JP2019184373A - Device and method for measuring particle size distribution and program for particle size distribution - Google Patents
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Abstract
Description
本発明は、検査光を粒子群に照射したときに生じる二次光の特性（例えば、回折／散乱光の空間強度分布やドップラーシフト等）に基づいて当該粒子群の粒子径分布を算出する粒子径分布測定装置に関するものである。 The present invention is a particle that calculates the particle size distribution of a particle group based on the characteristics of secondary light generated when the particle group is irradiated with inspection light (for example, spatial intensity distribution of diffraction / scattered light, Doppler shift, etc.) The present invention relates to a diameter distribution measuring apparatus.
従来の、例えば静的粒子径分布測定装置では、特許文献１に示すように、以下の式に基づいて粒子径分布を算出している。 In a conventional, for example, static particle size distribution measuring apparatus, as shown in Patent Document 1, the particle size distribution is calculated based on the following equation.
ω = M ν
ここで、ωは粒子群の周りに分散配置した複数の光検出器の出力信号から得られる二次光の空間強度分布を表すベクトル、νは粒子径分布を表すベクトル、Mは粒子群の屈折率等に係る物性と光検出器の配置位置によって一意的に定まる係数行列である。
ω = M ν
Here, ω is a vector representing the spatial intensity distribution of secondary light obtained from the output signals of a plurality of photodetectors distributed around the particle group, ν is a vector representing the particle diameter distribution, and M is the refraction of the particle group. It is a coefficient matrix uniquely determined by the physical properties related to the rate and the arrangement position of the photodetector.
ここで求めたいのは粒子径分布を表すベクトルνであるが、これが右辺にあるため、逆問題を解くことになる。 What we want to find here is a vector ν representing the particle size distribution, but since this is on the right side, the inverse problem is solved.
そのために従来は、例えば反復解法を用いてベクトルν（粒子径分布）を算出するようにしている。反復解法とは、最初に粒子径分布の仮想解を与え、その仮想解が所定条件を満たすまで次々更新し、その結果得られた仮想解を粒子径分布として算出するものである。発散することなく安定的に解を算出する反復解法の一例としては、解のエントロピー最大化を目指すLandweber、SIR、ART、Chahine、ModifiedChahine、Chahine-Twomey 法といったエントロピー最大化解法がある。 Therefore, conventionally, for example, a vector ν (particle size distribution) is calculated using an iterative solution. In the iterative solution method, a virtual solution of the particle size distribution is first given, the virtual solution is successively updated until a predetermined condition is satisfied, and the resulting virtual solution is calculated as the particle size distribution. An example of an iterative solution method that stably calculates a solution without divergence is an entropy maximization method such as Landweber, SIR, ART, Chahine, ModifiedChahine, or Chahine-Twomey method that aims to maximize the entropy of the solution.
しかしながら、例えばピケットフェンスなどのように、粒子径分布波形に複数のピークがあり、かつ、各ピーク波形の幅が狭い試料に対して、エントロピー最大化を目指す上記解法では、精度よく粒子径分布を測定することが難しい。 However, for example, a picket fence, where the particle size distribution waveform has a plurality of peaks and each peak waveform has a narrow width, the above-mentioned solution aiming at maximal entropy can accurately calculate the particle size distribution. Difficult to measure.
本発明は、かかる問題に鑑み、本発明者の鋭意検討の結果はじめてなされたものであって、やや安定性にはやや欠けるきらいはあるものの検出力が高い最尤法を利用したEM法を組み合わせることにより、前記逆問題を安定的に解くことができて、しかもピケットフェンスなどの試料に対しても精度よく粒子径分布を測定できる粒子径分布測定装置等を提供すべく図ったものである。 The present invention has been made for the first time as a result of the inventor's diligent study in view of such problems, and is combined with the EM method using the maximum likelihood method with high detection power although there is a slight lack of stability. Accordingly, the present invention is intended to provide a particle size distribution measuring apparatus and the like that can stably solve the inverse problem and can accurately measure the particle size distribution even for a sample such as a picket fence.
