Droplet particle size measurement method based on self-adaptive optimization of scattered light intensity difference

Abstract

The invention discloses a liquid drop particle size measurement method based on self-adaptive optimization of a scattered light intensity difference value, and the method comprises the steps: employing a reflection type measurement system based on a digital micromirror array to obtain the scattered light intensity, enabling laser to pass through a to-be-measured region through a beam expander, carrying out the light scattering, modulating a scattering pattern through the digital micromirror array, and reflecting the modulated scattering pattern to a photoelectric detector, transmitting to a computer through an acquisition card to obtain scattered light intensity distribution; the method comprises the following steps: establishing a closed-loop iteration process combined with a correction coefficient to reconstruct particle size distribution, firstly calculating a preliminary reconstruction result and an error, and updating the correction coefficient through an adaptive neural network; then, a reconstruction result is corrected by adopting a format fusing difference correction and historical iteration information, and is applied to next correction coefficient calculation; the iteration process is executed circularly until the preset iteration number is reached, and accurate particle size distribution is output. The method can effectively improve the reconstruction precision of droplet particle size distribution measurement, and has a wide application prospect in the field of spray droplet measurement.

Description

Technical Field

[0001] This invention relates to a droplet size measurement method based on adaptive optimization of scattered light intensity difference, belonging to the field of light scattering testing and measurement. Background Technology

[0002] Droplet size distribution is a key parameter in many industrial and scientific research fields such as fuel atomization, inkjet printing, and pharmaceutical spraying. Its accurate measurement is of great significance for optimizing process control and improving product quality. Laser diffraction is an advanced optical measurement method in the field of particle size measurement. Based on Mie scattering theory, particle size can be measured by analyzing the intensity of the scattered light after the laser passes through the particle to be measured and reconstructing it using relevant algorithms.

[0003] In recent years, laser diffraction has become the mainstream technology for online particle size measurement due to its significant advantages such as non-invasive measurement, wide dynamic range, and high measurement accuracy. In 2021, Sijs R et al. published an article entitled "Drop size measurement techniques for sprays: Comparison of image analysis, phase Doppler particle analysis, and laser diffraction" in Volume 11, Issue 1 of *AIP Advances*. This article compared three commonly used drop size measurement techniques: image analysis, phase Doppler particle analysis, and laser diffraction, and analyzed the advantages, disadvantages, and applicable ranges of each method. Laser diffraction has a wide measurement range and applicable scenarios, and can be used to measure the size distribution of various liquid and solid particles in the micrometer to millimeter range, such as sprays, powders, and emulsions. However, the measurement results are easily affected by the fitting method and droplet velocity, and may overestimate the number of small droplets. Therefore, it is necessary to select an appropriate measurement method based on the physical characteristics of the droplets and the expected size range. In 2022, Bittelli M et al. published an article entitled "Experimental evidence of laser diffraction accuracy for particle size analysis" in the journal Geoderma, Volume 409, page 115627. They experimentally demonstrated the accuracy of laser diffraction in particle size analysis and established a regression equation between the pipette method and laser diffraction, providing a new approach for the measurement and classification of solid soil particles. In 2025, Masui S et al. published an article titled "Precise characterization of individual microfluidic droplets using laser diffraction" in ACS Measurement Science. They applied laser diffraction to droplet measurement and developed a microfluidic droplet characterization system based on laser diffraction. This system can simultaneously measure the diameter and refractive index of droplets. Experiments verified the accuracy of the system in characterizing water-in-oil (O / W) and oil-in-water (W / O) droplets, as well as polystyrene particles. Furthermore, the system is integrated with a microscope, allowing for the simultaneous acquisition of scattering and bright-field images, facilitating more comprehensive analysis.

