JP3630919B2 - Spectral peak judgment method - Google Patents

Description

【００１５】
で与えられる。同様に２次微分スペクトルの各点の値ｄ_ｉ は、２次微分フィルタによって定まる係数をｇとして
【００１６】
【数２】

【００１７】
で与えられる。
【００１８】
次に、閾値を定める。この閾値は従来と同様に定めることができることは当然であるが、ここではノイズ標準偏差値Ｔ_ｉ を用いるものとする。ノイズ標準偏差値Ｔ_ｉ は次のようにして求めることができる。
【００１９】
さて、（２） 式と（３） 式から
【００２０】
【数３】

【００２１】
が得られる。なお、Ａ_ｊｋ＝ｇ_ｊｆ_ｋである。
【００２２】
ここで、ｄ_ｉ の分散をσ_ｉ ^２、ｐ_ｉ の分散をδ_ｉ ^２とすると、ｐ_ｉ は互いに独立であると仮定すれば、誤差伝搬の関係から
【００２３】
【数４】

【００２４】
となる。なお、ｐ_ｉ は互いに独立であるという仮定は厳密には正しくないが、ノイズ標準偏差値を求める計算には実際上差し支えないものである。ここで、測定が統計的な事象であることを利用すれば、
【００２５】
【数５】

【００２６】
となるから、
【００２７】
【数６】

【００２８】
で与えられることになる。この（７） 式を計算するのは容易ではないが、平滑化されたスペクトルの各点の値ｓ_ｉ と、測定によって得られたスペクトルｐ_ｉ とは大きな変化がないのが通常であるので
ｓ_ｉ ≒ｐ_ｉ …（８）
としても大きな誤りはなく、しかも上述したようにｐ_ｉ は互いに独立であると仮定することができるのと同様に、ｓ_ｉ も互いに独立であると仮定することができるので、（３） 式から２次微分スペクトルの分散σ_ｉ ^２は、
【００２９】
【数７】