すなわち、本発明に係る粒子径分布測定装置は、分散された粒子群に検査光を照射する光源と、前記検査光が粒子群に当たって生じる二次光を受光する受光部と、前記受光部の出力信号から得られる二次光の特性（以下、実二次光特性と言う。）に基づいて前記粒子群の粒子径分布を算出する演算部とを具備し、該演算部が、粒子径分布の仮想解から算出される仮想的な二次光の特性（以下、仮想二次光特性と言う。）を前記実二次光特性に近づけるべく前記仮想解を１回以上更新し、その結果得られた仮想解を粒子径分布として算出する反復解法を用いるものである。 That is, the particle size distribution measuring apparatus according to the present invention includes a light source that irradiates a dispersed particle group with inspection light, a light receiving unit that receives secondary light generated when the inspection light strikes the particle group, and an output of the light receiving unit. A calculation unit that calculates a particle size distribution of the particle group based on characteristics of secondary light obtained from the signal (hereinafter referred to as actual secondary light characteristics), and the calculation unit includes The virtual solution is updated at least once in order to bring the characteristics of the virtual secondary light calculated from the virtual solution (hereinafter referred to as virtual secondary light characteristics) closer to the actual secondary light characteristics, and the result is obtained. The iterative solution is used to calculate the virtual solution as the particle size distribution.
しかして、前記演算部の用いる反復解法が、EM法に属する反復解法である第1解法とChahine法に属する反復解法である第２解法とが所定の関係で組み合わせた組み合わせ反復解法であることを特徴とするものである。 Thus, the iterative solution used by the arithmetic unit is a combined iterative solution in which a first solution that is an iterative solution belonging to the EM method and a second solution that is an iterative solution belonging to the Chahine method are combined in a predetermined relationship. It is a feature.
より具体的には、前記第１解法がEMLS法であり、前記第２解法がModeified-Chahine法であることが好ましい。 More specifically, it is preferable that the first solution is an EMLS method and the second solution is a Moded-Chahine method.
前記組み合わせ反復解法の具体的な態様としては、例えば、第１解法を適用した後、それで得られた仮想解に第２解法を適用するといったように、第１解法と第２解法とをシーケンシャルに行う解法でもよいが、第１解法と第２解法との長所を引き出し短所を補うような組み合わせ解法をより簡便なアルゴリズムで実現するためには、前記組み合わせ反復解法が、所定の数式で表されるものであって、前記第1解法を示す式部分と前記第２解法を示す式部分とを含んだものにしておくことが望ましい。 As a specific aspect of the combined iterative solution method, for example, the first solution method and the second solution method are sequentially applied so that, after the first solution method is applied, the second solution method is applied to the virtual solution obtained by the first solution method. In order to realize a combined solution that draws out the advantages of the first solution and the second solution and compensates for the disadvantages with a simpler algorithm, the combined iterative solution is expressed by a predetermined mathematical formula. It is desirable to include an equation part indicating the first solution and an equation part indicating the second solution.
その場合において、前記第1解法と前記第２解法との寄与度を簡便に設定できるようにし、種々の試料においてより精度よく粒子径分布を測定できるようにするには、前記組み合わせ反復解法を示す所定の数式に、前記第１解法と前記第２解法との重み割合を定める重み係数が含まれていることが望ましい。 In that case, the combined iterative solution method is shown in order to make it possible to easily set the contribution between the first solution and the second solution and to measure the particle size distribution more accurately in various samples. It is desirable that a predetermined coefficient includes a weight coefficient that determines a weight ratio between the first solution and the second solution.
具体的な実施態様としては、前記組み合わせ反復解法に以下の数式が用いられるものを挙げることができる。 As a concrete embodiment, the following mathematical formula can be used for the combined iterative solution.
