JP2020160067A - Threshold calculation device, threshold calculation method, and measurement device - Google Patents

Abstract

To accurately calculate a threshold obtained from measurement data consisting of a plurality of measurement values when changing environmental variables without depending on a measurer.SOLUTION: When an environmental variable is changed, which is one of quantities representing the environment where the sample is placed, a plurality of measured values obtained from the sample are acquired, and the acquired measured values are used as the measurement data in association with the value of the environmental variable at that time. By setting the measurement data contained in the same analysis range, in which the environment variables are defined, as a target, the regression analysis by the minimum absolute error method and the regression analysis by the least square method are performed, and a threshold of the measurement data is calculated based on the regression analysis by the minimum absolute error method in an analysis range in which the ratio to the average of an absolute error of an average squared error becomes smaller than a predetermined value.SELECTED DRAWING: Figure 1

Description

The present invention relates to a threshold value calculation device, a threshold value calculation method, and a measurement device, and can be suitably used for calculating a threshold value from measurement data.

In the analysis of physical phenomena, there are many measurement methods for obtaining a threshold value. This is because the threshold value often reflects the physical property value. For example, in Photoelectron Yield Spectroscopy (PYS), the horizontal axis is the excitation energy of ultraviolet rays that irradiate a sample as excitation light, and the vertical axis is the photoelectron yield measured from the sample. The excitation energy at the point where the curve drawn by the measurement data rises sharply is calculated as the threshold. The obtained threshold value is interpreted as the work function or ionization potential of the sample to be measured.

In general, the curve drawn by the measurement data having a threshold value changes according to a function according to physical properties, such as 0 up to the threshold value in an ideal environment, proportional to the value on the horizontal axis, and proportional to the square after exceeding the threshold value. A method is adopted in which the vertical axis is set so that the curve after exceeding the threshold draws a straight line for the measured value itself, the square root of the measured value, etc., and the straight line is extrapolated to obtain the intercept with the horizontal axis as the threshold value. There is.

Patent Document 1 discloses a photoelectron emission threshold measuring device. The surface of the sample is irradiated with light while sequentially changing the wavelength, and the number of photoelectrons emitted is measured. As a prior art, Patent Document 1 states that "at the photoelectron emission start point, the increment of the pulse count (which measures the emitted photoelectrons) is small and it is difficult to accurately determine the emission start point (irradiation). The number of pulse counts for light energy (corresponding to the wavelength of light) is graphed in a linear relationship, and the threshold value is obtained from the intersection when this is extrapolated to the zero count side. " In Patent Document 1, a pulse signal irrelevant to the wavelength of the excitation light is generated and added to the pulse count number caused by photoelectrons, so that an error occurs in the required threshold value (No. 1 of the same document). See Figure 6).

In the invention described in the same document, a pulse count number that takes a constant value regardless of the energy of the excitation light is measured, subtracted from the measured pulse count number, and then matches the relationship of the pulse count number with respect to the excitation energy. The regression function is obtained by the least squares method, and the threshold value is specified (see Fig. 3 of the same document). The measured pulse count is not always proportional to the excitation energy, and the relationship differs depending on the substance. Therefore, the vertical axis is corrected so that the graph becomes a straight line. For example, when the sample is a metal, the vertical axis is the square root (1/2 power) of the pulse count number, and when it is a semiconductor, it is adjusted between 0.4 and 1.0 power. Further, when the sample is composed of a plurality of components, the data processing is performed assuming that the sample is a synthesis of a plurality of regression functions.

Japanese Unexamined Patent Publication No. 1-1838450

As a result of the present inventor examining Patent Document 1, it was found that there are the following new problems.

It has been found that the technique described in Patent Document 1 is not sufficient to absorb the error that actually occurs. As described above, in the technique described in the same document, the graph drawn by the adjusted and converted vertical axis and horizontal axis is smaller than the threshold value by adjusting the pulse count number as the vertical axis depending on the difference in substances. In the region, the slope is 0, and in the region larger than the threshold value, it becomes a straight line. In addition, when a plurality of components are included, data processing is performed on the premise that the characteristics appearing by each component are straight lines. That is, the characteristic curve that the conventional technique presupposes is a polygonal line with a threshold value in between. The region smaller than the threshold value and the region larger than the threshold value of the graph are approximated by straight lines, and the intersection is specified as the threshold value. Random noise is included in the actual measurement, and its characteristics can be approximated by the sigmoid curve. The threshold corresponds to the inflection point of the sigmoid curve.

Generally, in the measurement for obtaining the threshold value, another physical quantity when one physical quantity is changed is measured, and the relationship between the measured physical quantity and the changed physical quantity is expressed by the above-mentioned characteristic curve to obtain the threshold value. The physical quantity to be changed is called an influence variable, the measured physical quantity is called a measured value, and the corresponding pair of the value of the influence variable and the measured value is called the measurement data. The influence variable is a physical quantity that represents the environment in which the sample to be measured is placed, and affects the physical quantity that is the measured value. For example, in the photoelectron emission measurement disclosed in Patent Document 1, the light energy corresponding to the wavelength of the light irradiating the sample is the influence variable, and the number of emitted photoelectrons is the measured value. In addition, for example, there is a threshold value in the relationship of current with respect to voltage in semiconductor junction, voltage is an influence variable, and current is a measured value. As described above, there are many things having a threshold value in the relationship between the influence variable and the measured value.

The present inventor has studied a threshold value calculation method and a threshold value calculation device that can be universally applied to a measurement method for obtaining a threshold value from the relationship between an influence variable and a measured value.

As a result of the examination by the present inventor, it was found that the linear approximation of the measured value in the region where the influence variable is larger than the threshold value tends to have a large error, and as a result, the accuracy of the required threshold value is lowered. As described above, instead of directly setting the measured value to the vertical axis, the measured value adopts the vertical axis converted so that the graph becomes a straight line. The physical phenomenon that is the basis of such conversion has a remarkable effect on the measured value near the threshold value, but the influence of other physical phenomena becomes stronger as the distance from the threshold value increases, and the physical phenomenon that is the basis of the conversion becomes stronger. It is thought that this is because it is no longer dominant. Therefore, it was found that it is not always clear in which range of the horizontal axis (influence variable) the approximation should be performed. In addition, even when approximating with a sigmoid curve, a systematic error that increases as the distance from the threshold (inflection point) increases is superimposed, and in what range of the horizontal axis (influence variable) the approximation should be performed. It turns out that it is not always clear. Due to this background, in actual measurement, the value of the required threshold value varies depending on the knowledge and experience of the measurer who analyzes the measurement data, and even if the measurement data is the same, the required threshold value It turned out that the accuracy was reduced.

An object of the present invention is to improve the accuracy of the obtained threshold value in the measuring method for obtaining the threshold value. Furthermore, it is to eliminate the element that depends on the person who analyzes the measurement data.

Means for solving such problems will be described below, but other problems and novel features will become apparent from the description and accompanying drawings herein.

According to one embodiment of the present invention, it is as follows.
That is, it is a threshold value calculation device including a measurement unit and a control calculation unit, and is configured as follows.

When the environment variable, which is one of the quantities representing the environment in which the sample is placed, is changed, the measurement unit acquires a plurality of measurement values obtained from the sample and supplies them to the control calculation unit. The measured data is obtained by associating the supplied multiple measured values with the values of the environment variables at that time. The control calculation unit performs regression analysis by the least absolute error method and regression analysis by the least squares method on the measurement data included in the same analysis range defined for the environmental variables, and averages the absolute error of the square root of the square error. In the analysis range where the ratio to is smaller than the predetermined value, the threshold value of the measurement data is calculated based on the regression analysis by the least absolute error method.

The effects obtained by the above embodiment will be briefly described as follows.
That is, it is possible to provide a measuring device provided with a threshold value calculating means capable of accurately obtaining a threshold value obtained from measurement data consisting of a plurality of measured values when environment variables are changed, and the knowledge of the measurer and It is possible to calculate the threshold value that does not depend on experience.

FIG. 1 is a block diagram showing a configuration example of the threshold value calculation device according to the first embodiment. FIG. 2 is a flowchart showing a configuration example of the threshold value calculation method according to the second embodiment. FIG. 3 is a block diagram showing a configuration example of the measuring device according to the third embodiment. FIG. 4 is an explanatory diagram of the operation of the threshold value calculation device according to the first embodiment before narrowing the analysis range. FIG. 5 is an explanatory diagram of the operation of the threshold value calculation device according to the first embodiment after the analysis range is narrowed. FIG. 6 is a block diagram showing a configuration example of the threshold value calculation device according to the fourth embodiment. FIG. 7 is a flowchart showing a configuration example of the threshold value calculation method according to the fifth embodiment. FIG. 8 is a block diagram showing a configuration example of the measuring device according to the sixth embodiment. FIG. 9 is a block diagram showing a configuration example of the threshold value calculation device according to the seventh embodiment. FIG. 10 is a flowchart showing a configuration example of the threshold value calculation method according to the eighth embodiment. FIG. 11 is a block diagram showing a configuration example of the measuring device according to the ninth embodiment. FIG. 12 is a map diagram showing the implementation results according to the first embodiment.

1. 1. Outline of Embodiment First, an outline of a typical embodiment disclosed in the present application will be described. Reference numerals in the drawings referenced in parentheses in the schematic description of a typical embodiment merely exemplify those included in the concept of the component to which it is attached.

[1] <Threshold calculation device that performs regression analysis with a limited range based on the ratio of the square roots of the absolute error and the square error>
In a typical embodiment of the present invention, when an environmental variable, which is one of the quantities representing the environment in which the sample is placed, is changed, the measured value obtained from the sample is associated with the environmental variable at that time. It is a threshold calculation device (10) that calculates a threshold (9) from the measurement data (8) configured in the above, and is an input unit (7), a measurement data conversion unit (6), and a regression analysis range designation unit (3). ), The first and second regression analysis units (1, 2), the error evaluation unit (4), and the threshold calculation unit (5), and are configured as follows.