【００３０】
としてよく、従って、２次微分スペクトルの標準偏差σ_ｉ は
【００３１】
【数８】

【００３２】
で与えられることになる。
そして、正の係数ａを導入して、ノイズ標準偏差値Ｔ_ｉ を次のように定める。
【００３３】
【数９】

【００３４】
このノイズ標準偏差値Ｔ_ｉ を閾値として用いるのである。ここで、正の係数ａは経験的、実験的に定めればよいが、通常は ０．５〜 ３程度の範囲で設定すればよいことが確認されている。
【００３５】
次に、ピークの判定法について説明する。なお、以下では横軸をｘ軸とし、ｘ＝ｘ_ｉ（ｉ＝１，２，…，ｎ）における２次微分スペクトルの値及び閾値を、それぞれ、ｄ_ｉ ，Ｔ_ｉ とする。また、ｘの値の小さい方から順次２次微分スペクトルの値を注目していくものとする。
【００３６】
さて、このピーク判定法において、ピークの有無を判定するために用いる条件は次のようである。
【００３７】
▲１▼：ｄ_ｉ ＞Ｔ_ｉ のときには何もしない。
【００３８】
▲２▼：ｄ_ｉ ≦Ｔ_ｉ になったときには、その位置よりｘの値の大きい側に新たなピークの候補点があると判断する。
【００３９】
▲３▼：閾値以下の範囲において、２次微分スペクトルの値が減少して極小値ｄ_ｒｍｉｎをとり、その後増加していって
ｄ_ｉ −ｄ_ｒｍｉｎ ≧│Ｔ_ｉ│ （ただし、ｄ_ｉ ≦Ｔ_ｉ ） …（１２）
を満足する位置ｘ_ｉ があった場合、最初のｘ_ｉ の位置でピークが終了したと判定する。
【００４０】
▲４▼：閾値以下の範囲において、２次微分スペクトルの値が減少して極小値ｄ_ｒｍｉｎをとり、その後増加していったとき、（１２）を満足する位置ｘ_ｉ は存在しないが、そのまま増加していって閾値を越えた場合には、ピークが終了したと判定する。
【００４１】
▲５▼：閾値以下の範囲において、２次微分スペクトルの値が増加して極大値ｄ_ｒｍａｘをとり、その後減少していき、
ｄ_ｒｍａｘ −ｄ_ｉ ≧│Ｔ_ｉ│ …（１３）
を満足する位置ｘ_ｉ があった場合には、最初のｘ_ｉ の位置よりｘの値の大きい側に新たなピークの候補点があると判定する。
【００４２】
▲６▼：閾値以下の範囲において、２次微分スペクトルの値が減少して極小値ｄ_ｒｍｉｎをとり、その後増加して極大値ｄ_ｒｍａｘをとり、その後減少していったとき、当該極小値ｄ_ｒｍｉｎと極大値ｄ_ｒｍａｘとの差の絶対値が、当該極大値ｄ_ｒｍａｘをとる位置での閾値の絶対値より小さいときには、当該極小値ｄ_ｒｍｉｎをとる位置、及び次の極小値をとる位置をピークの候補点とする。
この条件は、条件▲５▼に優先する。
【００４３】
▲７▼：▲２▼または▲５▼によってｘの値の大きい側に新たなピークの候補点があると判定された後、▲３▼または▲４▼によって最初にピークが終了したと判定されるまでの間に極小値が一つしかない場合には、当該極小値をとる位置に正式なピークが存在すると判定する。
【００４４】
▲８▼：▲２▼または▲５▼によってｘの値の大きい側に新たなピークの候補点があると判定された後、▲３▼または▲４▼によって最初にピークが終了したと判定されるまでの間に極小値が複数ある場合には、これらの極小値の中で最小の値をとる極小値をとる位置に正式なピークが存在すると判定する。
【００４５】
次に、以上の条件▲１▼〜▲８▼によって、ピークの判定が具体的にどのように行われるかを例をあげて説明する。
［例１］いま、平滑化スペクトルの２次微分スペクトルが図１の実線で示すようであり、閾値が一点鎖線で示すようであり、ｘ_１ においてｄ_１ ＝Ｔ_１ となっているとすると、ｘ_１ より左側では条件▲１▼によって何の処理も行われず、ｘ_１ の時点で条件▲２▼によって、ｘ_１ の右側に新たなピークの候補点があると判定される。
【００４６】
そして、ｘ_２ において極小値ｄ_２ をとる。その後増加して、ｘ_３ の時点で、
△＝ｄ_３ −ｄ_２ ＝│Ｔ_３│ （ただし、ｄ_３＜Ｔ_３） …（１４）
となったとすると、条件▲３▼によってｘ_３ の位置でピークが終了したと判定される。そして、この場合には条件▲７▼によって原スペクトルのｘ_２ の位置に正式なピークが存在すると判定される。
【００４７】
その後、ｘ_４ においてｄ_４ ＝Ｔ_４ となるので、ｘ_４ より右側では条件▲１▼により何の処理も行われない。
【００４８】
［例２］いま、平滑化スペクトルの２次微分スペクトルが図２の実線で示すようであり、閾値が一点鎖線で示すようであり、ｘ_１ においてｄ_１ ＝Ｔ_１ となっているとすると、ｘ_１ より左側では条件▲１▼によって何の処理も行われず、ｘ_１ の時点で条件▲２▼によって、ｘ_１ の右側に新たなピークの候補点があると判定される。
【００４９】
そして、ｘ_２ において極小値ｄ_２ をとっている。その後増加を続け、ｘ_３ の位置で閾値をよぎっている。
そして、
ｄ_３ −ｄ_２ ＜│Ｔ_３│ …（１５）
であるとすると、条件▲４▼によってｘ_３ の時点でピークが終了したと判定される。そして、この場合には条件▲７▼によって原スペクトルのｘ_２ の位置に正式なピークが存在すると判定される。
ｘ_３ より右側では条件▲１▼により何の処理も行われない。
【００５０】
［例３］いま、平滑化スペクトルの２次微分スペクトルが図３の実線で示すようであり、閾値が一点鎖線で示すようであるとし、ｄ_１ ＝Ｔ_１ 、ｄ_８ ＝Ｔ_８ であり、ｘ_２ で極小値ｄ_２ をとり、ｘ_４ で極大値ｄ_４ をとり、ｘ_６ で極小値ｄ_６ をとるものとする。また、
△＝ｄ_３ −ｄ_２ ＝│Ｔ_３│ …（１６）
△′＝ｄ_４ −ｄ_５ ＝│Ｔ_５│ …（１７）
△″＝ｄ_７ −ｄ_６ ＝│Ｔ_７│ …（１８）
であるとすると、このとき、上記の［例１］と同様に、原スペクトルのｘ_２ の位置に正式なピークが存在すると判定される。
【００５１】
また、ｘ_５ の位置において条件▲５▼によってｘ_５ の右側に新たなピークの候補点があると判定され、その後、ｘ_７ の位置において条件▲３▼によってピークが終了したと判定されるので、条件▲７▼によって原スペクトルのｘ_７ の位置にも正式なピークが存在すると判定される。
ｘ_８ より右側では条件▲１▼により何の処理も行われない。
【００５２】
［例４］いま、平滑化スペクトルの２次微分スペクトルが図４の実線で示すようであり、閾値が一点鎖線で示すようであるとし、ｄ_１ ＝Ｔ_１ 、ｄ_６ ＝Ｔ_６ であり、ｘ_２ で極小値ｄ_２ をとり、ｘ_３ で極大値ｄ_３ をとり、ｘ_４ で極小値ｄ_４ をとるものとする。また、
ｄ_３ −ｄ_２ ＜│Ｔ_３│ …（１９）
△＝ｄ_５ −ｄ_４ ＝│Ｔ_５│ …（２０）
であるとする。
【００５３】
このときには、条件▲６▼によって二つの位置ｘ_２ ，ｘ_４ がピークの候補点として判定される。そして、ｘ_５ の位置において条件▲３▼によってピークが終了したと判定されることになるが、図４の場合にはｄ_２ ＞ｄ_４ であるので、条件▲８▼によって原スペクトルのｘ_４ の位置に正式なピークが存在すると判定されることになる。ｘ_６ より右側では条件▲１▼により何の処理も行われない。
【００５４】
以上、４つの例について説明したが、上記の条件▲１▼〜▲８▼によって実際の原スペクトルにおけるピークの有無を判定することができることが確認されている。
【００５５】
以上のように、このスペクトルのピーク判定方法によれば、２次微分スペクトルの値の変化の仕方、２次微分スペクトルの各点での値と閾値の関係、及び２次微分スペクトルの各点における近傍の極値からの変動分とそのときの閾値との関係等に基づいて原スペクトルにおけるピークの有無を判定しているので、従来は全体として一つのピークとして判定されていたような、二つのピークが近接して、一方のピークが他のピークの肩越しに瘤状に現れているような場合にも異なるピークとして分離判定することが可能となり、従って、上述したピーク判定法の処理を行うプログラムを作成して種々の分析装置に搭載し、測定の結果得られたスペクトルに対して上述した処理を実行させることによって、従来では分離されなかったピークを分離して検出することが可能となるので分析精度の向上を図ることができるものである。
【００５６】
なお、上述したような方法でノイズ標準偏差値が計算できるのは、信号検出の際、確率事象に基づいてノイズが発生する場合であり、本発明はそれに当てはまるＥＰＭＡ、Ａｕｇｅｒ分析装置、ＥＳＣＡ、蛍光Ｘ線分析装置等の分析機器より得られたスペクトルのピーク判定に適用することができる。
【００５７】