ν(k)は、前記組み合わせ反復解法をk回適用して得られた仮想解であり、kは反復回数を示す０以上の整数である。
αpは、EMLS法において計算の途中に用いられる中間値であり、βは、散乱光パターンなどの実二次光特性と仮想二次光特性との比である。
なお、ν(k)、p(k)、β(k)、a、ｂ、ｃはベクトル、Cm、α(k)、ｄは、スカラーである。
ν (k) is a virtual solution obtained by applying the combined iterative solution k times k, and k is an integer of 0 or more indicating the number of iterations.
αp is an intermediate value used during the calculation in the EMLS method, and β is a ratio between the real secondary light characteristic such as the scattered light pattern and the virtual secondary light characteristic.
Note that ν (k) , p (k) , β (k) , a, b, and c are vectors, and Cm, α (k) , and d are scalars.
前記重み係数Cmの好適な値としては、0より大きく0.1以下を挙げることができる。 A preferable value of the weighting factor Cm is greater than 0 and 0.1 or less.
以上に述べた本発明によれば、ピケットフェンスなどのような従来であれば粒子径分布の測定が難しい試料に対しても、安定的に、かつ精度よく粒子径分布を測定することができるようになる。 According to the present invention described above, it is possible to measure the particle size distribution stably and accurately even for a sample such as a picket fence that is difficult to measure in the past. become.
以下に本発明の一実施形態について図面を参照して説明する。 An embodiment of the present invention will be described below with reference to the drawings.
本実施形態に係る粒子径分布測定装置１は、図１に示すように、分散する粒子群Ｓに検査光Ｌを当てたときに生じる二次光である回折／散乱光ＬＳの特性、すなわち光強度の空間分布を検出することによってＭＩＥ散乱理論から粒子径分布を測定するものである。 As shown in FIG. 1, the particle size distribution measuring apparatus 1 according to the present embodiment has characteristics of diffracted / scattered light LS that is secondary light generated when the inspection light L is applied to the dispersed particle group S, that is, light. The particle size distribution is measured from the MIE scattering theory by detecting the spatial distribution of intensity.
同図中、符号Ｃは、分散媒中に分散させた測定対象である粒子群Ｓを収容するセルである。前記分散媒は、湿式の場合は水、乾式の場合は空気が一般的である。 In the figure, reference numeral C denotes a cell that accommodates a particle group S that is a measurement target dispersed in a dispersion medium. The dispersion medium is generally water in the case of wet and air in the case of dry.
符号２は、前記セルＣに検査光Ｌを照射する光源である。この実施形態では光源として、例えばコヒーレントなレーザ光を照射する半導体レーザを用いている。 Reference numeral 2 denotes a light source for irradiating the cell C with the inspection light L. In this embodiment, as a light source, for example, a semiconductor laser that emits coherent laser light is used.
符号３１、３２は、前記セルＣの周囲に配置した受光部たる光検出器であり、検査光Ｌが粒子群Ｓに当たって生じる回折／散乱光ＬＳの角度毎の光強度を検出する。 Reference numerals 31 and 32 are photodetectors that are light receiving portions arranged around the cell C, and detect the light intensity for each angle of the diffracted / scattered light LS generated when the inspection light L strikes the particle group S.
符号８は、光検出器３２の受光面中央に検査光Ｌが収斂するように設定された凸レンズである。 Reference numeral 8 denotes a convex lens that is set so that the inspection light L converges at the center of the light receiving surface of the photodetector 32.
符号４は、前記各光検出器３１、３２からの出力信号を受信し、変換等の処理を行うバッファ、増幅器等で構成されている信号処理部である。 Reference numeral 4 denotes a signal processing unit configured by a buffer, an amplifier, and the like that receive output signals from the photodetectors 31 and 32 and perform processing such as conversion.
