Particle measuring device and particle measuring method

Abstract

The objective of the present invention is to provide a technology with which it is easy to perform calibration to suppress differences between a plurality of devices, and with which it is possible to measure particle sizes using nonlinear detection signals ranging from the Rayleigh scattering region to the Mie scattering region. A particle measuring device according to the present invention acquires a normalized signal S obtained by dividing the maximum value of an interference signal generated by interference between a signal beam and a reference beam by a reference value, and measures the size of a particle using a function that describes a relationship between S and (d-d0), where d is the size of the particle and d0 is a measurement lower limit value of the size of the particle (see Fig. 2A).

Description

Particle measurement device and particle measurement method

[0001] The present invention relates to a technique for measuring the size of particles in a solvent using light.

[0002] In recent years, pharmaceutical development has been shifting from small molecule drugs to biopharmaceuticals. Because biopharmaceuticals are polymers, they are prone to aggregation, which can lead to toxicity. For example, the U.S. Food and Drug Administration and other organizations are seeking to strengthen regulations on aggregate concentration control. Therefore, a technology is needed to quantitatively measure the size distribution of aggregates at a desired density in the submicron range of 0.1 to 1 μm. Protein aggregates float in a solvent, and their position changes over time due to Brownian motion. This invention describes a technology for measuring the size and density of protein aggregates and standard particles such as polystyrene beads. These test objects are collectively referred to as "particles."

[0003] Patent Document 1 describes a technology for detecting particles using optical measurement. The document discloses an optical measurement method for focusing light to generate a light spot and measuring a test object approximately three times the size of the light spot, the method comprising: a signal acquisition step for detecting reflected light from the test object by irradiating the test object with the light while moving at least the focal position of the light in the optical axis direction; a step for acquiring correspondence data describing the correspondence between the intensity of the reflected light and the size of the test object; and a size calculation step for obtaining the size of the test object by referencing the correspondence data using the intensity of the reflected light (claim 1). The technology described in the document achieves high-resolution measurement without preprocessing by causing interference between the reflected light and a reference light to enhance the signal.

[0004] Patent Document 2 listed below discloses a technology that eliminates the need for phase adjustment of a reference light by mirror scanning in time domain OCT (Optical Coherence Tomography) by physically scanning an objective lens and receiving interference between signal light and interference light with four detectors with different phase conditions. Furthermore, based on the technology of Patent Document 1, a technology for speeding up scanning of a light spot is disclosed so as not to be affected by the movement of particles undergoing Brownian motion in a liquid.

[0005] Patent Document 3 discloses a technology for measuring biological tomographic images using a semiconductor laser as a light source, in which the coherence length is controlled within a predetermined range by superimposing a high frequency on the driving current, thereby reducing the effect of noise contained in the acquired tomographic image.

[0006] JP 2017-102032 A, WO 2020 / 144754 A, JP 2015-049204 A

[0007] The technology described in Patent Document 1 and Patent Document 2, which is based on Patent Document 1, can determine particle size from the measured maximum detection signal by acquiring correspondence data between particle size and the maximum detection signal obtained at the focal position in advance. Furthermore, particle density can be calculated from the number of detected particles. However, when suppressing differences between multiple devices of the same product model to manage performance, variations in the characteristics of individual components, such as the emission angle and current sensitivity of semiconductor lasers and the sensitivity of photodetectors, are unavoidable. According to Patent Documents 1 and 2, the aforementioned correspondence data must be acquired individually for each device. This is a cumbersome process, ultimately leading to increased device manufacturing costs.

[0008] Furthermore, the correspondence relationship data described in Patent Document 1 is a linear relationship as shown in Figure 17 of the same document. When such a linear relationship is used, it is not possible to deal with nonlinear characteristic changes from the Rayleigh scattering region to the Mie scattering region.

[0009] The present invention has been made in view of the above-mentioned problems, and aims to provide a technology that allows for easy calibration to suppress differences between multiple devices and that can measure particle size using nonlinear detection signals that range from the Rayleigh scattering region to the Mie scattering region.

[0010] The particle measuring device according to the present invention obtains a normalized signal S by dividing the maximum value of an interference signal generated by interference between a signal light and a reference light by a reference value, and measures the size of the particle using a function that describes the relationship between S and (d-d0), where d is the particle size and d0 is the lower measurement limit value of the particle size.

[0011] The particle measuring device according to the present invention is capable of suppressing differences between products in a particle measuring device that measures the size of particles contained in a liquid sample, and is capable of measuring particles over a wider size range than conventional devices. Problems, configurations, and advantages other than those described here will become clear from the description of the following embodiments.

[0012] 6A is a schematic diagram showing the relationship between defocus and detection signal in Patent Documents 1 and 2.

[0023] FIG. 6B is a simulation result of calculating the relationship between particle size and maximum detection signal using the interference detection optical system described in Patent Documents 1 and 2.

[0024] FIG. 6C is a diagram showing the simulation result of FIG. 2A with background scattering added. This shows a case where the background scattering level is equal to the interference signal of a particle with a size of 0.10 μm.

[0025] FIG. 6D is a flowchart showing the calibration procedure for the simplified device provided by the present invention.

[0026] FIG. 6E is an experimental result showing the relationship between the objective lens output power and detection signal when a reference sample is measured using a particle measuring device of the present invention.

[0027] FIG. 6F is a flowchart showing the procedure for obtaining a normalized signal of an evaluation sample.

[0028] FIG. 6G is an enlarged view of the experimental result of FIG. 6A.

[0029] FIG. 6H is a diagram showing the results of a model with order 1 among the results of applying the polynomial size conversion model of the present invention.

[0030] FIG. 6I is a diagram showing the results of a model with order 2 among the results of applying the polynomial size conversion model of the present invention.