以上、本発明の実施形態について説明したが、本発明は上記実施形態に限定されるものではなく種々の変形が可能である。例えば、上記の説明では測定の結果得られたスペクトルを平滑化するものとしたが、これは必須の要件ではなく省略することも可能である。その場合には（３） 式のｓ_ｉ＋ｊ としてはｐ_ｉ＋ｊ を用いればよい。
【図面の簡単な説明】
【図１】本発明に係るスペクトルのピーク判定方法を説明するための第１の例を示す図である。
【図２】本発明に係るスペクトルのピーク判定方法を説明するための第２の例を示す図である。
【図３】本発明に係るスペクトルのピーク判定方法を説明するための第３の例を示す図である。
【図４】本発明に係るスペクトルのピーク判定方法を説明するための第４の例を示す図である。
【図５】従来のスペクトルのピーク判定方法を説明すると共に、本発明が解決しようとする課題を説明するための図である。[0001]
[Industrial application fields]
The present invention relates to a method for determining a peak of a spectrum obtained from an analytical instrument such as an EPMA, Auger analyzer, ESCA, or fluorescent X-ray analyzer.
[0002]
[Prior art and problems to be solved by the invention]
In measurement using various analyzers, it is very important from the viewpoint of improving analysis accuracy to accurately detect a peak from the obtained spectrum. Therefore, a program for automatically determining the peak of a spectrum obtained as a result of measurement or a spectrum obtained by smoothing it (hereinafter collectively referred to as an original spectrum) is installed in the analyzer. Is normal.
[0003]
The peak determination method usually obtains a secondary differential spectrum from the original spectrum, and in the secondary differential spectrum, it is usually determined that the negative convex portion below the threshold is a significant peak. When there were a plurality of peaks, these peaks were not separated, and as a whole, only one peak was determined.
[0004]
An example will be described with reference to FIG. FIG. 5 (a) shows the original spectrum, and FIG. 5 (b) shows its second derivative spectrum. The horizontal axes in FIGS. 5A and 5B differ depending on the type of analyzer used to obtain the original spectrum. For example, if the original spectrum is obtained by EPMA or a fluorescent X-ray analyzer, the horizontal axis represents the wavelength or energy of the detected X-ray, and if the original spectrum is obtained by an Auger analyzer, the horizontal axis is It represents the energy of detected Auger electrons, and the horizontal axis represents binding energy if it is obtained by ESCA. Also, the vertical axis usually represents intensity or count value, but may be other.
[0005]
Now, the portion that is convex upward in the original spectrum has the property of being convex on the negative side in the secondary differential spectrum. 5 (a) and 5 (b), for P ₁ that is convex upward in the original spectrum, P ₁ ′ that is negatively convex appears at the same position of the secondary differential spectrum, and similarly P ₂ ′, P ₃ ′, and P ₄ ′ appearing on the negative side appear at the same position of the secondary differential spectrum with respect to P ₂ , P ₃ , and P ₄ that are convex above the original spectrum. Yes.
[0006]
Therefore, as shown in FIG. 5B, the value of the secondary differential spectrum is compared with the threshold value indicated by the alternate long and short dash line in the figure. Of course, the threshold value is a negative value. This threshold value can be determined by an appropriate method. For example, it may be a negative constant value or may be determined by another conventionally known method.
[0007]
And for the portion that is convex to the negative side below the threshold in the secondary differential spectrum, there is a significant peak that is not noise at the position of the minimum value of the portion that is convex to the negative side in the original spectrum. It is determined. Therefore, in FIG. 5B, it is determined that there are peaks at the positions of P ₁ ′ and P ₂ ′ in the original spectrum.
[0008]
