CN114965185A - Ultra-low concentration dynamic light scattering inversion method based on non-Gaussian autocorrelation function - Google Patents
Ultra-low concentration dynamic light scattering inversion method based on non-Gaussian autocorrelation function Download PDFInfo
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Abstract
An ultra-low concentration dynamic light scattering inversion method based on a non-Gaussian autocorrelation function belongs to the technical field of nanoparticle particle size detection. Step 1001, setting a fitting objective function and a fitting initial value; step 1002, determining an adjustment range of a focusing beam waist radius; step 1003, calculating the root mean square error of the autocorrelation function; step 1004, increasing the focus beam waist radius value; step 1005, w 0 Is greater than 0.1um, the step 1003 is returned to, w 0 If the sum is less than or equal to 0.1um, executing step 1006; step 1006, obtaining a minimum value of the root mean square error of the autocorrelation function; step 1007, obtaining the optimal value of the radius of the focusing beam waist to modify the non-Gaussian autocorrelation function model; step 1008, reconstructing a kernel matrix; step 1009, inversionParticle size distribution. In the ultralow-concentration dynamic light scattering inversion method based on the non-Gaussian autocorrelation function, the optimal focusing beam waist radius value is used for correcting the theoretical model of the non-Gaussian autocorrelation function to obtain a nuclear matrix matched with measured data, and the granularity inversion accuracy of ultralow-concentration dynamic light scattering measurement is remarkably improved.
Description
Technical Field
An ultra-low concentration dynamic light scattering inversion method based on a non-Gaussian autocorrelation function belongs to the technical field of nanoparticle particle size detection.
Background
Dynamic Light Scattering (DLS) has become a standard technique for measuring particle size and distribution of submicron and nanoparticles in liquid dispersions, and is widely used in scientific research and industrial production. The technique obtains Particle Size Distribution (PSD) by analyzing an Autocorrelation Function (ACF) of the scattered intensity of brownian motion particles. But DLS measurements are limited by particle concentration. When the particle concentration is too low, the number fluctuation due to the diffusion of particles in the scatterer causes the optical intensity ACF to add an additional slow attenuation (number fluctuation attenuation) over a long delay period, the additional attenuation containing both the particle size information and the concentration information. Since the attenuation section is not available in the conventional concentration measurement, estimating the PSD by using a data processing method for the conventional concentration treats this additional attenuation as an attenuation caused by brownian motion, so that a ghost peak occurs in a large particle size interval and the main peak is shifted toward the direction of particle size reduction.
For a long time, the problem of DLS particle size measurement at ultra-low concentration has not been solved well. To solve this problem, researchers in the field have studied various methods of removing the quantity fluctuation component:
(1) in documents A.W.Willemse, E.J.Nijman, J.C.M.Marijnissen, H.G.Merkus, and B.screens, "Photon Correlation Spectroscopy-extension of the limits of concentration," KONA Powder part.J.16, 102-115 (1998), a low-pass filter is used to filter out low-frequency scattered light intensity signals caused by fluctuations in the number of particles, and the particle size is determined using high-frequency signals. Although this approach is theoretically possible, adding a filter not only introduces additional noise, but also changes the mode of operation of the DLS real-time autocorrelation operation.
(2) Documents m.j.wang, j.shen, j.c.thomas, t.t.mu, w.liu, y.j.wang, j.f.pan, q.wang, and k.s.liu, "material size measurement using dynamic light scaling at ultra-low concentration for specific number fluctuations," Materials 14(19), "2025683 (2021), propose to cut off the number fluctuation component in the light intensity ACF by the baseline resetting method, but the cut-off position is greatly affected by noise, failing to recover an accurate PSD from the measured data.
(3) Documents q.wang, j.shen, m.j.wang, j.c.thomas, y.j.wang, w.liu, x.q.li, and x.f.li, "Measuring particulate size in ultra-low concentration distribution in number fluctuation compensation in dynamic light scattering," op.express 29(23), "38567-38581 (2021) propose to eliminate the effect of noise on the truncation position by differentiating the fitted light intensity ACF and thus to obtain a more accurate PSD.