[0031] FIG. 6J is a diagram showing the results of a model with order 3 among the results of applying the polynomial size conversion model of the present invention. 6A , 6B , and 6C show the results of a polynomial size conversion model of the present invention, where the model is of order 4; the results of a polynomial size conversion model of the present invention, where the model is of order 5; the results of a polynomial size conversion model of the present invention, where the model is of order 6; the experimental results showing the relationship between the order of the polynomial size conversion model of the present invention and the RMS error; the results of a first-order lag model of the exponential function size conversion model of the present invention, where the model is of order 5; the results of a second-order lag model of the exponential function size conversion model of the present invention, where the model is of order 6; the experimental results showing the relationship between the RMS error of the size conversion model based on the exponential function of the present invention and the converted particle size; the RMS error of particle sizes measured by the conventional technology and the present invention is shown; the results of a comparison of the relative error of the measured size obtained by the size conversion model for 0.107 μm (the minimum size shown in FIG. 6A ) between the conventional technology and the present invention; ０1 shows experimental results showing the relationship between the / λ value and the parameters of the size conversion model. Based on the experimental results, the range of particle sizes measured was changed by selecting the numerical aperture of the objective lens. ０ 10 is a numerical table showing an appropriate range of the / λ value.

[0013] <Background of the Invention> FIG. 1 is a schematic diagram showing the relationship between defocus and detection signal in Patent Documents 1 and 2. If the optical axis direction of the objective lens is z, the light spot diameter at the z position of the particle to be measured is determined by the wavelength of the light source, the numerical aperture of the objective lens, and the amount of defocus. The amount of reflected light from the particle is approximated and the detection signal increases or decreases depending on the ratio of the light spot diameter to the particle area. The left side of FIG. 1 is a schematic diagram showing a state in which the particle to be measured is defocused from the focal position of the objective lens. In this case, the size of the particle is relatively small compared to the light spot diameter, and the amount of reflected light received through the objective lens and the detection signal converted from that reflected light into an electrical signal are relatively small. On the other hand, the right side of FIG. 1 is a schematic diagram showing a state in which the particle to be measured is at the focal position of the objective lens. In this case, the size of the particle is maximized compared to the light spot diameter, and the amount of reflected light received through the objective lens and the detection signal, which are converted from that, are maximized. FIG. 17 of Patent Document 1 discloses that when the size (diameter) of the target particle is approximately three times or less the minimum light spot diameter at the focus, the particle size and the maximum detection signal obtained at the focus position are uniquely determined, and that by acquiring this correspondence data in advance, it is possible to determine the particle size from the measured maximum detection signal.

[0014] FIG. 2A shows the results of a simulation that calculated the relationship between particle size and maximum detection signal using the interference detection optical system described in Patent Documents 1 and 2. Here, the simulation was performed using a method that combined Mie scattering and Fraunhofer diffraction. The wavelength of the light source was 785 nm, the numerical aperture of the objective lens was 0.45, the refractive index of the particles was 1.58 corresponding to commercially available polystyrene beads, and the refractive index of the solvent was 1.333 corresponding to pure water. As shown in the figure, if the particle size is d, in the region d<0.1 μm, the maximum detection signal corresponds to Rayleigh scattering and is proportional to the cube of d, while in the region d>0.3 μm, the maximum detection signal corresponds to Mie scattering and is proportional to the first power of d. The linearity of the particle size and maximum detection signal in the region d>0.3 μm is consistent with Figure 17 of Patent Document 1.

[0015] To avoid any misunderstanding regarding these particle size dependencies, we will provide a more detailed explanation. It is generally known that the energy intensity of scattered light in Rayleigh scattering is proportional to the sixth power of the particle size d. The magnitude of the electrical signal obtained by photoelectrically converting reflected light with a photodetector is also proportional to the sixth power of d. The optical systems described in Patent Documents 1 and 2, as well as the present invention, utilize homodyne interference, which amplifies the interference between reflected light and a reference light. In this case, the "electric field amplitude" of the reflected light, rather than its "energy," is converted into an electrical signal, so the maximum detection signal is proportional to the third power of d. By using such an optical system, the change in the magnitude of the detection signal due to particle size is more gradual than in methods that photoelectrically convert the "energy" of reflected light, which is advantageous in widening the dynamic range of measurable particle sizes. When a semiconductor laser is used as the light source, it is possible to reduce laser noise, primarily caused by return light, by superimposing a high frequency on the drive current using the technology described in Patent Document 3.

[0016] When actually measuring a sample containing particles such as protein aggregates, the obtained interference signal contains components due to background scattering. The background scattering referred to in the present invention is the sum of (factor 1) Rayleigh scattering from protein molecules, surfactant molecules, and other molecules in the sample, and (factor 2) stray light in the optical system, including reflected light from the sample container, and laser noise. If the magnitude of the interference signal from the particle to be measured is smaller than the background scattering, the size of the particle cannot be measured. Therefore, background scattering provides a lower limit for the particle size measurement in the techniques described in Patent Documents 1 and 2, including the present invention.

[0017] Figure 2B shows the simulation results of Figure 2A with background scattering added. This example shows a case where the protein concentration in the sample is high, about 100 mg / mL, i.e., where background scattering is primarily determined by factor 1. The background scattering level (magnitude of the interference signal) is assumed to be equal to the interference signal of particles 0.25 μm in size. The lower limit of measurement size for this sample is 0.25 μm, and as can be seen in the figure, the interference signal of measurable particles is mainly Mie scattering. Therefore, the relationship between particle size and interference signal can be assumed to be linear. This shows a case where the linear relationship described in Figure 17 of Patent Document 1 is appropriate.

[0018] Figure 2C shows a case where the background scattering level is equal to the interference signal of a particle 0.10 μm in size. This corresponds to a case where the concentration of protein molecules contained in the sample is low, or where a diluted sample diluted approximately 1000 times is measured to examine the aggregate size distribution of the sample shown in Figure 2B in detail. In this case, the background scattering is mainly determined by factor 2. As can be seen from the figure, the interference signal of measurable particles includes Rayleigh scattering in addition to Mie scattering, so the relationship between particle size and interference signal is nonlinear.

