Ultra-low concentration dynamic light scattering inversion method based on non-Gaussian autocorrelation function

Abstract

The ultra-low concentration dynamic light scattering inversion method based on non-Gaussian autocorrelation function belongs to the technical field of nanoparticle size detection. Step 1001, set the fitting target function and the fitting initial value; step 1002, determine the adjustment range of the focusing waist radius; step 1003, calculate the root mean square error of the autocorrelation function; step 1004, increase the focusing waist radius value; step 1005, w0>0.1um, return to step 1003, w0≤0.1um, execute step 1006; step 1006, obtain the minimum value of the root mean square error of the autocorrelation function; step 1007, obtain the optimal value of the focusing waist radius to correct the non-Gaussian autocorrelation function model; step 1008, reconstruct the kernel matrix; step 1009, invert the particle size distribution. In this ultra-low concentration dynamic light scattering inversion method based on non-Gaussian autocorrelation function, the optimal focusing beam waist radius value is used to correct the non-Gaussian correlation function theoretical model to obtain a kernel matrix that matches the measured data, which significantly improves the particle size inversion accuracy of ultra-low concentration dynamic light scattering measurement.

Description

Technical Field

[0001] The invention discloses an ultra-low concentration dynamic light scattering inversion method based on non-Gaussian autocorrelation function, and belongs to the technical field of nanoparticle size detection. Background Art

[0002] Dynamic Light Scattering (DLS) has become a standard technique for measuring the particle size and distribution of submicron and nanoparticles in liquid dispersions, and is widely used in scientific research and industrial production. This technique obtains the particle size distribution (PSD) by analyzing the autocorrelation function (ACF) of the scattered light intensity of Brownian motion particles. However, DLS measurement is limited by particle concentration. When the particle concentration is too low, the number fluctuation caused by the diffusion of particles in the scatterer causes the light intensity ACF to add an additional slow decay (number fluctuation decay) during the long delay period. This additional attenuation contains both particle size information and concentration information. Since this attenuation segment is not available in conventional concentration measurements, the data processing method used for conventional concentration to estimate PSD will treat this additional attenuation as the attenuation caused by Brownian motion, resulting in false peaks in the large particle size range and the main peak shifting in the direction of decreasing particle size.

[0003] For a long time, the problem of DLS particle size measurement at ultra-low concentrations has not been well solved. To solve this problem, researchers in this field have studied various methods to remove the number fluctuation component:

[0004] (1) In the literature AW Wilemse, EJ Nijman, JCM Marijnissen, HG Merkus, and B. Scarlets, “Photon Correlation Spectroscopy–Extending the limits of concentration,” KONA Powder Part. J. 16, 102–115 (1998), a low-pass filter was used to filter out the low-frequency scattered light intensity signal caused by the fluctuation of the particle number, and the high-frequency signal was used to obtain the particle size. Although this method is theoretically feasible, adding a filter will not only introduce additional noise, but also change the working mode of the DLS real-time autocorrelation operation.

[0005] (2) MJ Wang, J. Shen, JC Thomas, TT Mu, W. Liu, YJ Wang, JF Pan, Q. Wang, and KS Liu, “Particle size measurement using dynamic light scattering at ultra-low concentration accounting for particle number fluctuations,” Materials 14(19), 5683(2021), proposed using the baseline reset method to truncate the number fluctuation component in the light intensity ACF, but the truncation position was greatly affected by noise and failed to recover the accurate PSD from the measured data.

[0006] (3) Q. Wang, J. Shen, M. J. Wang, J. C. Thomas, Y. J. Wang, W. Liu, X. Q. Li, and X. F. Li, “Measuring particle size in ultra-low concentration suspensions by removing the number fluctuation contribution in dynamic light scattering,” Opt. Express 29(23), 38567-38581 (2021) proposed to identify and separate the number fluctuation component by differentiating the fitted intensity ACF, eliminating the influence of noise on the cutoff position, thereby obtaining a more accurate PSD.

