WO2020067149A1

WO2020067149A1 - Fine particle detecting device

Info

Publication number: WO2020067149A1
Application number: PCT/JP2019/037583
Authority: WO
Inventors: 信宏茂木
Original assignee: 国立大学法人東京大学
Priority date: 2018-09-28
Filing date: 2019-09-25
Publication date: 2020-04-02
Also published as: JP7333637B2; JPWO2020067149A1

Abstract

A fine particle detecting device for detecting fine particles flowing through a flow cell is provided with: a laser radiator which radiates a laser beam; an optical system which prepares the laser beam to the extent that it is possible to approximate a Gaussian beam in the vicinity of a focusing spot; a light intensity detector which is disposed behind the focusing spot to detect light intensity; and a control device which identifies the fine particles on the basis of the light intensity detected by the light intensity detector. When the center of the focusing spot is an origin, an axis passing through the original parallel to the direction of flow of the fine particles in the flow cell is an x-axis, and an axis passing through the original perpendicular to the x-axis is a y-axis, the light intensity detector is configured from four detectors which are divided by means of a first straight line having an angle of elevation from the y-axis that is a prescribed angle at least equal to 15 degrees and at most equal to 75 degrees, and a second straight line having x-axis symmetry with the first straight line.

Description

Particle detector

The present invention relates to a particle detection device.

Conventionally, as this type of technology, a SPES method ( _{Single Particle Extinction and Scattering)} has been proposed (see Non-Patent Document 1). In the SPES method, the amplitude and phase of a scattered wave are measured by observing the spatial distribution of light intensity in the forward direction created by the interference between the incident wave of the converged laser beam and the scattered wave caused by particles traversing the beam. Measure at the same time. For this reason, it is shown that, after different particle types coexisting in the sample water are discriminated, the number concentration of each particle type by particle size can be measured.

In the SPES method, a TEM ₀₀ mode laser beam having a Gaussian intensity profile is converged by a condenser lens (so that the spot size at the beam waist is about several microns). The interference intensity pattern of the scattered wave and the incident wave generated by the particles crossing the vicinity of the beam waist is detected by a four-division photodiode, and the time waveform of the signal intensity is measured. Here, in the plane divided perpendicularly to the incident wave, the four-division photodiode has the origin at the center of the incident wave, the x-axis passes through the origin, and is parallel to the flow direction of the flow cell, and the flow of the flow cell passes through the origin. They are arranged in the first to fourth quadrants on the xy plane when the axis perpendicular to the direction is the y axis.

Then, from the time waveform of the measured light intensity while the fine particles flowing through the flow cell traverse the laser, the actual value of the complex scattering amplitude S (0) of the scatterer including information equivalent to the amplitude and phase of the scattered wave with respect to the incident wave is obtained. Derives the part and the imaginary part. For the real part of the complex scattering amplitude S (0), the light intensity (P1 + P2) observed by the photodiodes arranged in the first and second quadrants and the photodiodes arranged in the third and fourth quadrants The imaginary part of the complex scattering amplitude S (0) is located in the first to fourth quadrants based on the difference {(P1 + P2)-(P3-P4)} from the observed light intensity (P3 + P4). It is determined based on the light intensity (P1P2 + P3 + P4) observed by the photodiode. Since the complex scattering amplitude S (0) depends not only on the size of the scatterer but also on the complex permittivity, the particle type is empirically classified from the combination of the real part and the imaginary part of the complex scattering amplitude S (0). can do.

Natural water in the global environment, such as rainwater, river water, seawater, snow-melting water, etc., contains various solid particles (mineral particles, organic substances, viruses, plankton, plastics, etc.) and micellar liquid particles suspended at unknown concentrations. ing. Industrial water such as purified water for drinking water and food preservation, cleaning water for precision equipment, and purified water for medical use, though having a lower concentration than natural water, contains the same fine particles as contaminants. As described above, data on the number and concentration of fine particles in water by particle type and particle size are important as indices for understanding water pollution degree, pollution path, and environmental process.

In recent years, high-concentration air bubbles (fine bubbles) having a particle diameter of 1 μm or less, which are artificially generated and injected into water, have an effect of promoting washing of soil on clothes, pottery, and piping, an effect of promoting aquaculture of fish and shellfish, an effect of fresh seafood. It has been revealed that it has many useful effects, such as the promotion of preservation (oxidation suppression) and the cultivation of agricultural crops, and the research and application of fine bubble water are becoming active in various industrial fields.

However, until now, fine particles of various solids and liquids coexisting in water and fine bubbles can be clearly distinguished from each other, and the number concentration of each particle type / bubble by particle size can be measured in real time without pretreatment. Without technology, it was difficult to monitor contamination of fine particles in water and evaluate the quality of fine bubbles in environmental water. For this reason, fine particles and fine bubbles made of substances having different complex refractive indices are clearly distinguished from each other without any pretreatment for environmental water and industrial water, and real-time measurement of the number concentration of each particle size is performed. There is a need for enabling technology.

The main object of the particle detection device of the present invention is to more appropriately detect solid or liquid / gas particles in a liquid.

微粒子 The particle detecting device of the present invention employs the following means in order to achieve the above-mentioned main object.

The fine particle detection device of the present invention,
A fine particle detection device for detecting fine particles flowing in the flow cell,
A laser irradiator that irradiates a laser beam,
An optical system that adjusts the laser beam to a degree that can be approximated to a Gaussian beam in the vicinity of the focused spot;
A light intensity detector that is disposed behind the condensing spot and detects light intensity;
A control device for determining the fine particles based on the light intensity detected by the light intensity detector,
With
The light intensity detector has an origin at the center of the condensed spot, an x-axis passing through the origin and an axis parallel to the flow direction of the fine particles in the flow cell, and an y-axis passing through the origin and perpendicular to the x-axis. In this case, there are four detectors which are divided by a first straight line having a predetermined angle whose elevation angle from the y-axis is not less than 15 degrees and not more than 75 degrees and a second straight line symmetrical to the first straight line with respect to the x-axis. Yes,
It is characterized by the following.

In the particle detecting apparatus of the present invention, the light intensity detector has the origin at the center of the condensed spot, the axis parallel to the flow direction of the fine particles in the flow cell passing through the origin, and the x-axis passing through the origin. When a vertical axis is defined as a y-axis, there are four divided by a first straight line having a predetermined angle of elevation of 15 degrees or more and 75 degrees or less from the y-axis and a second straight line symmetrical to the first straight line with respect to the x-axis. It consists of a detector. For this reason, as compared with a configuration in which four detectors are provided in the first to fourth quadrants with respect to the xy axis, the dissipated power P _ext (AC) and the dissipated power P _ext (BD) Can be easily calculated, and solids in liquid and fine particles of liquid and gas can be detected more appropriately. It is more preferable that the first straight line and the second straight line are orthogonal straight lines.

In the particle detecting device of the present invention, the light intensity detector includes a first detector belonging to a region on the negative side of the x-axis when the particles in the flow cell flow from the negative direction to the positive direction on the x-axis, and a negative side on the y-axis. , A fourth detector belonging to the region, a third detector belonging to the region on the positive side of the x-axis, and a fourth detector belonging to the region on the positive side of the y-axis. The control device includes a first light intensity detected by the first detector, a second light intensity detected by the second detector, a third light intensity detected by the third detector, and the fourth detection. based on the sum of the fourth light intensity detected by the vessel to calculate the imaginary part of the complex scattering amplitude S _11, detected by the third detector and the first light intensity detected by the first detector based on the difference between the third light intensity calculating the real part of the complex scattering amplitude S ₁₁ , It is preferable to perform the determination of the fine particles on the basis of the real and imaginary parts of the calculated complex scattering amplitude S _11. In this way, it is possible to more appropriately determine the solid in the liquid or the fine particles of the liquid or gas.

In particle detector device of the invention that calculates a real part of the complex scattering amplitude S ₁₁ and an imaginary part, comprising a reference detector for detecting the light intensity of the reference laser beam separated from the laser beam, the control device Is a complex scattering based on the sum of the first light intensity, the second light intensity, the third light intensity, and the fourth light intensity minus the reference light intensity detected by the reference detector. or as to calculate the imaginary part of the amplitude S _11.

In particle detector device of the invention that calculates a real part of the complex scattering amplitude S ₁₁ and an imaginary part, said control device, of the complex scattering amplitude S ₁₁ that previously obtained for known complex dielectric constant of the fine particles Particles flowing in the flow cell may be determined using a relationship consisting of a real part and an imaginary part. In this way, it is possible to more appropriately determine whether or not the fine particles to be observed are known fine particles, and it is possible to more appropriately determine the solid in the liquid and the fine particles of the liquid / gas. In this case, the control device, when the particles flowing in the flow cell is determined to be any of the known fine particles, fine particles by the real part of the complex scattering amplitude S ₁₁ described above calculated using the complex dielectric constant of a known fine particles The volume may be derived. In this case, the volume of the fine particles can be detected.

In particle detector device of the invention that calculates a real part and an imaginary part of the complex scattering amplitude S _11, the control device, the first light intensity of the difference between the second light intensity and the fourth optical intensity The determination of the fine particles may be performed when the ratio of the difference between the third light intensity and the third light intensity is less than a predetermined value. This makes it possible to eliminate the detection of fine particles for which proper determination cannot be performed, and to more appropriately determine the solids in the liquid and the fine particles of the liquid / gas.

In the particle detecting device of the present invention, the light intensity detector includes a first detector belonging to a region on the negative side of the x-axis when the particles in the flow cell flow from the negative direction to the positive direction on the x-axis, and a negative side on the y-axis. , A fourth detector belonging to the region, a third detector belonging to the region on the positive side of the x-axis, and a fourth detector belonging to the region on the positive side of the y-axis. The control device includes a first light intensity detected by the first detector, a second light intensity detected by the second detector, a third light intensity detected by the third detector, and the fourth detection. the imaginary part of the complex scattering amplitude S ₂₂ calculated based on the sum of the fourth light intensity detected by the vessel, detected by the third detector and the first light intensity detected by the first detector based on the difference between the third light intensity calculating the real part of the complex scattering amplitude S ₂₂ It may be those based on the real and imaginary parts of the calculated complex scattering amplitude S ₂₂ discriminates particles. In this way, non-spherical solids and liquid / gas fine particles in the liquid can be more appropriately determined.

In particle detector device of the invention that calculates a real part of the complex scattering amplitude S ₂₂ and an imaginary part, comprising a reference detector for detecting the light intensity of the reference laser beam separated from the laser beam, the control device Is a complex scattering based on the sum of the first light intensity, the second light intensity, the third light intensity, and the fourth light intensity minus the reference light intensity detected by the reference detector. or as to calculate the imaginary part of the amplitude S _22.

In particle detector device of the invention that calculates a real part and an imaginary part of the complex scattering amplitude S _22, the controller of the complex scattering amplitude S ₂₂ that previously obtained for known complex dielectric constant of the fine particles Particles flowing in the flow cell may be determined using a relationship consisting of a real part and an imaginary part. In this way, it is possible to more appropriately determine whether or not the fine particles to be observed are known fine particles, and it is possible to more appropriately determine the solid in the liquid and the fine particles of the liquid / gas.

In particle detector device of the invention that calculates a real part of the complex scattering amplitude S ₂₂ and an imaginary part, and stores the real part and the imaginary part of the complex scattering amplitude S ₂₂ of a plurality of fine particles in the flow cell, the plurality of fine particles plotting the complex scattering amplitude S ₂₂ in the complex plane, among the plurality of microparticles plot of the complex scattering amplitude S _22, the complex scattering amplitude of the fine particles is estimated to particle volume are the same are different but complex refractive index S ₂₂ select may be one that calculates the complex refractive index and particle volume range for the complex scattering amplitude S ₂₂ of the selected particles. In this way, even for unknown particles in the environment, useful information for identifying the particle type can be obtained.