[0004] With advancements in hardware technologies such as optical devices and sensors, the measurement optical path of laser diffraction methods has been optimized. Some studies have proposed a series of novel designs, further improving measurement accuracy and applicability. In 2018, Xie H et al. published an article entitled "Particle sizing from Fraunhofer diffraction pattern using a digital micro-mirror device and a single photodiode" in Powder Technology, Volume 332, pp. 351-358. This article proposed a particle size measurement method based on a digital micro-mirror array (DMD) and a single photodiode. Through inverse Abel transform and integral inversion, accurate measurement of particle size distribution was achieved. This method has advantages such as simple structure, high accuracy, and automatic center positioning, effectively improving measurement efficiency and accuracy. In 2020, Hussain R et al. published an article titled "An ultra-compact particle size analyzer using a CMOS imagesensor and machine learning" in *Light: Science & Applications*, Volume 9, Issue 21. This article described a spatial light filter designed for light intensity acquisition, capable of collecting light intensity data at specific angles and combining it with a deep learning algorithm to predict the median volume diameter of particles. Through this filter, the photodetector can collect scattered light from specific angles. Compared to traditional methods that collect all diffracted light, this method reduces the sampling amount and mitigates the effects of multiple scattering. Experimental results show that the measurement system can achieve measurements in the range of 0.5–175 μm. With and without concentration as input parameters, the mean absolute percentage error for predicted particle size is 5.09% and 2.5%, respectively. Considering only spherical particles, the error reaches 0.72%.In 2021, Misawa T et al. published an article entitled "Imaging-based particle sizing system combining scattered-light imaging and particle-shade imaging for submicron particles" in Powder Technology, Volume 394, pp. 1218-1230. This article developed a submicron particle imaging particle size measurement system based on scattered-light imaging and particle-shade imaging. By combining the advantages of both imaging techniques and proposing a correction algorithm that considers light diffraction, the measurement range and accuracy can be effectively improved. Experimental results based on polystyrene standard spheres show that particle-shade imaging analysis can measure particles larger than 3 μm with an average particle size error of less than 10%, while scattered-light imaging analysis can accurately measure submicron particles with an average particle size error of less than 3.5%. In 2023, Chinese patent CN 220187647 U, "A Laser Diffraction Diameter Meter" (patent number: 202321642750.X), proposed a novel structure for a laser diffraction diameter meter. By combining an octahedron and a reflector, a motor can drive the octahedron to rotate at high speed and form a laser light curtain. By using an Fθ lens, a light-collecting tube, and a galvanometer mechanism, the light curtain is focused to form a measurement area. The incident laser angle can be flexibly adjusted to ensure the correctness and accuracy of the measurement results.

[0005] The relationship between particle size distribution and scattered light intensity distribution function constructed by laser diffraction is in the form of a first-kind Fredholm equation. Its kernel function exhibits strong ill-conditioned characteristics, making the solution process complex. Currently, two common solution methods exist: direct integral inversion and iterative numerical calculation. In 2009, Cao et al. published an article entitled "Integral inversion to Fraunhofer diffraction for particle sizing" in *Applied Optics*, Vol. 48, No. 25, pp. 4842-4850. They derived a double integral form of the traditional inversion formula by combining the Schlomilch equation and Hankel transform. While this method solves the problem of inaccurate integral reconstruction results in small particle measurements, it exhibits significant distortion in forward small-angle diffraction conditions. In 2018, Niu H et al. published an article entitled "Aniterative algorithm based on the dual integral inversion for particle sizing" in IEEE Transactions on Instrumentation and Measurement, Volume 67, pp. 1729-1737. This article proposed an iterative algorithm based on dual integral inversion, which overcomes the limitations of dual integral inversion in measuring the size of narrowly distributed particles. It achieves iterative correction of particle size distribution by simulating the deviation between the diffraction pattern and the measured pattern. Experimental results show that this algorithm can effectively improve the accuracy and robustness of particle size measurement.In 2019, Wang et al. published an article entitled "Optimal angular range for the Chin-Shifrin inversion algorithm for particle sizing by laser diffraction" in the Journal of Quantitative Spectroscopy and Radiative Transfer, Volume 224, pp. 319-324. By studying the influence of factors such as scattering angle on the particle size distribution inversion reconstruction effect, they proved that the upper and lower limits of diffraction angle and angular resolution are three key parameters. Based on this, they proposed optimization selection criteria for multiple parameters, providing important theoretical and technical support for improving the accuracy and stability of particle size distribution measurement.