[0019] The lower limit of particle size measurable by the particle measuring device of the present invention is determined by the magnitude of background scattering, which is determined by factors that depend on the sample (Factor 1) and the device implementation (Factor 2). The magnitude of background scattering due to (Factor 2) provides a lower limit of detection size that is independent of protein concentration, etc., and can be quantified by measuring, for example, a reference sample prepared by diluting a commercially available standard polystyrene bead suspension with cleanroom-grade pure water. The magnitude of background scattering measured in this case is a value specific to the device. Furthermore, in particle measuring devices that reduce background scattering due to (Factor 2) through improvements in device implementation, the relationship between particle size and interference signal becomes nonlinear, and therefore a size conversion model that describes the relationship between particle size and interference signal is required, replacing the linear relationship described in Figure 17 of Patent Document 1. In this case, if there is a size conversion model that describes the relationship between particle size and interference signal with sufficient accuracy for a reference sample with sufficiently small background scattering (no Rayleigh scattering from protein molecules), it is possible to accurately determine particle size from the interference signal within the measurable size range, even for samples in which background scattering is mainly determined by factor 1, as shown in Figures 2B and 2C.

[0020] In light of the problem to be solved by the present invention, it should be noted that hereinafter, unless otherwise specified, background scattering refers to background scattering measured by a reference sample, i.e., background scattering due to (factor 2).

[0021] In conventional techniques such as those described in Patent Documents 1 and 2, the relationship between particle size and detection signal is assumed to be linear. In contrast, the present invention targets a region ranging from Mie scattering to Rayleigh scattering, as shown in FIG. 2A. Therefore, the relationship between particle size and detection signal becomes nonlinear with a boundary near d = 0.2 to 0.3 μm. The present invention provides a technique that can accurately detect particle size even in such a nonlinear correspondence relationship between particle size and detection signal.

[0022] In the following description of the present invention, the explanation will be made in a unified coordinate system in which the optical axis direction is the z-axis. For simplicity of explanation, the maximum detection signal obtained when the particle size is at the focal position of the objective lens will be simply referred to as the detection signal, and the signal obtained by suppressing the instrumental difference will be referred to as the normalized signal.

[0023] First Embodiment: Regarding Normalized Signal Here, a normalized signal that suppresses differences among a plurality of devices will be described. The normalized signal S is defined as follows: s is the detection signal.

[0024]

[0025] s ０ is a reference signal that represents the detection sensitivity of the device, and is defined as follows: α is an intrinsic sensitivity coefficient that represents the light utilization efficiency of the optical system and the characteristics of the photodetector, η is a correction coefficient depending on the light emission power of the light source and temperature conditions, r is the Fresnel amplitude reflectance of the particle to be measured, R ０ is the Fresnel amplitude reflectance of the reference particle used in calibrating the instrument. ０ Arithmetically, s is calculated from the refractive index of the particle and the medium by ０ In Equation 3 and Equation 4, n ｏ is the refractive index of the particle to be measured, n ｓ is the refractive index of the particle to be measured, N ｏ is the refractive index of the particles of the reference sample, N ｓ is the refractive index of the solvent of the reference sample.

[0026]

[0027]

[0028]

[0029] 3 is a flow chart showing the simplified calibration procedure of the device provided by the present invention. In the sensitivity calibration procedure to suppress differences between multiple devices, the detection signal is measured using a reference sample. Specifically, this can be performed by the following steps:

[0030] In step S301, a reference sample is prepared. For example, a commercially available standard polystyrene bead suspension is diluted with pure water for clean rooms to obtain a particle density of 10 ７ The particle size is, for example, 1 μm. To ensure accuracy, it is desirable to measure the size of the particles contained in the suspension in advance using a scanning electron microscope. In this case, N ｏ = 1.58, N ｓ = 1.333 using a known refractive index such as R ０ Since the measurement target is a reference sample, r = R ０ is.

[0031] In step S302, the calibration target device is set to standard conditions. The light source is set to emit light at a predetermined standard light emission power, such as 1 mW, and the ambient temperature is maintained at a predetermined standard ambient temperature, such as 25° C. The correction coefficient at this time can be defined as η=1.

[0032] In step S303, the reference sample is measured using an apparatus set under standard conditions.

[0033] In step S304, the measured detection signal s indicates the inherent sensitivity coefficient of the light utilization efficiency of the optical system of the device and the photoelectric conversion characteristics of the detector. When the particle size contained in the reference sample is φ, α = s / φ is held as the magnitude of the detection signal per 1 μm. α is a constant inherent to the device and is saved in a device-dependent parameter file or the like for use.

[0034] Figure 4 shows experimental results showing the relationship between the objective lens output power and the detection signal when a reference sample is measured using a particle measuring device according to the present invention, which will be described later. As can be seen from the figure, there is a proportional relationship between the objective lens output power and the detection signal. This indicates that characteristics based on the basic equations of optical interference have been obtained. Therefore, the correction coefficient η in Equation 2, which is based on the light source emission power and temperature conditions, can be written as follows:

[0035]

[0036] P ０ is the output power under standard conditions, P is the output power during measurement, T is the temperature, η Ｔ (T) is a temperature correction coefficient that depends on the change in the emission spectrum of the semiconductor laser depending on the temperature, and in the device used, the sensitivity change is about 0.5% per 1°C at room temperature of 25°C. Ｔ (T) can be considered to be determined depending on the quantum well structure of the semiconductor laser used as the light source, and therefore can be treated as a group-specific characteristic determined by the model number or lot number of the selected semiconductor laser component, rather than being specific to the device.

[0037] 5 is a flowchart showing the procedure for obtaining a normalized signal of an evaluation sample. The procedure for obtaining a normalized signal of the present invention for an evaluation sample, such as a protein aggregate of a biopharmaceutical, prepared by a user will be described using FIG. 5. This flowchart can be implemented, for example, by a controller or computer attached to the measurement device.