However, the above three methods all lose the granularity information provided by the quantity fluctuation, and from the viewpoint of information utilization, the ideal PSD obtaining method is to analyze the non-gaussian light intensity ACF including the quantity fluctuation component, and directly establish the relationship between the non-gaussian ACF and the PSD by a Kernel Function Reconstruction (KFR) method to obtain the PSD. Although the method can obtain an ideal inversion result of the simulation data, the inversion result of the actual measurement data is far from the theoretical expectation because the actual measurement time is far shorter than the signal acquisition time required by the non-gaussian autocorrelation model, so that the actual measurement ACF data is not matched with the theoretical non-gaussian ACF model.
The measurement time is an important factor affecting the statistical accuracy of the optical strength ACF. This factor becomes even more important when the subject is an ultra low concentration suspension. Obtaining the correct optical strength ACF under the condition of ultra-low concentration requires the measurement time to last 10 5 s, whereas the measurement time for DLS is typically 1min to 10mins, such conventional measurement times result in distortion of the measured ACF, particularly the amount of fluctuations (non-gaussian terms) in the ACF.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method overcomes the defects of the prior art, and provides the ultralow concentration dynamic light scattering inversion method based on the non-Gaussian autocorrelation function, which determines the optimal value of the beam waist radius of the focused laser beam by using the root mean square error minimum value of the light intensity autocorrelation function, corrects the non-Gaussian autocorrelation theoretical model corresponding to the actually measured autocorrelation function data by using the optimal value, realizes the coincidence of the actually measured data and the corrected theoretical model, solves the problem of correlation function distortion caused by conventional measurement time, obtains a reconstructed nuclear matrix matched with the actually measured data, and remarkably improves the inversion accuracy of the actually measured data.
The technical scheme adopted by the invention for solving the technical problems is as follows: the ultra-low concentration dynamic light scattering inversion method based on the non-Gaussian autocorrelation function is characterized by comprising the following steps: the method comprises the following steps:
Preferably, in step 1006, the minimum value of the light intensity autocorrelation function root mean square error RMSE is expressed as
Wherein the content of the first and second substances,
and g (2) (τ) representing the fitted and measured light intensity autocorrelation functions, τ j The delay time corresponding to the jth channel of the photon correlator (j is more than or equal to 1 and less than or equal to M).
Preferably, in step 1001, the fitting objective function is:
wherein beta is a coherence factor, tau is a delay time, gamma is an attenuation line width, q is a scattering vector, w 0 For focusing the beam waist radius of the laser beam, a is the detector receiving aperture radius, C NG Is not a Gaussian term magnitude gamma<N>The fitting parameters of (1).
Preferably, in step 1003, a Levenberg-Marquard algorithm is used to perform autocorrelation function g on the measured scattered light intensity (2) (tau) fitting a non-linear least squares curve to obtain a fitted light intensity autocorrelation function
Compared with the prior art, the invention has the beneficial effects that:
in the prior art, the beam waist radius of a focused laser beam in a fixed experimental device is a fixed value, so that technicians in the field default to adopt the fixed parameter for corresponding calculation, common knowledge technical cognition universally existing in the technicians in the field is broken through in the ultra-low concentration dynamic light scattering inversion method based on the non-Gaussian autocorrelation function, the technical bias universally existing in the technicians in the field is overcome, the parameter of the beam waist radius of the focused laser beam is provided to correct a theoretical model of the non-Gaussian autocorrelation function corresponding to actually measured light intensity autocorrelation function data, the optimal beam waist radius value of the focused laser beam is selected according to the minimum value of the root mean square error of the light intensity autocorrelation function, the theoretical non-Gaussian autocorrelation model is corrected by using the optimal value, the distortion of the correlation function caused by conventional measurement time can be effectively solved, the corrected theoretical model is matched with the actually measured data, and a reconstructed kernel function matched with the measured data is obtained, and the inversion accuracy is obviously improved.
The inversion of the measured data shows that compared with the conventional kernel function reconstruction method, the inversion deviation of the particle size distribution caused by related function distortion is overcome, and the accuracy of the inversion result is improved. Under all ultralow particle concentrations, the relative error of the peak position of the inversion result is obviously lower than that of the conventional kernel function reconstruction method, and the inversion result which has no obvious difference from the conventional concentration measurement is obtained.
Drawings
FIG. 1 is a flow chart of an ultra-low concentration dynamic light scattering inversion method based on a non-Gaussian autocorrelation function.
FIG. 2 is a graph of simulated and fitted light strength ACF for a 200nm particle system with < N > -5, 10 and 50.