It is an explanatory view showing the outline of composition of particulate detection device 20 of an embodiment. FIG. 3 is an explanatory diagram illustrating an arrangement of a photodiode E for observation light. It is a flowchart which shows an example of the observation process performed when the control device 60 of the fine particle detection device 20 of an embodiment detects a fine particle. Radius is an explanatory diagram showing an example of the relationship between the complex permittivity and the complex scattering amplitude _{S 11} of the fine particles of 0.05 .mu.m ~ 0.3 [mu] m. FIG. 4 is an explanatory diagram showing definitions of a coordinate system and a unit vector of each coordinate. FIG. 3 is an explanatory diagram schematically illustrating an incident wave of a Gaussian beam. It is a graph which shows the dissipated power P _ext (AC) time difference (waveform width) [0.4 μs unit] of the time waveform of a sample of polystyrene particles having a diameter of 510 nm. The particle size and the complex refractive index is an explanatory diagram showing the real part of the complex scattering amplitude S ₁₁ as a real part and the theoretical value of the complex scattering amplitude S ₁₁ of the experimental example according to the known polystyrene standard particles. The particle size and the complex refractive index is an explanatory diagram showing the imaginary part of the complex scattering amplitude S ₁₁ as the imaginary part of the complex scattering amplitude S ₁₁ and the theoretical value of the experimental example according to the known polystyrene standard particles. FIG. 9 is an explanatory diagram showing an example of a measured waveform of a dissipated power P _ext (AC) of a fine particle having a real part Re (S ₁₁ ) of the complex scattering amplitude S ₁₁ larger than 0. FIG. 7 is an explanatory diagram showing an example of a measured waveform of the extinction power P _ext (AC) of a microbubble whose real part Re (S ₁₁ ) of the complex scattering amplitude S ₁₁ is smaller than 0. It is a flow chart which shows an example of observation processing performed at the time of detecting a particulate by control device 60 of particulate detection device 120 of a 2nd embodiment. It is an explanatory diagram showing experimental results showing the dependence of the volume and whether the diameter d _v of the complex scattering amplitude S _11. It is an explanatory diagram showing experimental results showing the dependence of the volume and whether the diameter d _v of the complex scattering amplitude S _11. FIG. 14 is an explanatory diagram plotting the absolute value of the F value and the particle size dependence of the argument for the same particle type as in FIG. 13. FIG. 15 is an explanatory diagram plotting the absolute value of the F value and the particle size dependence of the argument for the same particle type as in FIG. 14. It is explanatory drawing which shows the real part and imaginary part of complex refractive index in an example of the joint probability distribution of the parameter estimation value about a spherical particle. It is an explanatory view showing a volume equivalent particle size d _v of the first data point from the smaller real part of the complex refractive index of an exemplary joint probability distribution of the parameter estimates for the spherical particles. It is explanatory drawing which shows the real part and imaginary part of complex refractive index in an example of the joint probability distribution of the parameter estimation value about a spherical particle. It is an explanatory view showing a volume equivalent particle size d _v of the first data point from the smaller real part of the complex refractive index of an exemplary joint probability distribution of the parameter estimates for the spherical particles. It is explanatory drawing which shows the list | wrist of the parameter estimation result of the spherical particle of a complex refractive index. It is an explanatory view showing a list of results in S ₂₂ data of simulation for non-absorbable cubic grains tried to apply the parameter estimation algorithm with an assumption of spherical particles. Simulation is an explanatory diagram showing an example of applying the result parameter estimation algorithm with an assumption of fractal aggregates shape of microspheres generated S ₂₂ data. Simulation is an explanatory diagram showing an example of applying the result parameter estimation algorithm with an assumption of fractal aggregates shape of microspheres generated S ₂₂ data. It is explanatory drawing which shows an example of the experimental result with respect to the precipitation sample of Tokyo. It is explanatory drawing which shows an example of the experimental result with respect to the precipitation sample of Okinawa. FIG. 9 is an explanatory diagram showing an example of parameter estimation results assuming the particle shape of fractal agglomerates of microspheres for data of Category # 1 which is regarded as soot in a precipitation sample in Tokyo. FIG. 9 is an explanatory diagram showing an example of parameter estimation results assuming the particle shape of fractal aggregates of microspheres with respect to data of Category # 1 which is considered to be soot in a precipitation sample in Okinawa. FIG. 26 is an explanatory diagram showing an example of a result of parameter estimation assuming spherical particles with respect to the data of Category # 2 considered to be non-absorbable particles in FIG. 25. 27 is an explanatory diagram showing an example of a result of parameter estimation assuming spherical particles with respect to data of Category # 2 which is considered to be non-absorbable particles in FIG. 26. FIG. FIG. 27 is an explanatory diagram showing an example of a result of parameter estimation assuming spherical particles with respect to data of Category # 3 which is considered to be non-absorbable particles in FIG. 26.

Next, an embodiment for carrying out the present invention will be described. FIG. 1 is an explanatory diagram schematically showing a configuration of a particle detection device 20 according to the embodiment. As shown in the figure, the particle detection device 20 of the embodiment includes a laser irradiation device 22 that irradiates laser light, and an optical system 30 that guides the laser light from the laser irradiation device 22 to the irradiation unit of the flow cell 10 or guides the reference light. , The observation light photodiode 40 disposed on the side of the laser light traveling direction viewed from the flow cell 10, the reference light photodiode E for detecting the reference light, the observation light photodiode 40 and the reference light photodiode E And a control device 60 for controlling the entire apparatus.

The laser irradiation device 22 is preferably capable of irradiating an ideal Gaussian (TEM ₀₀ ) mode laser beam, for example, a linearly polarized HeNe laser (red HeNe laser: JDSU, model 1137P, 632.8 nm, <10 mW). ) Can be used.

The optical system 30 is an optical isolator 31 (for example, TH, IO-3D-633-VLP) for preventing reflected light from returning to the laser irradiation device 22, and for controlling a beam split ratio between observation light and reference light. A half-wave plate 32 (for example, TH, WPH05M-633) mounted on a rotary mount, a polarization beam splitter 33 (for example, TH, CCM1-PBS25-633 / M) for dividing observation light and reference light, A beam expander (for example, TH, GBE-10A) for expanding the beam diameter of the observation light (collimated beam) from the polarizing beam splitter 33, and a condensing lens (for example, TH, GBE-10A) for converging the observation light with the expanded beam diameter. AL2550H, φ = 25 mm, f = 50 mm). In the SPES method, it is necessary that the spatial distribution of the electric field in the vicinity of the converging spot can be approximated by an ideal Gaussian beam. The optical system 30 also includes a broadband dielectric mirror 36 (for example, TH, BB111-E02) for guiding the reference light from the polarization beam splitter 33 to the reference light photodiode E.

The observation light photodiode 40 detects the intensity of the observation light, and is constituted by four photodiodes A to D (for example, OSI, SPOT-9DMI) divided into four. FIG. 2 is an explanatory diagram illustrating the arrangement of the observation light photodiodes 40. When the axis parallel to the flow direction of the flow cell 10 is the x axis and the axis perpendicular to the flow direction of the flow cell 10 is the y axis, the photodiode A is orthogonal to the x axis and the y axis by 45 degrees. The photodiodes B to D are arranged on a plane at a position on the upstream side of the flow of the flow cell 10 among the four divided planes divided by the straight line, and the photodiodes B to D are arranged from the plane on which the photodiode A is arranged in the traveling direction of the observation light. They are arranged clockwise in this order. That is, the photodiode A is arranged on the upstream side (minus side of the x-axis) of the flow of the flow cell 10, the photodiode C is arranged on the downstream side (plus side of the x-axis), and the photodiode B is arranged on the minus side of the y-axis. Are arranged, and the photodiode D is arranged on the plus side of the y-axis. In the observation light photodiode 40, since it is necessary to observe the entire beam cross section, the distance from the beam waist position to the photocathode such that the exit beam diameter (1 / e ² ) of the divergent Gaussian beam is slightly smaller than the photocathode diameter. Adjust It is not desirable that the distance is made shorter than necessary because the mixing of scattered light that is not the object of observation only increases. In the embodiment, when 50 mm is used as the focal length of the condenser lens 35, this distance is set to 40 mm.

The reference light photodiode E detects the intensity of the reference light, and has the same light receiving sensitivity and inter-terminal capacitance as the four photodiodes A to D of the observation light photodiode 40 in order to match the noise characteristics. (For example, OSI, PIN-6D) is preferably used.

The stage 50 includes an x-direction actuator 52 and a y-direction actuator 54 for adjusting the positions of the observation light photodiode 40 and the reference light photodiode E in the x and y directions. In the SPES method, since the center of the observation photodiode 40 and the center of the diverging beam need to coincide (for example, coincide with a coaxial error of several μm or less), the x-direction actuator 52 and the y-axis The direction actuator 54 causes the center of the observation photodiode 40 to coincide with the center of the divergent beam. Note that the x-direction actuator 52 and the y-direction actuator 54 can use, for example, piezo motors.

The control device 60 is configured as, for example, a microcomputer mainly configured with a CPU, and includes a ROM, a RAM, an input / output port, and the like in addition to the CPU.

Next, the operation of the particle detecting device 20 according to the embodiment configured as described above will be described. FIG. 3 is a flowchart illustrating an example of an observation process performed when the control device 60 of the particle detection device 20 according to the embodiment detects a particle. In the following description, as an example, an operation when detecting a minute bubble will be described. In the observation processing, first, light intensities P (A) to P (D), P (E) detected by the four photodiodes A to D of the observation light photodiode 40 and the reference light photodiode E are acquired. (step S100), dissipated power _{_{P ext (Tot), P ext}} (a-C), calculates the _P ext (B-D) (step S110). Here, “dissipation” means a change in the time-average intensity of the incident field due to interference between the incident field and the forward scattered field behind the fine particles, and “dissipated power” means its energy. The dissipated power P _ext (Tot) is the sum of the dissipated powers of the four photodiodes A to D. The reference light photo is obtained from the sum of the light intensities P (A) to P (D) detected by the photodiodes A to D. It can be calculated by subtracting the light intensity P (E) detected by the diode E (P _ext (Tot) = P (A) + P (B) + P (C) + P (D) -P (E)). . The dissipated power P _ext ( _AC ) is obtained by subtracting the dissipated power P _ext (C) of the photodiode C from the dissipated power P _ext (A) of the photodiode A (P _ext ( _AC ) = P _ext ( A) −P _ext (C)), and subtracting the light intensity P (C) at the photodiode C from the light intensity P (A) at the photodiode A (P _ext ( _AC ) = P (A) − P (C)). The dissipated power P _ext (BD) is obtained by subtracting the dissipated power P _ext (D) of the photodiode D from the dissipated power P _ext (B) of the photodiode B (P _ext (BD) = P _ext ( B) −P _ext (D)), and subtracting the light intensity P (D) at the photodiode D from the light intensity P (B) at the photodiode B (P _ext (BD) = P (B) − P (D)).

Next, it is determined as the absolute value of the ratio of the calculated dissipation power P _ext (BD) to the dissipation power P _ext ( _AC ) (| P _ext (BD) / P _ext ( _AC ) |). A value J is calculated (step S120), and it is determined whether the calculated determination value J is less than 0.2 (step S130). When the determination value J is 0.2 or more, it is determined that observation is not possible, and the observation processing ends. The determination of whether or not observation is possible based on whether or not the determination value J is less than 0.2 will be described later.