[0006] There are various methods for iterative numerical computation, such as the Landweber algorithm, the Chahine algorithm, the Philips-Twomey algorithm, and various regularization algorithms. In 2020, Shan et al. published an article entitled "Inversion of particle size distribution based on iterative non-negative Philips-Twomey algorithm" in the Transactions of the Institute of Measurement and Control, Volume 42, Issue 4, pp. 805–812. Based on the traditional non-negative Philips-Twomey (NNPT) algorithm, they proposed an iterative non-negative Philips-Twomey (INNPT) algorithm. By introducing non-negativity constraints, they ensured that the inversion results conformed to the physical meaning of non-negative particle size. Combined with iterative optimization strategies, they improved the convergence and stability of the algorithm under complex scattering conditions. Experimental results using national standard particles showed that the INNPT algorithm outperformed the NNPT algorithm in terms of inversion accuracy and stability, reducing the inversion accuracy from 7.57% to 1.03%. This method performed particularly well under narrow distribution conditions, but its performance under wide distribution or bimodal distribution conditions needs improvement. In 2022, Liu et al. published an article entitled "Research on Tikhonov regularization parameter selection in dynamic lightscattering measurement of flowing particles" in the Journal of Optics, Volume 51, Issue 4, pp. 1038-1051. This article investigated the impact of regularization parameter selection criteria (GCV criterion and L-curve criterion) on the inversion accuracy of particle size distribution in flowing particles. The applicability of the two criteria under different noise levels, flow velocities, and distribution widths was analyzed, providing an important reference for parameter optimization in the Tikhonov regularization process and effectively reducing instability in solving the dynamic light scattering inverse problem.In 2023, Pawlata A et al. published an article titled "Application of thetikhonov and the modified twomey methods to calculate narrow microparticle size distributions by the laser diffraction technique" in *Opto-Electronics Review*, Volume 31, Issue 1. This article investigated the problem of oversmoothing in the measurement results of narrow particle size distributions using laser diffraction, particularly when the coefficient of variation was less than 5%. They proposed a new method for measuring narrow particle size distributions based on the Tikhonov method and a modified Twomey method. By using the Levenberg-Marquardt method to fit the calculated distribution to a Gaussian function and a bimodal Gaussian function, the oversmoothing problem in the reconstruction results of the bimodal narrow-peak distribution was effectively addressed. Comparative experiments with a nanoDS instrument verified that the modified Twomey method could not only accurately determine the location of the maxima but also the width of the studied narrow distribution.

[0007] Compared to solid particles, droplets typically possess a certain degree of transparency. Therefore, the influence of the droplet's complex refractive index on light scattering needs to be considered in measurements. Typically, the Fraunhofer diffraction theory approximation is no longer used; instead, the Mie scattering theory model is employed. In 2020, Martín J et al. published an article entitled "Computational study of the sensitivity of laser light scattering particle sizing to refractive index and irregularity" in the *Journal of Quantitative Spectroscopy and Radiative Transfer*, Volume 241, page 106745. This article systematically investigated the limitations of light scattering methods in measuring the size distribution of spheres and irregular particles. First, the particles were discretized and modeled using the discrete dipole approximation, simulating the scattering results of particles with different shapes. Then, the influence of complex refractive index was analyzed by comparing Mie scattering theory and Fraunhofer diffraction theory, quantifying the impact of refractive index and irregularity on particle size distribution reconstruction. In 2021, Darder ML et al. published an article titled "Comparing multifractal characteristics of soil particle size distributions calculated by Mie and Fraunhofer models from laser diffraction measurements" in *Applied Mathematical Modelling*, Volume 94, pp. 36-48. This study investigated the multifractal characteristics of particle size distributions calculated by the two models and found that the particle size distribution calculated using the Mie scattering model exhibited less scaling heterogeneity than that calculated using the Fraunhofer diffraction model. This is attributed to two factors: firstly, the Mie scattering model has a lower measurement limit; and secondly, the Mie scattering model comprehensively considers both particle shape and optical properties, providing a new approach for understanding and characterizing particle size distributions and complex structures. However, this method is primarily applied to solid soil particles and has not yet been extended to droplet measurements.In 2023, Báez-Chorro M et al. published an article entitled "Particle size inversion from spectrally resolved full-field forward scattering" in *Analytical Chemistry*, Volume 95, Issue 43, pp. 15994-16003. This paper applied coherent detection technology to particle size inversion in the terahertz band and improved the Twomey iterative method by using a forward model based on the complex refractive index according to the Waterman-Truell formula. This allowed the method to simultaneously utilize extinction and refractive index information, thus improving inversion accuracy. This method does not require prior assumptions or constraints on particle size distribution shape and can be applied to optically opaque media and matrix media with moderate absorption, expanding the application range of particle size measurement. However, this method is highly susceptible to sample concentration, requiring an experimental sample concentration not exceeding 10% by volume, making it difficult to apply to high-concentration particle measurements. In 2025, Su G et al. published a paper entitled "Laser diffraction modeling based on laser and particle behavior statistics for particle size characterization" in the Journal of Quantitative Spectroscopy and Radiative Transfer, Volume 337, page 109381. In an article on size characterization, a scattering model based on the Monte Carlo method (MCM) was developed to study the light scattering and extinction characteristics of a high-concentration mixed particle system irradiated by a non-collinear laser beam. A test system for measuring the energy distribution of scattered light was constructed. By combining the differential evolution algorithm and an improved coefficient matrix, the measurement error caused by non-collinear incident beams or multiple scattering effects in the traditional model was effectively corrected. The model successfully inverted two different particle sizes and mixing ratios of the mixed particle system. The absolute relative error with the reference value was reduced from 33.08% and 10.60% in the traditional model to within 3.00%. However, for droplet measurement scenarios, the model lacks consideration of complex refractive index and droplet deformation.