Fig. 3 is a graph of measured ACF and its fit to a 203nm particle suspension (< N > -35).
FIG. 4 is w 0 Fitting plots of measured ACF data for 203nm particle suspensions fitted using the Levenberg-Marquard algorithm at 27um, 10um, 5um, 2.5um, and 0.5 um.
FIG. 5 is w 0 The light intensity ACF root mean square error curve when the value is 0.5 um-5 umAnd (6) line drawing.
FIG. 6 is a graph showing the PSD inversion result of 203nm standard polystyrene latex particles by a conventional kernel function reconstruction method under different particle concentrations.
FIG. 7 is a graph showing the PSD inversion result of 203nm standard polystyrene latex particles by using an ultra-low concentration dynamic light scattering inversion method based on a non-Gaussian autocorrelation function under different particle concentrations.
FIG. 8 is a graph showing the PSD inversion result of 693nm standard polystyrene latex particles by a conventional kernel function reconstruction method under different particle concentrations.
FIG. 9 is a graph showing the PSD inversion result of 693nm standard polystyrene latex particles by using a non-Gaussian autocorrelation function-based ultra-low concentration dynamic light scattering inversion method under different particle concentrations.
Detailed Description
Fig. 1 to 9 are preferred embodiments of the present invention, and the present invention will be further described with reference to fig. 1 to 9.
As shown in fig. 1, the ultra-low concentration dynamic light scattering inversion method based on the non-gaussian autocorrelation function includes the following steps:
when DLS is applied to ultra low concentration systems, only a small number of particles diffuse within the scatterer and the measured fluctuations in scattered light intensity 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 fringe field is no longer Gaussian, and the light intensity ACFg (2) (τ) and electric field ACFg (1) (τ) the Siegert relationship is no longer satisfied and the light-intensity ACF contains non-Gaussian terms caused by fluctuations in the number of particles
Wherein the content of the first and second substances,
and
respectively a diffuse component and a magnitude-fluctuating component. g (1) (τ)＝exp(-Γτ)，Γ＝Dq 2 Is the attenuation line width, D is the translational diffusion coefficient, q is the scattering vector, beta is the coherence factor, tau is the delay time,<N>is the average number of particles in the scatterer, w 0 For focusing the beam waist radius of the laser beam, a is the detector receiving aperture radius, γ @<N>Is the magnitude of the non-gaussian term.<N>Below 100, the non-Gaussian terms are not negligible.
In the fitting process, according to equation (1), the objective function of the fitting is set as:
wherein, C NG Is not a Gaussian term magnitude gamma<N>The fitting parameters of (1). Pick the magnitude γ of a non-Gaussian term<N>Set as fitting parameter C NG The reason for this is that the amplitude cannot be determined by γ @ina limited measurement time<N>And (4) calculating.
The parameters beta, gamma and C in the formula (2) NG Is important physical information hidden in the measured data, and the three unknown parameters can be obtained from the measured data g (2) (τ) is obtained by a non-linear least squares fit using the Levenberg-Marquardt (L-M) algorithm. Because the L-M algorithm has the advantages of a gradient method and a Newton method, has low requirement on initial values, can search for a global optimal solution from any initial value, and randomly selects beta, gamma and C NG ]＝[1,100,0.5]As initial values for the fit.
In order to verify the applicability of the L-M algorithm to the light intensity ACF data under ultra-low concentration, the L-M algorithm is adopted to perform nonlinear least square fitting on the simulated light intensity ACF data of the 200nm single-peak PSD, and the fitting result is analyzed. The simulated PSD adopts log normal distribution, and the expression is as follows:
wherein d and f (d) are the particle size and the distribution thereof, respectively, d 1 Is the nominal diameter, σ, of the particle 1 The corresponding standard deviation.
The simulation experiment conditions are as follows: the wavelength of incident light is 532nm, the simulated 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, viscosity coefficient of the dispersion medium is 0.89X 10 -3 cP, scattering angle 90 °, β ═ 0.7, w 0 54um and 200 um. Get<N>Three particle concentrations of 5, 10 and 50. The simulated ACF and the fitted ACF of the 200nm particle system are shown in FIG. 2, in which the curve represented by the solid line is the fitted ACF. The values of the fitting parameters and the corresponding fitting errors are shown in table 1, with the subscripts true and fit representing the true and fitting values, respectively, and the error E ═ true-fit |/true.