When the determination value J is less than 0.2, it is determined that observation is possible, and the real part Re (S ₁₁ ) and the imaginary part of the complex scattering amplitude S ₁₁ are determined using the dissipated powers P _ext (Tot) and P _ext (AC). Im (S ₁₁ ) is calculated (step S140). This calculation will also be described later. Then, the real part Re (S ₁₁ ) and the imaginary part Im (S ₁₁ ) of the calculated complex scattering amplitude S ₁₁ are converted into the real part Re (S) of the complex scattering amplitude S ₁₁ of the observation target fine particles (hereinafter referred to as target fine particles). ₁₁₎ and determines whether or not the match the imaginary part Im _{(S 11)} (step S150, S160). Figure 4 is a radius of an explanatory view showing an example of the relationship between the complex permittivity and the complex scattering amplitude _{S 11} of the fine particles of 0.05 .mu.m ~ 0.3 [mu] m. In FIG. 4, microbubbles (air) having a dielectric constant smaller than water as fine particles, and a complex dielectric constant having a dielectric constant larger than water are 1.4 + 0.0i, 1.5 + 0.0i, 1.7 + 0.0i, 2.0 + 1. Five kinds of fine particles of 0i, 2.0 + 0.5i were used. As shown in the figure, the real part Re (S ₁₁ ) of the complex scattering amplitude S ₁₁ has a positive value for fine particles (solid particles such as metal) having a larger dielectric constant than water, and has a smaller dielectric constant than water (fine bubbles). (Gas particles such as (air)) has a negative value. Determination in step S150, the real part Re (S in the real part Re _{(S 11)} and the imaginary part Im _{(S 11)} of the target particles, such as shown in FIG. 4 complex scattering amplitude _{S 11} of the calculated complex scattering amplitude _{S 11} ₁₁ ) and the imaginary part Im (S ₁₁ ) are determined to be acceptable or not. Considering the case where the target particles is very small bubbles, or the real part Re of the complex scattering amplitude S ₁₁ that calculated (S ₁₁₎ and the imaginary part Im (S ₁₁₎ matches the acceptable degree in fine bubbles shown in FIG. 4 That is, it is determined based on whether it is not. When it is determined in steps S150 and S160 that the microparticle is not the target microparticle, the observation process ends. On the other hand, when the particulate is determined to be subject microparticles is determined in step S150, S160, the volume v of the particles was calculated from the real part Re of the complex scattering amplitude _{_{S 11 (S} 11)} _(step S170), ends the observation processing I do. The calculation of the volume v of the fine particles will be described later.

Next, dissipated power _{_{P ext (Tot), P ext}} (A-C) and the relationship between the complex scattering amplitude _{S 11,} the value J can be determined whether the observed by whether less than 0.2 The calculation of the volume v of the fine particles (fine bubbles) will be described below.

<Definition of light scattering theory and the complex scattering amplitude _{S 11>}
In many cases, a plane wave is assumed as an incident wave in a problem of scattering of an electromagnetic wave due to fine particles isolated in a uniform medium. This means that at a position far away (compared to the wavelength) from the electric dipole which is the radiation source of the wave, it behaves as a spherical wave spreading outward from the radiation source, and the spherical wave coming from the source far away from the fine particles has a radius of curvature. This is because it can be approximated as a plane wave much larger than the fine particles. A monochromatic plane wave having a frequency ω and a wave vector k is expressed as E ′ (r, t) = E ′ ₀ ^{ei (k · r−ωt)} as a function of the position r and the time t. Here, since a monochromatic wave is considered, the term e ^−ωt is implicitly assumed, and the electric field at the origin r = 0 is set to E ₀ . At this time, the electric field of the monochromatic plane wave can be expressed as E (r) = E ₀ e ^{ik · r} as a variable not in the time domain but in the frequency domain. However, E ₀ is a complex vector on a plane perpendicular to the wave vector k and can be decomposed into two independent polarization components. Here, the traveling direction of the incident wave is set to the + z direction, and the incident field is represented by Expression (1).

On the other hand, the scattering field E _sca (r) due to the fine particles placed near the origin r = 0 has two independent polarization components perpendicular to the wave vector at far-field far from the origin. It acts as a spherical wave. Also, the incident field and the scattering field have a linear relationship due to the linearity of the governing equation (Maxwell equation) of the electromagnetic field. For these two reasons, the relationship between the polarization components of the incident field and the scattered field can be expressed by equation (2) using a 2 × 2 complex scattering amplitude matrix S depending on the characteristics of the fine particles. However, since the scattering field E _sca (r) is a spherical wave, the polarization component is represented by a spherical coordinate system. FIG. 5 shows the definition of the coordinate system and the unit vector of each coordinate. In particular, in the forward direction θ = 0, the polarization component of the incident wave E _{inc0 and} the polarization component of the scattered field that are parallel on the xy plane interfere with each other (according to Fresnel-Arago's law). The change in the time-average intensity of the incident field due to the interference between the incident field and the forward (θ = 0) scattered field behind the particle is called “extinction”. Since φ can be arbitrarily selected for the forward scattered field of θ = 0, if φ = 0 is set, E _sca and _{θ = 0} = E _{sca, x} . Under this notation, the component of the scattered field that interferes with the x-linearly polarized incident field is represented by equation (3) in a Cartesian coordinate system.

In general, under the condition that the wave vectors of the incident field and the scattered field match, the relationship equivalent to the equation (3) holds for the electric field vector component of the scattered field parallel to the electric field vector component of the incident field on the wavefront. Therefore, the subscript x of both sides of Expression (3) is interpreted as a notation of an arbitrary direction vector component on a common wavefront of the incident field and the scattered field. In general, S ₁₁ (θ = 0) and S ₂₂ (θ = 0) are different for non-spherical particles, but when considering the average of many particle orientations, it is not necessary to distinguish them. Therefore, hereinafter, unless otherwise specified, when expressing a scattering field that interferes with a linearly polarized incident field, S ₁₁ (θ = 0) is simply written as S ₁₁ and the subscript x of the electric field is omitted (4) ) Is used. This relationship (equation (4)), for the scattered field of the wave vector and the polarization component in common with the incident field, that the phase and amplitude of the scattered field is represented by the complex scattering amplitude S ₁₁ that depends on the properties of the particles means. Equation (4) forms the basis of the principle of particle measurement by the SPES method.

<Relationship of the complex scattering amplitude _{S 11} and the SPES observed amount>
In the SPES method, a TEM ₀₀ mode laser beam having a Gaussian intensity profile (hereinafter, Gaussian beam) is used as an incident field E _inc (r). The Gaussian beam behaves as a plane wave near the beam waist and behaves as a spherical wave spreading from the beam waist center point farther from the beam waist. Therefore, the fine particles existing in the cross section near the beam waist of the Gaussian beam are excited by the local plane wave. Of the far scattered field that spreads out as a spherical wave from it, a Gaussian beam incident wave that spreads on a spherical surface within a finite solid angle in the forward direction and a wave vector coincide with each other and have a common polarization component interfere with the incident field ( (Fig. 6). Depending on the phase and amplitude of the scattered waves is determined by the source locations of the scattered field (position of the fine particles) and fine particles of the complex scattering amplitude S _11, it is different from the interference intensity distribution on the detection surface placed within a finite solid angle of forward direction Observed.

In the SPES method, a Gaussian beam diverging behind the beam waist is received by a multi-element photodetector (here, a four-division photodiode), and the intensity of each photocathode during the time when the particle to be measured crosses the beam waist. from the relationship between the time waveform of, (relative to the incident field) amplitude and phase scatter field, i.e. it is an object to determine the real and imaginary part of the complex scattering amplitude S _11. Hereinafter, we formulate the relationship between the observed quantity of the complex scattering amplitude _{S 11} and SPES. First, for a linearly polarized Gaussian beam incident field E _inc (r) propagating in the + z direction, the polarization component of the electric field vector (italic type of the incident field symbol in equation (5)) is expressed as in equation (5). Is done.

Here z ₀ is called Rayleigh length [m], as measured from the beam waist on the optical axis, approximate distance begins to transition to a spherical wave wavefront is approximated by infinity from the plane wave approximation near the beam waist Is interpreted as z ₀ is represented by Expression (7) by ω ₀ and the wavelength. At a position z≫λ far from the beam waist, Expression (6) can be approximated as Expression (8).

In formulating the interference between the Gaussian beam incident field and the forward scattered field, the beam center position on the beam waist section is set to the origin r = 0 of the position vector. At the position r _p = (x _p , y _p , 0) on the beam waist cross section, the incident field to which the fine particles are exposed is expressed by Expression (9) from Expressions (5) to (8). Further, it is assumed that the photodetector is placed sufficiently far than the spot size omega ₀ of the wavelength and the beam waist, and the solid angle thereof photocathode spanned is small. From Equations (4) and (9), the scattering field of the fine particles spreading as a spherical wave from r _p = (x _p , y _p , 0) indicates that on the photoelectric surface of the photodetector placed in front Σ _PD It can be expressed as in equation (10).

Approximate equality of formula (10) is within a small solid angle range detectors spanned when viewed from the origin means a assumed approximate a constant value of complex scattering amplitude S _11. In the formula (10), using a mathematical approximation equation (11), the scattered field in the photoelectric surface R∈shiguma _PD is expressed as Equation (12). On the other hand, the incident field at photocathode R∈shiguma _PD is the approximation to the formula (5) z → + ∞, denoted formula (13).

From this, the light receiving power (observation signal) of the four-division photodiode photocathode placed as shown in FIG. 2 is formulated using E _sca of Expression (12) and E _inc of Expression (13). Receiving power density at the position R∈shiguma _PD on the photocathode ^{[Wm -2]} is the formula (14). In the right side of equation (14), the first term is the contribution of the incident field, the second term is the contribution of the scattered field, and the third term is the contribution of interference (dissipation) between the incident field and the scattered field. The light receiving power of each photocathode is equal to the area on the photocathode of equation (14).

From the equation (13), the received light power P _inc of the incident field due to the entire four-segmented photodiode Σ _PD = Σ _{A + B + C + D is given} by equation (15). When the spot size ω (z) of the Gaussian beam on the photocathode is sufficiently smaller than the radius of the photocathode, the photocathode may be assumed to be infinitely wide in the area calculation of Expression (15), and the integration range of x and y is Each may be (-∞, + それぞれ). Using this approximation, the analytic integration of equation (15) can be performed, and expressing the result using equation (6) results in P _inc = P. This means that the received power of the incident field is equal to the beam power.

The received light power P _sca of the scattered field due to the entire four-segment photodiode ４ _PD = Σ _{A + B + C + D is given} by equation (16) using equation (12). In the last formula, in small solid angle range in which the photoelectric surface is put is assumed to S ₁₁ is a constant value. Here, if the position coordinates of the fine particles on the beam waist cross section are represented by a dimensionless parameter such as Expression (17), Expression (16) can be written as Expression (18).

Finally, the contribution of the dissipation field in the equation (14) is calculated. As a preparation, first, a mathematical expression of a complex scalar quantity (the left side of equation (19)) is obtained. Equation (12), and calculates equation (13) based on, _x p appearing in the phase term exp, when subjected to approximation to ignore the secondary small term of _{y p,} the following equation (19) Be guided. However, equation (20) was used for rearranging notations in equation (19). Here, when the position (x, y) on the photocathode is represented by polar coordinates and the expression of b is used, the expression (19) is expressed by the expression (21).

Based on the equation (21), 4 photocathode of the divided photodiode is trying to calculate the dissipated power P _exp for receiving. Observed quantities to be derived for P _ext are the following three.
(1) Total power dissipated by ΣA + B + C + D P _ext (Tot) = P _ext (A) + P _ext (B) + P _ext (C) + P _ext (D)
(2) Difference of dissipated power received by ΣA and ΣC P _ext (AC) = P _ext (A) -P _ext (C)
(3) Difference of dissipated power received by ΣB and ΣD P _ext (BD) = P _ext (B) −P _ext (D)

These dissipated powers P _ext can be expressed by the equations (22) to (24) as the area of the dissipated power density on the photocathode. In substituting equation (21) into each of the right sides of equations (22), (23), and (24) to calculate and arrange the integrals, the following complex integral formulas (25) and (26) are used. Used.

These formulas respectively represent the boundaries of the complex plane rectangular region {Re (z) =-t, tIm (z) = 0, c}, {Re (z) = 0, tIm (z) = 0, c}. Can be derived by integrating the complex function f (z) = z · exp (−a ² z ² ) in the closed path defined by and applying the residue theorem to t → ∞. Erfc (z) in equation (26) is the complementary error function of the complex variable. Using Expression (25), the right side of Expression (22) is expanded as Expression (27). Here, equation (28) and equation (29) are used in equation (27). However, equation (30) and equation (31) were used in equation (29).

