CN113654957A - Background interference elimination method based on baseline deduction - Google Patents
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Abstract
The invention provides a background interference elimination method based on baseline deduction, which comprises the following steps: step 1, firstly, obtaining a corrected sample scattered light energy distribution E by adopting a direct subtraction method; step 2, fitting a base line L of the E by using an asymmetric least square method; and 3, further correcting the scattered light energy distribution E of the sample by using the base line L to obtain a more accurate light scattering signal map, and providing an effective means for accurately measuring the particle size by a static light scattering method.
Description
Technical Field
The invention belongs to the fields of resources, environment and oceans, and particularly relates to a static light scattering signal background interference elimination method based on baseline subtraction.
Background
The suspended particles in the water body can deteriorate the water quality, prevent the self-purification of the water body and cause damage to fishes, and the particle size of the suspended particles is generally between several and hundreds of microns. Therefore, the automatic online measurement of the particle size of the suspended particles in the water body is carried out, and the method plays a crucial role in water environment protection. Currently, laser scattering technology is a relatively mature and widely used particle size measurement technology. The laser scattering technology generally adopts an annular photoelectric detector to detect a sample light scattering signal spectrum, but the annular photoelectric detector has the problems of complex process, high cost, alignment before measurement and the like. The CMOS detector can effectively solve the above problems, and thus, has become a new trend in the research of laser particle sizer. Due to the influence of factors such as the quality of a spatial filter and an optical element, the pollution of dust on the optical surface and the like, when the particle sample is measured by adopting a laser scattering technology, the background interference is inevitable. Therefore, to obtain an accurate sample light scattering signal profile, it is necessary to eliminate background interference. Background interference cancellation (hereinafter referred to as direct subtraction) is usually performed by subtracting the background light signal from the sample light scattering signal. However, when the CMOS detector adopts the direct subtraction method to eliminate the background interference, the optical energy information still has a large error in a small scattering angle region, and therefore, the spectrum needs to be further corrected.
Disclosure of Invention
Aiming at the problem that when a CMOS detector adopts a direct subtraction method to eliminate background interference, light energy information still has larger errors in a small scattering angle region, the invention provides a background interference elimination method based on base line subtraction.
The technical scheme of the invention is as follows: a background interference elimination method based on baseline subtraction specifically comprises the following steps: a background interference elimination method based on baseline subtraction comprises the following steps:
step 1, firstly, obtaining a corrected sample scattered light energy distribution E by adopting a direct subtraction method;
and 3, further correcting the scattered light energy distribution E of the sample by using the base line L to obtain a more accurate light scattering signal map.
Further, in the step 1, firstly, the corrected scattered light energy distribution E of the sample is obtained by adopting a direct subtraction method, which specifically comprises the following steps:
firstly, pure water is added into a sample cell as a control group, and a background light energy distribution graph E is measuredb(ii) a Adding samples to be detected in the sample cell respectively to obtain a sample scattered light energy distribution graph Es(ii) a From Es-EbGet the optical energy profile E.
Further, in the step 2, a baseline L of the luminous energy distribution graph E is fitted by using an asymmetric least square method; the method comprises the following specific steps:
fitting a light energy distribution baseline Ltarget by using an asymmetric least square algorithm as shown in formula (1):
wherein, wiIs a weight factor, delta is a second order difference operator, and lambda is a compromise factor; e and L are column vectors, i represents the corner mark of the element in the column vector; the first term represents the degree of asymmetric fit of the baseline to the light energy distribution(ii) a The second term is to ensure the smoothness of the baseline, and the compromise factor λ serves to balance the asymmetric approximation with the smoothness.
Minimizing equation (1) to obtain an equation system:
(W+λDTD)L＝WE (2)
where W is a diagonal matrix composed of vectors W, i.e., W ═ diag (W), and D is a matrix of second derivative fitted to the baseline L, i.e., DL ═ Δ ═2L; solving to obtain an estimated baseline:
L＝(W+λDTD)-1WE (3)
and fitting to obtain the optical energy distribution baseline L according to the asymmetric least square algorithm.
Further, in the step 3, the sample scattered light energy distribution E is further corrected by using the baseline L to obtain a more accurate light scattering signal spectrum, specifically, by subtracting the baseline, that is:
E'＝E-L
obtaining a sample light scattering signal spectrum E'.
Has the advantages that:
according to the background interference elimination method based on baseline subtraction, firstly, direct subtraction is adopted to obtain the scattering light energy distribution of a corrected sample, then, an asymmetric least square method is used for fitting the baseline of the light energy distribution, and finally, the scattering light energy distribution of the sample is further corrected by utilizing the baseline to obtain a more accurate light scattering signal map, so that an effective means is provided for the accurate measurement of the particle size by a static light scattering method.