Table 1200 nm particle system simulation ACF fitting parameter values and corresponding fitting errors
FIG. 2 and Table 1 show that the L-M algorithm can well fit the light intensity ACF data under ultra-low concentration and obtain relatively accurate fitting parameter values. Wherein beta and C NG The fitting value of (2) is closer to the true value, the fitting errors are all within 3 per mill, and the particle concentration is within the range<N>When equal to 50, C NG The fitting value of (b) is equal to the true value.
determining a focused laser beam waist radius w 0 Is given an initial value of w 0 54um, this initial value is determined by the experimental setup. The step length is adjusted to be l ═ 0.1 um. Selectively adjusting the beam waist radius w of the focused laser beam 0 The conclusion of the parameter is obtained by analyzing the non-Gaussian terms in the light intensity autocorrelation function, and the specific analysis process is as follows:
the conventional measurement time causes the distortion of the measured light intensity ACF, especially the non-Gaussian term part in the ACF, which is mainly reflected in that the amplitude of the non-Gaussian term is increased compared with the theoretical value (gamma/< N >) and the attenuation delay time is greatly shortened compared with the theoretical attenuation delay time.
In step 1001, the focused laser beam waist radius w in the objective function 0 And the value of the radius a of the receiver hole of the detector all influence the attenuation rate of a non-Gaussian term, and the smaller the value is, the faster the attenuation rate is and the shorter the attenuation delay time is. As can be seen by analyzing the non-gaussian terms,
the component is dominant in the non-Gaussian terms, the parameter w 0 The influence of the change in (c) on the decay characteristic time of the non-gaussian term is more significant. Reducing the parameter w 0 The value can reduce the decay delay time of the non-Gaussian term, namely, the problem that the decay delay time of the non-Gaussian term is greatly shortened compared with the theoretical decay delay time due to the conventional measurement time can be solved. Thus, the tuning parameter w is selected 0 And correcting the non-Gaussian term by the value to realize the coincidence of the theoretical non-Gaussian ACF model and the measured data.
autocorrelation function g of the measured scattered light intensity using Levenberg-Marquardt (L-M) algorithm (2) (tau) fitting a non-linear least squares curve to obtain a fitted light intensity autocorrelation function
And the Root Mean Square Error (RMSE) of the optical strength ACF is obtained.
First, at parameter w 0 At a value of 54um (determined by the experimental setup), the measured data was fitted using the L-M algorithm. The particle diameter is 203nm, and the average particle number is<N>For the example of 35 polystyrene latex suspension, the measured ACF data and the corresponding fitted curve are shown in fig. 3. It is clear that the brownian motion attenuation fit in the ACF was found to be good, while the magnitude ripple attenuation fit did not.
Then, the parameter w is decreased 0 Selecting a parameter w 0 27um, 10um, 5um, 2.5um and 0.5 um. FIG. 4 shows measured ACF data at different w 0 The fitting ACF obtained by the L-M algorithm under the value taking is shown in FIG. 4, and the parameter w in the fitting objective function 0 The value of (b) plays an important role in curve fitting. With parameter w 0 And the delay time of the quantity fluctuation attenuation section is shortened by reducing the value, and the obtained fitting curve is closer to the actually measured data. However, with w 0 Parameter w is too small compared to 2.5um 0 The fitting effect given by 0.5um is worse and fitting distortion occurs even in the brownian motion attenuation section.
In the present application, to select the beam waist radius w of the focused laser beam 0 Correcting the non-Gaussian correlation model, and introducing Root Mean Square Error (RMSE) of the light intensity ACF to measure the quality of the fitting effect, wherein the expression of the Root Mean Square Error (RMSE) is as follows:
in the formula (I), the compound is shown in the specification,
and g (2) (τ) represents the fitted light intensity ACF and the measured light intensity ACF, respectively. Smaller RMSE indicates that the fitted curve is closer to the measured data.
the RMSE of the light intensity autocorrelation function obtained in the step 1003 is stored and is saved to the RMSE i Then according to the preset step length (l ═ 0.1um), and focal laser beam waist radius w 0 Perform accumulation to adjust w 0 The values, namely: w is a 0 ＝w 0 +l。
determining the beam waist radius w of the focused laser beam 0 Whether or not it is less than or equal to 0.1um, i.e. w 0 Less than or equal to 0.1um, if the focused laser beam has a beam waist radius w 0 If the sum is more than 0.1um, returning to the step 1003, and sequentially executing the steps 1003-1004; if the focused laser beam has a beam waist radius w 0 Satisfy w 0 And if not more than 0.1um, executing the step 1006.
from the plurality of RMSEs saved in step 1004 i And selecting the minimum value from the values as the minimum value of the root mean square error of the light intensity autocorrelation function.