The measurement data conversion unit can generate conversion data composed of a plurality of conversion values by performing a predetermined conversion process on the plurality of measurement values input to the input unit.

The regression analysis range designation unit can specify an analysis range which is a range of environment variables in the first and second regression analysis units.

The first regression analysis unit performs regression analysis by the minimum absolute error method on the transformation data in the analysis range to obtain the first regression function, and the difference between the predicted value by the first regression function and the transformation data. The first error (MAE) can be calculated by averaging the absolute values of in the analysis range.

The second regression analysis unit performs regression analysis by the least squares method on the converted data in the analysis range to obtain a second regression function, and determines the difference between the predicted value by the second regression function and the converted data. The second error (RMSE) can be calculated by averaging the squared values in the analysis range and taking the square root.

The error evaluation unit compares the ratio of the second error to the first error with a predetermined value, and when the error ratio is larger than the predetermined value, the regression analysis range designation unit tells the environmental variable in the analysis range. The analysis range can be changed so as to reduce the upper end of the above, and the first and second regression analysis units can perform regression analysis in the changed analysis range, respectively.

The threshold value calculation unit can calculate the threshold value based on the first regression function when the error ratio becomes smaller than the predetermined value.

As a result, the accuracy of the threshold value obtained from the measurement data consisting of a plurality of measured values when the environment variable is changed can be improved, and the threshold value can be calculated without depending on the knowledge and experience of the measurer.

[2] <Error ratio RMSE / MAE = r <SQRT (2)>
In the threshold value calculation device of the item [1], the predetermined value is 1.414. Here, the theoretical value suitable as the predetermined value is the square root of 2, but when it is adopted for actual measurement including significant figures, it is adjusted in consideration of the error generated in the measurement. This also applies to the following items [6] and [10].

Thus, errors mean 0, when following Laplace distribution of the dispersed 2 [phi ^2, it is possible to eliminate the influence of measurement values that deviate greatly from the regression function, it is possible to improve the accuracy of the determined threshold.

[3] <Error ratio RMSE / MAE = r <SQRT (pi / 2)>
In the threshold value calculation device of the item [1], the predetermined value is 1.253. Here, the theoretical value appropriate as the predetermined value is the square root of half of the circumference ratio, but when it is adopted for actual measurement including significant figures, the error generated in the measurement is taken into consideration. Is adjusted. This also applies to the following items [7] and [11].

As a result, when the error follows a normal distribution with an average of 0 and a standard deviation σ, the influence of the measured value that greatly deviates from the regression function can be eliminated, and the accuracy of the required threshold value can be improved.

[4] <Photoelectron yield spectroscopy>
In the threshold value calculation device according to any one of items [1] to [3], the environment variable is the energy of the light applied to the sample (23), and the measured value is emitted from the sample. This is the photoelectron yield detected by the detector (Fig. 3).

Thereby, it is possible to provide a threshold value calculation device for calculating the threshold value from the measurement data measured by the photoelectron yield spectroscopy. At this time, the threshold value corresponds to the work function or ionization energy of the sample.

[5] <Threshold calculation method for performing regression analysis with a limited range based on the ratio of the square roots of the absolute error and the square error>
In a typical embodiment of the present invention, when an environmental variable, which is one of the quantities representing the environment in which the sample is placed, is changed, a plurality of measured values obtained from the sample are used as the environmental variable at that time. It is a threshold calculation method for calculating a threshold from the measurement data configured in association with each other, and is a measurement data input step (S1), a measurement data conversion step (S2), a regression analysis range designation step (S3), and a first. And the second regression analysis step (S4, S6), the first and second error calculation steps (S5, S7), the error ratio calculation step (S8), the error ratio determination step (S9), and the regression analysis range change. A step (S10) and a threshold calculation step (S11) are provided (FIG. 2).

In the measurement data input step, the plurality of measured values are input, and in the measurement data conversion step, a predetermined conversion process is performed on the plurality of measured values to generate conversion data composed of the plurality of converted values.

In the regression analysis range designation step, an analysis range which is a range of environment variables in the first and second regression analysis steps is designated. In the first regression analysis step, the transformation data in the analysis range is subjected to regression analysis by the minimum absolute error method to obtain a first regression function, and in the first error calculation step, prediction by the first regression function is performed. The first error is calculated by averaging the absolute value of the error between the value and the conversion data in the analysis range.

In the second regression analysis step, the transformation data in the analysis range is subjected to regression analysis by the least squares method to obtain a second regression function, and in the second error calculation step, the predicted value by the second regression function is obtained. The second error is calculated by averaging the squared value of the error between and the conversion data in the analysis range and taking the square root.

In the error ratio calculation step, the ratio of the second error to the first error is obtained and used as an error ratio, and in the error ratio determination step, the error ratio is compared with a predetermined value.

In the regression analysis range change step, the first and second regression analysis steps are performed while changing the analysis range to reduce the upper end of the environment variable in the analysis range until the error ratio becomes smaller than the predetermined value. , The first and second error calculation steps and the error ratio calculation step are repeated.

In the threshold value calculation step, when the error ratio becomes smaller than the predetermined value, the threshold value is calculated based on the first regression function.

As a result, as in item [1], the accuracy of the threshold value obtained from the measurement data consisting of a plurality of measured values when the environment variable is changed can be improved, and the threshold value does not depend on the knowledge and experience of the measurer. Can be calculated.

[6] <Error ratio RMSE / MAE = r <SQRT (2)>
In the threshold value calculation method of item [5], the predetermined value is 1.414.

Thus, errors mean 0, when following Laplace distribution of the dispersed 2 [phi ^2, it is possible to eliminate the influence of measurement values that deviate greatly from the regression function, it is possible to improve the accuracy of the determined threshold.

[7] <Error ratio RMSE / MAE = r <SQRT (pi / 2)>
In the threshold value calculation method of item [5], the predetermined value is 1.253.
As a result, when the error follows a normal distribution with an average of 0 and a standard deviation σ, the influence of the measured value that greatly deviates from the regression function can be eliminated, and the accuracy of the required threshold value can be improved.

[8] <Photoelectron yield spectroscopy>
In the threshold value calculation method of any one of items [5] to [7], the environment variable is the energy of the light applied to the sample (23), and the measured value is emitted from the sample and detected. The photoelectron yield detected by the vessel (26) (Fig. 3).

Thereby, it is possible to provide a threshold value calculation method for calculating the threshold value from the measurement data measured by the photoelectron yield spectroscopy. At this time, the threshold value corresponds to the work function or ionization energy of the sample.

[9] <Measuring device>
A typical embodiment of the present invention is a measuring device (20) including a measuring unit (21) and a control calculation unit (11), and is configured as follows.

The measuring unit can acquire a plurality of measured values obtained from the sample (23) and supply them to the control calculation unit. The control calculation unit measures a plurality of measured values obtained when an environment variable, which is one of the quantities representing the environment in which the sample is placed, is associated with the value of the environment variable at that time. It can be acquired as data. The control calculation unit has a first regression analysis (1) for obtaining a first regression function that minimizes an absolute error, and a square error for the measurement data included in the same analysis range defined for the environment variable. The second regression analysis (2) for obtaining the minimum second regression function is performed. The control calculation unit is in an analysis range in which the ratio of the square root (RMSE) of the mean square error in the second regression analysis to the average of the absolute error (MAE) in the first regression analysis is smaller than a predetermined value. The threshold of the measurement data can be calculated based on the one regression function (FIG. 3).

This makes it possible to provide a measuring device provided with a threshold value calculating means capable of accurately obtaining a threshold value obtained from measurement data consisting of a plurality of measured values when environment variables are changed, and depends on the measurer. It is possible to calculate the threshold value that does not exist.

[10] <Error ratio RMSE / MAE = r <SQRT (2)>
In the measuring device of item [9], the predetermined value is 1.414.

Thus, errors mean 0, when following Laplace distribution of the dispersed 2 [phi ^2, it is possible to eliminate the influence of measurement values that deviate greatly from the regression function, it is possible to improve the accuracy of the determined threshold.

[11] <Error ratio RMSE / MAE = r <SQRT (pi / 2)>
In the measuring device of item [9], the predetermined value is 1.253.

As a result, when the error follows a normal distribution with an average of 0 and a standard deviation σ, the influence of the measured value that greatly deviates from the regression function can be eliminated, and the accuracy of the required threshold value can be improved.

[12] <Photoelectron Yield Spectrometer>
In the measuring device (20) according to any one of items [9] to [11], the environment variable is the energy of the light applied to the sample (23), and the measured value is emitted from the sample. The photoelectron yield detected by the detector (26) (Fig. 3).

As a result, it is possible to provide a threshold value calculation means capable of automatically calculating the threshold value with high accuracy in the photoelectron yield spectroscope that calculates the threshold value from the measurement data measured by the photoelectron yield spectroscopy. At this time, the threshold value corresponds to the work function or ionization energy of the sample.

2. 2. Details of Embodiments The embodiments will be described in more detail.

[Embodiment 1]
FIG. 1 is a block diagram showing a configuration example of the threshold value calculation device according to the first embodiment.

The threshold calculation device 10 according to the first embodiment includes an input unit 7 into which measurement data 8 is input, a measurement data conversion unit 6, a regression analysis range designation unit 3, and a regression analysis unit 1 and a minimum two by the minimum absolute error method. It includes a regression analysis unit 2 by the multiplication method, an error evaluation unit 4, and a threshold value calculation unit 5, and outputs a threshold value 9. The measurement data 8 is a plurality of pairs in which the measured values obtained from the sample when the environment variable, which is one of the quantities representing the environment in which the sample is placed, are changed, are associated with the environment variable at that time. It is configured.

