CN113466092B - Root mean square error threshold method for determining optimal cut-off position of autocorrelation function - Google Patents
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Abstract
A root mean square error threshold method for determining the optimal cut-off position of an autocorrelation function belongs to the technical field of photon correlation spectroscopy. The method is characterized in that: the method comprises the following steps: step 1001, collecting scattered light intensity and calculating an autocorrelation function; step 1002, cutting off the electric field autocorrelation function at the 0.1 position; step 1003, inverting the particle size distribution; step 1004, calculating the root mean square error of the electric field autocorrelation function; step 1005, determining an electric field autocorrelation function root mean square error E RMS Whether greater than 0.0035; step 1006, reducing the number of electric field autocorrelation function points; step 1007, outputting the final result. In the root mean square error threshold method for determining the optimal cut-off position of the autocorrelation function, the optimal cut-off position of the autocorrelation function is selected by the root mean square error threshold method of the autocorrelation function, so that the method can adapt to measurement of particles with different sizes, has certain adaptability to the noise level of the autocorrelation function, and improves the accuracy and repeatability of inversion results.
Description
Technical Field
A root mean square error threshold method for determining the optimal cut-off position of an autocorrelation function belongs to the technical field of photon correlation spectroscopy.
Background
The photon correlation spectroscopy technology is to calculate an autocorrelation function by collecting scattered light intensity of nano particles and then invert to obtain particle size distribution, wherein the inversion process is solving of an unsuitable equation, and belongs to a disease state problem, namely, a tiny deviation of original data can cause huge difference of inversion results, and although various algorithms are proposed at present, the inversion problem is not solved well.
In the inversion process, the related function data of different points can influence the inversion result. Experimental data shows that the correlation function attenuated to the base line contains more noise, so that the inversion process contains more correlation function points, and an accurate particle size distribution result cannot be obtained. However, when the number of the related function points is small, the information of the sample is lost, and deviation of the inversion result is caused. The selection of the correlation function points depends on the size of the measured particles and the precision of the correlation function obtained by measurement, so that the key for improving the accuracy of the inversion result is how to determine the interception position of the correlation function, and the optimal correlation function points are selected.
In practical application, a fixed correlation function point number or a fixed correlation function threshold (FACFT) method is generally adopted to select the correlation function point number for inversion, but both methods cannot give consideration to the measured particle size and the correlation function precision.
The method for fixing the correlation function points does not consider the difference of the tested samples, and inversion is carried out by adopting the same correlation function points. However, in order to avoid introducing noise near the correlation function baseline, the correlation function points involved in the inversion cannot be excessive. Meanwhile, the correlation function of the small particles has faster attenuation, the correlation function of the large particles has slower attenuation, and the correlation function of the small particles has more points, so that the method for fixing the points of the correlation function cannot consider the samples of the large particles and the small particles, has poor adaptability and has poor inversion result.
And a method for fixing a correlation function threshold, cutting off the correlation function at a position where the correlation function value is smaller than the threshold, and inverting the particle size distribution by using the obtained correlation function data. However, under different noise levels, the number of the correlation function points selected by the method is basically the same, so the method has no self-adaptive capability and cannot select the number of the correlation function points according to the noise size of the correlation function.
It can be seen that, in both the fixed correlation function point number and the fixed correlation function threshold, the correlation function point number cannot be selected according to the measured particle size and the correlation function noise level. Therefore, designing a method for cutting off the noise of the correlation function and considering the size of the measured particles, selecting the number of the optimal correlation function points to obtain more accurate particle size distribution becomes a technical problem to be solved in the art.
Disclosure of Invention
The invention aims to solve the technical problems that: the root mean square error threshold method for determining the optimal cut-off position of the autocorrelation function, which can adapt to the measurement of particles with different sizes, has certain adaptability to the noise level of the correlation function, and improves the accuracy and repeatability of the inversion result, is provided.
The technical scheme adopted for solving the technical problems is as follows: the root mean square error threshold method for determining the optimal cut-off position of the autocorrelation function is characterized by comprising the following steps of: the method comprises the following steps:
Preferably, in step 1005, the preset threshold is 0.0035.
Preferably, in step 1005, the autocorrelation function root mean square error E RMS The calculation formula of (2) is as follows:
wherein,,
the j-th point, g, representing the fitting value of the electric field autocorrelation function (1) (τ j ) The j-th point of the electric field autocorrelation function measurement is represented.
Preferably, in said step 1001, the light intensity auto-correlation function g (2) Measurement g of (tau) and electric field autocorrelation function (1) (τ) satisfies the following relationship:
g (2) (τ)＝1+β|g (1) (τ)| 2
where τ represents the delay time and β represents the intercept of the correlation function.
Compared with the prior art, the invention has the following beneficial effects:
in the root mean square error threshold method for determining the optimal cut-off position of the autocorrelation function, the root mean square error threshold method of the correlation function is provided as a method for selecting the number of points of the optimal correlation function, the optimal cut-off position of the correlation function is selected through the root mean square error threshold method of the correlation function, the method can adapt to measurement of particles with different sizes, has certain adaptability to the noise level of the correlation function, and improves the accuracy and repeatability of inversion results. The method is not only suitable for unimodal distribution samples, but also suitable for bimodal distribution samples.