[0007] However, the above three methods all lose the granularity information provided by the number fluctuation. From the perspective of information utilization, the ideal PSD acquisition method is to analyze the non-Gaussian light intensity ACF including the number fluctuation component, and directly establish the relationship between the non-Gaussian ACF and PSD through the kernel function reconstruction (KFR) method to obtain the PSD. Although this method can obtain ideal simulation data inversion results, the inversion results of the measured data are far from the theoretical expectations. The reason is that the actual measurement time is much shorter than the signal acquisition time required by this non-Gaussian autocorrelation model, which leads to the inconsistency between the measured ACF data and the theoretical non-Gaussian ACF model.

[0008] The measurement time is an important factor affecting the statistical accuracy of the intensity ACF. This factor becomes even more important when the research object is an ultra-low concentration suspension. Under ultra-low concentration conditions, obtaining the correct intensity ACF requires a measurement time of 10 5s, while the measurement time of DLS is usually 1 min to 10 mins. Such conventional measurement time leads to distortion of the measured ACF, especially the distortion of the quantity fluctuation part (non-Gaussian term) in the ACF. Summary of the invention

[0009] The technical problem to be solved by the present invention is: to overcome the shortcomings of the prior art, to provide an ultra-low concentration dynamic light scattering inversion method based on non-Gaussian autocorrelation function, which determines the optimal value of the waist radius of a focused laser beam by using the minimum root mean square error of the light intensity autocorrelation function, and to use this optimal value to correct the non-Gaussian autocorrelation theoretical model corresponding to the measured autocorrelation function data, thereby achieving the consistency between the measured data and the corrected theoretical model, solving the correlation function distortion caused by conventional measurement time, obtaining a reconstructed kernel matrix matching the measured data, and significantly improving the inversion accuracy of the measured data.

[0010] The technical solution adopted by the present invention to solve the technical problem is: the ultra-low concentration dynamic light scattering inversion method based on non-Gaussian autocorrelation function is characterized by comprising the following steps:

[0011] Step 1001, setting the fitting objective function and the fitting initial value;

[0012] Step 1002, determining an adjustment range of a focused laser beam waist radius;

[0013] Step 1003: Fitting the measured light intensity autocorrelation function g (2) (τ) to get the fitted light intensity autocorrelation function And find the root mean square error of the light intensity autocorrelation function;

[0014] Step 1004, saving the root mean square error of the light intensity autocorrelation function, and increasing the waist radius of the focused laser beam according to the step size;

[0015] Step 1005, determining whether the focused laser beam waist radius w0 is less than or equal to 0.1um. If the focused laser beam waist radius w0>0.1um, returning to step 1003, and sequentially executing steps 1003 to 1004; if the focused laser beam waist radius w0 satisfies w0≤0.1um, executing step 1006;

[0016] Step 1006, obtaining the minimum value of the root mean square error of the light intensity autocorrelation function;

[0017] Step 1007, obtaining the optimal value of the waist radius w0 of the focused laser beam corresponding to the minimum root mean square error, and using the optimal value to correct the theoretical model of the non-Gaussian light intensity autocorrelation function;

[0018] Step 1008, calculating the equivalent electric field autocorrelation function, and reconstructing the kernel matrix of the inversion equation based on the modified autocorrelation function model;

[0019] Step 1009, obtaining the particle size distribution by inverting the equivalent electric field autocorrelation function.

[0020] Preferably, in step 1006, the expression for the minimum value of the root mean square error RMSE of the light intensity autocorrelation function is:

[0021]

[0022] in, and g (2) (τ) represent the fitted intensity autocorrelation function and the measured intensity autocorrelation function, τ j is the delay time corresponding to the j-th channel of the photon correlator (1≤j≤M).

[0023] Preferably, in step 1001, the fitting objective function is:

[0024]

[0025] Among them, β is the coherence factor, τ is the delay time, Γ is the attenuation line width, q is the scattering vector, w0 is the waist radius of the focused laser beam, a is the radius of the detector receiving aperture, C NG is the amplitude of the non-Gaussian term γ / <n>The fitting parameters of .