The measurement data conversion unit 6 generates conversion data composed of a plurality of conversion values by performing a predetermined conversion process on the plurality of measurement values input from the input unit 7. The predetermined conversion process is a conversion for matching the relationship of the measured values with respect to the influence variable to the regression function of the regression analysis adopted in the latter stage. For example, in the prior art disclosed in Patent Document 1, when the sample is a metal in order to perform a regression analysis that approximates the relationship of the pulse count number, which is a measured value to the light energy, which is an influential variable, to a linear function. The vertical axis is the square root (1/2 power) of the pulse count number, and in the case of a semiconductor, it is adjusted between 0.4 and 1.0 power.

The regression analysis unit 1 by the minimum absolute error method performs regression analysis by the minimum absolute error method in the analysis range which is the range of the environment variables specified by the regression analysis range designation unit 3, and obtains the absolute error MAE. Absolute error MAE is the absolute value of the difference between the predicted value by the regression function obtained by the regression analysis unit 1 by the minimum absolute error method and the converted data output from the measurement data conversion unit 6 in the specified analysis range. It is an average value.

The regression analysis unit 2 by the least squares method performs regression analysis by the least squares method in the same analysis range specified by the regression analysis range designation unit 3 to obtain the square root RMSE of the square error. The square root RMSE of the squared error is the average of the squared values of the difference between the predicted value by the regression function obtained by the regression analysis unit 2 by the least squares method and the converted data output from the measurement data conversion unit 6 in the analysis range. It is the square root of the value.

The error evaluation unit 4 compares the ratio (error ratio) of the square root RMSE of the squared error to the absolute error MAE with a predetermined value. When the error ratio is larger than the predetermined value, the regression analysis range specification unit 3 changes the analysis range so as to reduce the upper end of the environmental variable, and the regression analysis unit 1 by the minimum absolute error method and the regression analysis by the least squares method. Part 2 performs regression analysis in each of the modified analysis ranges. Along with this, the values of the absolute error MAE and the square root RMSE of the square error are updated. This process is repeated while gradually narrowing the analysis range until the error ratio, which is the ratio of the square root RMSE of the squared error to the absolute error MAE, becomes equal to or less than a predetermined value.

When the error ratio becomes equal to or less than a predetermined value, the threshold value calculation unit 5 calculates the threshold value 9 by using the regression function obtained by the regression analysis by the minimum absolute error method.

By appropriately determining a predetermined value for the ratio of the square root RMSE of the squared error to the absolute error MAE in the error evaluation unit 4, the threshold value obtained from the measurement data consisting of a plurality of measured values when the environment variables are changed. The accuracy can be improved.

For example, if the error follows a normal distribution with mean 0 and standard deviation σ, it is preferable to set the predetermined value to 1.253, and if the error follows a Laplace distribution with mean 0 and variance 2φ ² , the predetermined value is 1.414. Suitable. This is because the influence of the measured value that greatly deviates from the regression function can be eliminated, and the accuracy of the required threshold value can be improved. The above-mentioned 1.253 is theoretically the square root of half of the pi, and 1.414 is theoretically the square root of 2, but when it is used for actual measurement including significant figures, it should be noted. Should be adjusted in consideration of the error that occurs in the measurement.

[Principle for determining analysis range in threshold calculation of the present invention]
The principle of determining the analysis range in the threshold calculation of the present invention will be described.

Regression analysis includes the least absolute error method and the least squares method. The least absolute error method is a prediction method that minimizes the average of the absolute values of the errors of the predicted values y _p with respect to the measured value y _o , and the least squares method is a prediction method that minimizes the average value of the squares of the errors. The absolute error MAE and the square root RSME of the squared error are expressed by Equations 1 and 2 below, respectively. Here, n is the number of measurement data in the analysis range. N measurement values are input corresponding to n influence variable values, and n pairs of measurement data are obtained. The measured value y _o corresponds to the above-mentioned conversion data. The predicted value y _p is a value obtained by substituting the same influence variable value into the regression function.

Here, the absolute value e _i of the error is expressed by the following equation 3, so if equations 1 and 2 are rewritten using this, the equations 4 and 5 are obtained, respectively.

Since the absolute value e _{i of the} error takes only 0 or more, the mean MEAN (e _i ) is equal to the absolute error MAE (Equation 6), and the variance VAR (e _i ) is the variance derivation using the second moment and the first moment. According to the formula of, it is calculated as in Equation 7.

Using the above relationship, the ratio of the square root RMSE of the squared error to the absolute error MAE (error ratio) can be expressed as in Equation 8.

If the error follows a normal distribution with mean 0 and standard deviation σ, then the distribution of the absolute values e _i of the error is the distribution of the absolute values of the normal distribution. The probability density function pdf is expressed by Equation 9 below.

In this case, the mean MEAN (e _i ) and standard deviation VAR (e _i ) of the absolute values of the errors are expressed by equations 10 and 11 below.

Using the above relationship, the ratio of the square root RMSE of the squared error to the absolute error MAE (error ratio) can be expressed as in Equation 12 below.

When a good model can be constructed, the model represents the general characteristics of the data, and only the noise that follows the normal distribution remains as an error. In that case, it can be seen that the ratio (error ratio) of RMSE and MAE in the analysis result is close to 1.253.

When the probability density function follows the Laplace distribution defined by the equation below, the mean of the error is 0 and the variance is 2φ ² .

At this time, the ratio of the square root RMSE of the squared error to the absolute error MAE (error ratio) can be expressed by the following equation 14.

If the ratio of the square root RMSE of the squared error to the absolute error MAE (error ratio) exceeds 1.414, there may be data that is far from the prediction.

As described above, in a measurement system where the noise is only random noise and the error follows a normal distribution, 1.253 should be set as a predetermined value, and when sudden noise is included, the error follows the Laplace distribution. Since it is possible, it can be seen that 1.414 should be set as a predetermined value. However, since these values are theoretically derived values according to various assumptions in the derivation process, they are effective in consideration of the influence of systematic noise that is known to exist in an actual measurement system. It is advisable to make adjustments according to the actual situation, such as adjusting the number of digits of numbers.

The absolute error MAE and the square root RMSE of the squared error were adopted as the error evaluation method in the regression analysis for the following reasons. That is, the absolute error MAE reduces the weighting of the error evaluation as the error increases with respect to the square root RMSE of the square error. The square root of the squared error RMSE squared is expressed by Equation 15 below.

When the absolute error MAE is rewritten using this relationship, it becomes as shown in Equation 16 below.

In this way, the absolute error MAE is expressed in the form of being weighted by the inverse of the absolute value of the error y _{o −} y _p with respect to the square of the square root RMSE of the squared error, and the larger the error, the smaller the weight of the error evaluation. It has become a thing.

[Operation of threshold calculation device]
The operation of the threshold value calculation device 10 in the first embodiment will be described. 4 and 5 are explanatory views of the operation of the threshold value calculation device 10 in the first embodiment, FIG. 4 is before narrowing the analysis range, and FIG. 5 is after narrowing the analysis range. FIGS. 4 and 5 are graphs in which the influence variable is on the horizontal axis x and the conversion data obtained by performing a predetermined conversion process on the measured value is the vertical axis y. The regression function obtained by the regression analysis and the curve 32 are the regression functions obtained by the regression analysis by the least squares method. The intersection with the x-axis when the straight line portion of the curve 31 is extended in the x-axis direction is the threshold 33 obtained by the minimum absolute error method, and the intersection with the x-axis when the straight line portion of the curve 32 is extended in the x-axis direction. The intersection is the threshold 34 obtained by the least squares method. As shown in FIG. 4, when the analysis range is not limited, the curve 32 of the regression function by the least squares method is relatively faithful to the region where the influence variable x is larger than the curve 31 of the regression function by the least absolute error method. Is approximated to fit the measured data. This is because, as described above, the larger the error is, the smaller the weighting of the error evaluation is with respect to the square root RMSE of the square error. As a result, the threshold value 34 obtained by the least squares method is a value larger than the threshold value 33 obtained by the minimum absolute error method.

When the analysis range is gradually narrowed until the error ratio, which is the ratio of the square root RMSE of the squared error to the absolute error MAE, becomes less than a predetermined value, as shown in FIG. 5, the curve 32 of the regression function by the least squares method and the minimum absolute The deviation of the regression function by the error method from the curve 31 becomes small, and the deviation between the calculated thresholds 33 and 34 also becomes small. The repetition is completed when the error ratio becomes smaller than the predetermined value defined based on the assumed noise, and the threshold value is calculated using the regression function obtained by the regression analysis by the minimum absolute error method.

In this way, the range of regression analysis is narrowed to an appropriate range, the influence of measurement data away from the threshold value, which tends to increase the error, is suppressed, and the threshold value can be calculated with high accuracy. In addition, the calculation is automatically performed without depending on the experience and ability of the measurer.

The threshold value calculation device 10 can be implemented as an operation of a program installed in a processor built in the measurement device. Some or all of its functionality may be implemented as dedicated hardware. The threshold value calculation device 10 can be incorporated into various measuring devices. For example, it may be provided to the measurer as an additional function of the input / output interface. Further, as described above, since the threshold value calculation device of the present invention can be automatically executed without depending on the measurer, it can be increased by incorporating the threshold value into a mass production process that uses the threshold value as an index of quality control. It is possible to enable quality and efficient process control.

[Embodiment 2]
Since the threshold value calculation device 10 of the present invention can be functionally constructed as the operation of a program installed in the processor, the present invention can be positioned as a threshold value calculation method using a hardware system including a storage device and a computer. it can.

FIG. 2 is a flowchart showing a configuration example of the threshold value calculation method according to the second embodiment.