Particles beam center position (zeta, eta) = When in the (0,0), wherein the observed amount of (27) _P ext _P as contributions to (Tot) ext _{(Tot) 2} is zero _P ext (Tot) Only ₁ remains, resulting in equation (32). According to the relationship of equation (6), the quantity in the square brackets on the right side of equation (32) is equal to the power density of the incident field at the beam center position (ζ, η) = (0, 0). Further, by using Expression (33) as one of the defining expressions of the “dissipation cross-sectional area C _ext ” of the fine particles, Expression (34) that can be interpreted intuitively is obtained. Formula (34) is a definition formula of the extinction cross-section of the fine particles based on the observed light energy for the plane wave incident field having the above-mentioned power density. In the Gaussian beam incident field, it was shown that this relational expression holds only when the beam center position (ζ, η) = (0, 0).

On the other hand, when Expression (26) is used, the right sides of Expressions (23) and (24) are expanded as Expressions (35) and (36), respectively. In addition, it set as Formula (37) and Formula (38).

In the setting of the present apparatus, since fine particles move in the + x direction with time, ζ = ζ (t). In order to search for information that can be extracted from the observed signal waveform of P _ext , first, by taking the ratio of Equations (35) and (36), Equation (39) is obtained, and the observed amount P _ext (BD) and the observed amount P _ext ( the ratio of a-C), the beam dimensionless coordinates (zeta particulate on waist section, eta) only dependent, it can be seen that does not depend on the characteristics of the microparticles, such as the complex scattering amplitude S _11.

Further, as will be described later, the coordinate ζ (t) in the x direction along the flow of the fine particles can be restricted by the waveform of the observed amount P _ext ( _AC ). Therefore, the observed amount P _ext (BD) / P _ext ( _AC ) can be used as an index of the coordinate η of the fine particle in the y direction. Based on this index, it is possible to extract only the fine particles that cross the vicinity of the beam center (| η | ≪1). In this case, the observed amount P _ext is represented by Expressions (40) to (42).

Erfi (z) in equation (41) is an imaginary error function. Equation (40) is the same as equation (32) especially when the beam center ζ = 0. The function (equation 43) in equation (41) defines the waveform of P _ext (AC) (ζ) at | η | ≪1. The term on the right side erfi in equation (43) is an odd function and monotonically increasing, and the increase in its absolute value in the | ζ | ≫1 region is canceled by exp (−2ζ ² ). Therefore, f (ζ) has one minimum point and one maximum point (symmetrical with respect to the origin) in each of the positive and negative ζ regions, and f (0) = 0. The maximal point and the minimal point of f (求め) numerically obtained are expressed by equation (44).

According to the numerical calculation of Expression (39), | P _ext (BD) / P _ext ( _AC ) | <0.2 at a position ζ = ζ _{+ α} where P _ext ( _AC ) takes an extreme value. Then, | η | <0.2 is satisfied. At this time, the error of the approximate equations (40) and (41) is 2% smaller than the strict equations (27) and (35). Was found to be less than. Thus, in the present _{specification,} in the maximum position of _P ext (A-C) measured waveform _{_{| P ext (B-D)}} / P ext (A-C) | < only particle detection event satisfying 0.2 after having extracted the equation (40), assuming the equation _(41), is to derive the _P ext (a-C) and _P ext complex scattering amplitude _{S 11} from the waveform amplitude of the fine particles of (Tot). This method, equation to derive the real part of S ₁₁ and the imaginary part of the fine particles is Formula (45) and equation (46). However, in Expressions (45) and (46), the amplitude of the observed waveform is defined as in Expressions (47) and (48).

<Relationship between the particle characteristics and the complex scattering amplitude _{S 11>}
The problem of the scattering of the electromagnetic field of fine particles (or bubbles) made of a magnetic and isotropic material is represented by the following integral form (without approximation) derived from Maxwell's equation (without approximation) in the frequency domain. Can be represented by

非 In the non-magnetic material considered here, there is a relation that the square of the complex refractive index is equal to the complex permittivity. It is also assumed that the medium is non-absorbing (this assumption is approximately correct for water in the visible range). If r∈v in equation (49), and this equation is obtained by the product method for the electric field inside the particle, the scattering field due to the fine particles can be written as equation (50) as the second term on the right side of equation (49). . Under the condition that the particles are near the origin and the observation point is far enough from the origin compared to the particle size and wavelength (far-field), the following approximation can be used for the Green's function.

Now, by applying the situation of the measurement system of the SPES method, consider a forward scattered field due to an incident field that propagates in the first direction and the electric field is linearly polarized in the second direction. From Expressions (50) and (51), the polarization component of the scattered field propagating in the first direction in the second direction common to the incident field can be expressed by Expression (52).

Considering the case where the absolute value of the amplitude of the incident field is 1 without losing generality, the complex scattering amplitude S ₁₁ in the forward direction (θ = 0) can be obtained by comparing equation (52) with equation (3). It can be seen that is generally represented by the formula (53) using the internal electric field E (r ′) of the fine particles. Here, as dissipating structure factor (equation (54)), defining a dimensionless quantity that depends on the physical properties and geometry of the particles, from the equation (53), the complex scattering amplitude S ₁₁ is essentially to be seen from the observation It can be simply expressed as the product of the contribution of the complex dielectric constant and the particle volume v, which are the physical quantities of the fine particles, and the dimensionless quantity F, as in Expression (55).

In particular, for optically soft particles whose size is about the same as or smaller than the wavelength and whose complex permittivity is close to 1, the internal electric field E (r ') is affected by the incident field _Einc (r'). ) (Born approximation). As can be derived by substituting the incident field into the internal electric field in equation (54), F = 1 in the Born approximation. Even for general particles for which the Born approximation does not apply well, if the size is about the same as or smaller than the wavelength, the order of the real part and the imaginary part of the complex value F may be expressed by equation (56), respectively. The Born approximation is useful as a coarse approximation for many, rapid interpretations.

For any particle (or bubbles), each equation the real and imaginary parts of equation (55) (57), write an equation (58), the ratio of the real part and the imaginary part of the complex scattering amplitude S ₁₁ is the complex dielectric The rate and the dissipation structure factor have the relationship of equation (59). Especially for particles imaginary part of the complex dielectric constant is made of a non-absorptive material 0, the ratio of the real part and the imaginary part of the complex scattering amplitude S ₁₁ is equal to the ratio of the real part and the imaginary part of the dissipative structure factor F, Expression (60) is obtained. As described above, in data interpretation, it is key to know what value the dimensionless amount of dissipation structure factor F takes depending on the physical properties of the fine particles.

As described above, when the determination value J (J = | P _ext (BD) / P _ext ( _AC ) |) is 0.2 or more in step S130 in the observation processing of FIG. 3, it is determined that observation is not possible. The reason why observation is performed only when the judgment value J is less than 0.2 is that when the judgment value J is less than 0.2, the errors of the approximate equations (40) and (41) are strictly equal. It can be seen that it is based on the fact that it is less than 2% as compared with the equations (27) and (35).

Further, the calculation of the real part Re (S ₁₁ ) and the imaginary part Im (S ₁₁ ) of the complex scattering amplitude S ₁₁ in step S140 in the observation processing of FIG. 3 can be performed by the equations (45) and (46). Understand. Further, it can be understood that the calculation of the volume v of the fine particles (fine bubbles) in step S170 in the observation processing of FIG. 3 can be performed by equation (57).

Next, an experimental example using the particle detection device 20 of the embodiment will be described.
<Experimental example 1: Experimental example using polystyrene particles of known particle size>
A sample in which polystyrene particles of a known particle size (STADEX series, manufactured by JSR Corporation) were suspended in pure water was passed through the flow cell 10 to evaluate the performance of the fine particle detector 20. The spot size ω _{0 at the} beam waist was derived from the flow velocity at the center of the flow cell 10 determined by the flow rate driven by the tube pump, and the mode value of the waveform width of the dissipated power P _ext ( _AC ). FIG. 7 is a graph showing a time difference (waveform width) [0.4 μs unit] between the maximum and minimum of the dissipation power P _ext (AC) of the sample of polystyrene particles having a diameter of 510 nm. The spot size ω ₀ calculated from the mode value of the waveform width and the central flow velocity as understood from the figure is about 2.64 μm. This value is close to the spot size (about 2.5 μm) estimated from the paraxial ray theory based on the beam parameters of the laser irradiation device 22 (HeNe laser), the magnification of the beam expander 34, and the focal length of the condenser lens 35. (However, the influence of aberrations associated with the wall surface equivalent of the flow cell 10 was neglected). The fact that the spot size estimated value based on the flow velocity and the waveform width is slightly larger than the estimated value may be due to the influence of spherical aberration due to the flow cell wall surface. assuming ω ₀ = 2.64μm, was compared with the theoretical results of measurement of the complex scattering amplitude _{S 11.} Figure 8 is an explanatory diagram the particle size and the complex refractive index indicates the real part of the complex scattering amplitude S ₁₁ as a real part and the theoretical value of the complex scattering amplitude S ₁₁ of the experimental example according to the known polystyrene standard particles, Figure 9 is an explanatory diagram the particle size and the complex refractive index indicates the imaginary part of the complex scattering amplitude S ₁₁ as the imaginary part of the complex scattering amplitude S ₁₁ and the theoretical value of the experimental example according to the known polystyrene standard particles. As polystyrene standard particles, those having a diameter of 202 nm, 254 nm, 294 nm, 402 nm, and 510 nm were used. In the experimental example, as shown, both the real part and the imaginary part agree well with the theoretical values.

<Experimental example 2: Experimental example using _{fine bubble water} >
FIG. 10 is an explanatory diagram showing an example of a measured waveform of the extinction power P _ext (AC) of a particle whose real part Re (S ₁₁ ) of the complex scattering amplitude S ₁₁ is larger than 0. FIG. FIG. 9 is an explanatory diagram showing an example of a measured waveform of the extinction power P _ext ( _AC ) of a microbubble in which the real part Re (S ₁₁ ) of the scattering amplitude S ₁₁ is smaller than a value 0. As described above, the real part Re (S ₁₁ ) of the complex scattering amplitude S ₁₁ has a positive value for fine particles (solid particles such as metal) having a larger dielectric constant than water, and has a smaller dielectric constant than water (fine bubbles). (Gas particles such as (air)) has a negative value. For this reason, in the case of the microbubbles, the maximum and the minimum are inverted with respect to solid particles such as metal. Note that the second half of the waveform of the dissipated power P _ext ( _AC ) of the microbubbles is systematically disturbed, which may be due to the bubbles being deformed by some interaction with the laser.

In the particle detector 20 of the embodiment described above, the photodiode A is located upstream (minus side of the x-axis) of the flow of the flow cell 10, the photodiode C is located downstream (plus side of the x-axis), and the minus side of the y-axis. And a photodiode D on the positive side of the y-axis. When detecting the fine particles, the dissipated power P _ext (Tot) (P _ext (Tot) = P (A) + P (B) + P (C) + P (D) -P (E)) and the dissipated power P _ext ( _AC ) (P _ext ( _AC ) = P _ext (A) -P _ext (C)), dissipated power P _ext (BD) (P _ext (BD) = P _ext (B) -P _ext (D)) is calculated and dissipated power _P ext (a-C) on the basis to calculate the real part of the complex scattering amplitude _{S 11,} dissipated power _P ext (complex scattering based on Tot) amplitude _{S 11} Compute the imaginary part of. Then, fine particles by the real and imaginary parts of the calculated complex scattering amplitude S ₁₁ determines whether a target particle. Thereby, it is possible to determine only the target particles among the particles flowing through the flow cell 10. At this time, in the case where four photodiodes a to d are arranged in the first to fourth quadrants with respect to the xy axis, the dissipated power P _ext (a + bcd) and the dissipated power P _ext (a + db- Since it is only necessary to calculate the dissipated power P _ext (AC) and the dissipated power P _ext (BD) as compared with the case where c) needs to be calculated, it can be easily calculated. .