符号５は、信号処理部４で処理された各出力信号の値から得られる二次光の空間強度分布（請求項で言う実二次光特性に相当し、以下、実光強度分布と言う。）に基づいて、前記粒子群の粒子径分布を算出する演算部である。この演算部５は、ＣＰＵ、メモリなどから構成された所謂コンピュータ（データ処理装置）であり、前記メモリの所定領域に格納されたプログラムにしたがってＣＰＵやその周辺機器が協働することによって、図２に示すように、実光強度分布算出部５０、解法実行部５１、評価部５２などとしての機能を担う。 Reference numeral 5 denotes a spatial intensity distribution of secondary light obtained from the value of each output signal processed by the signal processing unit 4 (corresponding to the actual secondary light characteristic referred to in the claims, and hereinafter referred to as the actual light intensity distribution). ) To calculate the particle size distribution of the particle group. The arithmetic unit 5 is a so-called computer (data processing device) composed of a CPU, a memory, and the like, and the CPU and its peripheral devices cooperate in accordance with a program stored in a predetermined area of the memory. As shown in FIG. 4, the functions of the actual light intensity distribution calculation unit 50, the solution execution unit 51, the evaluation unit 52, and the like are performed.
実光強度分布算出部５０は、信号処理部４で処理された各出力信号の値から実光強度分布を算出するものである。 The actual light intensity distribution calculation unit 50 calculates the actual light intensity distribution from the value of each output signal processed by the signal processing unit 4.
解法実行部５１は、従来例で述べた式ω = M νをνについて解くことによって粒子径分布を算出するものである。 The solution execution unit 51 calculates the particle size distribution by solving the equation ω = Mν described in the conventional example for ν.
より具体的に説明すると、この解法実行部５１は、図２に示すように、粒子径分布の仮想解から算出される仮想的な二次光の空間強度分布（請求項で言う仮想二次光特性に相当し、以下、仮想光強度分布と言う。）を算出する仮想光強度分布算出部５１ａと、前記仮想光強度分布を前記実光強度分布に近づけるべく仮想解を更新する仮想解更新部５１ｂとを具備し、前記仮想光強度分布算出部５１ａと仮想解更新部５１ｂとの動作を交互に繰り返し行うことによって得られた仮想解を粒子径分布として算出するものである。なお、繰り返し回数（反復回数）は予め定めた一定回数でもよいし、後述する評価値が所定の閾値を超えた時点等で終了するようにしてもよい。 More specifically, as shown in FIG. 2, the solution execution unit 51, as shown in FIG. 2, calculates the spatial intensity distribution of the virtual secondary light calculated from the virtual solution of the particle size distribution (the virtual secondary light referred to in the claims). A virtual light intensity distribution calculating unit 51a that calculates a virtual light intensity distribution), and a virtual solution updating unit that updates the virtual solution to bring the virtual light intensity distribution closer to the actual light intensity distribution. The virtual solution obtained by alternately repeating the operations of the virtual light intensity distribution calculating unit 51a and the virtual solution updating unit 51b is calculated as a particle size distribution. Note that the number of repetitions (the number of repetitions) may be a predetermined fixed number, or may be terminated when an evaluation value, which will be described later, exceeds a predetermined threshold.
前記仮想光強度分布算出部５１ａは、従来例で述べた式であるω = Mνに基づいて、粒子径分布の仮想解ν(k)から仮想光強度分布ωvを算出するものである。 The virtual light intensity distribution calculating unit 51a calculates the virtual light intensity distribution ω v from the virtual solution ν (k) of the particle diameter distribution based on ω = Mν which is the formula described in the conventional example.