[0008] Against this background, this invention proposes a droplet size measurement method based on adaptive optimization of scattered light intensity deviation. First, a reflective laser diffraction measurement optical path is constructed based on a digital micromirror array to achieve high-precision measurement of the scattered light intensity distribution. For the measured light intensity distribution data, an iterative reconstruction process based on adaptive optimization of scattered light intensity deviation is established. Taking into account the errors and error changes in the iterative reconstruction process, an adaptive neural network is used to progressively update the correction coefficients. Based on historical reconstruction results and difference correction terms, a correction formula for the reconstruction results is constructed in conjunction with the correction coefficients. The reconstructed values ​​and reconstruction deviations are incorporated into the optimization process, and high-precision reconstruction is finally achieved through iterative calculation. Compared with traditional iterative reconstruction algorithms and integral reconstruction algorithms, this method effectively combines the reconstruction efficiency of direct integration with the optimization effect of iterative methods. The accuracy and speed of reconstruction can be controlled by adjusting the weight coefficient matrix and learning rate, thereby improving the efficiency and accuracy of solving the inverse light scattering problem. Summary of the Invention

[0009] (a) Technical problems to be solved

[0010] This invention proposes a droplet size measurement method based on adaptive optimization of scattered light intensity difference, aiming to solve the problem that the reconstruction process of laser diffraction is unstable and difficult to accurately measure the particle size distribution when considering droplet transparency and refractive index.

[0011] (II) Technical Solution

[0012] This invention relates to a droplet size measurement method based on adaptive optimization of scattered light intensity difference, the specific implementation process of which includes the following steps:

[0013] Step 1: Establish a scattered light intensity model based on Mie scattering theory, and reconstruct the particle size distribution by direct integration using the double integral formula; for a beam of light incident along the z-axis, let its amplitude be A, wavelength be λ, and wave vector be... The frequency is ω, the imaginary unit is i, the scattering angle is θ, and the azimuth angle is... Then at time t, the incident light u in Represented as:

[0014] u in =Ae iωt-ikz (1)

[0015] After passing through the particle system, the far-field scattered light u at a distance r from the particle system s Represented as:

[0016]

[0017] in, is the scattering amplitude function, characterizing the directional properties of the scattered light;

[0018] The intensity of scattered light is expressed as:

[0019]

[0020] in, This is called the scattering intensity function; according to Maxwell's equations of electromagnetism, the scattered light is decomposed into a parallel electric field E. s|| and vertical electric field E s⊥ Two directions:

[0021]

[0022] The intensity of scattered light in the two directions is expressed as:

[0023]

[0024] The intensity function I and amplitude function s are the scattering angle θ, and the relative refractive index m of the medium is a dimensionless parameter related to the particle size. The amplitude function is a function of the Bessel and Legendre functions; according to Mie scattering theory, the amplitude function is an infinite series composed of the Bessel and Legendre functions, expressed as...