Also, when the judgment value J (J = | P _ext (BD) / P _ext ( _AC ) |) is 0.2 or more, observation is not possible, and observation is performed only when the judgment value J is less than 0.2. By doing so, it is possible to increase the accuracy of determining whether or not the fine particles are the target fine particles.

Further, when the particles flowing in the flow cell 10 is determined to be subject microparticles, because to calculate the volume v of the particles on the basis of the real part of the complex scattering amplitude S _11, it is possible to detect the size of the fine particles.

In the particle detector 20 of the embodiment, the four photodiodes A to D of the observation light photodiode 40 are arranged such that an axis parallel to the flow direction of the flow cell 10 is an x axis and an axis perpendicular to the flow direction of the flow cell 10 is y. When placed on an axis, they were arranged on a four-divided plane divided by two straight lines orthogonal to each other at 45 degrees to the x-axis and the y-axis. However, the four photodiodes A to D are divided into a first straight line having a predetermined angle of 15 to 75 degrees from the y-axis and a second straight line symmetrical to the first straight line with respect to the x-axis. It may be arranged on a four-divided plane.

In the particle detector 20 of the embodiment, the observation is made when the judgment value J (J = | P _ext (BD) / P _ext ( _AC ) |) is less than 0.2. The observation may be performed when J is less than a predetermined value less than 0.2 (for example, 0.15 or 0.1). In this case, the fine particles can be determined with higher accuracy.

In the particle detecting device 20 of the embodiment, the volume v of the particle is calculated, but the volume v of the particle may not be calculated.

In the particle detection device 20 of the embodiment, the controller 60 controls the light intensity P (A) detected by the four divided photodiodes A to D of the observation light photodiode 40 and the reference light photodiode E. Based on -P (D), P (E), the dissipated power P _ext (Tot) (P _ext (Tot) = P (A) + P (B) + P (C) + P (D) -P (E)) , Dissipated power P _ext ( _AC ) (P _ext ( _AC ) = P _ext (A) -P _ext (C)), dissipated power P _ext (BD) (P _ext (BD) = P _ext (B) −P _ext (D)) was calculated. However, the light intensities P (A) to P (D), P () detected by the four photodiodes A to D and the reference light photodiode E between the observation light photodiode 40 and the control device 60. E), a circuit for calculating the dissipated power P _ext (Tot) (P _ext (Tot) = P (A) + P (B) + P (C) + P (D) -P (E)), and a dissipated power P _ext _(a-C) and a circuit for calculating the _{(P ext (a-C)} = P ext (a) -P ext (C)), dissipated power _{_{P ext (B-D) (}} P ext (B-D ) = P _ext (B) −P _ext (D)).

In an embodiment of the particle detector system 20 described above has focused on the complex scattering amplitude S ₁₁ because that is targeted to the spherical particles, such as micro-bubble as the target particles, when the target particle is a non-spherical particles it may be a replacement for the complex scattering amplitude _{S 11} to the complex scattering amplitude _{S 22.}

Next, a particle detector 120 according to a second embodiment of the present invention will be described. The particle detector 120 of the second embodiment has the same hardware configuration as the particle detector 120 of the first embodiment illustrated in FIG. In order to avoid redundant description, description of the hardware configuration of the particle detection device 120 according to the second embodiment will be omitted. In the particle detection device 120 of the second embodiment, between the observation light photodiode 40 and the control unit 60, dissipated power _P ext (Tot), dissipated power _P ext (A-C), dissipation power _{P ext} It is assumed that a preamplifier electronic circuit for calculating (BD) is provided. Further, the particle detection apparatus 120 of the second embodiment, since the detection of the particulate solid non-small bubbles (including non-spherical shape) as the target particles, the complex the complex scattering amplitude S ₁₁ in the description of the first embodiment replaced by a scattering amplitude _{S 22} will be described.

In the particle detection device 120 according to the second embodiment, the control device 60 executes an observation process illustrated in FIG. In the observation process of the second embodiment, the control device 60 firstly operates the dissipated power P _ext (Tot) and the dissipated power calculated by the preamplifier electronic circuit provided between the observation light photodiode 40 and the control device 60. P _ext (AC) and dissipation power P _ext (BD) are obtained (step S210). Subsequently, the absolute value of the ratio of the obtained dissipated power P _ext (BD) to the dissipated power P _ext ( _AC ) (| P _ext (BD) / P _ext ( _AC ) |) is determined. The value J is calculated (step S220), and it is determined whether the calculated determination value J is less than 0.2 (step S230). Determining whether observation is possible based on whether the determination value J is less than 0.2 has been described in the first embodiment.

If it is determined in step S230 that the determination value J is less than 0.2, the real part Re (S ₂₂ ) of the complex scattering amplitude S ₂₂ is calculated using the dissipated powers P _ext (Tot) and P _ext (AC). the imaginary part Im _{(S 22)} and calculates (step S240), the real part Re _{(S 22)} and the imaginary part Im _{(S 22)} of the calculated complex scattering amplitude _{S 22} and stores (step S250). Then, it is determined whether or not the observation is completed (step S260). If it is determined that the observation is not completed, the dissipation power P _ext (Tot), the dissipation power P _ext (AC), and the dissipation power P _ext (B− The process returns to step S210 for acquiring D). In the case where the determination value J is determined to be 0.2 or more, step S230 determines that the unobservable, the real part Re _{(S 22)} of the complex scattering amplitude _{S 22} and the imaginary part Im _{(S 22)} without calculating a It is determined whether or not the observation has been completed (step S260), and if it is determined that the observation has not been completed, the process returns to step S210. Therefore, the real part Re (S ₂₂ ) and the imaginary part Im (S ₂₂ ) of the complex scattering amplitude S ₂₂ are calculated for the fine particles having the judgment value J of less than 0.2 from the start of the observation to the end of the observation. The process of storing the data is repeatedly executed. Note that the determination of the end of observation in step S260 may be performed when instructed by the operator, when a predetermined number of particles are detected, or when the observation target cannot be detected for a predetermined time. it can. The calculation of the real part Re (S ₂₂ ) and the imaginary part Im (S ₂₂ ) of the complex scattering amplitude S ₂₂ will be described later.

If it is determined in step S260 that the observation has been completed, the complex scattering amplitude S22 of all the observed fine particles is plotted on a complex plane (step S270), and it is estimated that the particles are particles of the same material (a material having the same complex refractive index). The particle to be selected is selected (step S280). This selection can be made by the operator selecting the fine particles plotted on the complex plane. As shown in FIG. 4 and FIGS. 13 and 14 described later, the real part Re (S ₂₂ ) and the imaginary part Im (S ₂₂ ) of the complex scattering amplitude S ₂₂ on the complex plane have the same complex refractive index. Appears parabolically. For this reason, it is only necessary to presume that fine particles appearing in a parabolic shape are fine particles of the same material (a material having the same complex refractive index) and select them. As a selection method, the plotted fine particles may be individually selected, or may be selected by surrounding the plotted fine particles with a closed region. Then, the complex refractive index of the selected microparticle and the volume range of the selected microparticle are calculated (step S290). Then, it is determined whether or not to end the process (step S300). If it is determined that the process is not to be ended, the process returns to step S280 to select fine particles presumed to be the same material. finish. Therefore, when fine particles of a plurality of materials are observed, the fine particles can be selected for each of the plurality of materials, and the complex refractive index and the volume range of the selected fine particles can be calculated. It should be noted that the determination of the termination may be performed when the operator gives a termination instruction.

Calculation of the real part Re (S ₂₂ ) and the imaginary part Im (S ₂₂ ) of the complex scattering amplitude S ₂₂ of the fine particles, the method of selecting fine particles presumed to be fine particles of the same material, the complex refractive index of the selected fine particles, A method for calculating the volume range will be described.

<Definition of light scattering theory and the complex scattering amplitude _{S 22>}
In the problem of scattering of electromagnetic waves due to fine particles isolated in a uniform medium, as described above, the incident field when the traveling direction of the incident wave is in the + z direction is expressed by Expression (1). The relationship between the field and the polarization component of the scattering field can be expressed by equation (2) using a 2 × 2 complex scattering amplitude matrix S depending on the characteristics of the fine particles. Since φ can be arbitrarily selected for the forward scattered field of θ = 0, if φ = 0 is set, E _sca and _{θ = 0} = E _{sca, y} in equation (2). Under this notation, the component of the scattered field that interferes with the y-linearly polarized incident field is represented by the following equation (61) in a Cartesian coordinate system.

In general, under the condition that the wave vectors of the incident field and the scattered field match, the relationship equivalent to the equation (61) holds for the electric field vector component of the scattered field parallel to the electric field vector component of the incident field on the wavefront. Therefore, the subscript y of both sides of Expression (61) is interpreted as a notation of an arbitrary direction vector component on a common wavefront of the incident field and the scattered field. In general, S ₁₁ (θ = 0) and S ₂₂ (θ = 0) are different for non-spherical particles, but when considering the average of many particle orientations, it is not necessary to distinguish them. Therefore, hereinafter, unless otherwise specified, when expressing a scattering field that interferes with a linearly polarized incident field, S ₂₂ (θ = 0) is simply written as S _22, and the equation (62) omitting the subscript y of the electric field is omitted. ) Is used. This relationship (equation (62)), for the scattered field of the wave vector and the polarization component in common with the incident field, that the phase and amplitude of the scattered field is represented by the complex scattering amplitude S ₂₂ that depends on the characteristics of the fine particles means. Equation (62) forms the basis of the particle measurement principle by the SPES method.

<Relationship of the complex scattering amplitude _{S 22} and the SPES observed amount>
With respect to the linearly polarized Gaussian beam incident field E _inc (r) propagating in the + z direction, the polarization component of the electric field vector (italic type of the incident field symbol in equation (5)) is expressed as in equation (5). In formulating the interference between the incident field of the Gaussian beam and the forward scattered field, if the position of the beam center on the beam waist section is set to the origin r = 0 of the position vector, the position r _p = (x _p , Y _p , 0), the incident field to which the fine particles are exposed is expressed by the expression (9) from the expressions (5) to (8). It is assumed that the photodetector is located far enough from the wavelength and the spot size ω ₀ of the beam waist, and that the solid angle formed by the photocathode is small. From the equations (62) and (9), the scattering field of the fine particles spreading as a spherical wave from r _p = (x _p , y _p , 0) indicates that on the photoelectric surface of the photodetector placed in front Σ _PD It can be expressed as the following equation (63).

Approximate equality of formula (63) is within a small solid angle range detectors spanned when viewed from the origin is a complex scattering amplitude S ₂₂ means assumed approximate a constant value. In Expression (63), using the mathematical approximation of Expression (11), the scattered field at the photocathode r 面_PD is expressed by Expression (64). On the other hand, the incident field at photocathode R∈shiguma _PD is the approximation to the formula (5) z → + ∞, denoted formula (13).

From this, the light receiving power (observation signal) of the four-division photodiode photocathode placed as shown in FIG. 2 is formulated using E _{sca of} equation (64) and E _inc of equation (13). Receiving power density at the position R∈shiguma _PD on the photocathode ^{[Wm -2]} is the formula (14). From the equation (13), the received light power P _inc of the incident field due to the entire four-segmented photodiode Σ _PD = Σ _{A + B + C + D is given} by equation (15). When the spot size ω (z) of the Gaussian beam on the photocathode is sufficiently smaller than the radius of the photocathode, the photocathode may be assumed to be infinitely wide in the area calculation of Expression (15), and the integration range of x and y is Each may be (-∞, + それぞれ). Using this approximation, the analytic integration of equation (15) can be performed, and expressing the result using equation (6) results in P _inc = P. This means that the received power of the incident field is equal to the beam power.

The received light power P _sca of the scattered field due to the entire four-segment photodiode ４ _PD = Σ _{A + B + C + D is given} by equation (16) using equation (12). In the last formula, in small solid angle range in which the photoelectric surface is put is assumed to S ₂₂ is a constant value. Here, if the position coordinates of the fine particles on the beam waist cross section are expressed by a dimensionless parameter such as Expression (17), Expression (16) can be written as Expression (65).

