Solution cathode glow discharge spectrum detection limit improving method and system based on Abel inverse transformation

Abstract

The invention relates to the technical field of solution cathode glow discharge spectrums, and discloses a solution cathode glow discharge spectrum detection limit improving method and system based on Abel inverse transformation, and the method comprises the following steps: respectively collecting a spectral signal of a plasma transverse space of a to-be-detected element in a to-be-detected solution and a spectral signal of a blank solution; determining a plasma center position of the spectral signal of the plasma transverse space, and determining a unilateral transverse spectral intensity curve of the spectral signal of the plasma transverse space; fitting the unilateral transverse spectral intensity curve by a cubic spline function method to solve Abel inverse transformation, and obtaining a radial distribution curve of the radiance; and calculating the detection limit of the position where an extreme point appears in the radial distribution curve of the radiance, comparing the detection limit with the detection limit of the plasma center position, and taking the spectral signal acquisition position corresponding to the spectral intensity data value with the lower detection limit as the optimal acquisition area, thereby improving the detection limit of the solution cathode glow discharge element. The overall detection efficiency is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of atomic spectroscopy, in particular to a method and system for improving the detection limit of solution cathode glow discharge atomic emission spectrometry based on Abel inverse transformation. BACKGROUND

[0002] The rapid development of urban and suburban industries increases the risk of water pollution, especially heavy metal pollution, which poses a significant threat to human health and the ecological environment. Heavy metals in water can have adverse effects on the growth, reproduction, and metabolism of living organisms, leading to biological accumulation in the food chain and ultimately affecting human health and environmental quality. Residents mainly rely on groundwater as drinking water, which can lead to potential heavy metal exposure risks. Soil and water pollution by heavy metals can cause a variety of health problems, including chronic diseases, reproductive problems, and neurological diseases. Therefore, developing analytical methods for detecting heavy metals in water has always been a crucial research area.

[0003] Traditional analytical techniques, such as atomic absorption spectrometry, atomic fluorescence spectrometry, and inductively coupled plasma atomic emission spectrometry, have been widely used for heavy metal detection and have excellent analytical performance. However, these methods require expensive and bulky equipment, specific gas environments, complex experimental procedures, and suitable laboratory detection conditions. Therefore, it is necessary to develop a low-cost, simple, and portable metal detection instrument. Compared with traditional atomic spectroscopy techniques, Solution Cathode Glow Discharge-Atomic Emission Spectrometry (SCGD-AES) has many advantages, including lower cost, reduced power consumption, simplified sample preparation, smaller size, and reduced spectral interference. However, plasma parameters usually exhibit non-uniform spatial distribution during the discharge process, and the spectral intensity data obtained by line-of-sight integration may not directly reflect the true radial variation of these plasma parameters, making it difficult to obtain more accurate plasma spatial distribution to more accurately find the optimal region for collecting spectral data, thereby more accurately detecting element characteristics. Therefore, it is necessary to convert the spectral intensity data back to the original radial distribution to accurately obtain the spatial variation of the plasma. SUMMARY

[0004] The present application provides a method and system for improving the detection limit of solution cathode glow discharge atomic emission spectrometry based on Abel inverse transformation to solve the above problems.

[0005] The present application is implemented by the following technical solutions:

[0006] A method for improving the detection limit of solution cathode glow discharge atomic emission spectrometry based on Abel inverse transformation, comprising:

[0007] collecting a spectrum signal of a plasma transverse space of a to-be-tested element in a to-be-tested solution and a spectrum signal of a blank solution respectively;

[0008] determining a plasma center position of the spectrum signal of the plasma transverse space and determining a single-side transverse spectrum intensity curve of the spectrum signal of the plasma transverse space; meanwhile, obtaining a spectrum signal corresponding to the plasma center position in the blank solution as a blank solution center position and determining a single-side transverse spectrum intensity data based on the blank solution center position;

[0009] performing a cubic spline function fitting on the single-side transverse spectrum intensity curve to obtain an Abel inverse transform, thereby obtaining a radial distribution curve of radiance;

[0010] calculating a detection limit of a position of an extreme point of the radial distribution curve of radiance and comparing the detection limit with a detection limit of the plasma center position, and taking a spectrum signal collection position corresponding to a spectrum intensity data value with a lower detection limit as an optimal collection region, thereby improving an element detection limit of solution cathode glow discharge spectrum.

