-rays 7 dispersed (diffracted) by the spectroscopic element 6 form a spectral angle 2θ that is twice the incident angle θ. The interlocking means 10 changes the spectral angle 2θ to change the wavelength of the dispersed secondary X-rays 7, while rotating the spectroscopic element 6 about an axis O that passes through the center of its surface and is perpendicular to the paper surface, and rotating the detector 8 around the axis O by twice the rotation angle along a circle 12 so that the dispersed secondary X-rays 7 are incident on the detector 8. The value of the spectral angle 2θ (2θ angle) is input from the interlocking means 10 to the control means 11. In the present invention, the X-ray fluorescence analyzer may be a wavelength dispersive and multi-element simultaneous analysis type X-ray fluorescence analyzer, or an energy dispersive type X-ray fluorescence analyzer.

[0027] The fluorescent X-ray analyzer of this embodiment is provided with a quantification means 13 as a program installed in the control means 11, and the content ratios of components in the samples 1 and 14 are determined by the quantification means 13 using a calibration curve method that performs absorption excitation correction and overlap correction based on the measured intensity of the fluorescent X-rays 5. In determining the standard deviation of the theoretical quantitative values, the quantification means 13 first calculates the measured intensity I for the analytical component i and the correction components j and k, as in the case of conventional quantification means. ｉ , I ｊ , I ｋ Based on this, the content W of the analyte i can be calculated from the calibration curve equations for the analyte i and the correction components j and k, for example, the following calibration curve equations (1)-(3). ｉ Then, the content W of the analyte i is calculated. ｉ The first quantitative value Q ｉ１ Let's say.

[0028] W ｉ = (A ｉ I ｉ ３ +B ｉ I ｉ ２ +C ｉ I ｉ +D ｉ )(1+CＭ ｊｉ W ｊ ) + C Ｏ ｋｉ W ｋ …(1) W ｊ = (A ｊ I ｊ ３ +B ｊ I ｊ ２ +C ｊ I ｊ +D ｊ )(1+C Ｍ ｋｊ W ｋ ) … (2) W ｋ = (A ｋ I ｋ ３ +B ｋ I ｋ ２ +C ｋ I ｋ +D ｋ ) … (3) W ｉ : Content of analyte i W ｊ , W ｋ : Content of correction components j and k I ｉ : Measured intensity for analyte i I ｊ , I ｋ : Measured intensities of correction components j and k A, B, C, D: Calibration curve constants C Ｍ ｊｉ : Absorption excitation correction coefficient of j component for i component C Ｏ ｋｉ : Overlap correction coefficient of k component to i component

[0029] Furthermore, the quantification means 13 calculates the measured intensity I for the analyte i in the calibration curve formula (1) for the analyte i. ｉ is the content W of the analyte i ｉ In the direction of increasing or decreasing, for example, the content W ｉ In the direction of increasing, the right side of the calibration curve equation (1) is ｉ If the partial derivative value is positive, the measured intensity I ｉ is changed by a predetermined amount so that

[0030] In addition, in the calibration curve equations (2) and (3) for the correction components j and k, the measured intensity I ｊ , I ｋ is the measured intensity I for analyte i ｉ In this case, the content W of the analyte i is changed in the same direction as the direction in which ｉ The correction coefficient C Ｍ ｊｉ In the case of absorption correction, the content of correction component j is W ｊ As the amount of analyte i increases, the content of analyte i, W ｉ Therefore, the right side of the calibration curve equation (2) is expressed as the measured intensity I ｊ If the partial derivative value is positive, the measured intensity I ｊ For the overlap correction component, the content rate W of the correction component k is increased by a predetermined amount. ｋ When decreases, the content W of analyte i ｉ Therefore, the right side of the calibration curve equation (3) is expressed as the measured intensity I ｋ If the partial derivative value is positive, the measured intensity I ｋ Here, the predetermined amount to be changed is the amount by which each measurement intensity I ｉ , I ｊ , I ｋ Theoretical standard deviation σI ｉ , σI ｊ , σI ｋ and the measurement time t ｍｅａｓ Using this, σI = (I / 1000t ｍｅａｓ ) １／２ It can be calculated as follows.

[0031] Furthermore, the quantification means 13 calculates a set of measured intensities I for the analyte i and the correction components j and k. ｉ , I ｊ , I ｋ and the varied measurement intensities I for the analytical component i and the correction components j and k. ｉ +σI ｉ , I ｊ +σI ｊ , I ｋ -σI ｋ Based on this, the content W of the analyte i is calculated from the calibration curve equations (1)-(3) for the analyte i and the correction components j and k.ｉ That is, I ｉ I ｉ +σI ｉ And I ｊ I ｊ +σI ｊ And I ｋ I ｋ -σI ｋ As the content of the analyte i, W ｉ Then, the content W of the analyte i is calculated. ｉ The second quantitative value Q ｉ２ and the first quantitative value Q ｉ１ and the second quantitative value Q ｉ２ Difference | Q ｉ２ -Q ｉ１ |Theoretical quantitative value standard deviation σQ ｉ and displays it on a display 15 such as a liquid crystal display connected to the control means 11.