Finally, the contribution of the dissipation field in the equation (14) is calculated. As a preparation, first, a mathematical expression of a complex scalar quantity (the left side of Expression (66)) is obtained. Equation (64), and calculates equation (13) based on, _x p appearing in the phase term exp, when subjected to approximation to ignore the secondary small term of _{y p,} the following equation (66) Be guided. However, equation (20) was used for rearranging notations in equation (66). Here, when the position (x, y) on the photocathode is represented by polar coordinates and the expression of b is used, expression (66) is expressed by expression (67).

Based on the equation (67), 4 photocathode of the divided photodiode is trying to calculate the dissipated power P _exp for receiving. Observed quantities to be derived for P _ext are the following three.
(1) Total power dissipated by ΣA + B + C + D P _ext (Tot) = P _ext (A) + P _ext (B) + P _ext (C) + P _ext (D)
(2) Difference of dissipated power received by ΣA and ΣC P _ext (AC) = P _ext (A) -P _ext (C)
(3) Difference of dissipated power received by ΣB and ΣD P _ext (BD) = P _ext (B) −P _ext (D)

These formulas respectively represent the boundaries of the complex plane rectangular region {Re (z) =-t, tIm (z) = 0, c}, {Re (z) = 0, tIm (z) = 0, c}. Can be derived by integrating the complex function f (z) = z · exp (−a ² z ² ) in the closed path defined by and applying the residue theorem to t → ∞. Erfc (z) in equation (26) is the complementary error function of the complex variable. Using Expression (25), the right side of Expression (22) is expanded as Expression (27). Here, equation (68) and equation (69) are used in equation (27). However, equation (30) and equation (31) were used in equation (29).

Particles beam center position (zeta, eta) = When in the (0,0), wherein the observed amount of (27) _P ext _P as contributions to (Tot) ext _{(Tot) 2} is zero _P ext (Tot) Only ₁ remains, resulting in equation (70). According to the relationship of Expression (6), the amount in the brackets on the right side of Expression (70) is equal to the power density of the incident field at the beam center position (中心, η) = (0, 0). Further, by using the expression (71) as one of the defining expressions of the “dissipation cross-sectional area C _ext ” of the fine particles, the expression (34) that can be interpreted intuitively is obtained. Formula (34) is a definition formula of the extinction cross-section of the fine particles based on the observed light energy for the plane wave incident field having the above-mentioned power density. In the Gaussian beam incident field, it was shown that this relational expression holds only when the beam center position (ζ, η) = (0, 0).

On the other hand, when Expression (26) is used, the right sides of Expressions (23) and (24) are expanded as Expressions (72) and (73), respectively. In addition, it set as Formula (37) and Formula (38).

In the setting of the present apparatus, since fine particles move in the + x direction with time, ζ = ζ (t). In order to search for information that can be extracted from the observed signal waveform of P _ext , first, by taking the ratio of Equations (72) and (73), Equation (39) is obtained, and the observed amount P _ext (BD) and the observed amount P _ext ( the ratio of a-C), the beam waist dimensionless coordinates of the fine particles of the cross-section (zeta, eta) only dependent, it can be seen that does not depend on the characteristics of the microparticles, such as the complex scattering amplitude S _22. Further, the coordinate ζ (t) in the x direction along the flow of the fine particles can be restricted by the waveform of the observation amount P _ext ( _AC ). Therefore, the observed amount P _ext (BD) / P _ext ( _AC ) can be used as an index of the coordinate η of the fine particle in the y direction. Based on this index, it is possible to extract only the fine particles that cross the vicinity of the beam center (| η | ≪1). In this case, the observation amount P _ext is represented by Expression (74), Expression (75), and Expression (42).

Erfi (z) in equation (75) is an imaginary error function. Equation (74) is the same as equation (70) especially when the beam center ζ = 0. The function (equation 43) in equation (75) defines the waveform of P _ext (AC) (ζ) at | η | ≪1. The term on the right side erfi in equation (43) is an odd function and monotonically increasing, and the increase in its absolute value in the | ζ | ≫1 region is canceled by exp (−2ζ ² ). Therefore, f (ζ) has one minimum point and one maximum point (symmetrical with respect to the origin) in each of the positive and negative ζ regions, and f (0) = 0. The maximal point and the minimal point of f (求め) numerically obtained are expressed by equation (44).

According to the numerical calculation of Expression (39), | P _ext (BD) / P _ext ( _AC ) | <0.2 at a position ζ = ζ _{+ α} where P _ext ( _AC ) takes an extreme value. Then, | η | <0.2 is satisfied. At this time, the error of the approximate equations (74) and (75) is 2% smaller than the strict equations (27) and (72). Was found to be less than. Thus, in the present _{specification,} in the maximum position of _P ext (A-C) measured waveform _{_{| P ext (B-D)}} / P ext (A-C) | < only particle detection event satisfying 0.2 after having extracted the equation (74), assuming the equation _(75), is to derive the _P ext (a-C) and _P ext complex scattering amplitude _{S 22} from the waveform amplitude of the fine particles of (Tot). This method, equation to derive the real and imaginary part of the complex scattering amplitude S ₂₂ of the microparticles becomes Equation (76) Equation (77). However, in Expressions (76) and (77), the amplitude of the observed waveform is defined as Expressions (47) and (48).

The calculation of the real part Re (S ₂₂ ) and the imaginary part Im (S ₂₂ ) of the complex scattering amplitude S ₂₂ of the fine particles has been described above.

<Relationship between measured signal voltage and dissipated power>
Next, from three voltage signals V _sig (Tot-Ref), V _sig (AC), and V _sig (BD) output from the preamplifier circuit, the dissipated power P _ext (Tot) and the dissipated power P _ext ( AC) and a method of deriving the dissipated power P _ext (BD) will be described.

First, the voltage signal V _sig (Tot-Ref) is represented by Expression (78). R [AW ^-1 ] represents the light receiving sensitivity of the photodiode, K [VA ^-1 ] represents the amplification factor of the current-voltage conversion circuit, _and G _diff _{represents the differential amplification factor of the instrumentation amplifier. The superscripts QPD and rPD represent a quadrant} _{photodiode and a reference light photodiode, respectively} . α is the beam intensity division ratio between the incident light and the reference light. The division ratio α is adjusted so as to satisfy Expression (79), and two terms including the incident light power P _inc in Expression (78) are canceled. By this cancellation, the influence of the noise of the laser beam intensity can be largely eliminated. Even if the cancellation is not perfect, the DC component may be removed when extracting the signal waveform of the particles by the measurement software.

When the equation (78) is modified under the condition that two terms including the incident light power P _inc are canceled out, the equation (80) is obtained. Here, when the relative magnitudes of P _ext (Tot) and P _sca (Tot) on the left side of Expression (80) are estimated from Expressions (65) and (77), it is assumed that η is almost zero and Expression (81). Considering this as a function of particle size, _{it can be seen that in the} submicron particle size range, P _sca (Tot) _is _{not always negligibly small compared to} P _ext (Tot) _.

Therefore, _{it is} _{necessary to consider the contribution} _of P _sca (Tot) in _the _{data analysis} _{. As a preparation,} _instead _of Im (S ₂₂ ) _{in Expression} (77) _, [Im (S ₂₂ )] _SC is defined as Expression (82) as _{the sum} of Im (S ₂₂ ) and _{contribution of scattered light} . The equation (83) was used. As can be seen from Expressions (82) and (80), [Im (S ₂₂ )] _SC is a measured amount obtained from the signal V _sig (Tot-Ref). In particular _[Im (S _{22)] SC} when the _{_{_{P sca (Tot) amp «P ext}}} (Tot) amp is substantially equal to Im (S22).

On the other hand, the signal V _sig ( _AC ) is expressed as in equation (84). If the center position of the four-division photodiode is aligned with the beam center, the contributions of the incident light power P _inc and the received light power P _sca of the scattered field in equation (84) are canceled out by the photocathodes A and C, respectively. Under this canceling condition, Expression (84) is transformed into Expression (85). As can be seen from Expressions (85) and (76), Re (S22) is a measured amount obtained from the signal V _sig ( _AC ). In the data analysis method of the present apparatus, the complex refractive index and volume of particles are estimated based on bivariate measurement data {Re (S ₂₂ ), [Im (S ₂₂ )] _SC }.

<Model for calculating the complex scattering amplitude S ₂₂ of the fine particles>
In order to estimate the model parameters (complex refractive index, volume, shape) of the fine particles from the measurement data of the plurality of fine particles {Re (S ₂₂ ), [Im (S ₂₂ )] _SC }, the input values of the model parameters are used. forward model for calculating the complex scattering amplitude S ₂₂ is required. The formulation, calculation method and calculation result of the forward model are described below.

The problem of scattering of the electromagnetic field of fine particles (or bubbles) made of a non-magnetic and isotropic material is represented by the following integral form (without approximation) derived from Maxwell's equation (without approximation) in the frequency domain. ).

とき In the integration region in equation (78), this equation can be regarded as an integral equation for the electric field inside the particle. Assuming that the internal electric field of the particle, which is the solution of the integral equation, is obtained (by a numerical method described later), the scattered field by the particle can be written as the second term on the right side of the equation (85) as equation (86).

Under the condition that the particle is near the origin and the observation point r is far enough away from the origin compared to the particle size and wavelength (far-field), the approximation of Equation (87) can be used for the Green's function.

Applying the situation of the measurement system of the SPES method, consider a forward scattered field due to an incident field that propagates in the direction of equation (88) and the electric field is linearly polarized in the direction of equation (89). It is also assumed that the complex refractive index is constant within the particle volume. From Expressions (86) and (87), the polarization component of the scattering field propagating in the direction of Expression (88) in the direction of Expression (89) common to the incident field (the left side of Expression (90)) is expressed by Expression (90). Can be expressed. Here, a dimensionless quantity of a complex number appearing as a volume integral in the equation (90) is defined as an equation (91), and this is called a dissipative structure factor.

The dissipation structure factor is a volume average value of an inner product of an internal electric field and an incident field generated in a particle when a plane wave of a unit amplitude (Equation (92)) is incident. In particular, for optically soft particles whose size is about the same as or smaller than the wavelength, and whose m / m _med is close to the value 1, the internal electric field E (r∈ν) will have an incident field E _inc (R∈ν) (Born approximation). As can be derived by substituting the incident field into the internal electric field in equation (93), F = 1 in the Born approximation. Even for general particles to which the Born approximation does not apply well, when the size is about the same as or smaller than the wavelength, it is often | F | ～ 1 and arg (F) ～ 0 [rad]. In strongly absorbing particles, | F | tends to be smaller than the value 1 due to the small internal electric field. Further, it is derived from the long-wave limit of the Mie theory that the spherical particle having a size much smaller than the wavelength has the formula (93).

If the amplitude of the incident field (Equation (94)) is set to a value of 1 without loss of generality, Expression (90) is compared with Expression (61), and using the definition of F by Expression (91), the forward direction ( theta = 0 complex scattering amplitude _{S 22)} of it can be seen that expressed the equation (95). The ratio of the real part and the imaginary part of the complex scattering amplitude S ₂₂ has a complex refractive index m, the relationship between the dissipating structure factor F and equation (96). In particular, for particles made of a non-absorbable substance with _mi = 0, it is equal to the ratio of the real part to the imaginary part of F as shown in equation (97).

In the forward model calculations of the complex scattering amplitude S ₂₂ (the formula (95)), in some way, the wave number of the incident field dissipation structure factor F, the refractive index of the medium, it is necessary to calculate as a function of the parameters of the particles. In the present embodiment, in order to calculate the dissipation structure factor F, an analytical solution of the Mie theory is used for spherical particles, and a numerical solution by a discrete dipole method is used for non-spherical particles. For non-spherical particles, the particle orientation during traversal of the beam waist is unknown, so an average over a number of orientations was chosen. In order to efficiently calculate the orientation average value, the Block-Krylov subspace method was introduced to the iterative solution of a large-scale linear equation appearing in the discrete dipole method. An algorithm for FFT acceleration was implemented to speed up the calculation of the matrix-vector product in each iteration (Block-DDA). In addition, in order to be able to consider fractal aggregates of microspheres, which are particle shapes that are actually common in the environment, we have also developed software that automatically generates geometric coordinates of aggregates with known fractal dimensions (aggregate_gen ).