[0011] As an optimization, a specific process of collecting the spectrum signal of the plasma transverse space of the to-be-tested element in the to-be-tested solution is as follows:

[0012] obtaining a solution cathode glow discharge plasma between cathode rods and anode rods arranged vertically and at intervals through a solution cathode glow discharge technology;

[0013] obtaining the spectrum signal of the plasma through a light collection optical fiber structure, and moving the light collection optical fiber structure in the same vertical region between the cathode and the anode at intervals, thereby obtaining a spectrum signal of a transverse space of the plasma between the cathode and the anode.

[0014] As an optimization, a specific process of determining the single-side transverse spectrum intensity curve of the spectrum signal of the plasma transverse space is as follows:

[0015] taking an average value of a sum of left and right spectrum intensity data values as a spectrum intensity data value of a single-side corresponding position, and then preparing a curve based on the spectrum intensity data value of the single-side and a spectrum intensity data value of the plasma center position, thereby obtaining the single-side transverse spectrum intensity curve of the spectrum signal of the plasma transverse space.

[0016]

[0017] ​As optimization, the single-side transverse spectral intensity curve is subjected to cubic spline function fitting to obtain an Abel inverse transform, and a specific process for obtaining a radial distribution curve of the radiance is as follows:

[0018] The adjacent two spectral intensity data values (y i ,I i ) and (y i+1 ,I i+1 ) in the single-side transverse spectral intensity curve are approximated by a cubic polynomial, that is, I i (y) = a i0 +a i1 y+a i2 y 2 +a i3 y 3 , so as to obtain a first derivative I' i (y) and a second derivative I" i (y), wherein I' i (y) = b i +2c i y+3d i y 2 ; I" i (y) = 2c i +6d i y.

[0019] The first derivative I' i (y) and the second derivative I" i (y) are substituted into an Abel inverse transform formula , and a solution is obtained, so as to obtain the radiance E(r); r is a radial coordinate, represents a radial position of the plasma of interest, is used for describing the radial distribution of the radiance, is an integral variable related radial position parameter, R is an upper limit of integration, usually corresponds to a boundary position of a radial range of the plasma, that is, the integration is calculated from the radial position r of interest to the radial edge R of the plasma, y is an integral variable, is a variable used for representing a transverse position in the calculation related to the transverse spectral intensity curve of the plasma, and the conversion from the transverse spectrum to the radial radiance is realized by the integral operation thereof, I(y) represents a spectral intensity at the transverse position y (single-side transverse spectral intensity), is basic data obtained by previous collection and processing, and is used as an input of the Abel inverse transform for deducing the radial radiance distribution;

[0020] A radial distribution curve is drawn according to the radiance E(r).

[0021] As optimization, a calculation formula of the detection limit is as follows:

[0022]

[0023] Wherein, RSDb is the relative standard deviation of the blank solution, c is the element concentration, and SBR is the ratio of the spectral intensity data value of the measured solution to the background intensity.

[0024] The application further discloses a solution cathode glow discharge optical emission spectrum detection limit improving system based on Abel inverse transformation.

[0025] The spectrum signal acquisition module is configured to acquire the spectrum signal of the plasma transverse space of the to-be-detected element in the to-be-detected solution and the spectrum signal of the blank solution.

[0026] The data preprocessing module is configured to determine the plasma center position of the spectrum signal of the plasma transverse space and determine the one-side transverse spectrum intensity curve of the spectrum signal of the plasma transverse space.

[0027] The Abel inverse transformation module is configured to perform Abel inverse transformation on the one-side transverse spectrum intensity curve through cubic spline function fitting to obtain the radial distribution curve of the radiance.

[0028] The detection limit optimization comparison module is configured to calculate the detection limit of the position of the extreme point of the radial distribution curve of the radiance, compare the detection limit with the detection limit of the plasma center position, and take the acquisition position corresponding to the spectrum intensity data value with a lower detection limit as the optimal acquisition region, so as to improve the element detection limit of the solution cathode glow discharge optical emission spectrum.