[0032] According to the X-ray fluorescence analyzer of this embodiment, the quantification means 13 measures the measured intensities I ｉ , I ｊ , I ｋ A first quantitative value Q of analyte i based on ｉ１ In the calibration curve equations (1)-(3) for each component i, j, and k, the measured intensity I ｉ , I ｊ , I ｋ The content of analyte i, W ｉ The change in I ｉ +σI ｉ , I ｊ +σI ｊ , I ｋ -σI ｋ The second quantitative value Q of analyte i is calculated as ｉ２ Difference with |Q ｉ２ -Q ｉ１ | is the standard deviation σQ of the theoretical quantitative value of the analyte i ｉ The measured intensity I ｉ , I ｊ , I ｋ When varying the content W of the additional correction component k in the calibration curve formula (2) for the correction component j, ｋ In the above example, the change in the content W of component k is not taken into account.ｋ Considering the change in the measured intensity I ｋ is varied because component k is an overlapping correction component for analyte i in the calibration curve formula (1) for analyte i, but not because component j is an additional correction component for correction component j in the calibration curve formula (2) for correction component j. In this way, the number of measurement intensities to be varied is appropriately limited, so that the theoretical quantitative value standard deviation of analyte i can be determined and displayed within an acceptable time without actually performing repeated analyses and while appropriately incorporating the effects of correction components j and k.

[0033] The quantitative means 13 of the fluorescent X-ray analyzer of this embodiment can also determine the content ratios of components in the samples 1 and 14 by using a fundamental parameter method including overlap correction. In this case, in determining the standard deviation of the theoretical quantitative values, the quantitative means 13 first calculates the measured intensity I for each of a set of components i, as in the case of conventional quantitative means. ｉ Based on this, the content W of each component i in a set is calculated from the known theoretical strength formula for each component i in a set. ｉ Then, the content W of each component i is calculated. ｉ The first quantitative value Q ｉ１ Let's say.

[0034] In the case of the fundamental parameter method, corrections for all components in the sample are taken into consideration regarding absorption and excitation. Furthermore, as described in the background art, overlap corrections are also taken into consideration in the instrument sensitivity curve. Therefore, it is necessary to clarify whether each correction component j is an absorption or excitation component of the analytical line (fluorescent X-ray corresponding to analytical component i), and then calculate the analytical line intensity (measured intensity I ｊ ) of each component i. ｉ１ For a sample composition consisting of ｊ The theoretical analytical line intensity I of the analytical component i when each of Ｔｉｊ Then, calculate the theoretical intensity of this analytical line I Ｔｉｊ is the first quantitative value Q of each component i ｉ１ Theoretical analytical line intensity I for a sample composition consisting of Ｔｉ０If it is larger than j, it is determined that the correction component j excites the analytical line, and if it is smaller than j, it is determined that the correction component j absorbs the analytical line.

[0035] Furthermore, when excited, the analytical line intensity I of the correction component j ｊ is reduced by a predetermined amount, and if it is absorbed, the analytical line intensity I of the correction component j is ｊ Here, the intensity I is increased by a predetermined amount for the analytical lines of all components j except for the analytical component i in the sample. ｊ is varied to obtain the second quantitative value Q ｉ２ Although quantitative calculations may be performed to obtain the content W of the correction component j, ｊ Analysis line intensity I with respect to the change of Ｔｉｊ The calculation time can be reduced by setting a threshold value for the amount of change in the correction component j, and performing quantitative calculations for correction component j with a change amount equal to or less than the threshold value without changing the analysis line of correction component j.

[0036] For example, if the sample contains components i, j, and k, first, the measured intensity I ｉ , I ｊ , I ｋ Using the fundamental parameter method, the content W of each component i, j, k is calculated as the composition in the sample. ｉ , W ｊ , W ｋ The theoretical analytical line intensity of component i in this composition is calculated as I Ｔｉ０ Then, the content rate of j component W ｊ The theoretical intensity is calculated by changing the specified amount, and the theoretical intensity of the analysis line of the i component at that time is I Ｔｉｊ Let's say. Ｔｉｊ Ga I Ｔｉ０ If the intensity is greater than 1, the j component is excited with respect to the analytical line of the i component, so the analytical line intensity I of the corrected component j ｊ The same process is performed for the k component, and the analytical line intensity I of the corrected component k is ｋ Determine whether to increase or decrease by a predetermined amount.

