JPH0327065B2 - - Google Patents
Info
- Publication number
- JPH0327065B2 JPH0327065B2 JP59202281A JP20228184A JPH0327065B2 JP H0327065 B2 JPH0327065 B2 JP H0327065B2 JP 59202281 A JP59202281 A JP 59202281A JP 20228184 A JP20228184 A JP 20228184A JP H0327065 B2 JPH0327065 B2 JP H0327065B2
- Authority
- JP
- Japan
- Prior art keywords
- function
- diffraction image
- particle size
- size distribution
- transformation
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired
Links
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N15/00—Investigating characteristics of particles; Investigating permeability, pore-volume or surface-area of porous materials
- G01N15/02—Investigating particle size or size distribution
- G01N15/0205—Investigating particle size or size distribution by optical means
- G01N15/0211—Investigating a scatter or diffraction pattern
Landscapes
- Chemical & Material Sciences (AREA)
- Dispersion Chemistry (AREA)
- Physics & Mathematics (AREA)
- Health & Medical Sciences (AREA)
- Life Sciences & Earth Sciences (AREA)
- Analytical Chemistry (AREA)
- Biochemistry (AREA)
- General Health & Medical Sciences (AREA)
- General Physics & Mathematics (AREA)
- Immunology (AREA)
- Pathology (AREA)
- Investigating Or Analysing Materials By Optical Means (AREA)
- Length Measuring Devices By Optical Means (AREA)
Description
【発明の詳細な説明】
（産業上の利用分野）
本発明は、フラウンフオーフアー回折像の積分
変換を用いる粒度分布測定法に関する。粒子の大
きさやその分布状態を計測することは、粉粒体工
学、細胞学、大気汚染計測のみならず、鉄鉱、食
品、薬品などの製造業においても、品質管理、製
造工程制御などによつて極めて重要な問題となつ
ている。DETAILED DESCRIPTION OF THE INVENTION (Industrial Application Field) The present invention relates to a particle size distribution measuring method using integral transformation of a Fraunhofer diffraction image. Measuring the size of particles and their distribution state is used not only in powder and granule engineering, cytology, and air pollution measurement, but also in the manufacturing industry of iron ore, food, medicine, etc., for quality control, manufacturing process control, etc. This has become an extremely important issue.
（従来の技術）
従来、コヒーレント光を用いた粒度分布測定法
としては、光散乱分光法や、コヒーレント光の回
折像から行列計算により求める方法などが知られ
ている。(Prior Art) Conventionally, known methods for measuring particle size distribution using coherent light include light scattering spectroscopy and a method of determining particle size distribution by matrix calculation from a diffraction image of coherent light.
（発明が解決しようとする問題点）
しかしながら、従来のコヒーレント光を用いた
粒度分布測定法はいずれにおいても広範囲にわた
つて任意の粒度分布を導出することが原理的に不
可能であつた。(Problems to be Solved by the Invention) However, in any of the conventional particle size distribution measurement methods using coherent light, it is theoretically impossible to derive an arbitrary particle size distribution over a wide range.
本発明は、上記に鑑みなされたものであつて、
フラウンフオーフアー回折像を用いて連続的な粒
度分布を測定する方法を提供することを目的とす
る。 The present invention has been made in view of the above, and includes:
The object of the present invention is to provide a method for measuring continuous particle size distribution using a Fraunhofer diffraction image.
（問題点を解決するための手段及び作用）
上記目的は、次のステツプによつて達成され
る。(Means and actions for solving the problem) The above objective is achieved by the following steps.
() ランダムに分布している粒子にコヒーレン
ト光を投射してフラウンフオーフアー回折像を
形成し、
() このフラウンフオーフアー回折像の中心か
ら半径方向に沿つての距離ωの位置における回
折像強度Ｉ（ω）を光電変換装置によつて電気
信号として検出し、
() この回折像強度Ｉ（ω）に前記中心からの
距離ωを乗じた関数に１次のハンケル変換を施
してｘを変数とする関数Ｈ（ｘ）を得、
() この関数Ｈ（ｘ）にフーリエ変換を施して
ξを変数とする関数Ｆ（ξ）を得、
() この関数Ｆ（ξ）にξを乗じた関数に１次
のハンケル変換を施して粒度分布を求める。() Form a Fraunhofer diffraction image by projecting coherent light onto randomly distributed particles; () Diffraction at a position ω along the radial direction from the center of this Fraunhofer diffraction image. The image intensity I(ω) is detected as an electrical signal by a photoelectric conversion device, and () a function obtained by multiplying this diffraction image intensity I(ω) by the distance ω from the center is subjected to first-order Hankel transformation to obtain x Obtain a function H(x) with ξ as a variable, () Perform Fourier transform on this function H(x) to obtain a function F(ξ) with ξ as a variable, () Add ξ to this function F(ξ). A first-order Hankel transformation is applied to the multiplied function to obtain the particle size distribution.