The threshold calculation method of the present invention is implemented by software operating on a computer including a storage device, and includes a measurement data input step (S1), a measurement data conversion step (S2), a regression analysis range designation step (S3), and the like. First and second regression analysis steps (S4, S6), first and second error calculation steps (S5, S7), error ratio calculation step (S8), error ratio determination step (S9), and regression analysis. A range changing step (S10) and a threshold calculation step (S11) are provided. As an example of the first and second regression analysis, as illustrated in FIG. 2, the first regression analysis step (S4) is a regression analysis by the minimum absolute error method, and the first error calculation step (S5) is an absolute error (MAE). The second regression analysis step (S6) can be the regression analysis by the minimum square method, and the second error calculation step (S7) can be the square root (RMSE) of the squared error.

The measurement data input in the measurement data input step (S1) is a plurality of measurement values obtained from the sample when the environment variable, which is one of the quantities representing the environment in which the sample is placed, is changed. It is configured in association with the environment variables of.

In the measurement data conversion step (S2), conversion data composed of a plurality of conversion values is generated by performing a predetermined conversion process on the plurality of measurement values constituting the input measurement data. Since the predetermined conversion process is the same as the content described in the first embodiment, detailed description thereof will be omitted.

In the regression analysis range designation step (S3), the same analysis range is designated for the regression analysis step (S4) by the least absolute error method and the regression analysis step (S6) by the least squares method.

In the regression analysis step (S4) by the minimum absolute error method, the transformation data supplied from the measurement data conversion step (S2) is subjected to regression analysis by the minimum absolute error method to obtain the first regression function. In the absolute error (MAE) calculation step (S5), the absolute error (MAE) is calculated by averaging the absolute value of the difference between the predicted value obtained by the first regression function and the converted data in the specified analysis range.

In the regression analysis step (S6) by the least squares method, the regression analysis by the least squares method is performed on the conversion data supplied from the measurement data conversion step (S2) to obtain the second regression function. In the calculation step (S7) of the square root (RMSE) of the square error, the square root of the difference between the predicted value by the second regression function and the converted data is averaged in the specified analysis range to take the square root. Calculate the square root (RMSE) of.

In the error ratio calculation step (S8), the ratio of the square root (RMSE) of the squared error to the absolute error (MAE) is obtained and used as the error ratio r, and the error ratio r is compared with the predetermined value in the error ratio determination step (S9).

Regression by the least absolute error method and the least squares method while changing the analysis range to reduce the upper end of the environmental variable in the analysis range in the regression analysis range change step (S10) until the error ratio r becomes smaller than the predetermined value. The analysis step (S4, S6), the calculation step (S5, S7) of the square root (RMSE) of the absolute error (MAE) and the square error, and the error ratio calculation step (S8) are repeated.

In the threshold value calculation step (S11), when the error ratio r becomes smaller than a predetermined value, the threshold value is calculated based on the first regression function obtained by the regression analysis by the minimum absolute error method.

As a result, the accuracy of the threshold value obtained from the measurement data consisting of a plurality of measured values when the environment variable is changed can be improved, and the threshold value can be calculated without depending on the knowledge and experience of the measurer.

From the measurement data consisting of a plurality of measured values when the environmental variables are changed by appropriately determining the predetermined value for the error ratio r of the square root RMSE of the square root of the squared error with respect to the absolute error MAE in the error ratio determination step (S9). The accuracy of the required threshold can be improved. Similar to the first embodiment, when the error follows a normal distribution with an average of 0 and a standard deviation σ, it is preferable to set the predetermined value to 1.253, and when the error follows a Laplace distribution with an average of 0 and a variance of 2φ ² , it is predetermined. A value of 1.414 is preferred.

[Embodiment 3]
As described in the first embodiment, the threshold value calculation device 10 of the present invention can be incorporated into various measuring devices.

FIG. 3 is a block diagram showing a configuration example of the measuring device according to the third embodiment. The example shown in FIG. 3 is a photoelectron yield spectroscope.

The measuring device 20 includes a measuring unit 21 and a control calculation unit 11.

The measurement unit 21 can acquire a plurality of measured values obtained from the sample and supply them to the control calculation unit 11, and the control calculation unit 11 is an environment which is one of the quantities representing the environment in which the sample is placed. It is possible to acquire a plurality of measured values obtained when the variables are changed as measurement data in association with the values of the environment variables at that time.

The measuring unit 21 for performing photoelectron yield spectroscopy includes a sample stage 22 for holding the sample 23, an ultraviolet light source 24, a spectroscope 25, and a photoelectron detector 26. The spectroscope 25 can be mounted using, for example, a diffraction grating, and irradiates the sample 23 with light having a specific wavelength from the ultraviolet rays emitted from the ultraviolet light source 24. The angle of the diffraction grating that defines the wavelength is controlled by the control calculation unit 11. The photoelectron detector 26 is configured to count, for example, the number of photoelectrons amplified by a photomultiplier tube by a counter. Since the wavelength of the ultraviolet ray irradiating the sample 23 is specified by the spectroscope 25, the photoelectron yield emitted is measured corresponding to the wavelength. The light energy corresponding to the wavelength is the influence variable, the photoelectron yield is the measured value, and the pair is the measured data.

The control calculation unit 11 for performing photoelectron yield spectroscopy includes an irradiation light control unit 13 including a wavelength control unit 14 and a photoelectron yield measurement unit 12. The irradiation light control unit 13 controls the ultraviolet light source 24 of the measurement unit 21, and the wavelength control unit 14 controls the spectroscope 25 to control the wavelength of the light emitted to the sample 23. The photoelectron yield measuring unit 12 is connected to the photoelectron detector 26 of the measuring unit 21 to acquire the measured photoelectron yield.

In addition to this, the control calculation unit 11 may be configured to include the same means as the threshold value calculation device 10 described in the first embodiment, and FIG. 3 illustrates the configuration. However, the configuration is not limited to that. The control calculation unit 11 illustrated in FIG. 3 further includes a measurement data conversion unit 6, a regression analysis range designation unit 3, a regression analysis unit 1 by the least absolute error method, a regression analysis unit 2 by the least squares method, and an error evaluation unit 4. And the threshold calculation unit 5.

The measurement data conversion unit 6 performs a predetermined conversion process on the photoelectron yield input from the photoelectron yield measurement unit 12 to generate conversion data. Here, the predetermined conversion process is a conversion for matching the relationship of the measured value with respect to the influence variable to the regression function of the regression analysis, as described in the first embodiment, and in the example of the present photoelectron yield spectroscopic measurement, Similar to the prior art disclosed in Patent Document 1, when the sample is a metal in order to perform regression analysis that approximates the relationship of the pulse count number, which is a measured value to the light energy, which is an influential variable, to a linear function. The vertical axis is the square root (1/2 power) of the pulse count number, and in the case of a semiconductor, it may be adjusted between 0.4 and 1.0 power.

The regression analysis unit 1 by the minimum absolute error method and the regression analysis unit 2 by the least squares method perform their respective regression analysis in the same analysis range specified by the regression analysis range designation unit 3. The analysis range at this time is specified by the irradiation light control unit 13 for the wavelength defined by the wavelength control unit 14, that is, the light energy. Since the following configuration and operation are the same as those described with reference to FIG. 1 in the first embodiment, the repeated description will be omitted.

As a result, it is possible to provide a threshold value calculation means capable of automatically calculating the threshold value with high accuracy in the photoelectron yield spectroscope that calculates the threshold value from the measurement data measured by the photoelectron yield spectroscopy. At this time, the threshold value corresponds to the work function or ionization energy of the sample.

Further, the accuracy of the threshold can be improved by appropriately determining a predetermined value for the error ratio, which is the same as that of the first embodiment. For example, when the error follows a normal distribution with an average of 0 and a standard deviation σ. is preferable to a 1.253 a predetermined value, the average error is 0, when following Laplacian distribution of the dispersed 2 [phi ² is suitable when the predetermined value is 1.414.

The example shown in FIG. 3 is a photoelectron yield spectroscope, but the same configuration can be widely applied to other measuring devices. Similarly, in other measuring devices, the measuring device 20 may include a measuring unit 21 and a control calculation unit 11. The measurement unit 21 is configured so that a plurality of measured values obtained from the sample can be acquired and supplied to the control calculation unit 11, and the control calculation unit 11 is a quantity 1 representing the environment in which the sample is placed. It is configured so that a plurality of measured values obtained when one environment variable is changed can be acquired as measurement data in association with the value of the environment variable at that time. The control calculation unit 11 performs a regression analysis by the least absolute error method and a regression analysis by the least squares method on the measurement data included in the same analysis range defined for the environment variables. The control calculation unit 11 sets the threshold value of the measured data based on the regression function by the least absolute error method in the analysis range in which the ratio of the mean square error by the least squares method to the absolute error by the minimum absolute error method is smaller than a predetermined value. Can be calculated.

As a result, even in a general measuring device, a measuring device provided with a threshold value calculating means capable of accurately obtaining a threshold value obtained from measurement data consisting of a plurality of measured values when an environment variable is changed is provided. It is possible to calculate the threshold value that does not depend on the measurer.

Also, that it is possible to improve the threshold accuracy by properly determining that the predetermined value for the error ratio are the same as in Embodiment 1, for example, an error average 0, when following Laplacian distribution of the dispersed 2 [phi ² Is preferably 1.414 as the predetermined value, and 1.253 as the predetermined value when the error follows a normal distribution with an average of 0 and a standard deviation σ.

[Embodiment 4]
FIG. 6 is a block diagram showing a configuration example of the threshold value calculation device according to the fourth embodiment.

The threshold calculation device 50 according to the fourth embodiment includes an input unit 7 into which measurement data 8 is input, a measurement data conversion unit 6, a regression analysis unit 101, an error evaluation unit 102, a regression analysis range designation unit 103, and the like. The regression analysis range determination unit 104 and the threshold value calculation unit 105 are provided, and the threshold value 9 is output. Here, the measurement data conversion unit 6, the input unit 7, and the measurement data 8 are all the same as those in the first embodiment.