Drawings
FIG. 1 is a flowchart of a method for determining the root mean square error threshold of the optimal cut-off position of an autocorrelation function.
FIG. 2 is a graph of root mean square error values of correlation functions fitted at different points for a 30nm sample.
FIG. 3 is a graph of root mean square error values of correlation functions fitted at different points for 200nm samples.
FIG. 4 is a graph of root mean square error values of correlation functions fitted at different points for 550nm samples.
Fig. 5 is a plot of the truncated position of the correlation function at a noise level of 0.01.
Fig. 6 is a plot of the truncated position of the correlation function at a noise level of 0.04.
Fig. 7 is a plot of the truncated position of the correlation function at a noise level of 0.08.
Fig. 8 is a graph of root mean square error of the correlation function points you and the correlation function.
Detailed Description
FIGS. 1-8 illustrate preferred embodiments of the present invention, and the present invention will be further described with reference to FIGS. 1-8.
As shown in fig. 1, a root mean square error threshold method (RMSET) for determining an optimal cut-off position of an autocorrelation function includes the steps of:
the scattered light intensity of the nano particles is acquired through experimental equipment, and the light intensity autocorrelation function g is calculated (2) (τ) the intensity autocorrelation function g in the case of a scattered light field with Gaussian statistics (2) (tau) and an electric field autocorrelation function g (1) The measured value of (τ) satisfies the following relationship:
g (2) (τ)＝1+β|g (1) (τ)| 2
where τ represents the delay time, β represents the intercept of the correlation function, g (2) (τ) is a measurement of the experimentally measured autocorrelation function of the light intensity. Through the relation, the electric field autocorrelation function g is further calculated (1) A measurement of (τ).
in the vicinity of the baseline value of the long delay phase, the electric field correlation function has a large noise, so that it is necessary to remove the value in the vicinity of the baseline value of the electric field autocorrelation function in advance, in this embodiment, in the electric field correlationThe function being a truncated electric field autocorrelation function at 0.1, i.e. retaining g (1) (τ). Gtoreq.0.1.
autocorrelation function g for electric field truncated at 0.1 (1) (tau) inverting to obtain particle size distribution PSD;
fitting the particle size distribution PSD to obtain fitting value of the electric field autocorrelation function
Fitting value of the electric field autocorrelation function>
Electric field autocorrelation function g (1) Substituting the measured value of (tau) into the following formula to calculate and obtain the root mean square error E of the electric field autocorrelation function RMS ：
Wherein,,
the j-th point, g, representing the fitting value of the electric field autocorrelation function (1) (τ j ) The j-th point of the electric field autocorrelation function measurement is represented.
determining the root mean square error E of the electric field autocorrelation function RMS Whether or not it is greater than 0.0035, if E RMS Greater than 0.0035, step 1007 is performed if E RMS Less than or equal to 0.0035, step 1006 is performed;
the electric field is subjected to an autocorrelation function g (1) (τ) reduce one data point, return to execution step 1003;
and outputting the PSD obtained by inversion in the step 1003 as a final result.
The root mean square error threshold method for determining the optimal cut-off position of the autocorrelation function is further described below with reference to actual test data:
according to the correlation function root mean square error threshold method taking the fitting error of the correlation function as a judgment basis, the optimal correlation function point number is selected in a self-adaptive mode, and the accuracy of the inversion result is improved.
The correlation function is an exponential decay curve, the position of the curve beginning to decay indicates the average particle size of the sample, the gradient of the curve drop indicates the polydisperse characteristic of the sample, and the short delay area of the curve drop contains a large amount of information of the measured particles, so that the correlation function data of the short delay area should be kept as much as possible, and after the curve decays to a base line, little useful information is available. In addition, the noise near the baseline of the correlation function is far greater than the noise in the short delay stage, and particularly after the conversion into the electric field autocorrelation function, the noise is more remarkable. The particle size distribution is exactly inverted from the electric field autocorrelation function.
Inverting the correlation function to obtain a fitted correlation function, the degree of deviation between the fitted correlation function and the correlation function is generally measured by the magnitude of the fitting error of the correlation function, i.e. the root mean square error E obtained by the above formula RMS To characterize the correlation function fitting error. If the data noise level of the correlation function is low, the fitting correlation function and the correlation function can be well overlapped, so E RMS The value of (2) is relatively small; if a large amount of noise exists in the correlation function data, the fitting error of the correlation function is increased under the influence of the noise, and E is caused RMS Greatly increases.
From the distribution of noise in the correlation function: the noise of the short delay area with the declining correlation function curve is small, the noise near the baseline of the correlation function is large and is far larger than the noise of the short delay area, and E is known RMS The change of the curve with the number of points of the correlation function can be divided into two phases: first stage correlation function noise waterLeveling down, stage E RMS Slowly growing; the second stage of correlation function has high noise level, stage E RMS And grow rapidly. FIGS. 2-4 show 6 sets of measurement data for 3 samples, the root mean square error value E of the fitted correlation function obtained by inversion at different correlation function points RMS The law of variation thereof corresponds to the description above.