（実施例）
以下、添付図により本発明を説明する。第１図
は本発明の測定法の実施に用いる装置の一例であ
つて、被測定粒子のフラウンフオーフアー回折像
を得るための光学系ならびに信号処理系を示す。(Example) The present invention will be described below with reference to the accompanying drawings. FIG. 1 is an example of an apparatus used to carry out the measurement method of the present invention, and shows an optical system and a signal processing system for obtaining a Fraunhofer diffraction image of a particle to be measured.
光源１からはレーザー光等のコヒーレント光２
が放出される。このコヒーレント光２は光学系
３，３′によつて平行充にされた後ランダムに分
布する粒子群４に投射される。粒子群４を透過し
たコヒーレント光２はフーリエ変換レンズ５を透
過した後、面６においてフラウンフオーフアー回
折像（フーリエ変換像）を形成する。このフラウ
ンフオーフアー回折像の半径方向にわたつての各
位置の光強度Ｉ（ω）は光電変換装置７によつて
電気信号に変換される。この光電変換装置７とし
てはフオトマル、ダイオードアレイ、TVカメラ
等を使用できる。光電変換装置７から出力される
電気信号はデジタル化された後信号処理装置８に
入力される。この信号処理装置８は電気信号とし
て入力された回折像強度Ｉ（ω）を本発明のステ
ツプに従つて処理し、これによつて粒度分布が客
められる。ｆ（γ）のｎ次のハンケル変換Hn（ρ）
とフーリエ変換とには次のような関係、
ｆ（γ）ein〓←→2πHo（ρ）e-in〓
（但し、（γ、θ）および（ρ、η）は極座標で
あり、←→は２次元フーリエ変換を表わす。）があ
るので、ステツプ（）および（）のハンケル
変換を２次元フーリエ変換によつて達成すること
ができる。従つて、信号処理装置８としては、フ
ーリエ変換器、乗算器メモリを備えてなるものを
使用することができるが、汎用コンピユータに所
定のプログラムをストアすることによつても達成
することができる。求められた粒度分布は出力装
置によつて出力表示される。 Coherent light 2 such as laser light is emitted from light source 1.
is released. This coherent light 2 is collimated by optical systems 3 and 3' and then projected onto a randomly distributed particle group 4. The coherent light 2 that has passed through the particle group 4 passes through the Fourier transform lens 5 and forms a Fraunhofer diffraction image (Fourier transform image) on the surface 6 . The light intensity I(ω) at each position in the radial direction of this Fraunhofer diffraction image is converted into an electrical signal by a photoelectric conversion device 7. As this photoelectric conversion device 7, a photo camera, a diode array, a TV camera, etc. can be used. The electrical signal output from the photoelectric conversion device 7 is input into the signal processing device 8 after being digitized. This signal processing device 8 processes the diffraction image intensity I(ω) inputted as an electric signal according to the steps of the present invention, thereby determining the particle size distribution. n-th Hankel transformation of f(γ) Hn(ρ)
and the Fourier transform have the following relationship, f(γ)e in 〓←→2πH o (ρ)e -in 〓 (However, (γ, θ) and (ρ, η) are polar coordinates, and ← → represents a two-dimensional Fourier transform.) Therefore, the Hankel transform of steps () and () can be achieved by a two-dimensional Fourier transform. Therefore, as the signal processing device 8, one equipped with a Fourier transformer and a multiplier memory can be used, but the present invention can also be achieved by storing a predetermined program in a general-purpose computer. The determined particle size distribution is output and displayed by an output device.
次に、本発明によつて粒度分布が正確に求めら
れることを証明する。 Next, it will be demonstrated that the particle size distribution can be accurately determined by the present invention.
いま、粒度分布Ｎ(a)を次式で仮定する。 Now, assume that the particle size distribution N(a) is expressed by the following equation.
Ｎ(a)＝ｕ（ａ−３）ｕ（ｑ−ａ） ……(1) ここでｕ(a)は単位ステツプ関数を示す。 N(a)=u(a-3)u(q-a)...(1) Here, u(a) represents a unit step function.