The regression analysis unit 101 performs regression analysis by the minimum absolute error method on the transformation data in the analysis range to obtain the first regression function, and finds the difference between the first predicted value by the first regression function and the transformation data. The first error is calculated by averaging the absolute values in the analysis range, and the square root is taken by averaging the squared difference between the first predicted value and the converted data in the analysis range. The error can be calculated.

Alternatively, the transformation data in the analysis range is subjected to regression analysis by the least squares method to obtain the second regression function, and the squared difference between the second predicted value by the second regression function and the transformation data is analyzed. The third error is calculated by averaging over the range and taking the square root, and the fourth error is calculated by averaging the absolute value of the difference between the second predicted value and the converted data in the analysis range. Can be done.

The error evaluation unit 102 obtains the first error ratio, which is the ratio of the second error to the first error, or the second error ratio, which is the ratio of the third error to the fourth error, and obtains the first error ratio. The error ratio or the second error ratio is compared with the predetermined value, and when the error ratio is larger than the predetermined value, the regression analysis range designation unit is made to change the analysis range so as to reduce the upper end of the environmental variable in the analysis range. The regression analysis unit can execute regression analysis in the changed analysis range.

The regression analysis range designation unit 103 can specify an analysis range which is a range of environment variables in the regression analysis unit 101. Specifically, the upper limit of the range of regression analysis can be reduced.

The regression analysis range determination unit 104 can be designated as an indefinite value 110 in the analysis range designated by the regression analysis range designation unit 103. Specifically, when the analysis range is smaller than the specified value, it is determined that the value is indefinite 110.

The threshold value calculation unit 105 can calculate the threshold value based on the first regression function when the first error ratio becomes smaller than a predetermined value. Alternatively, when the second error ratio becomes smaller than the predetermined value, the threshold value can be calculated based on the second regression function.

In the fourth embodiment, the operations of the regression analysis unit 101 and the error evaluation unit 102 are performed as described above, so that (1) when the number of data points is small, (2) when there is a lot of noise as a whole, and (3) error. When the absolute value of is large, (4) it becomes a device for calculating a highly accurate threshold even in the case of an average error (uniform distribution error).

When (1) to (4) are concerned, it is preferable that the regression analysis unit 101 executes the above-mentioned first regression function, the first error, and the second error. That is, it is preferable to use the minimum absolute value error method for regression analysis in order to avoid the problems (1) to (4).

Further, in the fourth embodiment, (5) when there is a large noise even if the analysis range is reduced, for example, there is a large noise on the background side of low energy, optimization is performed even if the analysis range is reduced. Since the process does not proceed, the regression analysis range determination unit 104 has an effect of setting a lower limit of the analysis range reduction in advance, determining that the permissible value is indefinite 110, and alerting the user.

[Embodiment 5]
Since the threshold value calculation device 50 of the present invention can be functionally constructed as the operation of a program installed in the processor, the present invention uses a hardware system including a storage device and a computer as in the second embodiment. It can be positioned as a threshold calculation method to be performed.

FIG. 7 is a flowchart showing a configuration example of the threshold value calculation method according to the fifth embodiment.

The threshold calculation method of the present invention is implemented by software operating on a computer including a storage device, and includes a measurement data input step (S21), a measurement data conversion step (S22), a regression analysis range designation step (S23), and the like. An error in calculating the error ratio of at least one of the first error ratio and the second error ratio, and the selection step (S24) for selecting any one of the first error ratio calculation step and the second error ratio calculation step. It includes a ratio calculation step (S25-S31), an error ratio determination step (S32), a regression analysis range change step (S33), a regression analysis range determination step (S34), and a threshold calculation step (S36).

The measurement data input step (S21) is a step of inputting a plurality of measured values as in the second embodiment.

In the measurement data conversion step (S22), as in the second embodiment, conversion data composed of a plurality of conversion values is generated by performing a predetermined conversion process on the plurality of measurement values.

In the regression analysis range designation step (S23), the analysis range which is the range of the environment variables in the error ratio calculation step is designated as in the second embodiment.

The first error ratio calculation step includes a step (S25) of obtaining a first regression function by performing regression analysis by the minimum absolute error method on the converted data in the analysis range, and a first prediction by the first regression function. The step (S26) of obtaining the first error by averaging the absolute value of the difference between the value and the conversion data in the analysis range, and the squared value of the difference between the first predicted value and the conversion data are analyzed. It includes a step (S27) of calculating a second error by averaging over a range and taking a square root, and a step (S31) of calculating a first error ratio, which is the ratio of the second error to the first error. ..

The second error ratio calculation step includes a step (S28) of obtaining a second regression function by performing regression analysis by the least squares method on the converted data in the analysis range, and a second prediction by the second regression function. The step (S29) of obtaining the third error by averaging the squared value of the difference between the value and the converted data in the analysis range and taking the square root, and the absolute value of the difference between the second predicted value and the converted data A step (S30) for calculating a fourth error by averaging in the analysis range and a step (S31) for calculating a second error ratio, which is the ratio of the third error to the fourth error, are provided.

In the error ratio determination step (S32), the upper end of the environment variable in the analysis range is reduced in the regression analysis range change step (S33) until the error ratio is smaller than the predetermined value by comparing the error ratio with the predetermined value. to change the scope of analysis, the process proceeds to step (S34) for performing subsequent magnitude comparison of the specified value a ₁ and the analysis range. Then, when the analysis range is the designated value A ₁ or more, the error ratio calculation step is repeated, and when the analysis range is less than the designated value A ₁ , it is determined that the cognition is indefinite (S35).

In the threshold value calculation step (S36), when the error ratio becomes smaller than a predetermined value, the threshold value is calculated based on the selected first regression function or the second regression function.

In the fifth embodiment, the error ratio calculation step (S25-S31), the error ratio determination step (S32), the regression analysis range change step (S33), the regression analysis range determination step (S34), and the threshold value calculation step (S34) Since it has S36), (1) when the number of data points is small, (2) when there is a lot of noise as a whole, (3) when the absolute value of the error is large, and (4) average error (uniform). Even in the case of (distribution error), it is a method of calculating a highly accurate threshold.

When (1) to (4) are concerned, the error ratio calculation steps include steps S25, S26, and S27 for calculating the first regression function, the first error, and the second error described above. It is preferable to do so. That is, it is preferable to use the minimum absolute value error method for regression analysis in order to avoid the problems (1) to (4).

Further, in the fifth embodiment, (5) when there is a large noise even if the analysis range is reduced, for example, there is a large noise on the low energy background side, optimization is performed even if the analysis range is reduced. Since it does not proceed, if it falls below the lower limit of the analysis range reduction, it is determined that the permissible value is indefinite (S35), and there is an effect of calling attention to the user.

[Embodiment 6]
The threshold value calculation device 50 of the present invention can be incorporated into various measuring devices as in the third embodiment.

FIG. 8 is a block diagram showing a configuration example of the measuring device according to the sixth embodiment. The example shown in FIG. 8 is a photoelectron yield spectroscope.

The measuring device 60 includes a measuring unit 21 and a control calculation unit 201.

The measuring unit 21 conforms to the one described in the third embodiment.

The control calculation unit 201 includes an irradiation light control unit 13 and a photoelectron quantity measurement unit 12 based on those described in the third embodiment, a measurement data conversion unit 6 according to the fourth embodiment, a regression analysis unit 101, and an error. It includes an evaluation unit 102, a regression analysis range designation unit 103, a regression analysis range determination unit 104, and a threshold calculation unit 105.

As a result, it is possible to provide a threshold value calculation means capable of automatically calculating the threshold value with high accuracy in the photoelectron yield spectroscope that calculates the threshold value from the measurement data measured by the photoelectron yield spectroscopy. At this time, the threshold value corresponds to the work function or ionization energy of the sample.

The example shown in FIG. 8 is a photoelectron yield spectroscope, but the same configuration can be widely applied to other measuring devices as in the third embodiment. Similarly, in other measuring devices, the measuring device 60 may include a measuring unit 21 and a control calculation unit 201. The sixth embodiment can provide a measuring device provided with a threshold value calculating means capable of accurately obtaining a threshold value obtained from measurement data composed of a plurality of measured values when an environment variable is changed. It is possible to calculate a threshold value that does not depend on the person.

[Embodiment 7]
FIG. 9 is a block diagram showing a configuration example of the threshold value calculation device according to the seventh embodiment.

The threshold calculation device 70 according to the seventh embodiment includes an input unit 7 into which measurement data 8 is input, a measurement data conversion unit 6, a regression analysis unit 111, a coefficient of determination calculation / judgment unit 112, and an error evaluation unit 113. , A regression analysis range designation unit 114 and a threshold calculation unit 105 are provided, and a threshold 9 is output. Here, the measurement data conversion unit 6, the input unit 7, and the measurement data 8 are all the same as those in the first embodiment.

The regression analysis unit 111 is the same as the regression analysis unit 101 of the fourth embodiment. That is, the transformation data in the analysis range is subjected to regression analysis by the minimum absolute error method to obtain the first regression function, and the absolute value of the difference between the first predicted value by the first regression function and the transformation data is analyzed. The first error is calculated by averaging over the range, and the second error is calculated by averaging the squared difference between the first predicted value and the converted data in the analysis range and taking the square root. be able to. Alternatively, the transformation data in the analysis range is subjected to regression analysis by the least squares method to obtain the second regression function, and the squared difference between the second predicted value by the second regression function and the transformation data is analyzed. The third error is calculated by averaging over the range and taking the square root, and the fourth error is calculated by averaging the absolute value of the difference between the second predicted value and the converted data in the analysis range. Can be done.