[0038] In step S501, a correction coefficient η is calculated according to Equation 5 from the user-specified output power P and the output value T of a temperature monitor mounted near the semiconductor laser light source. At this time, if the difference between the refractive index of the particles being measured and that of the solvent is large, the detection signal will be large. Therefore, taking into consideration the dynamic range and resolution of the size measurement, it is advisable to reduce the output power of the objective lens. Conversely, if the difference in refractive index is small, it is preferable to set the output power to a large value. In actual measurement devices, convenience can be improved by having the measurement device determine appropriate output power settings for typical measurement targets, such as protein aggregates in biopharmaceuticals, commercially available antibodies, viral vectors, and coronavirus vaccines, and allowing the user to select the appropriate conditions depending on the measurement target.

[0039] In step S502, the Fresnel amplitude reflectance of the particle to be measured is calculated according to Equation 3 from the refractive indexes of the particle and medium contained in the evaluation sample.

[0040] In step S503, the reference signal s ０ Calculate.

[0041] In step S504, the light source and various motorized stages within the apparatus are appropriately controlled to prepare for measurement.

[0042] In step S505, detection signals obtained while scanning the light spot within the evaluation sample are acquired according to the method described in Patent Document 2 or the method described below, and three-dimensional image data is obtained. Individual particles are identified based on this, and then the maximum detection signal s at the focus of each individual particle is obtained.

[0043] In step S506, the normalized signal S of each particle is calculated according to Equation 1.

[0044] <First Embodiment: Summary> The obtained normalized signal S is in accordance with the above-mentioned sensitivity coefficient α, and can be said to directly reflect the relationship shown in the simplified form in Figure 17 of Patent Document 1, that is, the proportionality between the detection signal and the particle size. According to the technology disclosed in Patent Document 1, in order to obtain the normalized signal S, it is necessary to acquire the above-mentioned correspondence relationship data while changing the output power for various reference particle sizes individually for multiple devices. In contrast, according to this embodiment, this calibration process can be achieved in a single measurement step for the reference sample under the above-mentioned standard device conditions, which allows for a significant simplification of the process.

[0045] <Embodiment 2: Experimental Results of Measurement of Normalized Signals Using Multiple Devices> Four devices were prepared to demonstrate that the nonlinear size conversion model provided by the present invention can be applied to multiple devices. Each device shared the same type of semiconductor laser light source and objective lens, with a wavelength of 785 nm and a numerical aperture of 0.45. Other than that, each device was prepared with two types of optical system bases, two types of light spot scanning mirrors, two types of stages that drive the optical components and sample stage, and two types of adjustment for the origin of the optical path length of the reference light and signal light. The basic configuration and main components of the devices will be described later.

[0046] As a reference sample for measuring the particle size dependence of the normalized signal, a commercially available standard polystyrene bead suspension was diluted with pure water for clean room use to adjust the particle density to 10 ７Several samples were prepared, each adjusted to 1000 particles / mL. The size of the polystyrene particles contained in each standard sample was measured using a scanning electron microscope. The particle sizes prepared were 0.107 μm, 0.160 μm, 0.216 μm, 0.551 μm, 0.995 μm, and 1.510 μm.

[0047] 6A shows the experimental results of measuring each reference sample with each device for three types of output power, including the standard power, and plotting the relationship between the size of the reference particle and the normalized signal. As can be seen from the figure, the normalized signal provided by the present invention shows almost no variation across the four devices and three types of output power, and can be measured as a value determined solely by the particle size.

[0048] Figure 6B is an enlarged view of the experimental results of Figure 6A. When the particle size was the smallest, 0.107 μm, the effects of laser noise and Brownian motion of the particles were greatest, but the standard deviation of the normalized signal was 15%. For a particle size measurement device, it is desirable to keep the standard deviation below 10%.

[0049] <Embodiment 3: Nonlinear size conversion model applicable to multiple devices with a lower limit on measurement size (1) Polynomial> In embodiment 3 of the present invention, a polynomial model will be described as a size conversion model for determining particle size from the measurement results of normalized signals using multiple devices as shown in embodiment 2.

[0050] In the present invention, the normalized signal S is used to determine the lower limit of the measurement size d ０ (d ０ > 0) is introduced as a nonlinear model. ０ is the particle size at which the interference signal is approximately equal to the background scattering. In addition, the size conversion model shown here is not specific to the device, and therefore has the advantage over the technology described in Patent Document 1 that it can be commonly used for products of the same model (same model numbers for semiconductor laser and objective lens).

[0051] If the particle size obtained from the normalized signal is d, the size conversion model is defined as follows: N is the maximum order of the polynomial model, c ｎis a coefficient multiplied by the term of order n. In Equation 6, when the normalized signal S>0 and the right side is positive, the particle size d is within the measurement size lower limit d ０ In Equation 6, d ０ Since it may be easier to understand if you transpose it to the right side, we will show Equation 6' as a supplementary equation.

[0052]

[0053] The following describes the results of applying polynomials of degree N=1 to 6. Here, the size conversion model of Equation 6 is applied to the results of FIG. 6A, and the parameter (unknown) d ０ and c ｎ Multivariate optimization was performed using the Subplex method to minimize the error.

[0054] 7A shows the results of applying the polynomial size conversion model of the present invention, with the order of 1. The parameter d ０ and c １ and the number of parameters is two. A concrete example of this model is Equation 7A, which will be described later. In the figure, each plot shows the experimental results, and the straight lines show the model results. As can be seen from the figure, the error becomes large when the particle size is 0.2 μm or less and 1 μm or more. If this error can be tolerated, this model is a first-order linear equation, and is therefore very suitable for implementation in hardware such as FPGA.

[0055] FIG. 7B shows the results of the polynomial size conversion model of the present invention, with a degree of 2. The parameter d ０ , c １ , and c ２ and the number of parameters is three. A concrete example of this model is shown in Equation 7B, which will be described later. In the figure, each plot shows the experimental results, and the curve shows the model results. As can be seen from the figure, the error between the plots and the curve is smaller than in the case of degree 1. If the remaining error is acceptable, this model is a second-order polynomial, and is therefore suitable for implementation in hardware such as an FPGA.