With parameter w 0 The RMSE changes in a V shape when the value is reduced. Calculates parameter w 0 The RMSE of the light intensity ACF when the value is 0.5um to 5um, and the calculation result is shown in FIG. 5. It can be seen that with w 0 The root mean square error is reduced first and then increased, the minimum root mean square error corresponds to the optimal fitting curve, and the optimal fitting curve is matched with the actually measured data. On the basis, the method for determining the optimal w by using the minimum root mean square error of the optical intensity ACF is provided 0 According to the criteria of
In the formula (I), the compound is shown in the specification,
and g (2) (τ) represents the fitted light intensity ACF and the measured light intensity ACF, respectively.
in step 1006, the minimum value of the root mean square error of the autocorrelation function of the intensity is obtained, which corresponds to the beam waist radius w of the focused laser beam 0 The value is the optimum w 0 The value is obtained. Optimum w 0 The theoretical ACF model corresponding to the value is a non-Gaussian correlation model corrected according to the actually measured data, and the fitting values beta, gamma and C at the moment NG Closer to the actual measurement situation.
And calculating an equivalent electric field autocorrelation function, and reconstructing a kernel matrix of an inversion equation based on the modified non-Gaussian ACF model.
The ideal method for accurately acquiring the PSD is to directly analyze the non-Gaussian intensity ACF to establish the equivalent electric field ACF
And PSD, which can be realized by reconstructing kernel functions of the inversion equations. The discrete form of the equivalent electric field ACF can be written as:
wherein, tau j The delay time (j is more than or equal to 1 and less than or equal to M) corresponding to the jth channel of the photon correlator, f (d) i ) (i ═ 1,2,3, … …, K) is a discrete PSD, n 0 Refractive index of the suspending medium, k B Is Boltzmann constant, T is absolute temperature, eta is viscosity coefficient of dispersion medium, d is scattering particle diameter, q is scattering vector, lambda 0 θ is the scattering angle, which is the wavelength of the incident beam in vacuum.
Reconstructed kernel matrix A R From the element A R (j, i) composition:
the formula (6) can be simplified into
g e ＝A R f (8)
In the formula, g e Is a vector composed of equivalent electric field ACF data, the elements of which are
f is a vector consisting of discrete PSDs whose elements are f (d) i )。
the PSD is solved by adopting a constraint Tikhonov regularization method, which is as follows:
M α (f)＝||A R f-g e || 2 +α||Lf|| 2 s.t. f≥0 (9)
wherein M, α, L, | | · | | and | | | Lf | | 2 Respectively a stable functional, a regular parameter, a regular matrix, a Euclidean norm and a penalty factor. The stability and accuracy of the alpha control solution can be determined by the L curve criterion. And considering the smoothness of the PSD, the second-order difference matrix is selected as the regular matrix.
The ultra-low concentration dynamic light scattering inversion method based on the non-Gaussian autocorrelation function is evaluated by combining the actually measured data.
To evaluate whether the proposed method can improve inversion performance, it is compared with a conventional Kernel Function Reconstruction (KFR) method. Particle size measurements were performed on two different types of latex suspensions using standard polystyrene latex particles with average diameters of 203 + -5 nm (Duke Scientific,3200A) and 693 + -10 nm (GBW (E)120087), respectively, and a volume fraction of the raw latex suspension of 1.05%, and the raw latex suspension was diluted with distilled water to prepare two sets of samples with different particle concentrations, as shown in Table 2. The measurement time for all samples was 120 s.
TABLE 2 volume fraction of sample and corresponding particle number
PSD inversion is respectively carried out on the measured data by adopting a conventional kernel function reconstruction method and the proposed method, and the results are shown in FIGS. 6-9. The corresponding performance index is 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 The true peak particle size and the peak particle size obtained by inversion are respectively. At Normal Concentration (NC), the recovered PSD is also shown in FIGS. 6-9, with peak positions of 201nm and 698nm, respectively, and corresponding E p 0.010 and 0.007 respectively.