[0025]

[0026] The coefficients are expressed as follows:

[0027]

[0028] Where, ψ n (z) and ξ n (2) (z) are functions of the half-integer order Bessel function and the second kind of Hankel function, respectively:

[0029]

[0030] The complete form of the expression for scattered light intensity under Mie scattering theory is obtained by extending equation (1):

[0031]

[0032] For a particle system, which typically has a particle size distribution f(α) of a certain width, and assuming the distance between the particle and the receiving surface of the scattering pattern, i.e., the focal length of the lens, is f, then the light intensity distribution corresponding to the entire particle system is:

[0033]

[0034] Where a and b are the upper and lower limits of integration for the dimensionless parameters of particle size, and f is the focal length of the lens;

[0035] For the first type of Fredholm equation shown in equation (10), the particle size distribution is calculated using the double integral reconstruction method:

[0036]

[0037] Step 2: Establish an iterative correction formula based on adaptive optimization of scattered light intensity difference. The correction coefficient is calculated by an adaptive neural network based on the reconstruction error and error change during the iteration process. This network structure includes an input layer, a processing layer, and an output layer. First, the reconstruction error corresponding to different β and γ is calculated through an traversal algorithm to determine the initial value range and give the initial value of the correction coefficient. The initial input is set to uniform distribution, and the reconstruction error is given by the mean square error of the light intensity. The initial error e0 and the error change Δe0 are set to 0. When k≥2, the iterative reconstruction error e is calculated. k-1 With the change in error Δe k-1 :

[0038]

[0039] In the formula, I m For the measured light intensity distribution, I k To reconstruct the theoretical light intensity distribution corresponding to the particle size distribution; construct the input vector x. k-1 =[e k-1 ,Δe k-1 ];

[0040] A dual-neuron structure is used to design the processing layer optimization network. Each neuron corresponds to a dynamically adjusted correction coefficient. Within the range of the correction coefficient's value, the correction coefficient and the error are approximately linearly related. The computational logic of the neurons is a linear weighted operation, and its computation matrix is ​​as follows:

[0041]

[0042] Among them, w β =[w β1 w β2 ] and w γ =[w γ1 w γ2 These are the neuron weight matrices with two correction coefficients, and the update rule uses the least mean square algorithm for online adaptive adjustment.

[0043]

[0044] Where, η β and η γ These represent the neural network learning rates for the two correction coefficients.

[0045] Based on the previous value of the correction coefficient, the updated value is calculated as follows:

[0046]

[0047] Step 3: Construct an iterative format that integrates historical iteration information and difference correction. Based on the reconstruction results of the first two steps and a difference correction term, adjust the reconstruction results using the corresponding correction coefficients. When k≥2, the reconstruction results f from the first two steps are... k-2 and f k-1 As the initial input for the iteration, Equation (10) is then used to calculate the light intensity distribution I corresponding to the reconstructed particle size distribution. t,k-2 and I t,k-1 The difference in light intensity distribution, calculated using the correction factor β, is:

[0048] I diff,k-1 =I t,k-1 -βI k,k-2 (16)

[0049] And calculate and compare with the measured light intensity data I m Difference in light intensity distribution:

[0050] ΔI k-1 =(1-β)I m -I diff,k-1 (17)

[0051] Calculate the particle size distribution difference term corresponding to the light intensity distribution difference according to equation (11):

[0052]

[0053] Construct a correction formula for reconstructing particle size distribution by combining the correction factor γ:

[0054] f k =f k-1 -β k ·f k-2 +γ k ·Δf k-1 (19)

[0055] The first two items are the reconstruction results of the first two steps, and the third item is the difference correction item;

[0056] The quality of the reconstruction is measured by the mean square error s between the theoretical light intensity distribution calculated from the reconstructed particle size distribution and the measured light intensity distribution.

[0057] A smaller s-value indicates higher reconstruction accuracy;

[0058] The corrected particle size distribution is substituted back into the second step of the iterative process until the preset number of iterations is reached, at which point the final reconstruction result is output. Thus, by constructing an iterative framework using historical reconstruction information and the difference in scattered light intensity during the iterative process, the correction coefficients are adaptively optimized, thereby gradually correcting the reconstruction result and reducing the error of single-step direct integration reconstruction.

[0059] (III) Beneficial Effects

[0060] The beneficial effects of this invention lie in proposing a droplet size measurement method based on adaptive optimization of scattered light intensity difference. According to Mie scattering theory and the double integral formula, an iterative correction and reconstruction model is established. For the measured light intensity distribution data, a correction term is constructed to incorporate the reconstructed value and reconstruction error into the iterative optimization process. Specifically, an adaptive update mechanism for the correction coefficients is established based on an adaptive neural network to progressively optimize the calculation of the correction coefficients. This method is applicable to light scattering cases considering the complex refractive index of droplets, effectively reducing the instability of reconstruction solutions in laser diffraction-based droplet size distribution measurement and improving reconstruction accuracy. Attached Figure Description

[0061] Figure 1 Flowchart of the specific implementation of this method

[0062] Figure 2 Schematic diagram of the droplet size measurement system using reflection laser diffraction in this method.