[0026] Preferably, in step 1003, the Levenberg-Marquard algorithm is used to measure the autocorrelation function g of the scattered light intensity. (2) (τ) is subjected to nonlinear least squares curve fitting to obtain the fitted light intensity autocorrelation function

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] In the prior art, the waist radius of the focused laser beam in the fixed experimental device is a fixed value, so technical personnel in the field all default to using this fixed parameter for corresponding calculations. However, in the ultra-low concentration dynamic light scattering inversion method based on the non-Gaussian autocorrelation function, the common common technical cognition of ordinary technical personnel in this field is broken through, and the common technical prejudice of ordinary technical personnel in this field is overcome. It is proposed to adjust the parameter of the waist radius of the focused laser beam to correct the non-Gaussian autocorrelation function theoretical model corresponding to the measured light intensity autocorrelation function data. The optimal waist radius value of the focused laser beam is selected by the minimum value of the root mean square error of the light intensity autocorrelation function, and then this optimal value is used to correct the theoretical non-Gaussian correlation model. This can effectively solve the correlation function distortion caused by conventional measurement time, achieve the consistency between the corrected theoretical model and the measured data, and obtain a reconstructed kernel function that matches the measured data, which significantly improves the inversion accuracy.

[0029] The inversion of measured data shows that compared with the conventional kernel function reconstruction method, the particle size distribution inversion deviation caused by the correlation function distortion is overcome, and the accuracy of the inversion results is improved. At all ultra-low particle concentrations, the relative error of the peak position of the inversion result is significantly lower than that of the conventional kernel function reconstruction method, and the inversion results are no significantly different from those of conventional concentration measurements. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a flow chart of the ultra-low concentration dynamic light scattering inversion method based on non-Gaussian autocorrelation function.

[0031] Figure 2 for <n>=5, 10 and 50 for the 200nm particle system with simulated intensity ACF and fitted intensity ACF.

[0032] Figure 3 For a 203 nm particle suspension ( <n>=35) and its fitted curve.

[0033] Figure 4 The fitting curve graph obtained by fitting the measured ACF data of 203nm particle suspension using Levenberg-Marquard algorithm when w0=27um, 10um, 5um, 2.5um and 0.5um.

[0034] Figure 5 This is the ACF root mean square error curve of light intensity when w0 is 0.5um~5um.

[0035] Figure 6 The graph shows the PSD inversion results of 203nm standard polystyrene latex particles using the conventional kernel function reconstruction method at different particle concentrations.

[0036] Figure 7 The figure is a graph showing the PSD inversion results of 203nm standard polystyrene latex particles at different particle concentrations using the ultra-low concentration dynamic light scattering inversion method based on non-Gaussian autocorrelation function.

[0037] Figure 8 This is a graph showing the PSD inversion results of 693nm standard polystyrene latex particles using the conventional kernel function reconstruction method at different particle concentrations.

[0038] Fig. 9 The PSD inversion result curve of 693nm standard polystyrene latex particles under different particle concentrations using the ultra-low concentration dynamic light scattering inversion method based on non-Gaussian autocorrelation function. DETAILED DESCRIPTION

[0039] Figures 1 to 9 The best embodiment of the present invention is shown below in conjunction with the attached Figures 1 to 9 The present invention is further described.

[0040] like Figure 1 As shown, the ultra-low concentration dynamic light scattering inversion method based on non-Gaussian autocorrelation function includes the following steps:

[0041] Step 1001, setting the fitting objective function and the fitting initial value;

[0042] When DLS is applied to ultra-low concentration systems, only a small number of particles diffuse in the scatterer, and the measured scattered light intensity fluctuations come not only from Brownian motion but also from changes in the number of particles in the scatterer. In this case, the amplitude distribution of the scattered field is no longer a Gaussian distribution, and the light intensity ACFg (2) (τ) and electric field ACFg (1) (τ) no longer satisfies the Siegert relation, and the intensity ACF contains non-Gaussian terms caused by the fluctuation of the number of particles.