On the other hand, if the original spectrum of FIG. 5 (a) is seen, it is determined that there are peaks at the positions of P ₃ and P ₄ respectively. In FIG. 5 (b), P ₃ ′ and P _{3 Since} the maximum value between ₄ 'is smaller than the threshold value, it is not determined as a different peak but is determined as one peak. In this case, the peak position is the position of the minimum value, which is the position of P ₄ ′ in FIG. In FIG. 5B, if the maximum value between P ₃ ′ and P ₄ ′ is larger than the threshold value, it is natural that the peaks are determined as different peaks.
[0009]
As described above, in the conventional peak determination method, peaks that exist apart like P ₁ and P _{2 in} FIG. 5A are determined as different peaks, but two peaks such as P ₃ and P ₄ are determined. When two peaks are close to each other and one peak appears in the shape of a bump over the shoulder of the other peak, there is a case where it is determined as only one peak as a whole.
[0010]
This invention solves said subject, Comprising: When two peaks adjoin and one peak appears in the shape of a bump over the shoulder of the other peak, it determines with a different peak Therefore, an object of the present invention is to provide a spectrum peak determination method capable of improving the analysis accuracy.
[0011]
[Means for Solving the Problems]
In order to achieve the above-described object, the spectrum peak determination method according to claim 1 is a method in which there is a minimum value that is equal to or less than a threshold value at each position in a spectrum region where the second-order differential spectrum value is negative. When there is only one position where the secondary differential spectrum value takes the minimum value, it is determined that there is a peak at the position where the minimum value is taken, and when there are a plurality of the minimum values, the secondary differential spectrum value is If there is a position that increases from a certain minimum value, takes a maximum value, then decreases, and the difference of the second derivative spectrum value from the maximum value is equal to or greater than the absolute value of the threshold at that position, Assuming that there is a new peak candidate point on the side larger than the position, the second derivative spectrum value has increased from the minimum value, and the difference in the second derivative spectrum value from the minimum value is the threshold value at that position. Absolute value or more It is determined that the peak has ended at a position where
The spectrum peak determination method according to claim 2 uses the noise standard deviation value obtained based on the standard deviation of the secondary differential spectrum as described in claim 2 as the threshold value in claim 1.
[0012]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments will be described with reference to the drawings.
First, the spectrum obtained as a result of the measurement is smoothed and a second derivative spectrum is obtained. The smoothing of the spectrum may be performed by using the Savitzky-Golay method, which is performed by taking as many smoothing points as the average half width of the peak around each point of the spectrum. According to this, if the number of smoothing points taken around the spectrum is 2m + 1 (m is a natural number), the step width of the spectrum is t, and the peak half-value width in the spectrum is w, m is m = [w / t]. ... (1)
It is known that the degree is sufficient. Here, [] indicates a Gaussian symbol taking an integer part in parentheses.
[0013]
Now, assuming that the value of each point of the spectrum obtained as a result of the measurement is p _i (i = 1, 2,..., N), the value s _i of each point of the smoothed spectrum is determined by the smoothing filter. The coefficient is f.
[Expression 1]