前記仮想解更新部５１ｂは、この実施形態では、組み合わせ反復解法に基づいて仮想光強度分布を算出するものである。ここでいう組み合わせ反復解法とは、EM法（expectation-maximization algorithm）とChahine法とを組み合わせたものである。ここでＥＭ法は、観測できない変数が存在する確率モデルにおいてパラメータの最尤推定値を求めるための手法である。Chahine法は、一般に漸化式ν(k)= VProd(γ(k),ν (k))で（γ(k)はベクトル係数）で表される反復解法である。本実施形態では特にEMLS（expectation-maximization algorithm least square）法とModified-Chahine法とを組み合わせた以下の式で表される解法を用い、メモリの所定領域中に関数として記憶されている。仮想解更新部５１ｂは、この関数を呼び出して演算を行う。 In this embodiment, the virtual solution update unit 51b calculates a virtual light intensity distribution based on a combined iterative solution. The combined iterative solution here is a combination of the EM method (expectation-maximization algorithm) and the Chahine method. Here, the EM method is a method for obtaining a maximum likelihood estimation value of a parameter in a probability model in which a variable that cannot be observed exists. The Chahine method is an iterative method generally expressed by a recursion formula ν (k) = VProd (γ (k) , ν (k) ) (where γ (k) is a vector coefficient). In the present embodiment, a solution represented by the following expression, which is a combination of the EMLS (expectation-maximization algorithm least square) method and the Modified-Chahine method, is used, and is stored as a function in a predetermined area of the memory. The virtual solution update unit 51b performs an operation by calling this function.
この式（数２）において、Cmは、0以上1以下の値をとる重み係数（スカラー）であり、オペレータによる入力など外部から変更設定可能なようにメモリに予め記憶されている。しかして、Cmが0のとき、本式はEMLS法を表す式と合致し、Cmが1のときはModified-Chahine法を表す式と合致する。この実施形態では、Cmは0.03に設定してあり、この組み合わせ解法が、検出力の高いEMLS法の重み割合を大きくしてこれを主体としつつ、安定度の高いModified-Chahine法を補正項として加えたものとなるように設定してある。 In this equation (Equation 2), Cm is a weighting coefficient (scalar) having a value of 0 or more and 1 or less, and is stored in advance in a memory so that it can be changed and set from the outside such as an input by an operator. Thus, when Cm is 0, this equation matches the equation representing the EMLS method, and when Cm is 1, it agrees with the equation representing the Modified-Chahine method. In this embodiment, Cm is set to 0.03, and this combined solution increases the weight ratio of the EMLS method with high power and mainly uses it, and the highly stable Modified-Chahine method is used as a correction term. It is set to be added.
ここで、kは反復回数を示す０以上の整数である。 Here, k is an integer of 0 or more indicating the number of iterations.
ν(k)は、粒子径分布の仮想解（ベクトル）である。したがって、ν(0)が初期仮想解となるが、その値（各要素の値）は、オペレータによる入力など外部から変更設定可能なようにメモリに予め記憶されている。 ν (k) is a virtual solution (vector) of the particle size distribution. Therefore, although ν (0) is an initial virtual solution, its value (value of each element) is stored in advance in a memory so that it can be changed and set from the outside such as an input by an operator.
αpは、EMLS法において計算の途中に用いられる中間値（ベクトル）であり、現在の解（k-1回目の解）から、次の解への差分（現在の解の微分係数）を表す。 αp is an intermediate value (vector) used during the calculation in the EMLS method, and represents a difference (differential coefficient of the current solution) from the current solution (k−1 solution) to the next solution.
βは、実光強度分布（ベクトル）と仮想光強度分布（ベクトル）との各対応要素の比で表される係数ベクトルである。Chahine法を基にした改良解法では、各要素に重み付けされる場合もある。 β is a coefficient vector represented by the ratio of each corresponding element between the real light intensity distribution (vector) and the virtual light intensity distribution (vector). In the improved solution based on the Chahine method, each element may be weighted.