Determination coefficient calculation, determination unit 112, the coefficient of determination R ² the following formula determined by (17), the coefficient of determination R ² If the value is 0 or more and 1 or less in error evaluation unit 113 first or second error ratio If the value of the coefficient of determination R ² is negative, it is determined that the cognitive indefinite 110 is obtained.

Further, it is possible to compare the magnitude of the value of the coefficient of determination R ² when changing the regression analysis range. If equal the value of the coefficient of determination R ² is small when the narrow regression analysis range, calculates a threshold value by the threshold value calculation unit 105. On the other hand, when the value of the coefficient of determination R ² is large, the error evaluation unit 113 is executed.
Here, n is the number of measurement data in the measurement range, x _j is the j-th environmental variable of the measured value, y _{0, j} is the j-th measured value, and f (x _j ) is the first regression function or the second. The regression function and μY are simple averages of the measured values within the measurement range.

The error evaluation unit 113, like the error evaluation unit 102 of the fourth embodiment, has a first error ratio which is a ratio of the second error to the first error, or a ratio of the third error to the fourth error. The second error ratio is obtained, and the first error ratio or the second error ratio can be compared with a predetermined value (loss variable re). Here, the loss variable re is 1.414 in the case of the first error ratio and 1.253 in the case of the second error ratio. It is preferable to set these values as default settings for the loss variable re, but in some cases, it can be set manually.

The regression analysis range designation unit 114 can change the analysis range so as to reduce the upper end of the environment variable in the analysis range.

The threshold value calculation unit 105 can calculate the threshold value based on the first regression function or the second regression function, as in the fourth embodiment.

The threshold value calculation device of the seventh embodiment can obtain preferable effects on the items (1) to (4) described in the fourth embodiment as in the fourth embodiment. Further, regarding the item (5), it is not necessary to set the lower limit of the regression analysis range in advance.

[Embodiment 8]
Since the threshold value calculation device 70 of the present invention can be functionally constructed as the operation of a program installed in the processor, the present invention uses a hardware system including a storage device and a computer as in the fifth embodiment. It can be positioned as a threshold calculation method to be performed.

FIG. 10 is a flowchart showing a configuration example of the threshold value calculation method according to the eighth embodiment.

The threshold calculation method of the present invention is implemented by software operating on a computer including a storage device, and includes a measurement data input step (S51), a measurement data conversion step (S52), a first error ratio calculation step, and a second error. A selection step (S53) for selecting any one of the ratio calculation steps, a loss variable designation step (S54), and a first error ratio for calculating at least one of the first error ratio and the second error ratio. the error ratio calculation step (S57-S62, S65), and the first coefficient of determination ^{R 2} calculation step (S63), and the first coefficient of determination ^{R 2} determination step (S64), the first error ratio calculation step ( S65), the first error ratio determination step (S67), the regression analysis range change step (S68-S71) constituting the i-th loop, the error ratio calculation step (S72-S77, S80), and the coefficient of determination. A calculation / determination step (S78, S79) and a regression analysis range determination step (S81) are provided, and finally the threshold is calculated in the threshold calculation step (S82). Here, i is an integer of 1 or more and represents the number of changes in the regression analysis range.

The measurement data input step (S51) is a step of inputting a plurality of measured values as in the second embodiment.

The measurement data conversion step (S52) generates conversion data composed of a plurality of conversion values by performing a predetermined conversion process on the plurality of measurement values.

The selection step (S53) is a step of selecting any one of the first error ratio calculation step and the second error ratio calculation step, as in the fifth embodiment.

The loss variable designation step (S54) is a step in which the value of the loss variable re is automatically set depending on whether the first error ratio calculation step is selected or the second error ratio calculation step is selected in the selection step (S53). is there. Here, the loss variable re is set to 1.414 when the first error ratio calculation step is selected, and 1.253 when the second error ratio calculation step is selected.

After the loss variable specification step (S54), the work of the first loop is executed. In order to make the explanation easier, the number variable i will be used here. First, i is set to 1 (S55).

The first error ratio calculation step is the same first error ratio calculation step as in the fifth embodiment, and a regression analysis is performed on the converted data in the analysis range by the minimum absolute error method to obtain a first regression function. A step (S57), a step (S58) of obtaining the first error by averaging the absolute value of the difference between the first predicted value by the first regression function and the converted data in the analysis range, and the first step. The ratio of the second error to the first error in the step (S59) of calculating the second error by averaging the squared value of the difference between the predicted value and the conversion data in the analysis range and taking the square root. The step (S65) for calculating the first error ratio is provided.

The second error ratio calculation step is the same second error ratio calculation step as in the fifth embodiment, and is a step of obtaining a second regression function by performing regression analysis by the minimum square method on the converted data in the analysis range. (S60) and the step (S61) of obtaining the third error by averaging the squared value of the difference between the second predicted value by the second regression function and the converted data in the analysis range and taking the square root. The step (S62) of calculating the fourth error by averaging the absolute value of the difference between the second predicted value and the converted data in the analysis range, and the second, which is the ratio of the third error to the fourth error. The step (S65) for calculating the error ratio of

The coefficient of determination calculated, determination step calculates a determination coefficient ^{R 2} of the formula (17) (S63), the coefficient of determination ^{R 2} is judged whether it is greater than or less than 0 0 (S64), determines When the coefficient R ² is 0 or less, it is determined that the cognition is indefinite (S66).

The error ratio determination step (S67) is a step of comparing the error ratio with the predetermined value re, and when the error ratio is smaller than or equal to the predetermined value re, the threshold value calculation step (S82) is executed and the error ratio is executed. If is larger than the predetermined value re, the regression analysis range change step (S68-S71) is executed, and the process proceeds to the i-th loop.

Regression analysis range changing step (S68-S71) includes a a step of reduction of the regression analysis range, for example, i-th decision in the loop coefficient ^R 2 (i) and determining a threshold value Y (i) (S68), A step (S69) in which 1 is added to i to replace the value of i, a step (S70) in which the upper limit of the regression analysis range is reduced, and a step (S71) in which the regression analysis range is specified in Ar (i) are provided.

The first error ratio calculation step of the i-th loop has the same configuration as the first error ratio calculation step of the first loop, and regression analysis is performed by the minimum absolute error method for the converted data in the analysis range. The step of obtaining the first regression function (S72) and the step of obtaining the first error by averaging the absolute value of the difference between the first predicted value by the first regression function and the converted data in the analysis range (S72). S73) and the step (S74) of calculating the second error by averaging the squared value of the difference between the first predicted value and the converted data in the analysis range and taking the square root, and the first error. The step (S80) for calculating the first error ratio, which is the ratio of the second error to the relative error, is provided.

The second error ratio calculation step of the i-th loop also has the same configuration as the first second error ratio calculation step, and regression analysis by the minimum square method is performed on the converted data in the analysis range. The third error is obtained by averaging the squared root of the step (S75) for obtaining the second regression function and the squared difference between the second predicted value and the converted data by the second regression function in the analysis range. (S76), the step of calculating the fourth error by averaging the absolute value of the difference between the second predicted value and the converted data in the analysis range (S77), and the third with respect to the fourth error. The step (S80) for calculating the second error ratio, which is the ratio of the errors of

The coefficient of determination calculation and determination step in the i-th loop is the coefficient of determination R ² (i) calculated by Eq. (17) (S78), and the coefficient of determination R ² when the regression analysis range is changed. The magnitudes of the values are compared (S79), and when the value of the coefficient of determination R ² is smaller or equal to that when the analysis range is narrower than when it is wider, that is, when R ² (i) ≤ R ² (i-1). In the case, the threshold calculation step (S82) is executed using the analysis range when the analysis range is wide.

The regression analysis range determination step (S81) in the i-th loop is a step of comparing the error ratio with the predetermined value re, and if the error ratio is smaller than or equal to the predetermined value re, the threshold value calculation step (S82) is executed. If the error ratio is larger than the predetermined value re, the process returns to the regression analysis range change step (S68-S71) and the loop step is continued.

The threshold value calculation step (S82) calculates the threshold value based on the selected first regression function or the second regression function.

The threshold value calculation method of the eighth embodiment has a preferable effect on the items (1) to (4) described in the fifth embodiment as in the fifth embodiment. Further, regarding the item (5), it is not necessary to set the lower limit of the regression analysis range in advance.

[Embodiment 9]
The threshold value calculation device 80 of the present invention can be incorporated into various measuring devices as in the sixth embodiment.

FIG. 11 is a block diagram showing a configuration example of the measuring device according to the ninth embodiment. The example shown in FIG. 11 is a photoelectron yield spectroscope.

The measuring device 80 includes a measuring unit 21 and a control calculation unit 202.

The measuring unit 21 conforms to the one described in the third embodiment.

The control calculation unit 202 determines the irradiation light control unit 13 and the photoelectron amount measurement unit 12 based on those described in the third embodiment, the measurement data conversion unit 6 according to the seventh embodiment, and the regression analysis unit 111. It includes a coefficient calculation / determination unit 112, an error evaluation unit 113, a regression analysis range designation unit 114, and a threshold value calculation unit 105.

As a result, it is possible to provide a threshold value calculation means capable of automatically calculating the threshold value with high accuracy in the photoelectron yield spectroscope that calculates the threshold value from the measurement data measured by the photoelectron yield spectroscopy. At this time, the threshold value corresponds to the work function or ionization energy of the sample.

The example shown in FIG. 11 is a photoelectron yield spectroscope, but the same configuration can be widely applied to other measuring devices as in the sixth embodiment. Similarly, in other measuring devices, the measuring device 80 may include a measuring unit 21 and a control calculation unit 202. Embodiment 9 can provide a measuring device provided with a threshold value calculating means capable of accurately obtaining a threshold value obtained from measurement data composed of a plurality of measured values when an environment variable is changed. It is possible to calculate a threshold value that does not depend on the person.