The particles of various complex refractive index and shape shows the calculation results of the complex scattering amplitude S ₂₂ defined by formula (95) in FIG. 13 and FIG. 14. As can be seen from FIGS. 13 and 14, the value of the complex scattering amplitude S ₂₂ has a value on the specific curve particle species in the complex plane. Attention is first focused on the small particle size limit near the origin in FIGS. F values in the vicinity of the origin from being approximated by Equation (93), the curve of the complex scattering amplitude S ₂₂ extends from the origin in a direction which depends only on the value of the complex refractive index. When the particle diameter increases to some extent away from the origin, the curve starts to bend not only depending on the complex refractive index but also on the particle shape. As described later, the depending on the particle size of in the complex plane curve of the complex scattering amplitude S ₂₂ bends are by particle size dependence of the argument arg (F) of the dissipative structure factor F. First, focusing only on spherical particles, it can be seen that the curve strongly depends on both the real and imaginary parts of the complex refractive index.For sample particles that are known to be spherical, complex scattering it is expected that can estimate the real and imaginary part of the complex refractive index from the measured values of the amplitude S _22. For relatively spherical near cubic grains (cube), the curve of the complex scattering amplitude S ₂₂ although fairly close to spherical particles, having a slight shift trend towards the curve of the refractive index is small spherical particles (FIG. 14). On the other hand, very high non-sphericity, the fractal aggregate particles of microspheres (diameter 0.04 · / U> m) ( aggregate), the curve of the complex scattering amplitude S ₂₂ is in the form close to a straight line extending from the origin.

Such the significant particle species dependent curve shape of the complex scattering amplitude S ₂₂ can be discussed on the basis of the particle species dependent F value defined by equation (91). FIGS. 15 and 16 are explanatory diagrams in which the absolute value of the F value and the particle size dependence of the argument are plotted for the same particle type as in FIGS. 13 and 14. First, in a spherical particle (sphere, m = 1.4 + 0i) whose refractive index is close to the medium (here, water), since the internal electric field of the particle volume is close to the incident field, the dissipative structure factor F takes a value close to the real number 1. , Does not depend much on the particle size. Therefore the curve of the complex scattering amplitude S ₂₂ on the complex plane, close to a straight line, the slope of passes through the origin determined from equation (93) (95). When the particle shape is the same, the difference between the amplitude and phase of the incident field and the internal electric field increases with the particle size as the difference in the refractive index from the medium increases. With the shift of the internal electric field, the argument arg (F) of the dissipation structure factor F shows a particle size dependence as shown in FIGS. In the case of fractal aggregate particles of microspheres, the particle surface area is remarkably large with respect to the particle volume, and the incident field easily penetrates into the particle volume. small. Therefore, the smaller situations than the particle size or wavelength comparable, F value without departing significantly from the small径極limit value of the formula (93), the curve of the complex scattering amplitude S ₂₂ extends from the origin It has a shape close to a straight line.

<Estimation of particle parameters based on the data of the complex scattering amplitude S _22>
Next, the inverse problem of estimating the parameters of the particles based on the measurement data of the plurality of fine particles {Re (S ₂₂ ), [Im (S ₂₂ )] _SC } and the _two models of the complex scattering amplitude S ₂₂ is calculated. The solution of will be described. This solution consists of n S ₂₂ data points (the real part Re (S ₂₂ ) and the imaginary part Im of the complex scattering amplitude S ₂₂ corresponding to n particles having the same shape parameter and complex refractive index but different volumes only. (S ₂₂ )) is used as an input value to estimate the complex refractive index and n volumes of the particle group. Using this solution imposes an assumption that the particle shape and the complex index of refraction are the same for n data points used as input values. As an index of validity of the assumption, for example, extraction and density distribution in the complex plane of the S ₂₂ data points were, S ₂₂ theoretical curve of particles having a specific shape parameter and the complex refractive index (FIGS. 13 and 14) Can be used. In practice, such data point cloud extraction is performed manually or using some automatic algorithm. Within the scope of the second embodiment, the search for the automatic algorithm was not performed, and the extraction was performed manually. The extracted n pieces of _{S 22} data points specified as equation (98). The model parameters estimated by the algorithm are represented as in equation (99). Here, _mr and _mi represent the real and imaginary parts of the complex refractive index, respectively, and v _j (j = 1,..., N) represents the j-th particle volume counting from the smaller one.

In the range of the second embodiment, in order to avoid difficulties in the amount of calculation, the particle shape is preliminarily selected from several types of candidates _{and is not included in} the model parameters _{. It is assumed that the occurrence probabilities of each element of the data have a normal distribution independent of each other. At this time, the probability distribution (likelihood function) of the data under the condition of the model parameter} can be expressed by Expression (100). _{_{{Re (S 22) j,}} [Im (S 22) j] SC} are the model parameters _{_{(m r, m i, ν}} j) calculated by the forward model for particles of _{{Re (S} 22), [ Im (S ₂₂ )] _SC }.

統計 Statistical error of measurement data consists of contribution of relative error and background noise. The relative error is caused by the deviation of the crossing position of the particle from the center of the beam waist, and the background noise is caused by the noise of the electronic circuit and the noise of the laser light source. The magnitude of each contribution of the relative error and the background noise can be estimated from waveform simulations and experiments.

According to Bayes' theorem, _{the posterior probability p of the model parameter} can be expressed as Expression (101) by the _{likelihood function L and the prior probability p0} .

If there is no prior information that restricts the existence range of the model parameters, a uniform distribution is adopted as the prior probability. In order to efficiently calculate the posterior probability of {Re (S ₂₂ ) j, [Im (S ₂₂ ) j] _SC }, the Metropolis-Hasting (MH) algorithm of the Markov chain Monte Carlo method (MCMC method) [Reference: Aster et al. 2013 etc.] were used. The number of MCMC calculation steps was 1,200,000, and the first 200,000 steps were excluded as burn-in-time. In addition, in order to eliminate artificial correlation depending on the algorithm, sampling points every 100 steps (total 10,000 points) were used for analysis. In each calculation step of MCMC methods Upon executing a forward calculation of the values of the complex scattering amplitude S _22, in the case of spherical particles directly running the semi-analytical calculation of Mie theory in the case of non-spherical particles with pre-calculated Equation (95) was evaluated using an F value calculated by linearly interpolating the numerical value table of F (k, ν, m, shape) in a multidimensional manner. Under the calculation condition of n = 4, the time required for 1200,000 steps in the single core calculation of the Intel Core i7-7660 CPU @ 2.5 GHz was several seconds in both spherical and non-spherical cases.

<Verification of estimation method of particle parameters>
In order to verify the performance of the particle parameter estimation method, we first show the results of applying it to ideal data without noise generated by simulation. FIGS. 17 to 20 show a part of the joint probability distribution of parameter estimation values for spherical particles of m = 1.5 + 0i and 1.5 + 0.1i, respectively. 17 and 19 shows the real and imaginary part of the complex index of refraction, 18 and 20 show the volume equivalent particle size d _v of the first data point from the smaller real part of the complex refractive index. FIG. 21 shows a list of parameter estimation results (values at 5%, 50%, and 95% points of the probability density distribution) of other spherical particles having a complex refractive index including these particles.

As for the spherical particles, it can be seen that the real and imaginary parts and the volume of the complex refractive index can be estimated to be almost correct. However, for example, m = 1.5 + particle volume in the case of 0.1i (d _{v, 1st)} as can be remarkably observed in the real part of the refractive index (m _r), in that there is a correlation parameter between (degenerate) Please be careful. The uncertainty width of the parameter estimation, that is, the width of the posterior distribution becomes wider as the degeneracy between different parameters increases. The degree of degeneracy between the parameters depends on the region of the particle volume included in the input data point group (Equation (98)). If If, in grain volume region containing the S ₂₂ data points, if dissipative structure factor F is constant value, as can be seen from equation (95), the particle volume and the complex refractive index in the information data includes has completely degenerated, it is recovered from S ₂₂ data the true value of the grain volume and the complex refractive index independently becomes impossible. For example, when _S22 data of only one point is used, the particle volume and the complex refractive index completely degenerate, and the functional relationship between the real part and the imaginary part of the complex refractive index can be restricted, but the values are determined. Can not. On the other hand, if if the particle volume in the region containing the S ₂₂ data points, if the dissipation structure factor F, depending on the particle volume has changed, the degeneracy of the grain volume and the complex refractive index in the information data includes It is likely to be resolved, and if fully resolved, each can be restored independently. Therefore, when it is desired to precisely estimate the real and imaginary part and particle volume of the complex refractive index is at least, particle volume area S ₂₂ dissipate data points structure factor F is changed to some extent used for input (Figure 15 and 16 (see FIG. 16).

In this data analysis algorithm, it is necessary to presuppose the particle shape in advance, but in the particle measurement in the environment, the exact particle shape is often unknown. To examine how the parameter estimation results or systematic errors occur when the assumption of particle shape was incorrect, the S ₂₂ data of simulation for non-absorbable cubic grains (random orientation average), parameters assuming spherical particles I applied the estimation algorithm (see the table in FIG. 22). As a result, the real part of the complex refractive index tended to be estimated to be slightly smaller than the true value, and the particle volume tended to be estimated to be slightly larger than the true value. The imaginary part of the complex index of refraction gave an approximate correct estimate near zero. This result suggests that the complex refractive index and particle volume of non-spherical particles such as cubes can be estimated to some extent by the estimation algorithm assuming spherical particles.

Next, we simulated fractal aggregates of light-absorbing microspheres (diameter 0.04 // U> m) that mimic soot particles in the atmospheric environment, and whose volume equivalent particle size is smaller than the wavelength. in the generated S ₂₂ data, shows the result of applying the parameter estimation algorithm with an assumption of fractal aggregates shape of the microspheres 23 and 24. For particles in the form of fractal aggregates of microspheres, when the volume equivalent particle size is smaller than the wavelength, the value of the dissipation structure factor F does not depend much on the particle volume and is close to the value of the small particle size limit. Therefore, the parameter to each other of the grain volume and the complex refractive index in the information contained in the S ₂₂ data are degenerated strongly, to estimate each independently is extremely difficult. However, if positively utilizing it less dependent on the F value is the particle size and fractal dimension in a small area than the volume equivalent particle diameter of the wavelength (FIGS. 15 and 16), Ya extracted particle size range of S ₂₂ data There is a possibility that the "relational expression between the real part and the imaginary part of the complex refractive index" can be restricted without being influenced by the assumed value of the fractal dimension. As it can be seen from FIGS. 23 and 24, the existence range of the parameter in the model soot particles, hardly depends on the assumed value and size range were extracted S ₂₂ data fractal dimension, certain constraints on the one-dimensional space Have been. In particular, the real and imaginary parts of the complex refractive index are constrained on a straight line passing through the true value. This is the actual soot particles also, by applying a parameter estimation algorithm with an assumption of fractal aggregate shape S ₂₂ data, constraint of the presence area of the real part of the complex refractive index and the imaginary part on the one-dimensional space Suggests that you can.