評価部５２は、前記仮想解ν(k)の確からしさを示す評価値を算出するとともに、その評価値に応じて、前記解法実行部５１の算出した仮想解を最終的な粒子径分布として出力するか、あるいは、再度、解法実行部５１に仮想解を更新させるかを決定するものである。前記評価値とは、基本的には、評価したい仮想解から算出される仮想光強度分布と実光強度分布との距離を表す値のことである。ここでは仮想光強度分布と実光強度分布との残差平方和を算出しているが、その他に尤度などでも構わない。 The evaluation unit 52 calculates an evaluation value indicating the probability of the virtual solution ν (k) , and outputs the virtual solution calculated by the solution execution unit 51 as a final particle size distribution according to the evaluation value. Or it is determined again whether the solution execution unit 51 should update the virtual solution. The evaluation value is basically a value representing the distance between the virtual light intensity distribution calculated from the virtual solution to be evaluated and the actual light intensity distribution. Here, the residual sum of squares of the virtual light intensity distribution and the actual light intensity distribution is calculated, but likelihood or the like may be used.
次に、かかる構成の粒子径分布測定装置１の動作を図に基づいて説明する。 Next, operation | movement of the particle diameter distribution measuring apparatus 1 of this structure is demonstrated based on figures.
測定したい粒子群に検査光が照射されると、実光強度分布算出部５０が、各光検出器３１、３２の出力信号の値から、回折／散乱光の光強度分布（光強度分布ベクトル）である実光強度分布ωrを算出する（ステップＳ１）。 When the inspection light is irradiated to the particle group to be measured, the actual light intensity distribution calculating unit 50 calculates the light intensity distribution (light intensity distribution vector) of the diffracted / scattered light from the output signal values of the photodetectors 31 and 32. The actual light intensity distribution ω r is calculated (step S1).
次に、前記仮想光強度分布算出部５１ａが、k = 0として初期仮想解ν(0)を取得し、前記式（数２）に基づいて、初期仮想解ν(0)から仮想光強度分布ωvを算出する（ステップＳ２〜Ｓ４）。 Next, the virtual light intensity distribution calculating unit 51a obtains an initial virtual solution ν (0) with k = 0, and based on the equation (Equation 2), the virtual light intensity distribution from the initial virtual solution ν (0). ω v is calculated (steps S2 to S4).
次に評価部５２が、実光強度分布ωrと仮想光強度分布ωvとに基づいて、評価値Nを算出する（ステップＳ５）。 Next, the evaluation unit 52 calculates an evaluation value N based on the actual light intensity distribution ω r and the virtual light intensity distribution ω v (step S5).
この評価値Nが予め定められた閾値以内の場合は、評価部５２は、前記仮想解ν(k)を粒子径分布の測定結果として出力する（ステップＳ９）。 When the evaluation value N is within a predetermined threshold value, the evaluation unit 52 outputs the virtual solution ν (k) as a measurement result of the particle size distribution (step S9).
他方、そうでない場合は、仮想光強度分布算出部５１ａが、kをインクリメントした後、前記式（数２）に基づいて、仮想解ν(k)を算出更新する（ステップＳ７、Ｓ８）。そして、前記ステップＳ４に戻る。 On the other hand, if not, the virtual light intensity distribution calculation unit 51a increments k, and then calculates and updates the virtual solution ν (k) based on the equation (Equation 2) (steps S7 and S8). Then, the process returns to step S4.
次に、以上のように構成した本実施形態の効果について説明する。 Next, the effect of the present embodiment configured as described above will be described.
図４は、ピケットフェンスと称される試料を、EMLS法（Cm = 0）、本組み合わせ解法（Cm = 0.03）及びModified-Chahine法（Cm =1）の３つで測定した結果を示している。 Fig. 4 shows the results of measuring a sample called a picket fence by three methods: EMLS method (Cm = 0), this combined solution method (Cm = 0.03), and Modified-Chahine method (Cm = 1). .
前述したように、本組み合わせ解法によれば、他の解法による測定結果よりも精度が良いことがわかる。 As described above, according to this combined solution, it can be seen that the accuracy is better than the measurement results obtained by other solutions.