[0056] FIG. 7C shows the results of applying the polynomial size conversion model of the present invention, with a degree of 3. The parameter d ０ , c １ , c ２ , and c ３ and the number of parameters is four. A specific example of this model is Equation 7C, which will be described later. In the figure, each plot shows the experimental results, and the curve shows the model results. As can be seen from the figure, the error between the plot and the curve, especially when the particle size is 1 μm, is significantly smaller than in the case of degree 2. If the remaining error can be tolerated, this model is a third-order polynomial, and therefore is suitable for implementation in hardware such as FPGA.

[0057] FIG. 7D shows the results of the polynomial size conversion model of the present invention, with a degree of 4. The parameter d ０ , c １ , c ２ , c ３ , and c ４ and the number of parameters is 5. A specific example of this model is Equation 7D, which will be described later. In the figure, each plot shows the experimental results, and the curve shows the model results. As shown in the figure, although no significant improvement in error is visible compared to the case of degree 3, the numerical error has been reduced. If the remaining error and the increase in calculation time due to the increase in the number of parameters can be tolerated, this model is a fourth-order polynomial, and therefore is relatively suitable for implementation in hardware such as an FPGA.

[0058] FIG. 7E shows the results of applying the polynomial size conversion model of the present invention, with a degree of 5. The parameter d ０ , c １ , c ２ , c ３ , c ４ , and c ５and the number of parameters is 6. A specific example of this model is Equation 7E, which will be described later. In the figure, each plot shows the experimental results, and the curve shows the model results. As shown in the figure, although no significant improvement in error is visible compared to the case of degree 4, the numerical error has been reduced. If the remaining error and the increase in calculation time due to the increase in the number of parameters can be tolerated, this model is a fifth-order polynomial, and therefore is relatively suitable for implementation in hardware such as an FPGA.

[0059] FIG. 7F shows the results of applying the polynomial size conversion model of the present invention, with a degree of 6. The parameter d ０ , c １ , c ２ , c ３ , c ４ , c ５ , and c ６ and the number of parameters is 7. A specific example of this model is equation 7F, which will be described later. In the figure, each plot shows the experimental results, and the curve shows the model results. As shown in the figure, although no significant improvement in error is visible compared to the case of degree 5, the numerical error has been reduced. If the remaining error and the increase in calculation time due to the increased number of parameters can be tolerated, this model is a sixth-order polynomial, and therefore is relatively suitable for implementation in hardware such as an FPGA.

[0060]

[0061] FIG. 8 shows experimental results illustrating the relationship between the order and RMS error of the polynomial-based size conversion model of the present invention. FIG. 8 summarizes the RMS (Root Mean Square) error when converting normalized signals to particle sizes for the results shown in FIGS. 7A to 7F. As can be seen from the figure, the RMS error decreases as the order of the polynomial increases. The RMS error ranges from a maximum of approximately 0.07 μm to a minimum of approximately 0.01 μm. As the order of the polynomial increases, the calculation time increases when processed by a CPU, and the circuit size and power consumption increase when implemented in hardware such as an FPGA. When utilizing the technology disclosed in this invention, the error (i.e., size measurement accuracy), calculation time, or circuit size can be taken into consideration to select an appropriate solution that meets the specifications.

[0062] The above examples are given for polynomial models of degrees 1 to 6. In the present invention, as shown in Equation 6, polynomial models of degrees 7 or higher can also be used in the same manner, by evaluating the RMS error of the particle size converted from the normalized signal based on the model equation, and it is possible to select a model that matches the circuit scale and precision specifications.

[0063] <Embodiment 4: Nonlinear size conversion model applicable to multiple devices with a lower limit on measurement size (2) In the case of an exponential function> In embodiment 4 of the present invention, an exponential function model will be described as a size conversion model for determining particle size from the measurement results of normalized signals using multiple devices as shown in embodiment 2.

[0064] In the present invention, the normalized signal S is used to determine the lower limit of the measurement size d ０ (d ０ > 0) is introduced as a nonlinear model. ０is the particle size at which the interference signal is approximately equal to the background scattering. Furthermore, the size conversion model shown here is not specific to the device, and can be used for products of the same model (same model numbers for the semiconductor laser and objective lens), which is an advantage over the technology described in Patent Document 1. At the same time, the following model has a relatively small number of parameters (three), making it easier to grasp the physical meaning of each parameter compared to the polynomial model described above. This point leads to the advantage that the size conversion model is easier to manage, for example, when a second-generation device is designed to achieve higher resolution by changing the wavelength of the light source or the numerical aperture of the objective lens compared to the first-generation device.

[0065] Taking into consideration that the intensity distribution of the light spot is approximated by a Gaussian distribution, that the reflected light from the target particle is interference-amplified by a homodyne optical circuit (described later) and converted into a detection signal as an electrical signal corresponding to an electric field amplitude proportional to the 1 / 2 power of the light intensity, and that the reflected light from particles equal to or larger than the light spot size is saturated due to its size effect, three size conversion models are presented below. These are a basic first-order lag model and its advanced second-order lag model and a Gaussian distribution model. To derive each parameter, a multivariate optimization process was performed using the Subplex method based on the results of Figure 6A to minimize the error.

[0066] (1) First-order lag model To facilitate understanding, a model that represents the normalized signal S obtained when the particle size d is given is shown in Equation 8. ０ (>0) indicates the particle size at which the interference signal is nearly equal to the background scattering, D(>0) is the light spot size constant that indicates the saturation of the normalized signal due to the size of the light spot, and A(>0) is a constant that indicates the magnitude of the saturation signal. These parameters each have physical meanings, so for example, when developing a new second-generation device with a light spot size that is 1 / 2, if D in the above formula is close to 1 / 2, it can be interpreted that the prototype device has been assembled correctly. To convert from the normalized signal S to the size of the measured particle, the inverse function of formula 8 is used. Specifically, it becomes formula 8' below. d ０ The form obtained by transferring the above to the right side is the following formula 8''.