[0063] In the diagram: 101-Laser, 102-Continuously zoomable beam expander, 103-Adjustable aperture, 104-Particle to be measured, 105-Lens, 106-Digital micromirror array, 107-Light shield, 108-Lens, 109-Photodetector and data acquisition card, 110-Computer Figure 3 Comparison of the reconstruction results of the RR distribution by this method and the direct integration method.

[0064] Figure 4 Comparison of reconstruction results of bimodal distribution using this method and the direct integration method. Detailed Implementation

[0065] In the attached diagram Figure 1 This is a flowchart illustrating the specific implementation of this method. Figure 2 This is a schematic diagram of the optical path for particle size measurement using laser diffraction. Figure 3 and Figure 4 The reconstruction results for the RR distribution and the bimodal distribution are shown below, with specific operation steps for an example:

[0066] Step 1: The 450nm laser emitted by laser 101 is expanded by the continuously variable beam expander 102, and then adjusted to a suitable diameter by the adjustable aperture 103, so that it passes through the particle under test and undergoes Mie scattering. The original light and the scattered light are converged on the mirror surface of the digital micromirror array 106 by lens 105. This digital micromirror array has a resolution of 1920×1080 and a maximum flip frequency of 9.5kHz. Let the long side axis be the x-axis and the short side axis be the y-axis. The flip direction of the micromirrors in different areas is adjusted by the control software. 192 10×1080 reflection areas are constructed along the x-axis and 108 10×1920 reflection areas are constructed along the y-axis. The reflected beam is reflected sequentially by lens 108 to the photodetector 109 and the data acquisition card. The light intensity signal is converted into an electrical signal and input into the computer 110. The x-axis light intensity matrix is ​​initially displayed [I]. x1 I x2 I x2 …I x192 ] and y-axis light intensity matrix [I y1 I y2 I y2 …I y108 ] T The intensity distribution is used to locate the center of the diffraction pattern. Within this area, the mirrors are flipped sequentially to determine the precise location of the center. The light beam from the micromirror area where the center is located is reflected to the 107 light-blocking plate, while the remaining effective intensity areas are reflected to the detector for normal acquisition. Based on the principle of inverse Abelian transform, the radial intensity distribution I0(θ) is calculated from the tangential intensity distribution and used as the original intensity input for the inversion and reconstruction calculation.

[0067] Step 2: Establish a particle light scattering model based on Mie scattering theory, and construct a functional model relationship between particle size distribution and scattered light intensity distribution:

[0068]

[0069] The calculation method for the preliminary reconstruction results is given by the direct integration method formula:

[0070]

[0071] Based on the closed-loop control principle, a correction framework for the reconstruction results is constructed. The update of the correction coefficients is achieved by an adaptive neural network based on the reconstruction error and its change during the iteration process. An adaptive neural network is constructed, and an ergonomic algorithm is used to calculate the reconstruction error corresponding to different β and γ values ​​to determine the initial value range. In this example, the calculation range is approximately β∈[1.3,1.8], γ∈[-0.45,-0.25]. The initial distribution is set to uniform distribution, and the reconstruction error is given by the mean square error of the light intensity. The initial error e0 and the error change Δe0 are set to 0. When k≥2, the iterative reconstruction error e is calculated. k-1 With the change in error Δek-1 :

[0072]

[0073] In the formula, I m For the measured light intensity distribution, I k To reconstruct the theoretical light intensity distribution corresponding to the particle size distribution; construct the input vector x. k-1 =[e k-1 ,Δe k-1 ];

[0074] A dual-neuron structure is used to design the processing layer optimization network. Each neuron corresponds to a dynamically adjusted correction coefficient. Within the range of the correction coefficient's value, the correction coefficient and the error are approximately linearly related. The computational logic of the neurons is a linear weighted operation, and its computation matrix is ​​as follows:

[0075]

[0076] Among them, w β =[w β1 w β2 ] and w γ =[w γ1 w γ2 These are the neuron weight matrices with two correction coefficients, and the update rule uses the least mean square algorithm for online adaptive adjustment.

[0077]

[0078] Where, η β and η γ These represent the neural network learning rates for the two correction coefficients.