The invention made by the present inventor has been specifically described above based on the embodiments, but it goes without saying that the present invention is not limited thereto and can be variously modified without departing from the gist thereof.

[Example 1]
The threshold calculation methods of Embodiments 4 to 6 are applied to the measurement of the photoelectron yield measuring device that measures the photoelectron yield by irradiating the sample with the dispersed light, and the Fitting calculated value by the least squares method is used for comparison. The effect of the present invention was verified.

There, a total of 87 measurements were made using various samples such as Al and Cu. The discrepancy between the photoelectron yield judgment value by the researcher and the predicted value by the threshold calculation method was evaluated. The mapping data of the measured values are shown in FIG. 12, and the results summarized as a table are shown in Table 1.

From this result, it can be seen that the threshold value calculation method of the present invention has high accuracy.

1 Regression analysis unit by the minimum absolute error method 2 Regression analysis unit by the minimum square method 3 Regression analysis range specification unit 4 Error evaluation unit 5 Threshold calculation unit 6 Measurement data conversion unit 7 Input unit 8 Measurement data 9 Threshold 10 Threshold calculation device 11 Control Calculation unit 12 Photoelectron yield measurement unit 13 Irradiation light control unit 14 Wavelength control unit 20 Measuring device 21 Measuring unit 22 Sample stage 23 Sample 24 Ultraviolet light source 25 Spectrometer 26 Photoelectron detector 30 Measured value 31 Regression function by minimum absolute error method 32 Minimum Regression function by square method 33 Threshold by minimum absolute error method 34 Threshold by minimum square method 50 Threshold calculation device 60 Measuring device 70 Threshold calculation device 80 Measuring device 101 Regression analysis unit 102 Error evaluation unit 103 Regression analysis range specification unit 104 Regression analysis range Judgment unit 105 Threshold calculation unit 110 Indefinite value 111 Regression analysis unit 112 Decision coefficient calculation, judgment unit 113 Error evaluation unit 114 Regression analysis range specification unit 201 Control calculation unit 202 Control calculation unit

Claims (20)