TABLE 3203 nm and 693nm Standard polystyrene latex particles PSD Performance index
As can be seen from fig. 6 to 9 and table 3, under the same particle concentration, the distribution obtained by the conventional kernel function reconstruction method is seriously deviated from the true value, and the inversion result of the proposed method is significantly improved and is similar to that of the conventional concentration measurement. In addition, for two groups of unimodal particle systems of 203nm and 693nm, under all particle concentrations, the peak values of inversion results obtained by the method are 201nm and 698nm respectively, and the corresponding peak value position relative errors are as low as 0.010 and 0.007 respectively, which are completely consistent with the errors of the inversion results of conventional concentration measurement.
Therefore, the optimal beam waist radius value of the focused laser beam is selected according to the minimum value of the root mean square error of the light intensity autocorrelation function to correct the theoretical model of the non-Gaussian autocorrelation function, and the method can adapt to the correction of actually measured data under different low particle concentrations. Based on the modified non-Gaussian autocorrelation function model, a kernel function is reconstructed, a kernel matrix matched with the measured data is obtained, the inversion deviation of particle size distribution caused by the distortion of the correlation function is overcome, the inversion precision is improved, an inversion result without obvious difference with the conventional concentration measurement is obtained, and the measurement range of the dynamic light scattering is enlarged.
The foregoing is directed to preferred embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope of the technical solution of the present invention.
Claims (4)
1. The ultra-low concentration dynamic light scattering inversion method based on the non-Gaussian autocorrelation function is characterized by comprising the following steps: the method comprises the following steps:
step 1001, setting a fitting objective function and a fitting initial value;
step 1002, determining an adjustment range of the beam waist radius of a focused laser beam;
step 1003, fitting the measured light intensity autocorrelation function g (2) (tau) obtaining a fitted light intensity autocorrelation function
And solving the root mean square error of the light intensity autocorrelation function;
step 1004, storing the root mean square error of the light intensity autocorrelation function, and increasing the beam waist radius of the focused laser beam according to the step length;
step 1005, determining the beam waist radius w of the focused laser beam 0 If it is less than or equal to 0.1um, if the focused laser beam has a beam waist radius w 0 If the sum is more than 0.1um, returning to the step 1003, and sequentially executing the steps 1003-1004; if the focused laser beam has a beam waist radius w 0 Satisfy w 0 If the sum is less than or equal to 0.1um, executing step 1006;
step 1006, obtaining a minimum value of the root mean square error of the light intensity autocorrelation function;
step 1007, obtaining the beam waist radius w of the focused laser beam corresponding to the minimum value of the root mean square error 0 And correcting the theoretical model of the non-Gaussian light intensity autocorrelation function by using the optimal value;
step 1008, calculating an equivalent electric field autocorrelation function, and reconstructing a kernel matrix of an inversion equation based on the corrected autocorrelation function model;
step 1009, find the particle size distribution by inverting the equivalent electric field autocorrelation function.
2. The ultra-low concentration dynamic light scattering inversion method based on non-gaussian autocorrelation function as claimed in claim 1, wherein: in step 1006, the minimum value of the light intensity autocorrelation function root mean square error RMSE is expressed as
Wherein the content of the first and second substances,
and g (2) (τ) representing the fitted and measured light intensity autocorrelation functions, τ j The delay time corresponding to the jth channel of the photon correlator (j is more than or equal to 1 and less than or equal to M).
3. The ultra-low concentration dynamic light scattering inversion method based on non-gaussian autocorrelation function as claimed in claim 1, wherein: in step 1001, the fitting objective function is:
wherein beta is a coherence factor, tau is a delay time, gamma is an attenuation line width, q is a scattering vector, w 0 For focusing the beam waist radius of the laser beam, a is the detector receiving aperture radius, C NG Is not a Gaussian term magnitude gamma<N>The fitting parameters of (1).
4. The ultra-low concentration dynamic light scattering inversion method based on non-gaussian autocorrelation function as claimed in claim 1, wherein: in step 1003, a Levenberg-Marquard algorithm is used to apply an autocorrelation function g to the measured scattered light intensity (2) (tau) fitting a non-linear least squares curve to obtain a fitted light intensity autocorrelation function
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