[0015]
Given in. Similarly, the value d _i of each point of the secondary differential spectrum is represented by g as a coefficient determined by the secondary differential filter.
[Expression 2]

[0017]
Given in.
[0018]
Next, a threshold value is determined. Naturally, this threshold value can be determined in the same manner as in the prior art, but here, the noise standard deviation value T _i is used. The noise standard deviation value T _i can be obtained as follows.
[0019]
From equations (2) and (3),
[Equation 3]

[0021]
Is obtained. Note that A _jk = g _j f _k .
[0022]
Here, assuming that the variance of d _i is σ _i ² and the variance of p _i is δ _i ² , assuming that p _i are independent from each other, from the relationship of error propagation,
[Expression 4]

[0024]
It becomes. Although p _i is strictly incorrect assumption that are independent of each other, in which no problem practically the calculation for obtaining the noise standard deviation value. If we take advantage of the fact that the measurement is a statistical event,
[0025]
[Equation 5]

[0026]
So,
[0027]
[Formula 6]

[0028]
Will be given. This (7) is not easy to calculate the formula, the value s _i of smoothed points of the spectrum, since the there is no significant change in the spectral p _i obtained by measurement is usual s _i ≒ p _i (8)
No major errors as, moreover Just as p _i can be assumed to be independent of each other as described above, since the s _i can be assumed to be independent of each other, from (3) The variance σ _i ² of the ^second derivative spectrum is
[0029]
[Expression 7]

[0030]
Therefore, the standard deviation σ _i of the second derivative spectrum is
[Equation 8]

[0032]
Will be given.
Then, a positive coefficient a is introduced to determine the noise standard deviation value T _i as follows.
[0033]
[Equation 9]