[0043]

[0044] in, and are the diffusion component and the quantity fluctuation component respectively. (1) (τ)=exp(-Γτ), Γ=Dq 2 is the attenuation line width, D is the translational diffusion coefficient, q is the scattering vector, β is the coherence factor, τ is the delay time, <n>is the average number of particles in the scatterer, w0 is the waist radius of the focused laser beam, a is the radius of the detector receiving hole, γ / <n>is the magnitude of the non-Gaussian term. <n>When <100, the non-Gaussian term cannot be ignored.

[0045] In the fitting process, according to formula (1), the objective function of the fitting is set as:

[0046]

[0047] Among them, C NG is the amplitude of the non-Gaussian term γ / <n>The amplitude of the non-Gaussian term γ / <n>Set as the fitting parameter C NG The reason is that the amplitude cannot be expressed as γ / <n>calculate.

[0048] The parameters β, Γ and C in formula (2) NG It is the important physical information hidden in the measured data. These three unknown parameters can be obtained from the measured data g (2) (τ) is obtained by nonlinear least squares fitting using the Levenberg-Marquardt (LM) algorithm. Since the LM algorithm has the advantages of both the gradient method and the Newton method and has low requirements on the initial value, it can start from any initial value and find the global optimal solution, so [β,Γ,C NG ]=[1,100,0.5] as the initial value for fitting.

[0049] In order to verify the applicability of the LM algorithm to the light intensity ACF data at ultra-low concentrations, the LM algorithm was used to perform nonlinear least squares fitting on the simulated light intensity ACF data of the 200nm single-peak PSD, and the fitting results were analyzed. The simulated PSD adopts a logarithmic normal distribution, and its expression is:

[0050]

[0051] Where d and f(d) are the particle size and its distribution, d1 is the nominal diameter of the particle, and σ1 is the corresponding standard deviation.

[0052] The simulation experimental conditions are as follows: the incident light wavelength is 532nm, the simulation temperature is 298.15K, the refractive index of the dispersion medium is 1.33, and the Boltzmann constant is 1.3807×10 -23 J / K, the viscosity coefficient of the dispersion medium is 0.89×10 -3 cP, scattering angle is 90°, β=0.7, w0=54um, a=200um. <n>= 5, 10 and 50 for three particle concentrations. The simulated ACF and fitted ACF of the 200 nm particle system are shown in Figure 2 As shown in the figure, the solid line represents the ACF obtained by fitting. The fitting parameter values ​​and the corresponding fitting errors are shown in Table 1. The subscripts true and fit represent the true value and the fitting value respectively, and the error E = |true-fit| / true.

[0053]

[0054] Table 1 Fitting parameter values ​​and corresponding fitting errors of 200 nm particle system simulated ACF

[0055] Figure 2 Table 1 shows that the LM algorithm can fit the ACF data of light intensity under ultra-low concentration very well, and obtain relatively accurate fitting parameter values. NG The fitting value is closer to the true value, and the fitting error is within 3‰. <n>=50, C NG The fitted value of is equal to the true value.

[0056] Step 1002, determining an adjustment range of a waist radius of a focused laser beam;

[0057] The initial value of the focused laser beam waist radius w0 is determined to be w0 = 54um, which is determined by the experimental device. The adjustment step is l = -0.1um. The conclusion of selecting the parameter of adjusting the focused laser beam waist radius w0 is obtained by analyzing the non-Gaussian term in the intensity autocorrelation function. The specific analysis process is as follows:

[0058] Conventional measurement time leads to the distortion of the measured light intensity ACF, especially the non-Gaussian term in the ACF, which is mainly manifested in that the amplitude of the non-Gaussian term is larger than the theoretical value (γ / <n>) The rise and decay delay time is much shorter than the theoretical decay delay time.