また、図５に、１０万種類の６ピークピケットフェンスをシミュレーションで評価した例を示す。このグラフでは、D50の相対差の頻度分布（Density distribution）を対数軸にプロットしてあり、本組み合わせ解法によるCm = 0.03のときが、もっとも差が少ないことがわかる。すなわち、従来解法（Cm=0.0 および 1.0）では、対数軸が0の付近に高い頻度のピークが存在するが、Cm=0.03 のときは、このピークが抑制されており、フィッティングの失敗が大きく改善されている。また、頻度のメインピークも従来解法より左側に位置しており、これは残差がより少ない、優れた解法であることを示している。 FIG. 5 shows an example in which 100,000 types of 6-peak picket fences are evaluated by simulation. In this graph, the frequency distribution of the relative difference of D50 (Density distribution) is plotted on the logarithmic axis, and it can be seen that the difference is the smallest when Cm = 0.03 according to the combined solution method. In other words, in the conventional solution (Cm = 0.0 and 1.0), there is a high-frequency peak near the logarithmic axis of 0, but when Cm = 0.03, this peak is suppressed and fitting failure is greatly improved. Has been. The main frequency peak is also located on the left side of the conventional solution, indicating that this is an excellent solution with fewer residuals.
なお、本発明は前記実施形態に限られない。例えば、Cmは、0.03のみならず、0.03±0.003の範囲で設定してもよい。試料および測定機器の光学系によっては、0より大きく0.1以下の間、特に0.02~0.1の間で変更してさらに好適な結果を得ることができる。また、組み合わせ解法に用いる２種の反復解法は、検出力の高いEM法に属する反復解法と安定力の高いChahine法に属する反復解法であればよい。その組み合わせ式も前記実施形態に限られるものではない。 The present invention is not limited to the above embodiment. For example, Cm may be set within a range of 0.03 ± 0.003 as well as 0.03. Depending on the optical system of the sample and the measuring instrument, a more preferable result can be obtained by changing between 0 and 0.1 or less, particularly 0.02 to 0.1. In addition, the two types of iterative solutions used for the combination solution may be an iterative solution belonging to the EM method having high power and an iterative solution belonging to the Chahine method having high stability. The combination formula is not limited to the above embodiment.
演算部５に関し、粒子径分布測定装置１とは独立したコンピュータにおいて本願発明に係るプログラムを実行することによって、演算部５における少なくとも解法実行部５１および評価部５２と同様の機能を有するデータ処理装置を実現しても良い。すなわち、データ処理装置において、粒子径分布測定装置１から取り込むなどの手段で得た実光強度分布のデータに対して組み合わせ反復解法を適用し、粒子径分布を算出しても良い。 A data processing device having at least functions similar to those of the solution execution unit 51 and the evaluation unit 52 in the calculation unit 5 by executing the program according to the present invention in a computer independent of the particle size distribution measuring device 1 with respect to the calculation unit 5. May be realized. That is, in the data processing device, the particle size distribution may be calculated by applying a combined iterative solution to the actual light intensity distribution data obtained by means such as taking in from the particle size distribution measuring device 1.
その他、本発明の趣旨に反しない限りにおいて様々な実施形態の変形や組み合わせを行っても構わない。 In addition, various modifications and combinations of the embodiments may be made without departing from the spirit of the present invention.