得られる粒子のフラウンフオーフアー回折像の
光強度を表わす電気信号Ｉ（ω）は、
Ｉ（ω）＝k∫∞ 0｛J1（aω）／aω｝2
Ｎ(a)a4da ……(2)
（ただし、ωは回折像面上の動径座標、ｋは定
数）で表わされる。第２図にＩ（ω）ωを表わす
関係曲線を示した。 The electrical signal I(ω) representing the light intensity of the resulting Fraunhofer diffraction image of the particle is I(ω)=k∫ ∞ 0 {J 1 (aω)/aω} 2 N(a)a 4 da... ...(2) (where ω is the radial coordinate on the diffraction image plane, and k is a constant). FIG. 2 shows a relational curve representing I(ω)ω.
この電気信号Ｉ（ω）ωにωJ1（2xω）を乗じ
〔０、∞〕の範囲で積分するすなわち１次のハン
ケル変換をすると、新たな関数Ｈ（ｘ）は次式で
表わされる。 When this electric signal I(ω)ω is multiplied by ωJ 1 (2xω) and integrated in the range [0, ∞], that is, subjected to first-order Hankel transformation, a new function H(x) is expressed by the following equation.
Ｈ（ｘ）＝∫∞ 0Ｉ（ω）ωJ1（2xω）ωdω＝∫
∞ x√2−2Ｎ(a)da……(3)
ただしｘ＞０）
これは第３図に示す関係曲線となる。 H(x)=∫ ∞ 0 I(ω)ωJ 1 (2xω)ωdω=∫
∞ x √ 2 − 2 N(a)da...(3) where x>0) This results in the relationship curve shown in Figure 3.
Ｈ（ｘ）が偶関数となるようにｘ＜０でＨ（ｘ）
を拡張し、Ｈ（ｘ）のｘ＝０での値は、ｘを限り
なく０に近づけたＨ（ｘ）の極限値で置き換える。 H(x) at x<0 so that H(x) is an even function
is expanded, and the value of H(x) at x=0 is replaced by the limit value of H(x) that brings x as close to 0 as possible.
このＨ（ｘ）を次式に従つてフーリエ変換して
Ｆ（ξ）を求めると第４図に示す関係曲線となる。 When this H(x) is Fourier-transformed according to the following equation to obtain F(ξ), the relationship curve shown in FIG. 4 is obtained.
Ｆ（ξ）＝∫∞ ∞Ｈ（ｘ）ei〓xdx ……(4)
そして、Ｆ（ξ）ξを作り、これを次式のよう
に１次のハンケル変換をして、Ｎ(a)を求めると第
５図の粒度分布曲線が得られる。 F(ξ)=∫ ∞ ∞ H(x)e i 〓 x dx ...(4) Then, create F(ξ)ξ, perform first-order Hankel transformation as shown in the following equation, and obtain N( When a) is determined, the particle size distribution curve shown in FIG. 5 is obtained.
Ｎ(a)＝∫∞ 0Ｆ（ξ）ξJ1（ξa）ξdξ ……(5)
図５から仮定した分布が良く再生されているの
がわかる。本発明によれば、任意の粒度分布を精
度良く測定できることが理解される。 N(a)=∫ ∞ 0 F(ξ)ξJ 1 (ξa)ξdξ ...(5) It can be seen from FIG. 5 that the assumed distribution is well reproduced. It is understood that according to the present invention, any particle size distribution can be measured with high accuracy.
なお、本発明によつて粒度分布Ｎ(a)が求められ
ると、粒度、面積、体積の平均値が求まることは
言うまでもない。また、本発明はコヒーレント光
の回折像を用いるために、粒子の直径が光の半波
長程度から、第１図の光学系３，３′，５を変え
ることにより数cm程度までの粒子の粒度分布が測
定できる。 It goes without saying that when the particle size distribution N(a) is determined according to the present invention, the average values of particle size, area, and volume are determined. In addition, since the present invention uses a diffraction image of coherent light, the diameter of the particles can be increased from about half the wavelength of light to about several centimeters by changing the optical systems 3, 3', and 5 in FIG. Distribution can be measured.