[0059] In step 1001, the values ​​of the focused laser beam waist radius w0 and the detector receiving aperture radius a in the objective function affect the decay rate of the non-Gaussian term. The smaller the value, the faster the decay rate and the shorter the decay delay time. By analyzing the non-Gaussian term, we can see that: The component is dominant in the non-Gaussian term, and the change of parameter w0 has a more significant impact on the decay characteristic time of the non-Gaussian term. Reducing the value of parameter w0 can shorten the decay delay time of the non-Gaussian term, which can solve the problem that the decay delay time of the non-Gaussian term is much shorter than the theoretical decay delay time due to the conventional measurement time mentioned above. Therefore, the adjustment of parameter w0 value is chosen to correct the non-Gaussian term to achieve the consistency between the theoretical non-Gaussian ACF model and the measured data.

[0060] Step 1003, obtaining a fitted light intensity autocorrelation function, and calculating a root mean square error of the light intensity autocorrelation function;

[0061] The Levenberg-Marquardt (LM) algorithm is used to measure the autocorrelation function of the scattered light intensity g. (2) (τ) is subjected to nonlinear least squares curve fitting to obtain the fitted light intensity autocorrelation function And calculate the root mean square error (RMSE) of the light intensity ACF.

[0062] First, when the parameter w0 is 54 μm (determined by the experimental device), the LM algorithm is used to fit the measured data. <n>= 35 polystyrene latex suspension as an example, the measured ACF data and its corresponding fitting curve are shown in Figure 3 It is obvious that the Brownian motion decay in the measured ACF is well fitted, while the number fluctuation decay is not.

[0063] Then, the value of parameter w0 is reduced, and parameter w0=27um, 10um, 5um, 2.5um and 0.5um are selected. Figure 4 The fitted ACF obtained by the LM algorithm for the measured ACF data at different w0 values ​​is shown. Figure 4 It can be seen that the value of parameter w0 in the fitting objective function plays an important role in curve fitting. As the value of parameter w0 decreases, the delay time of the quantity fluctuation decay section is shortened, and the obtained fitting curve is closer to the measured data. However, compared with w0=2.5um, the too small parameter w0=0.5um gives a worse fitting effect, and even fitting distortion occurs in the Brownian motion decay section.

[0064] In this application, in order to select the optimal value of the waist radius w0 of the focused laser beam, the non-Gaussian correlation model is corrected and the root mean square error (RMSE) of the intensity ACF is introduced to measure the quality of the fitting effect. The expression of the root mean square error (RMSE) is:

[0065]

[0066] In the formula, and g (2) (τ) represents the fitted light intensity ACF and the measured light intensity ACF respectively. The smaller the RMSE, the closer the fitted curve is to the measured data.

[0067] Step 1004, saving the root mean square error of the light intensity autocorrelation function, and increasing the waist radius of the focused laser beam according to the step size;

[0068] The RMSE of the intensity autocorrelation function obtained in step 1003 is saved and saved to RMSE i Then, according to the preset step size (l = -0.1um), the w0 value is adjusted by adding it to the focused laser beam waist radius w0, that is: w0 = w0 + l.

[0069] Step 1005, whether the value of the waist radius w0 of the focused laser beam is less than or equal to 0.1 um;

[0070] Determine whether the focused laser beam waist radius w0 is less than or equal to 0.1um, that is, w0≤0.1um. If the focused laser beam waist radius w0>0.1um, return to step 1003 and execute steps 1003 to 1004 in sequence; if the focused laser beam waist radius w0 satisfies w0≤0.1um, execute step 1006.

[0071] Step 1006, obtaining the minimum value of the root mean square error of the light intensity autocorrelation function;

[0072] The RMSE values ​​saved from step 1004 are i The minimum value is selected from the values ​​as the minimum value of the root mean square error of the light intensity autocorrelation function.

[0073] As the value of parameter w0 decreases, the RMSE changes in a "V" shape. The RMSE of the light intensity ACF when the parameter w0 is 0.5um to 5um is calculated. The calculation results are as follows: Figure 5 As shown. It can be seen that as w0 decreases, the root mean square error first decreases and then increases. The minimum root mean square error corresponds to the optimal fitting curve, and the optimal fitting curve coincides with the measured data. On this basis, the criterion for determining the optimal w0 using the minimum root mean square error of the light intensity ACF is proposed, that is,

[0074]

[0075] In the formula, and g (2) (τ) represents the fitted light intensity ACF and the measured light intensity ACF, respectively.