[0034]
This noise standard deviation value T _i is used as a threshold value. Here, the positive coefficient a may be determined empirically and experimentally, but it has been confirmed that the positive coefficient a should normally be set in the range of about 0.5 to 3.
[0035]
Next, a peak determination method will be described. In the following description, the horizontal axis is the x-axis, and the values and threshold values of the secondary differential spectrum at x = x _i (i = 1, 2,..., N) are d _i and T _i , respectively. In addition, it is assumed that the value of the secondary differential spectrum is sequentially focused from the smaller value of x.
[0036]
Now, in this peak determination method, the conditions used for determining the presence or absence of a peak are as follows.
[0037]
(1): Do nothing when d _i > T _i .
[0038]
{Circle around (2)} When d _i ≦ T _i , it is determined that there is a new peak candidate point on the side where the value of x is larger than that position.
[0039]
▲ 3 ▼: in the range of the threshold value, taking the second derivative spectrum value minimum value _{d rmin} decreases, went increased thereafter _{d i -d rmin ≧ │T i │} ( although, _{d i} ≦ T _i ) (12)
If there is a position x _i that satisfies the above, it is determined that the peak has ended at the first position of x _i .
[0040]
▲ 4 ▼: in the range of the threshold value, taking the second derivative spectrum value minimum value d _rmin decreases, then increased when went, but no position x _i that satisfies (12), as it If it has increased and exceeded the threshold, it is determined that the peak has ended.
[0041]
(5): In the range below the threshold value, the value of the second derivative spectrum increases to take the maximum value _drmax , and then decreases.
_{d rmax -d i ≧ │T i │} ... (13)
If there is a position x _i that satisfies the above, it is determined that there is a new peak candidate point on the larger x value side than the first x _i position.
[0042]
{Circle around (6)}: When the value of the secondary differential spectrum decreases and takes a minimum value _drmin within a range below the threshold value, then increases to take a maximum value _drmax , and then decreases, the minimum value d _When the absolute value of the difference between _rmin and the maximum value _drmax is smaller than the absolute value of the threshold at the position where the maximum value _drmax is taken, the position where the minimum value _drmin is taken and the position where the next minimum value is taken. The candidate point for the peak.
This condition has priority over condition (5).
[0043]
(7): After determining that there is a new peak candidate point on the larger x value side by (2) or (5), it is determined by (3) or (4) that the peak has ended first. If there is only one minimum value until the end of the period, it is determined that a formal peak exists at the position where the minimum value is obtained.
[0044]
(8): After it is determined by (2) or (5) that there is a new peak candidate point on the larger x value side, it is determined by (3) or (4) that the peak has ended first. If there are a plurality of local minimum values, it is determined that a formal peak exists at the position of the local minimum value that takes the minimum value.
[0045]
Next, how the peak determination is specifically performed under the above conditions (1) to (8) will be described with an example.
[Example 1] Now, it is assumed that the second derivative spectrum of the smoothed spectrum is indicated by a solid line in FIG. 1, the threshold value is indicated by an alternate long and short dash line, and d ₁ = T _{1 at} x ₁ . x ₁ from the left condition ▲ 1 without performing any processing by ▼, the conditions ▲ 2 ▼ at the time of x _1, it is determined that there is a candidate point of a new peak to the right of x _1.
[0046]
Then, the minima _{d 2} in _{x 2.} And it increased thereafter, at the time of the _{x 3,
△ = d 3 -d 2 = │T} 3 │ ( _{where, d 3 <T 3) ...} (14)
When becomes, it is determined that the peak at the position of x ₃ by conditions ▲ 3 ▼ is completed. The formal peaks at x ₂ the original spectrum by conditions ▲ 7 ▼ in this case is determined to be present.
[0047]
Thereafter, since d ₄ = T _{4 at} x ₄ , no processing is performed on the right side of x ₄ due to condition (1).
[0048]
[Example 2] Now, assuming that the second derivative spectrum of the smoothed spectrum is shown by a solid line in FIG. 2, the threshold is shown by a one-dot chain line, and d ₁ = T _{1 at} x ₁ , x ₁ from the left condition ▲ 1 without performing any processing by ▼, the conditions ▲ 2 ▼ at the time of x _1, it is determined that there is a candidate point of a new peak to the right of x _1.
[0049]
Then, taking a minimum value _{d 2} in _{x 2.} Thereafter it continued to increase, which crossed the threshold at the position of x _3.
And
d ₃ -d ₂ <| T ₃ | (15)
When it is determined that the peak has ended at the time of x ₃ by conditions ▲ 4 ▼. The formal peaks at x ₂ the original spectrum by conditions ▲ 7 ▼ in this case is determined to be present.
_{On the} right side of x3, no processing is performed due to condition (1).
[0050]
[Example 3] Now, it is assumed that the second-order differential spectrum of the smoothed spectrum is indicated by a solid line in FIG. 3, the threshold value is indicated by a one-dot chain line, and d ₁ = T ₁ and d ₈ = T ₈ , takes a minimum value _{d 2} in x _2, takes a maximum value _{d 4} in _{x 4,} it is assumed that the minima _{d 6} at _{x 6.} Also,
Δ = d ₃ −d ₂ = | T ₃ | (16)
Δ ′ = d ₄ −d ₅ = | T ₅ | (17)
Δ ″ = d ₇ −d ₆ = | T ₇ | (18)
When it is, this time, in the same manner as Example 1 above, it is determined that the official peak exists at the position of x ₂ in the original spectrum.