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FIG. 1: testing a 120-micron standard sample, and analyzing a test result by using a light energy distribution curve;
FIG. 2: 120 μm standard inversion results: (a) the background is not eliminated; (b) eliminating background by direct subtraction; (c) eliminating background by a baseline method;
FIG. 3: the invention discloses a background interference elimination method based on baseline subtraction.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments, and all other embodiments obtained by a person skilled in the art based on the embodiments of the present invention belong to the protection scope of the present invention without creative efforts.
According to an embodiment of the present invention, a background interference elimination method based on baseline subtraction for particle size measurement of suspended particles in water by using a static light scattering method is provided, as shown in fig. 3, specifically including the following steps:
step 1, firstly, obtaining a corrected sample scattered light energy distribution E by adopting a direct subtraction method;
and 3, further correcting the scattered light energy distribution E of the sample by using the base line L to obtain a more accurate light scattering signal map.
According to an embodiment of the present invention, in step 1, a direct subtraction method is first adopted to obtain a corrected scattered light energy distribution E of the sample, which is specifically as follows:
firstly, pure water is added into a sample cell as a control group, and a background light energy distribution graph E is measuredb(ii) a Adding samples to be detected in the sample cell respectively to obtain a sample scattered light energy distribution graph Es(ii) a From Es-EbThe light energy distribution E is obtained.
According to an embodiment of the invention, in the step 2, a baseline L of E is fitted by using an asymmetric least square method; the method comprises the following specific steps:
fitting a light energy distribution baseline Ltarget by using an asymmetric least square algorithm as shown in formula (1):
wherein, wiIs a weight factor, delta is a second order difference operator, and lambda is a compromise factor; e and L are column vectors, i represents the corner mark of the element in the column vector; the first term represents the asymmetric approximation of the baseline and the light energy distributionThe degree of synthesis; the second term is to ensure the smoothness of the baseline, and the compromise factor λ serves to balance the asymmetric approximation with the smoothness.
Minimizing equation (1) to obtain an equation system:
(W+λDTD)L＝WE (2)
bold E denotes the light energy distribution column vector, EiDenote the elements in E, the base line L is the column vector, LiAlso represents an element in L;
where W is a diagonal matrix composed of vectors W, i.e., W ═ diag (W), and D is a matrix of second derivative fitted to the baseline L, i.e., DL ═ Δ ═2And L. Solving to obtain an estimated baseline:
L＝(W+λDTD)-1WE (3)
and fitting to obtain the optical energy distribution baseline L according to the asymmetric least square algorithm.
According to an embodiment, in step 3, the sample scattered light energy distribution E is further corrected by using the baseline L to obtain a more accurate light scattering signal spectrum, specifically, by subtracting the baseline, the method is as follows:
E'＝E-L
obtaining a sample light scattering signal spectrum E'.
The static light scattering method for measuring the suspended particles in the water body is different from the traditional spectral analysis method. The invention innovatively applies the asymmetric least square method to the baseline fitting deduction of the static light scattering method water body suspended particle measurement, improves the measurement precision of the static light scattering method water body suspended particle, and obtains a more accurate light scattering signal map.
According to one embodiment of the present invention, the light energy distribution curve analysis test is performed using water as a medium, and the sample is a national standard sample of 120 μm (hereinafter referred to as a 120 μm standard sample) of the national academy of metrology sciences, and is made of polystyrene. By utilizing the background interference elimination method based on baseline subtraction provided by the invention, a 120-micron standard sample is tested, the analysis and test result of the light energy distribution curve is shown in figure 1, and when the background interference is not eliminated, the light energy distribution of the standard sample and water linearly rises after 6600 microns (as shown in a local graph in figure 1), which is not in accordance with the theoretical value. And (3) processing by adopting a direct subtraction method and a baseline deduction method, wherein the coincidence degree of the optical energy distribution curve obtained by the baseline deduction method and the Mie scattering theoretical model is higher than that of the optical energy distribution curve obtained by the direct subtraction method.