[0037] In summary, the quantitative determination means 13 in the fluorescent X-ray analyzer of this embodiment determines the content W of a component j other than the analyzed component in the theoretical intensity formula for each component i. ｊis increased by a predetermined amount one by one to obtain the theoretical intensity I Ｔｉ increases to or above a predetermined threshold, the measured intensity I for a component j other than the analyte ｊ is varied by decreasing it by a predetermined amount, and the theoretical intensity I Ｔｉ If decreases below a predetermined threshold, the measured intensity I for a component j other than the analyte is ｊ is increased by a predetermined amount.

[0038] Here, the measured intensity I ｉ , I ｊ , I ｋ The predetermined amount to be changed is each measurement intensity I ｉ , I ｊ , I ｋ Theoretical standard deviation σI ｉ , σI ｊ , σI ｋ and the measurement time t ｍｅａｓ Using this, σI = (I / 1000t ｍｅａｓ ) １／２ In addition, the content of component j other than the analyzed component, W ｊ The predetermined amount to be increased is, for example, W ｊ × 0.01, and the theoretical strength I Ｔｉ For example, I Ｔｉ × 1.01 or more, and the theoretical strength I Ｔｉ The predetermined threshold value for I is, for example, Ｔｉ × 0.99 or less.

[0039] Furthermore, the quantification means 15 calculates a set of measured intensities I for each component i. ｉ and the varied measured intensity I for each component i ｉ +σI ｉ or I ｉ -σI ｉ Based on this, the content W of each component i in a set is calculated from the theoretical intensity formula for each component i in a set. ｉ Then, the content W of each component i is calculated. ｉ The second quantitative value Q ｉ２ For each component i, the first quantitative value Q ｉ１ and the second quantitative value Q ｉ２ Difference | Q ｉ２-Q ｉ１ |Theoretical quantitative value standard deviation σQ ｉ is displayed on the display 15.

[0040] According to the X-ray fluorescence analyzer of this embodiment in which the quantitative determination means 13 uses the fundamental parameter method including overlap correction, the quantitative determination means 13 calculates the measured intensity I for each component i. ｉ The first quantitative value Q based on ｉ１ and the theoretical intensity I for the analytical component i in the theoretical intensity formula for each component i Ｔｉ The measurement intensity I has a large effect on ｊ , I ｋ The content W of the analyte i ｉ The second quantitative value Q obtained by varying in the direction of increasing ｉ２ The difference between the theoretical quantitative value and the standard deviation σQ ｉ Therefore, the theoretical quantitative value standard deviation σQ can be calculated by appropriately incorporating the influence of the correction components j and k in an allowable time without actually performing repeated analysis. ｉ can be calculated and displayed.

[0041] Although the preferred embodiment has been described above with reference to the drawings, those skilled in the art will readily understand various changes and modifications within the scope of the present invention, which are within the scope of the present invention as defined by the appended claims.

[0042] 1, 14 Sample 3 Primary X-ray 5 Fluorescent X-ray 13 Quantification means 15 Display

Claims

1. An X-ray fluorescence analyzer that irradiates a sample with primary X-rays and determines the content of a component in the sample by a quantitative means using a calibration curve method that performs absorption excitation correction and overlap correction based on the measured intensity of the generated fluorescent X-rays, wherein the quantitative means: determines the content of the analyte from a calibration curve equation for the analyte and correction component based on the measured intensities of the analyte and correction component, as a first quantitative value; fluctuates the measured intensity of the analyte by a predetermined amount in a direction in which the content of the analyte increases or decreases, in the calibration curve equation for the analyte; fluctuates the measured intensity of the correction component by a predetermined amount in the same direction as the direction in which the measured intensity of the analyte was fluctuated, in the calibration curve equation for the correction component; determines the content of the analyte from the calibration curve equation for the analyte and correction component based on the measured intensities of the analyte and correction component and the fluctuated measured intensities of the analyte and correction component, as a second quantitative value; and displays the difference between the first quantitative value and the second quantitative value on a display as the standard deviation of the theoretical quantitative value.

2. An X-ray fluorescence analyzer which irradiates a sample with primary X-rays, and determines the content of a component in the sample based on the measured intensity of the generated fluorescent X-rays using a quantitative determination means which employs a fundamental parameter method including overlap correction, wherein the quantitative determination means: determines the content of each component from a theoretical intensity formula for each component based on the measured intensity of each component to obtain a first quantitative value; in the theoretical intensity formula for each component, the content of components other than the analytical component is increased by a predetermined amount one by one, and when the theoretical intensity of the analytical component increases to or exceeds a predetermined threshold value, the measured intensity of the component other than the analytical component is decreased by a predetermined amount to vary the content; and when the theoretical intensity of the analytical component decreases to or below the predetermined threshold value, the measured intensity of the component other than the analytical component is increased by a predetermined amount to vary the content; determines the content of each component from the theoretical intensity formula for each component based on the measured intensity of each component and the varied measured intensity of each component to obtain a second quantitative value; and displays the difference between the first quantitative value and the second quantitative value for each component on a display as the standard deviation of the theoretical quantitative value.

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