[0079] Calculate the updated value by combining the correction coefficient from the previous step:

[0080]

[0081] Step 3: Construct the iterative correction formula:

[0082] f k =f k-1 -β k ·f k-2 +γ k ·Δf k-1 (7)

[0083] The first two terms are the reconstructed values ​​from the first two steps, the third term is the difference correction term, and β and γ are the correction coefficients.

[0084] The results of the first two steps of particle size distribution reconstruction are calculated using equation (2). k-2 and f k-1As the initial input for the iteration, Equation (1) is then used to calculate the light intensity distribution I corresponding to the reconstructed particle size distribution. t,k-2 and I t,k-1 The intensity difference is calculated using the correction factor β as follows:

[0085] I diff,k-1 =I t,k-1 -βI t,k-2 (8)

[0086] Based on measured light intensity data I m Calculate the light intensity difference:

[0087] ΔI k-1 =(1-β)I m -I diff,k-1 (9)

[0088] The particle size distribution difference Δf corresponding to the light intensity difference is calculated according to equation (2). k-1 Substitute this into the iterative correction formula (7);

[0089] Theoretical light intensity distribution I calculated from reconstructed particle size distribution k Compared with the measured light intensity distribution I m The mean square error (S-value) measures the quality of the reconstruction:

[0090]

[0091] A smaller s-value indicates higher reconstruction accuracy;

[0092] The corrected particle size distribution is substituted back into the second step of the iterative process until the preset number of iterations is reached. The final reconstructed particle size distribution f(d), reconstruction accuracy s, and the curve of change with the number of iterations are obtained. Thus, by constructing an iterative framework with the historical reconstruction information and the difference in scattered light intensity during the iterative process, the correction coefficient is adaptively optimized, thereby gradually correcting the reconstruction results and reducing the error of single-step direct integration reconstruction.

[0093] The above description of the present invention and its embodiments is not limited thereto, and the accompanying drawings are only one embodiment of the present invention. Any structure or embodiment similar to this technical solution designed without departing from the spirit of the present invention shall fall within the protection scope of the present invention.

Claims

1. A droplet size measurement method based on adaptive optimization of scattered light intensity difference, characterized in that: A reflective laser diffraction system based on a digital micromirror array (DMI) is used to obtain the intensity distribution of scattered light. The components include a laser, a beam expander, a lens, a DMI, a photodetector, a data acquisition card, and a computer. After passing through the beam expander, the laser light scatters as it passes through the droplet region. The scattered light is then focused by the lens and modulated and reflected by the DMI to the photodetector. The light is then transmitted to the computer via the data acquisition card, where the intensity distribution of the scattered pattern is calculated. A mathematical model for solving the light scattering and inverse problem is established based on Mie scattering theory and the double integral formula, enabling forward calculation of light intensity and particle size reconstruction. An iterative process for adaptive optimization of the scattered light intensity difference is established, setting the initial distribution and calculating the preliminary reconstruction results and errors. Based on the reconstruction error and its variation, the correction coefficients are optimized and updated using an adaptive neural network. An iterative correction formula is constructed, adopting a format that integrates historical iteration information and difference correction. Based on the reconstruction results of the first two steps and a difference correction term, the reconstruction result is corrected by combining the corresponding correction coefficient, and then used for the calculation of the correction coefficient in the next step. This iterative process is executed repeatedly until the number of iterations reaches a preset value, and then the final reconstructed particle size distribution is output, realizing high-precision measurement of the particle size distribution of the droplet to be measured.