[0067]

[0068] Figure 9A shows the results of applying the exponential size conversion model of the present invention to a first-order lag model. In the figure, each plot represents the experimental results under various conditions for the four devices mentioned above, and the curve represents the results of the size conversion model. As can be seen from the figure, there is good agreement between the size conversion model and the experimental results. This is due to the effect of introducing a lower limit on the measurement size that models the effects of the normalized signal and Rayleigh scattering provided by the present invention. Because this model is a transcendental function, the circuit size and power consumption will increase when implemented in hardware such as an FPGA. However, the calculation time is only slightly extended when processed using a general CPU with a built-in numerical calculation processor.

[0069] (2) Second-order lag model To facilitate understanding, the model representing the normalized signal S obtained when the particle size d is given is shown in the following equation 9. ０ (>0) indicates the lower limit of the measurement size due to the influence of Rayleigh scattering, D (>0) is the light spot size constant that indicates the saturation of the normalized signal due to the size of the light spot, and A (>0) is a constant that indicates the magnitude of the saturation signal. When converting the normalized signal S into the size of the measured particle, the inverse function of Equation 9 is used. Specifically, it is expressed as Equation 9' below. d ０ The form obtained by transferring the above to the right side is the following formula 9''.

[0070]

[0071] Figure 9B shows the results of applying the size conversion model based on the exponential function of the present invention, using a second-order lag model. In the figure, each plot represents the experimental results under various conditions for the four aforementioned devices, and the curve represents the results of the size conversion model. As can be seen, the size conversion model and the experimental results are in good agreement. Comparing Figure 9A with the curve representing the model, it can be seen that the rising region for particle sizes of 0.2 μm or less exhibits a smooth transition. This is a characteristic suitable for devices with a high S / N ratio and reduced laser noise. At the same time, it can be seen that the saturation effect of the normalized signal is large in the region for particle sizes of 1 μm or more. This is a characteristic suitable for detecting large particles. Because this model is a transcendental function, implementing it in hardware such as an FPGA increases the circuit size and power consumption, but the calculation time is minimal when processed using a general CPU with a built-in numerical calculation processor.

[0072] (3) Gaussian Distribution Model To facilitate understanding, a model that represents the normalized signal S obtained when the particle size d is given is shown in Equation 10. ０ (>0) indicates the lower limit of the measurement size due to the influence of Rayleigh scattering, D (>0) is the light spot size constant that indicates the saturation of the normalized signal due to the size of the light spot, and A (>0) is a constant that indicates the magnitude of the saturation signal. When converting the normalized signal S into the size of the measured particle, the inverse function of Equation 10 is used. Specifically, it is the following Equation 10'. d ０ The form obtained by transferring the above to the right side is the following formula 10''.

[0073]

[0074] Figure 9C shows the results of applying the exponential size conversion model of the present invention to a Gaussian distribution model. In the figure, each plot represents the experimental results under various conditions for the four aforementioned devices, and the curve represents the results of the size conversion model. As can be seen, the size conversion model and the experimental results closely match. Comparing Figures 9A and 9B, the overall error is larger. Furthermore, the rising region for particle sizes of 0.2 μm or less exhibits a smoother transition, a characteristic suitable for devices with a high S / N ratio and reduced laser noise. At the same time, the saturation effect of the normalized signal in the region of particle sizes of 1 μm or more is even greater. This characteristic is suitable for detecting large particles. Because this model is a transcendental function, implementing it in hardware such as an FPGA increases the circuit size and power consumption, but the calculation time is minimal when processed using a general CPU with a built-in numerical calculation processor.

[0075] Figure 10 shows experimental results showing the relationship between the size conversion model based on the exponential function formula of the present invention and the RMS error of the converted particle size, and is a summary of the results shown in Figures 9A to 9C. As can be seen from the figure, the RMS errors of the first-order lag model and the second-order lag model are almost equal at approximately 0.02 μm, while the RMS error of the Gaussian distribution model is slightly larger at approximately 0.055 μm. When using the technology disclosed in this invention, it is possible to select an appropriate model that meets the specifications, taking into account the RMS error (= measurement accuracy) shown here and the aforementioned rise region and saturation characteristics.

[0076] The above describes three size conversion models based on exponential functions. However, the present invention is not limited to these, and size conversion models combining higher-order exponential functions and the polynomial models shown above can also be applied. In such cases, by evaluating the RMS error of particle size converted from the normalized signal based on the model formula using a procedure similar to that shown here, a model suited to the amount of calculation and accuracy specifications can be used as appropriate.

[0077] <Embodiment 5: Comparison of size measurement accuracy between the present invention and conventional techniques> In embodiment 5 of the present invention, the improvement in size measurement accuracy according to the present invention will be summarized. Here, as a conventional size conversion model, a model in which the normalized signal is proportional to the particle size is used, based on the results shown in FIG. 17 of Patent Document 1. The model formula is as follows: d is the particle size, S is the normalized signal, c is the particle size, １ and represent the proportionality coefficients. Comparing with Equation 7A, the lower limit of the measurement size d ０ The absence of the above is a difference from the present invention.

[0078]

[0079] FIG. 11A shows the RMS error of particle size measured by the conventional technology and the present invention. The horizontal axis of the figure represents the number of parameters, with the conventional technology having a parameter number of 1, the polynomial model having a parameter number of order + 1, and the exponential model having a parameter number of 3. As can be seen from the figure, the RMS error for each model is approximately 0.07 μm or less, which is a reasonable result for the measurement accuracy of particle size in the submicron range. The first-order polynomial model (number of parameters = 2) of the present invention has an RMS error almost equivalent to that of the conventional technology. The effect of the present invention is more pronounced in the second-order or higher polynomial model and the exponential model, and it can be seen that the RMS error is improved to a minimum of approximately 0.01 μm.