（発明の効果）
以上、詳細に説明したように本発明は、サンプ
ルに特別な加工を必要としないために、製造工程
への導入が容易にでき、オンラインでしかもイン
プロセスでの計測ができ、計算機処理の高速化に
より実時間の測定が可能となる。したがつて本発
明は、任意の粒度分布が精度良く求まることによ
り、製造品の異常検出や、原材料の最適パラメー
タの決定など、品質管理、工程管理の迅速化、高
精度化に寄与することができる。(Effects of the Invention) As explained above in detail, the present invention does not require any special processing on the sample, so it can be easily introduced into the manufacturing process, and measurement can be performed online and in-process. Real-time measurement becomes possible due to faster computer processing. Therefore, the present invention can contribute to faster and more accurate quality control and process control, such as detecting abnormalities in manufactured products and determining optimal parameters for raw materials, by determining a desired particle size distribution with high precision. can.
第１図は本発明に用いる装置の光学系と信号処
理系の一例を示す概略図、第２図は本発明を説明
するために用いた、仮定した粒度分布から成る粒
子の回折像強度と位置座標の積Ｉ（ω）ωを表わ
すグラフ、第３図は第２図に対して１次のハンケ
ル変換をした後の関数（Ｈ（ｘ））を示すグラフ、
第４図はＨ（ｘ）のフーリエ変換をした後のＦ
（ξ）を示すグラフ、第５図はＦ（ξ）ξに１次の
ハンケル変換をして得られた粒度分布Ｎ(a)を示す
グラフ。
図中の符号：１……光源、２……コヒーレント
光、３，３′……光学系、４……被測定面、５…
…フーリエ変換レンズ、６……回折像が得られる
面、７……光電変換装置、８……信号処理装置。
Fig. 1 is a schematic diagram showing an example of the optical system and signal processing system of the apparatus used in the present invention, and Fig. 2 is a diffraction image intensity and position of particles having an assumed particle size distribution used to explain the present invention. A graph representing the product of coordinates I(ω)ω, FIG. 3 is a graph showing the function (H(x)) after performing first-order Hankel transformation on FIG. 2,
Figure 4 shows F after Fourier transform of H(x).
FIG. 5 is a graph showing the particle size distribution N(a) obtained by applying first-order Hankel transformation to F(ξ)ξ. Codes in the figure: 1...Light source, 2...Coherent light, 3, 3'...Optical system, 4...Measurement surface, 5...
...Fourier transform lens, 6... Surface from which a diffraction image is obtained, 7... Photoelectric conversion device, 8... Signal processing device.
Claims (1)
光を投射してフラウンフオーフアー回折像を形成
し、 このフラウンフオーフアー回折像の中心から半
径方向に沿つての距離ωの位置における回折像強
度Ｉ（ω）を光電変換装置によつて電気信号とし
て検出し、 この回折像強度Ｉ（ω）に前記中心からの距離
ωを乗じた関数に１次のハンケル変換を施してｘ
を変換とする関数Ｈ（ｘ）を得、 この関数Ｈ（ｘ）にフーリエ変換を施してξを
変数とする関数Ｆ（ξ）を得、 この関数Ｆ（ξ）にξを乗じた関数に１次のハ
ンケル変換を施して粒度分布を求めることを特徴
とする粒度分布測定法。[Claims] 1. A Fraunhofer diffraction image is formed by projecting coherent light onto randomly distributed particles, and the distance ω along the radial direction from the center of this Fraunhofer diffraction image is The diffraction image intensity I(ω) at the position is detected as an electrical signal by a photoelectric conversion device, and a first-order Hankel transformation is applied to a function obtained by multiplying this diffraction image intensity I(ω) by the distance ω from the center. x
Obtain a function H(x) whose transformation is .Fourier transform is applied to this function H(x) to obtain a function F(ξ) whose variable is ξ.The function obtained by multiplying this function F(ξ) by ξ is A particle size distribution measuring method characterized by obtaining a particle size distribution by applying a first-order Hankel transformation.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP59202281A JPS6179139A (en) | 1984-09-27 | 1984-09-27 | Particle size distribution measurement method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP59202281A JPS6179139A (en) | 1984-09-27 | 1984-09-27 | Particle size distribution measurement method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPS6179139A JPS6179139A (en) | 1986-04-22 |
| JPH0327065B2 true JPH0327065B2 (en) | 1991-04-12 |
Family
ID=16454936
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP59202281A Granted JPS6179139A (en) | 1984-09-27 | 1984-09-27 | Particle size distribution measurement method |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JPS6179139A (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101793665B (en) * | 2010-03-19 | 2011-07-27 | 北京航空航天大学 | Limited distribution integral inversion algorithm for grain diameter measurement |
-
1984
- 1984-09-27 JP JP59202281A patent/JPS6179139A/en active Granted
Also Published As
| Publication number | Publication date |
|---|---|
| JPS6179139A (en) | 1986-04-22 |
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