The threshold is calculated from the measurement data configured by associating the measured value obtained from the sample with the environmental variable at that time when the environmental variable, which is one of the quantities representing the environment in which the sample is placed, is changed. A threshold calculation device including an input unit, a measurement data conversion unit, a regression analysis range designation unit, first and second regression analysis units, an error evaluation unit, and a threshold calculation unit.
The measurement data conversion unit can generate conversion data composed of a plurality of conversion values by performing a predetermined conversion process on the plurality of measurement values input to the input unit.
The regression analysis range designation unit can specify an analysis range which is a range of environment variables in the first and second regression analysis units.
The first regression analysis unit performs regression analysis by the minimum absolute error method on the transformation data in the analysis range to obtain the first regression function, and the difference between the predicted value by the first regression function and the transformation data. The first error can be calculated by averaging the absolute values of
The second regression analysis unit performs regression analysis by the least squares method on the converted data in the analysis range to obtain a second regression function, and determines the difference between the predicted value by the second regression function and the converted data. The second error can be calculated by averaging the squared values in the analysis range and taking the square root.
The error evaluation unit compares the ratio of the second error to the first error with a predetermined value, and when the error ratio is larger than the predetermined value, the regression analysis range designation unit tells the environmental variable in the analysis range. The analysis range can be changed so as to reduce the upper end of the above, and the first and second regression analysis units can execute regression analysis in the changed analysis range, respectively.
The threshold value calculation unit can calculate the threshold value based on the first regression function when the error ratio becomes smaller than the predetermined value.
Threshold calculation device. When the environmental variable, which is one of the quantities representing the environment in which the sample is placed, is changed, the threshold value is calculated from the measurement data configured by associating the measured value obtained from the sample with the environmental variable at that time. It is a threshold calculation device, and includes an input unit, a measurement data conversion unit, a regression analysis range designation unit, a regression analysis range determination unit, a regression analysis unit, an error evaluation unit, and a threshold calculation unit.
The measurement data conversion unit can generate conversion data composed of a plurality of conversion values by performing a predetermined conversion process on the plurality of measurement values input to the input unit.
The regression analysis range designation unit can specify an analysis range which is a range of environment variables in the regression analysis unit.
The regression analysis range determination unit can be designated as an indefinite value in the analysis range specified by the regression analysis range designation unit.
The regression analysis unit performs regression analysis by the minimum absolute error method on the transformation data in the analysis range to obtain a first regression function, and obtains a first predicted value by the first regression function and the transformation data. The first error is calculated by averaging the absolute value of the difference with the above analysis range, and the squared value of the difference between the first predicted value and the conversion data is averaged in the analysis range. The second error can be calculated by taking the square root,
Alternatively, the transformation data in the analysis range is subjected to regression analysis by the least squares method to obtain a second regression function, and the difference between the second predicted value by the second regression function and the transformation data is squared. The third error is calculated by averaging the obtained values in the analysis range and taking the square root, and by averaging the absolute value of the difference between the second predicted value and the conversion data in the analysis range. The fourth error can be calculated,
The error evaluation unit obtains a first error ratio, which is the ratio of the second error to the first error, or a second error ratio, which is the ratio of the third error to the fourth error. ,
Compare the first error ratio or the second error ratio with the predetermined value,
When the error ratio is larger than the predetermined value, the regression analysis range designation unit is made to change the analysis range so as to reduce the upper end of the environmental variable in the analysis range, and the regression analysis unit is changed to the analysis range. Regression analysis can be performed individually
The threshold value calculation unit can calculate the threshold value based on the third regression function when the first error ratio becomes smaller than the predetermined value, or the second error ratio is the said. When it becomes smaller than the predetermined value, the threshold value can be calculated based on the fourth regression function.
Threshold calculation device. In claim 1 or 2, the predetermined value is 1.414.
Threshold calculation device. In claim 1 or 2, the predetermined value is 1.253.
Threshold calculation device. The threshold is calculated from the measurement data configured by associating the measured value obtained from the sample with the environmental variable at that time when the environmental variable, which is one of the quantities representing the environment in which the sample is placed, is changed. It is a threshold calculation device, and includes an input unit, a measurement data conversion unit, a regression analysis unit, a determination coefficient calculation, a judgment unit, an error evaluation unit, a regression analysis range designation unit, and a threshold calculation unit.
The measurement data conversion unit can generate conversion data composed of a plurality of conversion values by performing a predetermined conversion process on the plurality of measurement values input to the input unit.
The regression analysis unit obtains a first regression function by performing a regression analysis on the transformed data by the minimum absolute error method, and finds a difference between the first predicted value by the first regression function and the transformed data. The first error is calculated by averaging the absolute values in the analysis range, and the squared value of the difference between the first predicted value and the conversion data is averaged in the analysis range to take the square root. The second error can be calculated more
Alternatively, the transformation data in the analysis range is subjected to regression analysis by the least squares method to obtain a second regression function, and the difference between the second predicted value by the second regression function and the transformation data is squared. The third error is calculated by averaging the obtained values in the analysis range and taking the square root, and by averaging the absolute value of the difference between the second predicted value and the conversion data in the analysis range. The fourth error can be calculated,
The coefficient of determination calculation / determination unit obtains the coefficient of determination R ² by the following equation (1).
If the value of the coefficient of determination R ² is 0 or more and 1 or less calculates the first or second error ratio in the error evaluation unit, determines the value of the coefficient of determination R ² is the case of the negative and cognitive indefinite Can be
Further, it is possible to compare the magnitude of the coefficient of determination R ² value when changing the regression analysis range,
The error evaluation unit obtains a first error ratio, which is the ratio of the second error to the first error, or a second error ratio, which is the ratio of the third error to the fourth error. ,
The first error ratio or the second error ratio can be compared with a predetermined value.
The regression analysis range designation unit can change the analysis range so as to reduce the upper end of the environment variable in the analysis range.
The threshold value calculation unit can calculate the threshold value based on the first regression function or the second regression function.
Threshold calculation device.
Here, n is the number of the measured data in the measurement range, x _j is the j-th environmental variable of the measured value, y _{0, j} is the j-th measured value, and f (x _j ) is the first regression function. Alternatively, the second regression function and μY are simple average values of the measured values within the measured range. In any one of claims 1 to 5, the environment variable is the energy of light irradiating the sample, and the measured value is the photoelectron yield detected by the detector after being emitted from the sample. ,
Threshold calculation device. When the environmental variable, which is one of the quantities representing the environment in which the sample is placed, is changed, a threshold value is set from the measurement data configured by associating a plurality of measured values obtained from the sample with the environmental variable at that time. It is a threshold calculation method to calculate, and is an error ratio of a measurement data input step, a measurement data conversion step, a regression analysis range specification step, a first and second regression analysis step, a first and second error calculation step, and an error ratio. It includes a calculation step, an error ratio determination step, a regression analysis range change step, and a threshold calculation step.
In the measurement data input step, the plurality of measured values are input.
The measurement data conversion step generates conversion data composed of a plurality of conversion values by performing a predetermined conversion process on the plurality of measurement values.
The regression analysis range designation step specifies an analysis range which is a range of environment variables in the first and second regression analysis steps.
In the first regression analysis step, the first regression function is obtained by performing regression analysis by the minimum absolute error method on the transformation data in the analysis range.
In the first error calculation step, the first error is calculated by averaging the absolute value of the difference between the predicted value by the first regression function and the conversion data in the analysis range.
In the second regression analysis step, a second regression function is obtained by performing regression analysis by the least squares method on the transformed data in the analysis range.
In the second error calculation step, the second error is calculated by averaging the squared value of the difference between the predicted value by the second regression function and the conversion data in the analysis range and taking the square root.
In the error ratio calculation step, the ratio of the second error to the first error is obtained and used as the error ratio.
In the error ratio determination step, the error ratio is compared with a predetermined value, and the error ratio is compared with a predetermined value.
In the regression analysis range change step, the first and second regression analysis steps are performed while changing the analysis range to reduce the upper end of the environment variable in the analysis range until the error ratio becomes smaller than the predetermined value. , The first and second error calculation steps and the error ratio calculation step are repeated.
The threshold value calculation step calculates the threshold value based on the first regression function when the error ratio becomes smaller than the predetermined value.
Threshold calculation method. In claim 7, the predetermined value is 1.414.
Threshold calculation method. In claim 7, the predetermined value is 1.253.
Threshold calculation method. When the environmental variable, which is one of the quantities representing the environment in which the sample is placed, is changed, a threshold value is set from the measurement data configured by associating a plurality of measured values obtained from the sample with the environmental variable at that time. A selection step for selecting one of a measurement data input step, a measurement data conversion step, a regression analysis range designation step, a first error ratio calculation step, and a second error ratio calculation step, which is a threshold calculation method for calculation. An error ratio calculation step for calculating an error ratio of at least one of the first error ratio and the second error ratio, an error ratio determination step, a regression analysis range change step, and a threshold calculation step are provided.
In the measurement data input step, the plurality of measured values are input.
The measurement data conversion step generates conversion data composed of a plurality of conversion values by performing a predetermined conversion process on the plurality of measurement values.
The regression analysis range designation step specifies an analysis range that is a range of environment variables in the error ratio calculation step.
In the first error ratio calculation step, the transformation data in the analysis range is subjected to regression analysis by the minimum absolute error method to obtain the first regression function, and the first predicted value by the first regression function is obtained. The first error is calculated by averaging the absolute value of the difference from the conversion data in the analysis range, and the squared value of the difference between the first predicted value and the conversion data is calculated in the analysis range. The second error is calculated by taking the square root on average, and the first error ratio, which is the ratio of the second error to the first error, is calculated.
In the second error ratio calculation step, the transformation data in the analysis range is subjected to regression analysis by the least squares method to obtain a second regression function, and the second predicted value by the second regression function and the said. The third error is calculated by averaging the squared value of the difference from the converted data in the analysis range and taking the square root, and the absolute value of the difference between the second predicted value and the converted data is analyzed. The fourth error is calculated by averaging in the range, and the second error ratio, which is the ratio of the third error to the fourth error, is calculated.
In the error ratio determination step, the upper end of the environmental variable in the analysis range is reduced in the regression analysis range change step until the error ratio is smaller than the predetermined value by comparing the error ratio with the predetermined value. The range is changed, and if the analysis range is equal to or greater than the specified value, the error ratio calculation step is repeated, and if the analysis range is less than the specified value, it is determined that cognition is indefinite.
In the threshold value calculation step, when the error ratio becomes smaller than the predetermined value, the threshold value is calculated based on the first regression function or the second regression function for which the selection is made.
Threshold calculation method. In claim 10, the predetermined value is 1.414 when the first error ratio is used as the error ratio for comparison with the predetermined value, and when the second error ratio is used, the predetermined value is 1.414. 1.253,
Threshold calculation method. When the environmental variable, which is one of the quantities representing the environment in which the sample is placed, is changed, a threshold value is set from the measurement data configured by associating a plurality of measured values obtained from the sample with the environmental variable at that time. A method for calculating a threshold, which is at least one of a measurement data input step, a measurement data conversion step, a selection step, a loss variable designation step, a regression analysis range designation step, and a first error ratio and a second error ratio. It is provided with an error ratio calculation step for calculating the error ratio of 1 or 1, a determination coefficient calculation, a judgment step, an error ratio judgment step, a regression analysis range change step, and a threshold calculation step.
The measurement data input step is a step of inputting the plurality of measured values.
The measurement data conversion step generates conversion data composed of a plurality of conversion values by performing a predetermined conversion process on the plurality of measurement values.
The selection step is a step of selecting any one of the first error ratio calculation step and the second error ratio calculation step.
The loss variable designation step automatically sets the value re of the loss variable to 1.414 when the first error ratio calculation step is selected and 1.253 when the second error ratio calculation step is selected. It is a step to set to
The regression analysis range designation step specifies an analysis range that is a range of environment variables in the error ratio calculation step.
In the first error ratio calculation step, the transformation data in the analysis range is subjected to regression analysis by the minimum absolute error method to obtain the first regression function, and the first predicted value by the first regression function is obtained. After obtaining the first error by averaging the absolute value of the difference from the converted data in the analysis range, the squared value of the difference between the first predicted value and the converted data is averaged in the analysis range. The second error is calculated by taking the square root, and the first error ratio, which is the ratio of the second error to the first error, is calculated.
In the second error ratio calculation step, the transformation data in the analysis range is subjected to regression analysis by the least squares method to obtain a second regression function, and the second predicted value by the second regression function and the said. After obtaining the third error by averaging the squared value of the difference with the converted data in the analysis range and taking the square root, the absolute value of the difference between the second predicted value and the converted data is analyzed. The fourth error is calculated by averaging in the range, and the second error ratio, which is the ratio of the third error to the fourth error, is calculated.
In the coefficient of determination calculation / determination step, the coefficient of determination R ² represented by the following equation (2) is calculated, it is determined whether the coefficient of determination R ² is greater than 0 or less than or equal to 0, and the coefficient of determination R ² is 0. in the following cases, it is determined that cognitive indefinite, also compares the values of the coefficient of determination R ² value when changing the regression analysis range, the coefficient of determination than if it is large when the analytical range is narrow R ^When the value of ² is small or equal, the threshold calculation step is executed using the analysis range when the analysis range is wide.
The error ratio determination step is a step of comparing the error ratio with the predetermined value re, and when the error ratio is smaller than the predetermined value re, the threshold value calculation step is executed and the error ratio is the predetermined value. If it is equal to or greater than re, the regression analysis range change step is executed.
In the regression analysis range change step, the analysis range is changed so that the upper end of the environment variable in the analysis range is reduced, and after the regression analysis range change step is executed, the error ratio calculation step is performed in the changed analysis range. And / or execute the coefficient of determination calculation and determination steps,
The threshold calculation step calculates the threshold value based on the first regression function or the second regression function for which the selection is made.
Threshold calculation method.
Here, n is the number of the measured data in the measurement range, x _j is the j-th environmental variable, y _{0, j} is the j-th measured value, and f (x _j ) is the first regression function or the above. The second regression function and μY are simple average values of the measured values within the measured range. In any one of claims 7 to 12, the environment variable is the energy of light irradiating the sample, and the measured value is the photoelectron yield detected by the detector after being emitted from the sample. ,
Threshold calculation method. A measuring device including a measuring unit and a control calculation unit.
The measuring unit can acquire a plurality of measured values obtained from the sample and supply the measured values to the control calculation unit.
The control calculation unit measures a plurality of measured values obtained by changing an environmental variable, which is one of the quantities representing the environment in which the sample is placed, in association with the value of the environmental variable at that time. The first regression analysis that finds the first regression function that minimizes the absolute error and the smallest square error for the measurement data that can be acquired as data and is included in the same analysis range defined for the environment variables. In the analysis range where the ratio of the average squared error in the second regression analysis to the average of the absolute error in the first regression analysis is smaller than a predetermined value by performing the second regression analysis to obtain the second regression function. The threshold value of the measurement data can be calculated based on the first regression function.
measuring device. In claim 14, the predetermined value is 1.414.
measuring device. In claim 14, the predetermined value is 1.253.
measuring device. A measuring device including a measuring unit and a control calculation unit.
The measuring unit can acquire a plurality of measured values obtained from the sample and supply the measured values to the control calculation unit.
The control calculation unit measures a plurality of measured values obtained when the environmental variable, which is one of the quantities representing the environment in which the sample is placed, is associated with the value of the environmental variable at that time. The first regression function is obtained by performing regression analysis by the minimum absolute error method on the measurement data that can be acquired as data and is included in the same analysis range defined for the environment variables. The first error is calculated by averaging the absolute value of the difference between the first predicted value by the regression function and the converted data in the analysis range, and the difference between the first predicted value and the converted data. The second error can be calculated by averaging the squared values of and taking the square root in the analysis range.
Alternatively, the transformation data in the analysis range is subjected to regression analysis by the least squares method to obtain a second regression function, and the difference between the second predicted value by the second regression function and the transformation data is squared. The third error is calculated by averaging the obtained values in the analysis range and taking the square root, and by averaging the absolute value of the difference between the second predicted value and the conversion data in the analysis range. The fourth error can be calculated,
The error evaluation unit obtains a first error ratio, which is the ratio of the second error to the first error, or a second error ratio, which is the ratio of the third error to the fourth error. ,
In the analysis range where the first error ratio is smaller than a predetermined value, the threshold value of the measurement data can be calculated based on the first regression function.
Alternatively, the threshold value of the measurement data can be calculated based on the second regression function in the analysis range in which the second error ratio is smaller than a predetermined value.
measuring device. In claim 17, the predetermined value is 1.414 when the first error ratio is used as the error ratio for comparison with the predetermined value, and when the second error ratio is used, the predetermined value is 1.414. 1.253,
measuring device. A measuring device including a measuring unit and a control calculation unit.
The measuring unit can acquire a plurality of measured values obtained from the sample and supply the measured values to the control calculation unit.
The threshold value according to claim 5, wherein the control calculation unit includes a measurement data conversion unit, a regression analysis unit, a coefficient of determination calculation, a determination unit, an error evaluation unit, a regression analysis range designation unit, and a threshold value calculation unit. Equipped with a calculation device,
measuring device. In any one of claims 14 to 19, the environment variable is the energy of light irradiating the sample, and the measured value is the photoelectron yield detected by the detector after being emitted from the sample. ,
measuring device.