E RMS The trend of increasing points with the correlation function can be divided into two phases, once E RMS The rapid increase indicates that the noise contained in the correlation function data increases and the data reliability decreases, so E will RMS The rapidly-growing position is taken as the interception position, so that the number of points of the optimal correlation function can be effectively selected, and the influence of noise near a base line on an inversion result is avoided. FIGS. 2-4 show E for different samples at different correlation function points RMS Curve, E in the figure RMS The rapidly growing positions of the curves are all below 0.0035, and in order to avoid introducing more correlation function noise and utilize effective data of the correlation function as much as possible, the application provides a root mean square error threshold method of the correlation function as a method for selecting the number of points of the optimal correlation function, namely 0.0035 is used as E RMS Threshold value E RMS And the maximum point number is the optimal correlation function inversion point number in the correlation function point numbers corresponding to less than 0.0035. As can also be seen from FIGS. 2-4, E RMS The number of correlation function points corresponding to =0.0035 can increase as the measured particles increase.
The "triangle" marks in fig. 5-7 are positions selected by RMSET method, and at noise levels of 0.01, 0.04 and 0.08, the number of selected correlation function points is 96, 88 and 84, respectively, and the number of selected points is related to the noise level of the correlation function. The number of selection points with low noise level is more, and the number of selection points with high noise level is less. The RMSET method has a certain noise adaptation capability. As can be observed from fig. 5 to 7, the interception position of the FACFT method does not change much, and the interception position of the RMSET method changes with the noise variation of the correlation function.
The 3 samples in fig. 2 to 4 are subjected to 60 experimental measurements, and inversion is performed by using an RMSET method and a FACFT method, and the results show that the particle size distribution norm and the particle size fluctuation of the inversion result of the RMSET method are relatively small, so that the stability and the repeatability of the measurement result of the RMSET method are superior to those of the FACFT method.
FIG. 8 is a graph of 6 sets of correlation functions for bimodal distribution of particle samples, E at different inversion points RMS As can be seen from FIG. 8, E RMS The change rule of the values is consistent with that of the unimodal distribution particles, and E RMS The rapidly growing positions are all below 0.0035.
Therefore, the RMSET method is used for selecting the optimal interception position of the correlation function, so that the method can adapt to measurement of particles with different sizes, has certain adaptability to the noise level of the correlation function, and improves the accuracy and repeatability of an inversion result. The method is not only suitable for unimodal distribution samples, but also suitable for bimodal distribution samples.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the invention in any way, and any person skilled in the art may make modifications or alterations to the disclosed technical content to the equivalent embodiments. However, any simple modification, equivalent variation and variation of the above embodiments according to the technical substance of the present invention still fall within the protection scope of the technical solution of the present invention.
Claims (3)
1. A method for determining a root mean square error threshold for an optimal truncation position of an autocorrelation function, comprising: the method comprises the following steps:
step 1001, collecting scattered light intensity, and calculating to obtain a light intensity autocorrelation function g (2) (τ) and then further calculate the electric field autocorrelation function g (1) A measurement of (τ);
step 1002, deleting the point where the electric field autocorrelation function is smaller than 0.1 to obtain the truncated electric field autocorrelation function g (1) (τ)；
Step 1003, inverting the cut-off electric field autocorrelation function to obtain particle size distribution PSD;
step 1004, fitting the particle size distribution PSD to obtain a fitting value of the electric field autocorrelation function
Then calculate the root mean square error E of the electric field autocorrelation function RMS ：
Step 1005, determining an electric field autocorrelation function root mean square error E RMS Whether or not it is greater than a preset threshold, if E RMS Greater than a preset threshold, go to step 1006, if E RMS Less than or equal to a preset threshold, step 1007 is performed;
step 1006, the electric field autocorrelation function g (1) (τ) reduce one data point, return to execution step 1003;
step 1007, outputting the PSD obtained by inversion in step 1003 as a final result;
in step 1005, the predetermined threshold is 0.0035.
2. The method for determining an rms error threshold value of an optimal cutoff location for an autocorrelation function according to claim 1, wherein: in step 1005, the autocorrelation function root mean square error E RMS The calculation formula of (2) is as follows:
wherein,,
the j-th point, g, representing the fitting value of the electric field autocorrelation function (1) (τ j ) The j-th point of the electric field autocorrelation function measurement is represented.
3. The method for determining an rms error threshold value of an optimal cutoff location for an autocorrelation function according to claim 1, wherein: in said step 1001, the light intensity autocorrelation function g (2) (tau) and an electric field autocorrelation function g (1) The measured value of (τ) satisfies the following relationship:
g (2) (τ)＝1+β|g (1) (τ)| 2
where τ represents the delay time and β represents the intercept of the correlation function.
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