[0051]
Also, depending on the conditions ▲ 5 ▼ at the position of x ₅ it is determined that a candidate point of a new peak on the right side of the x _5, then the peak by the condition ▲ 3 ▼ at the position of x ₇ is determined to have ended According to the condition ( ₇₎ , it is determined that a formal peak exists at the x7 position of the original spectrum.
conditions on the right side than x ₈ ▲ 1 nothing is done by the ▼.
[0052]
[Example 4] Now, it is assumed that the second derivative spectrum of the smoothed spectrum is indicated by a solid line in FIG. 4 and the threshold value is indicated by an alternate long and short dash line, and d ₁ = T ₁ and d ₆ = T ₆ , takes a minimum value _{d 2} in x _2, takes a maximum value _{d 3} in _{x 3,} it is assumed that the minima _{d 4} in _{x 4.} Also,
d ₃ −d ₂ <| T ₃ | (19)
Δ = d ₅ −d ₄ = | T ₅ | (20)
Suppose that
[0053]
At this time, two positions x ₂ and x ₄ are determined as peak candidate points according to the condition (6). Then, it will be determined that the peak by the condition ▲ 3 ▼ at the position of x ₅ is completed, since in the case of FIG. 4 is a d _2> d _4, conditions ▲ 8 ▼ by the original spectrum x ₄ It is determined that a formal peak exists at the position of. nothing is done by the conditions ▲ 1 ▼ on the right side than x _6.
[0054]
Although four examples have been described above, it has been confirmed that the presence or absence of a peak in the actual original spectrum can be determined by the above conditions (1) to (8).
[0055]
As described above, according to the peak determination method of this spectrum, the method of changing the value of the secondary differential spectrum, the relationship between the value and the threshold value at each point of the secondary differential spectrum, and the point at each point of the secondary differential spectrum Since the presence or absence of a peak in the original spectrum is determined based on the relationship between the fluctuation from the nearby extreme value and the threshold at that time, two peaks that were conventionally determined as one peak as a whole It is possible to separate and determine as different peaks even when the peaks are close to each other and one peak appears over the shoulder of the other peak, and therefore the program for performing the above-described peak determination method processing And mount it on various analyzers, and perform the above-mentioned processing on the spectrum obtained as a result of measurement, thereby separating peaks that were not previously separated Since it is possible to detect Te is capable of improving the accuracy of analysis.
[0056]
Note that the noise standard deviation value can be calculated by the above-described method when noise is generated based on a probability event at the time of signal detection, and the present invention is applicable to EPMA, Auger analyzer, ESCA, fluorescence. The present invention can be applied to peak determination of a spectrum obtained from an analytical instrument such as an X-ray analyzer.
[0057]
As mentioned above, although embodiment of this invention was described, this invention is not limited to the said embodiment, A various deformation | transformation is possible. For example, in the above description, the spectrum obtained as a result of the measurement is smoothed, but this is not an essential requirement and can be omitted. In that case, p _{i + j} may be used as s _{i + j in} equation (3).
[Brief description of the drawings]
FIG. 1 is a diagram showing a first example for explaining a spectrum peak determination method according to the present invention.
FIG. 2 is a diagram showing a second example for explaining a spectrum peak determination method according to the present invention.
FIG. 3 is a diagram showing a third example for explaining a spectrum peak determining method according to the present invention.
FIG. 4 is a diagram showing a fourth example for explaining a spectrum peak determining method according to the present invention.
FIG. 5 is a diagram for explaining a conventional spectrum peak determination method and a problem to be solved by the present invention.

Claims (2)

In the case where there are local minimum values below the threshold at each position in the spectral region where the second derivative spectrum value is negative,
If there is only one position where the secondary differential spectrum value takes the minimum value, it is determined that a peak exists at the position where the minimum value is taken,
When there are a plurality of the minimum values, the secondary derivative spectrum value increases from a certain minimum value to take a maximum value, and then decreases, and the difference between the second derivative spectrum values from the maximum value is the position. If there is a position that is equal to or greater than the absolute value of the threshold value in the above, it is assumed that there is a new peak candidate point on the side larger than the position, and the secondary differential spectrum value increases from the minimum value, and the minimum value A method for determining a peak of a spectrum, characterized in that it is determined that a peak has ended at a position where a difference between the second-order differential spectrum values from the position becomes equal to or greater than an absolute value of a threshold value at that position . 2. The spectrum peak determination method according to claim 1 , wherein the threshold value is a noise standard deviation value obtained based on a standard deviation of a secondary differential spectrum .

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