[0029] As an optimization, the spectrum signal acquisition module comprises a peristaltic pump, a cathode rod, an anode rod, a power supply, a light receiving optical fiber structure and a spectrometer, the cathode rod and the anode rod are electrically connected to the power supply, the cathode rod is vertically arranged in a container, the container is connected to the peristaltic pump, so that the peristaltic pump draws the to-be-detected liquid or the blank solution into the container, the cathode rod is in contact with the to-be-detected liquid or the blank solution, the cathode rod and the anode rod are vertically and oppositely arranged at intervals, the light receiving optical fiber structure is located on the side of the interval between the cathode rod and the anode rod, and is configured to acquire the spectrum signal of the plasma generated between the cathode rod and the anode rod, and the light receiving optical fiber structure is connected to a computing terminal through the spectrometer.

[0030] Compared with the prior art, the application has the following advantages and beneficial effects:

[0031] Existing technologies, such as traditional atomic spectroscopy analysis methods, often require expensive and complex large-scale equipment, are cumbersome to operate, and demand highly skilled operators. In contrast, this invention's method for acquiring the spatial distribution characteristics of solution cathode glow discharge plasma based on inverse Abel transform requires relatively simple equipment, mainly consisting of solution cathode glow discharge devices and common spectral acquisition equipment, significantly reducing equipment costs. In terms of operation, the clearly defined steps, from equipment parameter adjustment to data processing, are easy to master, reducing experimental errors and time costs caused by operational complexity, and improving overall detection efficiency.

[0032] Existing technologies often struggle to accurately reconstruct the true radial distribution when processing spectral data. This invention utilizes the powerful mathematical tool of the inverse Abel transform to precisely convert spectral intensity data obtained by integrating along the line of sight into a true radial emissivity distribution. Multi-step data processing ensures the accuracy and reliability of the acquired spatial distribution characteristics. Compared to other detection methods, this approach provides a more comprehensive and detailed representation of the distribution patterns of different elements and substances within the plasma, offering more valuable data support for scientific research and practical applications.

[0033] Traditional detection methods may be ineffective when dealing with different types of solution cathode glow discharge plasmas due to equipment limitations or methodological limitations. The method of this invention has broad applicability, and can meet the needs of blank solutions with different compositions or the detection of multiple target elements by flexibly adjusting experimental parameters and analytical steps.

[0034] In existing technologies, only lateral adjustments are made to find the position of maximum spectral intensity or optimal detection limit for light collection, generally at the center position, which is the cumulative intensity of the tangent of the circle. However, the detection limit corresponding to this invention is the maximum intensity at the radial position, where elements can be detected more sensitively.

[0035] The method of this invention can obtain the radial distribution law of metal ions in the plasma excitation source, which is the true distribution law of metal ions; at the same time, by exploring the true spatial distribution law, the optimal position of the detection limit can be found, thereby improving the detection capability. Attached Figure Description

[0036] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0037] Figure 1 The flowchart is a method for improving the detection limit of solution cathode glow discharge spectroscopy based on Abel inverse transform, as described in this invention.

[0038] Figure 2This is a connection diagram of a solution cathode glow discharge spectral detection limit enhancement system based on Abel inverse transform as described in this invention.

[0039] Figure 3 This is a schematic diagram of a plasma image;

[0040] Figure 4 This is a schematic diagram illustrating the geometric interpretation of the inverse Abel transform in cylindrical symmetric plasma. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0042] Existing research indicates that plasma parameters typically exhibit a non-uniform spatial distribution during discharge, and the spectral intensity data obtained by integrating along the line of sight may not directly reflect the true radial variations of these parameters.

[0043] To address the problems existing in the background technology, there is an urgent need to design a new method to accurately acquire the spatial distribution characteristics of SCGD spectral data. This invention utilizes the inverse Abel transform to obtain the radial distribution of emissivity, thereby improving the detection performance of SCGD. Furthermore, compared to traditional methods, the method for acquiring the spatial distribution characteristics of solution cathode glow discharge plasma based on the inverse Abel transform requires relatively simple equipment, mainly consisting of solution cathode glow discharge devices and common spectral acquisition equipment, significantly reducing equipment costs.

[0044] Example 1 discloses a method for improving the detection limit of solution cathode glow discharge spectroscopy based on inverse Abel transform, such as... Figure 1 As shown, it includes:

[0045] S1. Collect the spectral signals of the plasma transverse space of the element to be tested in the test solution and the spectral signals of the blank solution, respectively.