[0080] Figure 11B shows a comparison of the relative error of the measured size determined by the size conversion model for 0.107 μm (the smallest size shown in Figure 6A) between the conventional technology and the present invention. As mentioned above, one of the main objectives of the present invention is to address the characteristic changes in particle size and detection signal in the Rayleigh scattering region. As can be seen from the figure, the size measurement error for the conventional technology is approximately 67%. On the other hand, the size conversion model of the present invention significantly improves the error to approximately 34% or less. It can be seen that a polynomial model with four or more parameters (order ≥ 3) and exponential models with first-order and second-order lags are suitable for reducing the size measurement error for particles of approximately 0.1 μm to 10% or less. The results shown here are based on the wavelength (= 0.785 μm) and objective lens (numerical aperture = 0.45) of the four instruments prepared. When using the technology disclosed in this invention, the appropriate specifications can be selected taking into account the evaluation method of the size conversion model shown here.

[0081] <Embodiments 1 to 5: Supplementary Information Regarding Calibration> In the above embodiments, d0 is fixed depending on the model of particle measurement device, and there is no need to consider differences in d0 between devices. Devices in which background scattering measured using a reference sample falls outside a predetermined range indicate an abnormality in the device implementation, such as stray light or laser noise, and the device can be shipped after appropriate measures such as readjustment of the optical system are taken. Furthermore, the calibration process can be simplified by applying the same size conversion model to devices in which background scattering falls within a predetermined range.

[0082] <Embodiment 6: Lower limit d of measurement size in the present invention> ０ In the sixth embodiment of the present invention, the measurement size lower limit d ０ Regarding the appropriate numerical range, we will discuss. As is well known, in Rayleigh scattering and Mie scattering, the scattering characteristics are determined by the value obtained by dividing the particle size by the wavelength. Here, we will consider the selection of the light source wavelength of the device and determine the value of d ０The appropriate numerical range for / λ (λ is the wavelength of the light source) will be described below.

[0083] FIG. 12A shows the ０ The experimental results show the relationship between the / λ value and the parameters of the size conversion model. The wavelength of the light source of the four devices prepared is 0.785 μm, and the numerical aperture of the objective lens is 0.45. As can be seen in the figure, ０ / λ was in the range of 0.01 to 0.14. Figure 12B shows the results of experiments in which the range of particle sizes measured was changed by selecting the numerical aperture of the objective lens. ０ The experimental conditions shown in the figure are as shown above.

[0084] d ０ The minimum value of / λ is determined mainly by Rayleigh scattering, and it is appropriate to set the minimum value at 0.01 as shown in the figure.

[0085] d ０ The maximum value of / λ can be considered to increase or decrease in proportion to the light spot size. It is well known that the light spot size is proportional to 1 / numerical aperture. When measuring the particle size distribution of large sizes (approximately 1 to 30 μm) using the technology of the present invention, it is advisable to select the numerical aperture of the objective lens to be about 0.1. In this case, the light spot size will be 4.5 times that of the experimental conditions, and d ０ The maximum value of / λ is 0.63. On the other hand, when measuring the particle size distribution of small particles (approximately 0.03 to 1 μm) using the technology of the present invention, it is recommended to select the numerical aperture of the objective lens to be about 0.95. In this case, the light spot size is 0.47 times that of the experimental condition, and d ０ The maximum value of / λ is 0.07.

[0086] As described above, in the size conversion model provided by the present invention, the parameter d ０ , where λ is the wavelength of the light source, d ０ The appropriate range of / λ is 0.01 to 0.63.

[0087] 13 is a diagram showing an example of the configuration of a particle measuring device according to a seventh embodiment of the present invention. Laser light emitted from a light source 100, whose light emission state is controlled by a laser driver 101 that controls high-frequency superposition and output power, is converted into parallel light by a collimating lens 102, and after the polarization direction is adjusted by a λ / 2 plate 103 whose optical axis is set at approximately 22.5 degrees with respect to the horizontal direction, the light is separated into signal light and reference light by a polarizing beam splitter 104.

[0088] The reference light is converted into a circularly polarized state by the λ / 4 plate 105, then reflected by the reference light mirror 106. The λ / 4 plate 105 causes the reference light to be polarized in a state where its polarization is rotated 90 degrees from that of the outbound path, and the signal light is then reflected by the polarizing beam splitter 104. The signal light is deflected in its traveling direction by the XY-direction composite deflection element 107, then converted into a circularly polarized state by the action of the built-in λ / 4 plate, and focused within the sample 204 held in the sample container 200 by the objective lens 108. The drive mechanism 109, which moves the sample in the Z-axis direction, has the function of scanning the focal position of the signal light along the Z-axis (optical axis direction). The signal light components reflected from individual particles contained in the sample 204 are deflected in the same direction as that of the outbound path by the XY-direction composite deflection element 107, and are polarized circularly by the action of the built-in λ / 4 plate, with their polarization rotated 90 degrees from that of the outbound path, and are transmitted through the polarizing beam splitter 104. Here, the sample container 200 holds a sample 204 in a well and guides signal light into the sample through a transparent window 202. 203 is a resin member that forms the well of the sample container. The base plate 201 comes into contact with the transparent window 202 and mechanically holds the sample container 200 while stabilizing the temperature of the sample.

[0089] The signal light and the reference light are combined by the polarizing beam splitter 104, guided to the detection optical system 112, and split into transmitted light and reflected light by the half beam splitter 113 via the pinhole 111.

[0090] The reflected light passes through a λ / 4 plate 114, whose optical axis is set at approximately 45 degrees with respect to the horizontal direction, and is then focused by a focusing lens 115 and split into two by a polarizing beam splitter 116. The two beams are then photoelectrically converted by photodetectors 150 and 151, and differentially amplified by a current differential amplifier 152 to become a detection signal 123.