According to one embodiment of the present invention, a particle size distribution curve test is performed, and the particle size inversion results of 120 μm standards are shown in FIG. 2. The red line in FIG. 2 shows the cumulative percent inversion results for the 120 μm standard. As can be seen, when the background interference is not eliminated, the cumulative percentage of the 120 μm standard sample increases significantly from 5 μm to 100 μm and from 180 μm to 500 μm, which does not meet the trend of the cumulative percentage of the single-particle-size sample increasing stepwise. After the direct subtraction method is adopted to eliminate background interference, the inversion result of the 120 mu m standard sample is obviously increased from 30 mu m to 64 mu m accumulation percentage, and the trend that the accumulation percentage of a single-particle-size sample is increased in a step mode is not met. After background interference is eliminated by adopting a baseline deduction method, the cumulative percentage of the standard sample with the particle size of 120 mu m obviously rises from 110 mu m to 126 mu m and is gradually gentle, and the cumulative percentage of the standard sample with the particle size of single particle is in accordance with the distribution of step-type increase of the cumulative percentage of the sample with the single particle size.
The darkest color curve in FIG. 2 shows the inversion of the 120 μm percent standard particle size. (a) As background is not eliminated; (b) background is eliminated for direct subtraction; (c) background is eliminated for the baseline method; the half height width of the peak of the particle size percentage was 30 μm without eliminating the background interference. After eliminating background interference by adopting a direct subtraction method, the half-height width of the peak of the particle size percentage is 40 mu m. After background interference is eliminated by adopting a baseline deduction method, the peak half-height width of the particle size percentage is 15 mu m. The half-height width of the grain size percentage obtained by the baseline deduction method is narrow, and the grain size distribution of a single grain size sample is better met.
According to one embodiment of the invention, a particle size distribution parameter test was performed, the parameters characterizing the particle size distribution being D10, D50, D90 and Dmax. D represents the diameter of the powder particles, Dx represents the corresponding particle diameter when the cumulative particle size distribution percentage of the sample reaches x%, and Dmax represents the highest particle diameter. And (4) counting the particle size distribution parameters of the sample to be detected according to the particle size inversion result, wherein the result is shown in table 1. As can be seen from Table 1, the relative error between D10 and D90 is above 70% when the background interference is not eliminated. After the direct subtraction method eliminates background interference, the relative errors of D50, D90 and Dmax in the inversion result are small, but the error of D10 is still as high as 61.2%. After background interference is eliminated by the baseline deduction method, the maximum error of the inversion result does not exceed 10%, and the relative error of each characterization parameter of the inversion result is effectively controlled within a reasonable range.
Table 1120 μm Standard sample size inversion results
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, but various changes may be apparent to those skilled in the art, and it is intended that all inventive concepts utilizing the inventive concepts set forth herein be protected without departing from the spirit and scope of the present invention as defined and limited by the appended claims.
Claims (4)
1. A background interference elimination method based on baseline subtraction is characterized by comprising the following steps:
step 1, firstly, obtaining a corrected sample scattered light energy distribution E by adopting a direct subtraction method;
step 2, fitting a base line L of the E by using an asymmetric least square method;
and 3, further correcting the scattered light energy distribution E of the sample by using the base line L to obtain a more accurate light scattering signal map.
2. The method for eliminating background interference based on baseline subtraction according to claim 1, wherein step 1, the corrected sample scattered light energy distribution E is obtained by a direct subtraction method, specifically as follows:
firstly, pure water is added into a sample cell as a control group, and a background light energy distribution graph E is measuredb(ii) a Then respectively adding the sample to be tested into the sample cellObtaining a scattered light energy distribution graph E of the samples(ii) a From Es-EbGet the optical energy profile E.
3. The method for eliminating background interference based on baseline subtraction according to claim 1, wherein in the step 2, a baseline L of the luminous energy distribution graph E is fitted by using an asymmetric least square method; the method comprises the following specific steps:
fitting a light energy distribution baseline Ltarget by using an asymmetric least square algorithm as shown in formula (1):
wherein, wiIs a weight factor, delta is a second order difference operator, and lambda is a compromise factor; e and L are column vectors, i represents the corner mark of the element in the column vector; the first term represents the degree of asymmetric fit of the baseline to the light energy distribution; the second term is to ensure the smoothness of the base line, and the compromise factor lambda plays a role in balancing the asymmetric approximation degree and the smoothness;
minimizing equation (1) to obtain an equation system:
(W+λDTD)L＝WE (2)
where W is a diagonal matrix composed of vectors W, i.e., W ═ diag (W), and D is a matrix of second derivative fitted to the baseline L, i.e., DL ═ Δ ═2L; solving to obtain an estimated baseline:
L＝(W+λDTD)-1WE (3)
and fitting to obtain the optical energy distribution baseline L according to the asymmetric least square algorithm.
4. The method for eliminating background interference based on baseline subtraction according to claim 1, wherein in step 3, the sample scattered light energy distribution E is further corrected by using the baseline L to obtain a more accurate light scattering signal spectrum, specifically, by subtracting the baseline:
E'＝E-L
obtaining a sample light scattering signal spectrum E'.
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