[0046] The spectral signals of the test solution and the blank solution were collected sequentially. The blank solution did not contain the analyte. The blank solution was typically acidified deionized water.

[0047] In some embodiments, the specific process of acquiring the spectral signal of the plasma transverse space of the element to be tested in the solution is as follows:

[0048] S1.1 Plasma is obtained between vertically spaced cathode and anode rods using solution cathode glow discharge technology;

[0049] S1.2. The spectral signal of the plasma is acquired through a light-collecting fiber structure, and the light-collecting fiber structure is moved within the same vertical region between the cathode and anode to obtain the spectral signal of the plasma in the transverse space between the cathode and anode. Here, the spectral signal refers to the spectral line intensity.

[0050] The optical fiber structure here mainly refers to the optical fiber in the three-dimensional optical receiving platform (existing equipment). By moving the optical fiber between the upper and lower ends of the plasma (with a certain distance between the optical fiber and the plasma), the transverse spectral signals at different positions of the plasma in vertical space are collected. The transverse distribution of the spectral intensity of the element to be measured is obtained by collecting spectral data multiple times.

[0051] S2. Determine the plasma center position of the spectral signal in the transverse space of the plasma, and determine the single-sided transverse spectral intensity curve of the spectral signal in the transverse space of the plasma. Simultaneously, acquire the spectral signal in the blank solution corresponding to the plasma center position as the blank solution center position, and determine the single-sided transverse spectral intensity data at the blank solution center position.

[0052] After obtaining the spectral signals of the transverse space of the plasma, we can know the spectral intensity data values ​​of these spectral signals. The maximum value of these spectral intensity data values ​​is the center position of the plasma. This is because, under normal circumstances, the transverse spectral signals of elements increase first and then decrease from left to right, and the middle position is the position of the maximum value of the spectral signal.

[0053] In some embodiments, the specific process for determining the single-sided transverse spectral intensity curve of the spectral signal in the transverse space of the plasma is as follows:

[0054] S2.1. Starting from the center position of the plasma, acquire n / 2 spectral intensity data values ​​on the left and right sides of the center position of the plasma respectively. It should be noted that in the acquired spectral signals, the step size is 0.01mm, that is, starting from the center position of the plasma, the spectral signals on both sides are acquired multiple times with an interval of 0.1mm.

[0055] S2.2. Take the average of the sums of the two spectral intensity data values ​​symmetrical about the center position of the plasma as the spectral intensity data value of the corresponding position on one side. Then, based on the spectral intensity data value of the one side and the spectral intensity data value of the center position of the plasma, a curve is prepared to obtain the one-sided transverse spectral intensity curve of the spectral signal of the transverse space of the plasma.

[0056] In other words, after determining the location of the plasma center, find n spectral intensity data values ​​that are collected diffusely from the plasma center, n / 2 on each side, where n is a positive even number. Average the symmetrical spectral intensities along the center to obtain n / 2+1 unilateral variation values ​​of spectral intensities.

[0057] It should be noted that spectral signals from the same location are collected for both the blank solution and the test solution, with each sample being n+1. After obtaining the spectral signal corresponding to the plasma center position, this signal is used as the center position of the blank solution. Then, n / 2 spectral intensity data values ​​are collected from both the left and right sides, and the single-sided transverse spectral intensity curve of the blank solution is calculated. This curve is used to subsequently calculate the detection limit at each location based on the spectral signal intensity and signal-to-noise ratio of the blank solution and the test solution at the same location.

[0058] For example, after determining the center position of the acquisition, the spectral signal intensity is measured by moving the acquisition point to the left and right every 0.1 mm. The spectral intensity at the position 0.1 mm to the left is I1, and the spectral intensity at the position 0.1 mm to the right is I2. Then, (I1+I2) / 2 is the average spectral intensity at each 0.1 mm position.

[0059] S3. Perform a cubic spline function fit on the single-sided transverse spectral intensity curve to obtain the inverse Abel transform and the radial distribution curve of the emissivity.