１００・・・粒子径分布測定装置
２・・・光源
３１、３２・・・受光部
５・・・演算部
DESCRIPTION OF SYMBOLS 100 ... Particle size distribution measuring apparatus 2 ... Light source 31, 32 ... Light-receiving part 5 ... Calculation part
Claims (7)
前記演算部が、粒子径分布の仮想解から算出される仮想的な二次光の特性（以下、仮想二次光特性と言う。）を前記実二次光特性に近づけるべく前記仮想解を１回以上更新し、その結果得られた仮想解を粒子径分布として算出する反復解法を用いるものであって、
前記演算部が、EM法に属する反復解法である第1解法とChahine法に属する反復解法である第２解法とを所定の関係で組み合わせた反復解法である組み合わせ反復解法を用いるものであることを特徴とする粒子径分布測定装置。 A light source for irradiating inspection light to the particle group to be dispersed, a light receiving part for receiving secondary light generated when the inspection light hits the particle group, and characteristics of secondary light obtained from an output signal of the light receiving part (hereinafter referred to as real two) A calculation unit that calculates the particle size distribution of the particle group based on the following light characteristics),
The calculation unit sets the virtual solution to 1 so that the virtual secondary light characteristic (hereinafter referred to as virtual secondary light characteristic) calculated from the virtual solution of the particle size distribution approaches the real secondary light characteristic. It uses an iterative solution that updates more than once and calculates the resulting virtual solution as a particle size distribution,
The arithmetic unit uses a combination iterative solution that is an iterative solution in which a first solution that is an iterative solution that belongs to the EM method and a second solution that is an iterative solution that belongs to the Chahine method are combined in a predetermined relationship. Characteristic particle size distribution measuring device.
ν(k)は、前記組み合わせ反復解法をk回適用して得られた仮想解であり、kは反復回数を示す０以上の整数である。
αpは、EMLS法において計算の途中に用いられる中間値であり、βは、散乱光パターンなどの実二次光特性と仮想二次光特性との比である。
なお、ν(k)、p(k)、β(k)、a、ｂ、ｃはベクトル、Cm、α(k)、ｄは、スカラーである。 The particle size distribution measuring apparatus according to claim 2, wherein the combined iterative solution method uses the following mathematical formula.
ν (k) is a virtual solution obtained by applying the combined iterative solution k times k, and k is an integer of 0 or more indicating the number of iterations.
αp is an intermediate value used during the calculation in the EMLS method, and β is a ratio between the real secondary light characteristic such as the scattered light pattern and the virtual secondary light characteristic.
Note that ν (k) , p (k) , β (k) , a, b, and c are vectors, and Cm, α (k) , and d are scalars.
前記反復解法として、EM法に属する反復解法である第1解法とChahine法に属する反復解法である第２解法とを所定の関係で組み合わせた反復解法である組み合わせ反復解法を用いることを特徴とする粒子径分布測定方法。 The dispersed particle group is irradiated with inspection light, and the particle size distribution of the particle group is calculated based on the characteristics of secondary light generated when the inspection light hits the particle group (hereinafter referred to as actual secondary light characteristics). In this case, the virtual solution is updated a plurality of times in order to bring the virtual secondary light characteristic (hereinafter referred to as virtual secondary light characteristic) calculated from the virtual solution of the particle size distribution closer to the actual secondary light characteristic. In the particle size distribution measurement method, which uses an iterative method for calculating the resulting virtual solution as a particle size distribution,
As the iterative solution method, a combined iterative solution method that is an iterative solution in which a first solution method that is an iterative solution method that belongs to the EM method and a second solution method that is an iterative solution method that belongs to the Chahine method is combined in a predetermined relationship is used. Particle size distribution measurement method.
前記演算部に、EM法に属する反復解法である第1解法とChahine法に属する反復解法である第２解法とを所定の関係で組み合わせた反復解法である組み合わせ反復解法を用いて粒子径分布を算出する機能を発揮させることを特徴とする粒子径分布算出用プログラム。 Data provided with an arithmetic unit for calculating the particle size distribution of the particle group based on data indicating the characteristic of secondary light generated when the inspection light strikes the dispersed particle group (hereinafter referred to as actual secondary light characteristic) A program installed in a processing device,
In the calculation unit, the particle size distribution is calculated by using a combination iterative solution that is an iterative solution in which a first solution that is an iterative solution that belongs to the EM method and a second solution that is an iterative solution that belongs to the Chahine method are combined in a predetermined relationship. A program for calculating a particle size distribution characterized by having a function of calculating.
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