<Experimental results: Particles contained in precipitation>
Next, as early application examples, precipitation samples collected on the day in Tokyo (collected on August 8, 2018, Hongo Campus of the University of Tokyo) and precipitation samples collected in Okinawa and stored refrigerated (2016 FIG. 25 and FIG. 26 show the results of analysis of the particles contained in the sample (collected at Cape Hedo, Okinawa Prefecture, March 19-20). FIG. 25 shows the experimental results of a rain sample in Tokyo, and FIG. 26 shows the experimental results of a rain sample in Okinawa. 25 and 26, the measurement data range of Fullerene soot (Alfa Aesar, stock # 40971), which is one of the standard samples of soot particles, is superimposed on the measurement data of the precipitation sample. Fullerene soot has a high [ImS ₂₂ ] _SC / ReS ₂₂ ratio because the imaginary part of the complex refractive index is large. In the precipitation sample, particles that appear to be soot having an [ImS ₂₂ ] _SC / ReS ₂₂ ratio close to Fullerene soot and particles that appear to be non-absorbent having a low [ImS ₂₂ ] _SC / ReS ₂₂ ratio are mixed. _Here, the data group found soot on the complex plane of the _{S 22} data the Category 1 Distant, among the data points appear to _{non-absorbent,} the Category to _[ImS _22] SC / _ReS 22 ratio is relatively large data group 2. A data group whose [ImS ₂₂ ] _SC / ReS ₂₂ ratio is relatively small is referred to as Category 3. Here, Category classification is performed visually and subjectively, several representative data points are appropriately selected from each Category (markers in the figure), and they are input to the parameter estimation algorithm (Equation (91)). Used as Category 1 is defined as a data point that satisfies [ImS ₂₂ ] _SC / ReS ₂₂ > 1, and as a representative data point, first, data that satisfies [ImS ₂₂ ] _SC <0.34 is linearly fitted, and the regression line is obtained. Four points where the ReS ₂₂ value was 0.04, 0.08, 0.12, and 0.16 were selected above. The reason why the [ImS ₂₂ ] _SC value was given an upper limit in Category 1 data analysis was that the target of analysis was that the volume equivalent particle size, whose parameter estimation result was hardly affected by the particle size and shape of the selected data point, was smaller than the wavelength. Is also limited to small particles (see FIGS. 23 and 24).

First, for the data of Category 1, which is considered to be soot, the parameter estimation results assuming the particle shape of the fractal aggregate of microspheres (0.04 μm in diameter) are shown in FIGS. 27 and 28. It can be seen that the estimated values of the real part and the imaginary part of the complex refractive index are constrained on a one-dimensional space (straight line) that hardly depends on the assumed value of the fractal dimension (D _f = 2.5, 2.7). . Although Tokyo constraints straight line of Okinawa sample is fairly close, _[ImS _22] of Okinawa better elected data points for SC / _{ReS 22} ratio is greater, _{_m} i / _m _r ratio, which is derived is slightly larger I have.

FIG. 29 and FIG. 30 show the results of parameter estimation assuming spherical particles for the data of Category 2, which is considered to be non-absorbable particles in FIG. 25 and FIG. Data of the Category 2 _{_is,} m r = 1.45 ~ _1.55, a _m i ~ 0, it is presumed to be a mineral dust particles mainly containing such silicate. FIG. 31 shows the results of parameter estimation assuming spherical particles for the data of Category 3 which is considered to be non-absorbable particles in FIG. Data of the Category 3 _{_is,} m r = 1.37 ~ _1.38, a _m i ~ 0, it is inferred that the microorganism particles containing much moisture organics or water. It is presumed that the reason why there are many Category 3 precipitation samples in Okinawa is that microorganisms have propagated in the samples since they were kept refrigerated for about two years.

As described above, in the fine particle detection device 120 according to the second embodiment, it is understood that, even with unknown particles in the environment, useful information for identifying the particle type can be obtained by the data analysis algorithm. Although not shown here, if the complex refractive index is determined, the particle volume is also determined, and the number of detections per unit time can be converted into a number concentration. Therefore, from the data shown in FIGS. Several concentrations can also be derived.

In the particle detector 120 according to the second embodiment described above, the photodiode A is located on the upstream side (minus side of the x-axis) of the flow of the flow cell 10, the photodiode C is located on the downstream side (plus side of the x-axis), and the y-axis is on the downstream side. A photodiode B is arranged on the minus side, and a photodiode D is arranged on the plus side of the y-axis. Further, the light intensities P (A) to P (D) and P (E) detected by the four photodiodes A to D and the reference light photodiode E are input, and the dissipated power P _ext (Tot) is calculated. a circuit for a circuit for calculating the dissipated power _P ext (a-C), a pre-amplifier electronic circuit and a circuit for calculating the dissipated power _P ext (B-D) is provided. Preamplifier electronics dissipation from the power _P ext (Tot), dissipated power _P ext (A-C), the real part Re _{(S 22)} and imaginary of the complex scattering amplitude _{S 22} based on the dissipated power _P ext (B-D) The part Im (S ₂₂ ) is calculated. The real part Re (S ₂₂ ) and the imaginary part Im (S ₂₂ ) of the complex scattering amplitude S ₂₂ of the plurality of fine particles calculated in this way are stored. Then, plot the complex scattering amplitude S ₂₂ of a plurality of particles in the complex plane, and select the plurality of complex scattering amplitude S ₂₂ which is presumed to be the same complex index of refraction, the plurality of complex scattering amplitude S ₂₂ selected Calculate the complex refractive index and particle volume of the fine particles using a data analysis algorithm. As a result, even for unknown particles in the environment, useful information for identifying the particle type can be obtained.

Further, for an observation target having a judgment value J (J = | P _ext (BD) / P _ext ( _AC ) |) of less than 0.2, the real part Re (S ₂₂ ) of the complex scattering amplitude S ₂₂ and the imaginary Since the part Im (S ₂₂ ) is stored, the accuracy of determining whether or not the microparticle is the target microparticle can be increased.

Also in the particle detector 120 of the second embodiment, the four photodiodes A to D of the observation light photodiode 40 are arranged such that the axis parallel to the flow direction of the flow cell 10 is the x-axis and the axis perpendicular to the flow direction of the flow cell 10. Is the y axis, they are arranged on a four-divided plane divided by two straight lines perpendicular to the x axis and the y axis at 45 degrees. However, the four photodiodes A to D are divided into a first straight line having a predetermined angle of 15 to 75 degrees from the y-axis and a second straight line symmetrical to the first straight line with respect to the x-axis. It may be arranged on a four-divided plane.

In the particle detection device 120 according to the second embodiment, for the observation target whose judgment value J (J = | P _ext (BD) / P _ext ( _AC ) |) is less than 0.2, the complex scattering amplitude S ₂₂ Although the real part Re (S ₂₂ ) and the imaginary part Im (S ₂₂ ) are stored, the observation target whose judgment value J is less than 0.2 (eg, 0.15 or 0.1) is less than 0.2. May store the real part Re (S ₂₂ ) and the imaginary part Im (S ₂₂ ) of the complex scattering amplitude S ₂₂ .

As described above, the embodiments for carrying out the present invention have been described using the embodiments. However, the present invention is not limited to these embodiments at all, and various forms may be provided without departing from the gist of the present invention. Of course, it can be implemented.

The present invention can be used in the manufacturing industry of fine particle detection devices.

10 flow cell, 20 particle detector, 22 laser irradiator, 30 optical system, 31 optical isolator, 32 half-wave plate, 33 polarization beam splitter, 34 beam expander, 35 condenser lens, 36 broadband dielectric mirror, 40 Observation light photodiode, 50 ° stage, 52 ° x-direction actuator, 54 ° y-direction actuator, 60 ° control device, AD photodiode, E reference light photodiode.

Claims

A fine particle detection device for detecting fine particles flowing in the flow cell,
A laser irradiator that irradiates a laser beam,
An optical system that adjusts the laser beam to a degree that can be approximated to a Gaussian beam in the vicinity of the focused spot;
A light intensity detector that is disposed behind the condensing spot and detects light intensity;
A control device for determining the fine particles based on the light intensity detected by the light intensity detector,
With
The light intensity detector has an origin at the center of the condensed spot, an x-axis passing through the origin and an axis parallel to the flow direction of the fine particles in the flow cell, and an y-axis passing through the origin and perpendicular to the x-axis. In this case, there are four detectors which are divided by a first straight line having a predetermined angle whose elevation angle from the y-axis is not less than 15 degrees and not more than 75 degrees and a second straight line symmetrical to the first straight line with respect to the x-axis. Yes,
Particle detector.
The particle detecting device according to claim 1,
The first straight line and the second straight line are orthogonal straight lines;
Particle detector.
The particle detection device according to claim 1 or 2,
The light intensity detector includes a first detector that belongs to a region on the negative side of the x-axis when the particles in the flow cell flow from a negative direction to a positive direction on the x-axis, and a second detector that belongs to the region on the negative side of the y-axis. And a third detector that belongs to the region on the positive side of the x-axis and a fourth detector that belongs to the region on the positive side of the y-axis.
The control device includes a first light intensity detected by the first detector, a second light intensity detected by the second detector, a third light intensity detected by the third detector, and the fourth light intensity. the imaginary part of the complex scattering amplitude S 11 calculated based on the sum of the fourth light intensity detected by the detector, is detected by the first light intensity and the third detector detected by the first detector and third, based on the difference between the light intensity to calculate the real part of the complex scattering amplitude S 11, discriminates particles on the basis of the real and imaginary parts of the calculated complex scattering amplitude S 11,
Particle detector.
The particle detection device according to claim 3, wherein
With a reference detector for detecting the light intensity of the reference laser beam separated from the laser beam,
The control device is based on a value obtained by subtracting a reference light intensity detected by the reference detector from a sum of the first light intensity, the second light intensity, the third light intensity, and the fourth light intensity. Te to calculate the imaginary part of the complex scattering amplitude S 11,
Particle detector.
The fine particle detection device according to claim 3 or 4,
The control device determines the fine particles flowing through the flow cell using a composed of a real part and an imaginary part of the complex scattering amplitude S 11 that previously obtained for known complex dielectric constant of the particulate relationship,
Particle detector.
The particle detection device according to claim 5, wherein
Wherein the controller, when the particles flowing in the flow cell is determined to be any of the known particulate, derives the volume of particles by the real part of the complex scattering amplitude S 11 described above calculated using the complex dielectric constant of a known fine particles Do
Particle detector.
The fine particle detection device according to any one of claims 3 to 6, wherein
The controller determines the particles when the ratio of the difference between the second light intensity and the fourth light intensity to the difference between the first light intensity and the third light intensity is less than a predetermined value.
Particle detector.
The particle detection device according to claim 1 or 2,
The light intensity detector includes a first detector that belongs to a region on the negative side of the x-axis when the particles in the flow cell flow from a negative direction to a positive direction on the x-axis, and a second detector that belongs to the region on the negative side of the y-axis. And a third detector that belongs to the region on the positive side of the x-axis and a fourth detector that belongs to the region on the positive side of the y-axis.
The control device includes a first light intensity detected by the first detector, a second light intensity detected by the second detector, a third light intensity detected by the third detector, and the fourth light intensity. the imaginary part of the complex scattering amplitude S 22 calculated based on the sum of the fourth light intensity detected by the detector, is detected by the first light intensity and the third detector detected by the first detector and third, based on the difference between the light intensity to calculate the real part of the complex scattering amplitude S 22, discriminates particles on the basis of the real and imaginary parts of the calculated complex scattering amplitude S 22,
Particle detector.
The particle detecting device according to claim 8, wherein
With a reference detector for detecting the light intensity of the reference laser beam separated from the laser beam,
The control device is based on a value obtained by subtracting a reference light intensity detected by the reference detector from a sum of the first light intensity, the second light intensity, the third light intensity, and the fourth light intensity. Te to calculate the imaginary part of the complex scattering amplitude S 22,
Particle detector.
The fine particle detection device according to claim 8, wherein:
The control device determines the fine particles flowing through the flow cell using a composed of a real part and an imaginary part of the complex scattering amplitude S 22 that previously obtained for known complex dielectric constant of the particulate relationship,
Particle detector.
The fine particle detection device according to any one of claims 8 to 10, wherein
Storing the real and imaginary parts of the complex scattering amplitude S 22 of a plurality of particles in the flow cell,
Plotting the complex scattering amplitude S 22 of the plurality of fine particles on a complex plane;
Among a plurality of microparticles plot of the complex scattering amplitude S 22, the particle volume selects the complex scattering amplitude S 22 of different but particles complex refractive index is estimated to be the same,
Calculating the complex refractive index and particle volume range for the complex scattering amplitude S 22 of the selected particles,
Particle detector.