[0060] In some embodiments, the specific process of fitting the single-sided transverse spectral intensity curve with the cubic spline function method to obtain the inverse Abel transform and thus the radial distribution curve of the radiance is as follows:

[0061] S3.1, in the single-sided transverse spectral intensity curve, two adjacent spectral intensity data points (y i ,I i ) and (y i+1 ,I i+1 It can be approximated by a cubic polynomial, i.e., I i (y)=a i0 +a i1 y+a i2 y 2 +a i3 y 3 Thus, the first differential I′ is obtained. i (y) and the second derivative I″ i (y), where I′ i (y)=b i +2c i y+3d i y 2 ;I″ i (y)=2c i +6d i y;

[0062] Each spectral intensity data value is calculated using this formula (location, spectral intensity). i I represents the position of the i-th spectral intensity data point. i This represents the spectral intensity data value of the i-th spectral intensity data point.

[0063] On the subinterval [y i ,y i+1 ], I(y)=I i Since (y) is a cubic polynomial, I″(y) is a linear function of x. I (y i+1 ) = M i+1 and I″ I (y i ) = M i Linear interpolation shows that:

[0064]

[0065] Integrate the above equation twice, and use the boundary value I of the interpolation. i+1 and I i The following formula can be obtained:

[0066]

[0067] Let h i =y i+1 -y i According to the above formula, we get:

[0068]

[0069] S3.2, the first-order differential I′ i (y) and the second derivative I″ i Substitute (y) into the inverse Abel transform formula And solve for it to obtain the emissivity E(r);

[0070] Solve for the coefficients a of the cubic polynomial i0 a i1 a i2 a i3 First, find the n+1 unknowns: M1, ..., M i+1 To ensure continuity at nodes, the following conditions must be met:

[0071] I' i-0 =I′ i+0 .

[0072] Assuming the plasma has an axisymmetric shape, there are n-1 nodes (data points) between the measurement points, thus allowing the establishment of n-1 linear algebraic equations. At the center, the first derivative of the radiation intensity is 0; and at the plasma boundary, r = R, the first derivative of the intensity is also assumed to be 0. These conditions provide the necessary boundary constraints for solving the spatial distribution of the plasma. I′(0) = I′(R) = 0. Through the above conditions, two additional equations can be obtained. Combined with the n-1 node equations, a total of n+1 linear equations are formed, used to solve for n+1 second derivatives M. Substituting these derivatives into the coefficients of the cubic polynomial, the radial emissivity distribution E(r) of the plasma can be obtained, thus fully describing its spatial characteristics.

[0073] S3.3. Draw a radial distribution curve based on the emissivity E(r).

[0074] In this step, the unilateral transverse spectral intensity curves corresponding to the test solution and the blank solution will be executed.

[0075] S4. Calculate the detection limit of the location where the radial distribution curve of the emissivity shows an extreme point, and compare it with the detection limit of the plasma center location. The spectral signal acquisition location corresponding to the spectral intensity data value with the lower detection limit is taken as the optimal acquisition area, thereby improving the element detection limit of the solution cathode glow discharge spectrum.

[0076] The detection limit is the lowest concentration of a metal element that can theoretically be detected. The calculation of the detection limit uses the radial distribution curves of the emissivity of the test solution and the blank solution.

[0077] The formula for calculating the detection limit is:

[0078]

[0079] Where RSDb is the relative standard deviation of the blank solution, c is the element concentration, and SBR is the ratio of the spectral intensity of the test solution to the spectral intensity of the blank solution, obtained by the radial distribution curves of the emissivity of the test solution and the blank solution.

[0080] RSDb: Calculated by collecting 11 spectral signal intensities of a blank solution at the emission wavelength of a certain element. RSDb = standard deviation / average value. Element concentration: the configured concentration, which is a known value.

[0081] Finally, the radial distribution of the obtained emissivity E(r) shows an extreme point. The detection limit at this location is calculated to be lower than that at the center of the plasma, and the detection limit can be improved to some extent.

[0082] The radial distribution of emissivity can be obtained through the inverse Abel transform. This distribution will have a maximum point. The detection limit at this location is higher than the detection limit of the maximum spectral intensity point measured in the past. That is, the detection limit of the maximum point of the radial distribution is lower than the detection limit at the center of the plasma, indicating that elements can be more easily detected in the region corresponding to the maximum point of the radial distribution.

[0083] Example 2 discloses a solution cathode glow discharge spectral detection limit enhancement system based on inverse Abel transform, such as... Figure 2 As shown, the method for improving the detection limit of solution cathode glow discharge spectrum based on inverse Abel transform described in Example 1 includes a spectral signal acquisition module, a data preprocessing module, and a detection limit optimization and comparison module. The function and principle of each module will be described in detail below.