[0091] The transmitted light passes through a λ / 2 plate 118, whose optical axis is set at approximately 22.5 degrees relative to the horizontal direction, and is then focused by a focusing lens 119 and split into two by a polarizing beam splitter 120. The two beams are then photoelectrically converted by photodetectors 153 and 154, and differentially amplified by a current differential amplifier 155 to become a detection signal 122.

[0092] The detection optical system 112 shown here constitutes a homodyne phase diversity method, and the real part component 122 and imaginary part component 123 of the detection signal are electrical signals corresponding to the real part and imaginary part of the electric field amplitude of the signal light reflected from individual particles contained in the sample 204. The detection signal is calculated in the signal processing unit 124 as a numerical value obtained by calculating the sum of the squares of these and then calculating the square root.

[0093] The signal processing unit 124 combines the time-series data of the acquired detection signals to form three-dimensional image data in the X, Y, and Z directions within the sample, and also separates and tracks the data of individual particles contained therein to calculate the maximum value of the detection signal obtained under the focusing conditions for each particle. The signal processing unit 124 further calculates the reference signal and the normalized signal according to the flows shown in Figures 3 and 5 and Equations 1 to 5. Finally, the signal processing unit 124 calculates the particle size from the normalized signal using the size conversion model shown in embodiments 3 and 4 of the present invention, and presents the results to the user after organizing them into graphs, numerical tables, etc.

[0094] The signal processing unit 124 in the figure is implemented by an embedded microcomputer built into the device, or by a computer placed outside the device that enables the exchange of necessary signals via an interface board, etc. If there are time or power constraints on the processing items of the signal processing unit 124, a dedicated processing circuit implemented by an FPGA or the like may be used as an auxiliary computing unit.

[0095] The memory unit 126 can store, for example, a measurement lower limit value d0 measured in advance for each particle measuring device. The signal processing unit 124 can calculate the particle size d using the d0 stored in the memory unit 126 by the method described in the above embodiment.

[0096] <Regarding Modifications of the Present Invention> The present invention is not limited to the above-described embodiments and includes various modifications. For example, the above-described embodiments have been described in detail to clearly explain the present invention, and the present invention is not necessarily limited to those including all of the described configurations. Furthermore, it is possible to replace part of the configuration of one embodiment with the configuration of another embodiment, and it is also possible to add the configuration of another embodiment to the configuration of one embodiment. Furthermore, it is possible to add, delete, or replace part of the configuration of each embodiment with other configurations.

[0097] In the above embodiments, the signal processing unit 124 can be built into the particle measuring device, or the particle measuring device can be configured to acquire only data describing the results of measuring a sample, and the signal processing unit 124 can be located outside the particle measuring device to receive that data. In either case, the configuration of the particle measuring device according to the present invention is the same as that described in the above embodiments.

[0098] 100: Light source 101: Laser driver with high frequency superposition function 108: Objective lens 109: Driving mechanism for sample container 112: Detection optical system 124: Signal processing unit 200: Sample container 201: Base plate 202: Transparent window 203: Resin member forming well

Claims

1. A particle measuring device for measuring the size of particles contained in a liquid sample, comprising: a light source for emitting light; a branching section for branching the light from the light source into signal light and reference light; an irradiation section for focusing the signal light and irradiating it onto the sample; a detection section for detecting an interference signal obtained by causing the light reflected from the particle to interfere with the reference light; and a processing section for measuring the size of the particle using the interference signal, wherein the processing section obtains a normalized signal S by dividing the maximum value of the interference signal detected by the detection section by a reference value, and the processing section measures the size of the particle using a function that describes the relationship between S and (d-d0), where d is the size of the particle and d0 is the lower limit of the size of the particle at which the interference signal is equal to or lower than the signal level of background scattering caused by the liquid.

2. The particle measuring device according to claim 1, characterized in that the function is configured to connect the portion of the interference signal caused by Mie scattering of the particle and the portion of the interference signal caused by Rayleigh scattering in a range equal to or greater than the lower limit value in a plot of the interference signal and the size.

3. The particle measuring device according to claim 1, wherein the function is a polynomial function or an exponential function.

4. The above function is expressed as follows, where N is a natural number and Cn is a constant:

2. The particle measuring device according to claim 1, characterized in that the particle measuring device is represented by the following formula:

5. The function is expressed as follows, where A and D are positive constants:

2. The particle measuring device according to claim 1, characterized in that the particle measuring device is represented by the following formula:

6. The particle measuring device according to claim 1, characterized in that the reference value is a value calculated using at least an apparatus-specific sensitivity constant α obtained from the results of measuring a reference sample under predetermined standard conditions, a correction value η representing the effects of light emission power or temperature, a Fresnel reflectance R of particles in the reference sample, and a Fresnel reflectance r of the particles contained in the sample.

7. The particle measuring device according to claim 1, wherein said processing section measures the size of said particles of 0.2 μm or less.

8. The particle measuring device according to claim 1, further comprising a memory unit that stores the lower limit value d0, and the processing unit measures the size of the particle using the lower limit value d0 stored in the memory unit.

9. The particle measuring device according to claim 1, wherein the value obtained by dividing the lower limit by the wavelength of the light is 0.01 to 0.

63.

10. The particle measuring device according to claim 1, characterized in that the processing unit is composed of at least one of an arithmetic unit built into the particle measuring device, or an arithmetic unit arranged outside the particle measuring device and acquiring the interference signal from the detection unit.

11. A particle measuring method for measuring the size of particles contained in a liquid sample, comprising: a step of emitting light; a step of splitting the light into signal light and reference light; a step of concentrating the signal light and irradiating the sample; a step of detecting an interference signal obtained by interfering between the light reflected from the particle and the reference light; and a step of measuring the size of the particle using the interference signal, wherein in the measuring step, a normalized signal S is obtained by dividing the maximum value of the interference signal detected in the detecting step by a reference value, and in the measuring step, the size of the particle is measured using a function that describes the relationship between S and (d-d0), where d is the size of the particle and d0 is the lower limit of the size of the particle at which the interference signal is equal to or lower than the signal level of background scattering caused by the liquid.

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