2. The droplet size measurement method based on adaptive optimization of scattered light intensity difference according to claim 1, characterized in that: A reflective laser diffraction measurement system based on a digital micromirror array is used to accurately measure the scattered light intensity distribution of the droplet under test. Based on Mie scattering theory, a positive correlation model from particle size distribution to light intensity distribution is established, extending the applicability of laser diffraction to the measurement of droplet particle size distribution with adjustable transmittance and complex refractive index. An inverse problem solution model based on adaptive optimization of scattered light intensity difference is constructed. First, an adaptive neural network is used to update the correction coefficients, specifically including the following steps: Step 1: Establish a mathematical model for reconstructing the intensity distribution and particle size distribution of Mie scattered light; for a beam of light incident along the z-axis, let the wavelength be λ and the wave vector be... The frequency is ω, the scattering angle is θ, and the azimuth angle is... The intensity I of the far-field scattered light at a distance r after being scattered by a particle with a diameter of d s Represented as: in, This is called the scattering amplitude function. This is called the scattering intensity function; According to Mie's light scattering theory, for a spherical particle, the amplitude function is an infinite series composed of the Bessel function and the Legendre function; and according to Maxwell's equations of electromagnetism, the scattered light is decomposed into two directions, parallel and perpendicular, and the intensity of the scattered light in the two directions is expressed as: Among them, a n ,π n ,b n ,τ n The Mie scattering coefficient is a dimensionless parameter relating the scattering angle θ, the relative refractive index m of the medium, and the particle size. The function of ; then the complete form of the scattered light intensity expression under the Mie scattering theory is obtained by extending equation (1): For a particle system, which typically has a particle size distribution f(α) of a certain width, the light intensity distribution corresponding to the entire particle system is as follows: Where a and b are the upper and lower limits of integration for the dimensionless parameters of particle size, and f is the focal length of the lens; The initial particle size distribution reconstruction process was calculated using the double integral reconstruction method: Step two: the correction coefficient is calculated adaptively based on the difference of scattered light intensity; the calculation process of the correction coefficient is realized by the adaptive neural network according to the reconstruction error and the error change in the iterative process, and the network structure includes an input layer, a processing layer, and an output layer; first, the reconstruction error corresponding to different β and γ is calculated by the traversal algorithm to determine the preliminary value range, and the initial value of the correction coefficient is given; the initial distribution is set as a uniform distribution, the reconstruction error is given by the mean square error of the light intensity, the initial error e0 and the error change Δe0 are set as 0; when k≥2, the reconstruction error e k-1 and the error change Δe k-1 : In the formula, I m For the measured light intensity distribution, I t,k-1 To reconstruct the theoretical light intensity distribution corresponding to the particle size distribution; based on this, an input vector x is constructed. k-1 =[e k-1 ,Δe k-1 ]; A dual-neuron structure is used to design the processing layer optimization network. Each neuron corresponds to a dynamically adjusted correction coefficient. Within the range of the correction coefficient's value, the correction coefficient and the error are approximately linearly related. The computational logic of the neurons is a linear weighted operation, and its computation matrix is ​​as follows: Among them, w β =[w β1 w β2 ] and w γ =[w γ1 w γ2 These are the neuron weight matrices with two correction coefficients, and the update rule uses the least mean square algorithm for online adaptive adjustment. Where, η β and η γ These represent the neural network learning rates for the two correction coefficients. Based on the previous value of the correction coefficient, the updated value is calculated as follows: The updated values ​​of the correction coefficients are used to correct the next step of the reconstruction results in the iterative correction formula.

3. The droplet size measurement method based on adaptive optimization of scattered light intensity difference according to claim 1, characterized in that: The theoretical light intensity distribution corresponding to the particle size distribution is reconstructed by using Mie scattering theory, and the deviation from the measured light intensity distribution is calculated. An adaptive neural network is used to gradually update the correction coefficients during the iteration process. An iterative format integrating historical iteration information and error correction is constructed. Based on the reconstruction results of the first two steps and a difference correction term, the reconstruction results are corrected using the corresponding correction coefficients. The specific steps are as follows: Step 1: Calculate the difference correction term based on the two-step reconstruction results and the correction coefficients; first, calculate the two-step reconstruction result f. k-2 with f k-1 As the initial input for the iteration, a uniform distribution is initially used as the particle size distribution for the first step; the light intensity distribution I corresponding to the reconstructed particle size distribution is calculated using equation (4). t,k-2 and I t,k-1 The difference in light intensity distribution, calculated using the correction factor β, is: AND diff,k-1 =I t,k-2 -β k AND t,k-1 (10) Based on the measured light intensity distribution I m The difference in light intensity distribution is calculated using the correction factor: ΔI k-1 =(1-β k )I m -I diff,k-1 (11) Calculate the particle size distribution difference corresponding to the light intensity distribution difference according to equation (5): Step 2: Construct an iterative correction formula for reconstructing the particle size distribution; based on the reconstruction results and difference correction terms from the first two steps, and combining the two correction coefficients, construct the complete iterative correction formula: f k =f k-1 -β k ·f k-2 +γ k ·Δf k-1 (13) The first two terms are the reconstructed values ​​from the first two steps, and the third term is the difference correction term. The difference between the light intensity distribution corresponding to the corrected particle size distribution and the measured light intensity is calculated. This process is repeated until the preset number of iterations is reached, and the final reconstruction result is output.

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