[0076] Step 1007, obtaining the optimal value of the waist radius of the focused laser beam to correct the non-Gaussian light intensity autocorrelation function model;

[0077] In step 1006, the minimum value of the root mean square error of the intensity autocorrelation function is obtained, and the value corresponding to the focused laser beam waist radius w0 is the optimal w0 value. The theoretical ACF model corresponding to the optimal w0 value is the non-Gaussian correlation model modified according to the measured data, and the fitting values ​​β, Γ and C at this time are NG Closer to the actual measured situation.

[0078] Step 1008: reconstruct the kernel matrix of the inversion equation based on the modified non-Gaussian ACF model.

[0079] The equivalent electric field autocorrelation function is calculated, and the kernel matrix of the inversion equation is reconstructed based on the modified non-Gaussian ACF model.

[0080] The ideal method to accurately obtain PSD is to directly analyze the non-Gaussian light intensity ACF to establish the equivalent electric field ACF. The inversion equation between and PSD can be achieved by reconstructing the kernel function of the inversion equation. The discrete form of the equivalent electric field ACF can be written as:

[0081]

[0082] Among them, τ j is the delay time corresponding to the jth channel of the photon correlator (1≤j≤M), f(d i )(i=1,2,3,……,K) is the discrete PSD, n0 is the refractive index of the suspension medium, k B is the Boltzmann constant, T is the absolute temperature, η is the viscosity coefficient of the dispersion medium, d is the particle size of the scattering particles, q is the scattering vector, λ0 is the wavelength of the incident light beam in vacuum, and θ is the scattering angle.

[0083] Reconstructed kernel matrix A R By element A R (j,i) composition:

[0084]

[0085] Formula (6) can be simplified as

[0086] g e =A R f (8)

[0087] In the formula, g e is a vector composed of equivalent electric field ACF data, whose elements are f is a vector composed of discrete PSDs, whose elements are f(d i ).

[0088] Step 1009, obtaining the particle size distribution by inverting the equivalent electric field autocorrelation function;

[0089] The constrained Tikhonov regularization method is used to solve the PSD as follows:

[0090] M α (f)=||A R fg e || 2 +α||Lf|| 2 st f≥0 (9)

[0091] Where M, α, L, ||·|| and ‖Lf‖ 2 They are stability functional, regularization parameter, regularization matrix, Euclidean norm and penalty factor respectively. α controls the stability and accuracy of the solution and can be determined by the L-curve criterion. Considering the smoothness of PSD, the regularization matrix uses the second-order difference matrix.

[0092] Next, the ultra-low concentration dynamic light scattering inversion method based on the non-Gaussian autocorrelation function of the present application is evaluated in combination with the measured data.

[0093] In order to evaluate whether the proposed method can improve the inversion performance, it is compared with the conventional kernel function reconstruction (KFR) method. The particle size of two different types of latex suspensions was measured. The average diameters of the standard polystyrene latex particles used were 203±5nm (Duke Scientific, 3200A) and 693±10nm (GBW(E)120087), respectively. The volume fraction of the original latex suspension was 1.05%. The original latex suspension was diluted with distilled water to prepare two groups of samples with different particle concentrations, as shown in Table 2. The measurement time for all samples was 120s.

[0094]

[0095] Table 2 Volume fraction of samples and corresponding particle number

[0096] The conventional kernel function reconstruction method and the proposed method are used to perform PSD inversion on the measured data. The results are shown in Figures 6 to 9 The corresponding performance indicators are shown in Table 3, where the relative error of the peak position is E P =|(P true -P meas ) / P true |,P true and P meas are the true peak particle size and the peak particle size obtained by inversion. Under normal concentration (NC), the restored PSD is also Figures 6 to 9 The peak positions are 201nm and 698nm respectively, and the corresponding E p They are 0.010 and 0.007 respectively.

[0097]

[0098] Table 3 PSD performance indicators of 203nm and 693nm standard polystyrene latex particles

[0099] from Figures 6 to 9 It can be seen from Table 3 that at the same particle concentration, the distribution obtained by the conventional kernel function reconstruction method deviates seriously from the true value, while the inversion results of the proposed method are significantly improved and similar to the inversion results of conventional concentration measurements. In addition, for the two groups of single-peak particle systems of 203nm and 693nm, at all particle concentrations, the peak values ​​of the inversion results obtained by the proposed method are 201nm and 698nm, respectively, and the corresponding relative errors of the peak positions are as low as 0.010 and 0.007, respectively, which are completely consistent with the errors of the inversion results of conventional concentration measurements.

[0100] Therefore, the optimal focused laser beam waist radius value is selected by the minimum value of the root mean square error of the intensity autocorrelation function to correct the non-Gaussian autocorrelation function theoretical model, which can adapt to the correction of measured data under different low particle concentrations. Based on the modified non-Gaussian autocorrelation function model, the kernel function is reconstructed to obtain a kernel matrix that matches the measured data, overcome the particle size distribution inversion deviation caused by the correlation function distortion, improve the inversion accuracy, obtain an inversion result that is not significantly different from the conventional concentration measurement, and increase the measurement range of dynamic light scattering.

[0101] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.< / n> < / n> < / n> < / n> < / n> < / n> < / n> < / n> < / n> < / n> < / n> < / n> < / n>

Claims

1. An ultra-low concentration dynamic light scattering inversion method based on non-Gaussian autocorrelation function, characterized by: The steps include: Step 1001, setting the fitting objective function and the fitting initial value; Step 1002, determining an adjustment range of a focused laser beam waist radius; Step 1003: Fitting the measured light intensity autocorrelation function g (2) (τ) to get the fitted light intensity autocorrelation function And find the root mean square error of the light intensity autocorrelation function; Step 1004, saving the root mean square error of the light intensity autocorrelation function, and increasing the waist radius of the focused laser beam according to the step size; Step 1005, determining whether the focused laser beam waist radius w0 is less than or equal to 0.1um. If the focused laser beam waist radius w0>0.1um, returning to step 1003, and sequentially executing steps 1003 to 1004; if the focused laser beam waist radius w0 satisfies w0≤0.1um, executing step 1006; Step 1006, obtaining the minimum value of the root mean square error of the light intensity autocorrelation function; Step 1007, obtaining the optimal value of the waist radius w0 of the focused laser beam corresponding to the minimum root mean square error, and using the optimal value to correct the theoretical model of the non-Gaussian light intensity autocorrelation function; Step 1008, calculating the equivalent electric field autocorrelation function, and reconstructing the kernel matrix of the inversion equation based on the modified autocorrelation function model; Step 1009, obtaining the particle size distribution by inverting the equivalent electric field autocorrelation function; In step 1001, the fitting objective function is: Among them, β is the coherence factor, τ is the delay time, Γ is the attenuation line width, q is the scattering vector, w0 is the waist radius of the focused laser beam, a is the radius of the detector receiving aperture, C NG is the amplitude of the non-Gaussian term γ / <n> The fitting parameters of< / n> In step 1003, the Levenberg-Marquard algorithm is used to calculate the measured scattered light intensity autocorrelation function g (2) (τ) is subjected to nonlinear least squares curve fitting to obtain the fitted light intensity autocorrelation function 2. The ultra-low concentration dynamic light scattering inversion method based on non-Gaussian autocorrelation function according to claim 1 is characterized in that: In step 1006, the expression for the minimum value of the root mean square error RMSE of the light intensity autocorrelation function is: in, and g (2) (τ) represent the fitted intensity autocorrelation function and the measured intensity autocorrelation function, τ j is the delay time corresponding to the j-th channel of the photon correlator (1≤j≤M).

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