[0084] The spectral signal acquisition module is used to acquire the spectral signals of the plasma transverse space of the analyte in the test solution and the spectral signals of the blank solution, respectively.

[0085] In some embodiments, the spectral signal acquisition module includes a peristaltic pump, a cathode rod, an anode rod, a power supply, a light-collecting fiber structure, and a spectrometer. The cathode rod and the anode rod are electrically connected to the power supply, and the cathode rod is vertically arranged in a container. The container is connected to the peristaltic pump, so that the peristaltic pump draws the liquid to be tested or a blank solution into the container, bringing the cathode rod into contact with the liquid to be tested or the blank solution. The cathode rod and the anode rod are vertically spaced facing each other. The light-collecting fiber structure is located on the side of the space between the cathode rod and the anode rod, and is used to collect the spectral signal of the plasma when plasma is generated between the cathode rod and the anode rod. The light-collecting fiber structure is connected to a computing terminal through the spectrometer.

[0086] The optical fiber receiving structure includes two plano-convex quartz lenses and optical fibers, with the planes of the two plano-convex quartz lenses arranged opposite each other (i.e., the convex surfaces are arranged opposite each other).

[0087] This invention designs a spectral signal acquisition module specifically for the area between the electrodes of a solution cathode glow discharge plasma, capable of accurately capturing the spectral signals emitted by different elements during the discharge process between the electrodes. Through optimized optical path design, the comprehensiveness and accuracy of signal acquisition are ensured, avoiding signal omissions or interference. For many common elements, such as K, In, Rb, Ag, Ca, Cu, Mn, and Cd, the spectral intensity distribution can be acquired, providing a rich data foundation for subsequent in-depth analysis. This device can obtain the distribution of spectral intensity, signal-to-background ratio, and detection limit of various elements between the electrodes.

[0088] In other words, the spectral signal acquisition module of this invention is designed to detect the spectral signals between the two electrodes of a solution cathode glow discharge plasma. The module is equipped with an optical sensor that can accurately acquire the spectral signals released by different elements during the discharge process. Through optimized design of the optical path system, aberration interference is reduced. For many common elements such as K, In, Rb, Ag, Ca, Cu, Mn, and Cd, this module can comprehensively acquire their spectral intensity distribution data, providing rich and reliable data support for subsequent in-depth analysis. Furthermore, this device can also acquire the distribution of spectral intensity, signal-to-background ratio, and detection limit of various elements between the electrodes, providing crucial information for evaluating element detection performance.

[0089] More specifically, this spectral signal acquisition module primarily uses a motorized three-dimensional platform to move the optical fiber and acquire spectral intensity signals at different locations. The signal-to-background ratio and detection limit are calculated from the measured spectral signals. The plasma spectral signal is transmitted to the end of the optical fiber through two plano-convex quartz lenses (China Daheng Optics, f=60mm, diameter=25mm). The discharge plasma is imaged into the fiber optic head using a lens at a 1:1 scale. The opening size of the optical fiber cable is 600μm. The other end of the optical fiber is connected to a Czerny-Turner spectrometer with a spectral range of 200-1100nm.

[0090] The data preprocessing module is used to determine the plasma center position of the spectral signal in the transverse space of the plasma, and to determine the one-sided transverse spectral intensity curve of the spectral signal in the transverse space of the plasma. Simultaneously, it acquires the spectral signal in the blank solution corresponding to the plasma center position as the center position of the blank solution, and determines the one-sided transverse spectral intensity data at the center position of the blank solution. In other words, the data preprocessing module processes the acquired spectral signals. For the acquired n spectral signals, by determining the center position signal, the symmetrical spectral intensities are averaged along the center to obtain (n / 2+1) one-sided variation values ​​of the spectral intensities.

[0091] The Abel inverse transform module is used to perform a cubic spline function fit on the single-sided transverse spectral intensity curve to obtain the radial distribution curve of the emissivity.

[0092] The inverse Abel transform module performs an inverse Abel transform on the transverse unilateral spectral intensity to obtain the radial distribution of emissivity. This is further extended to the acquisition and analysis of the transverse distribution of eight elements. By optimizing the acquisition process and data processing methods, and again utilizing the inverse Abel transform, the radial distribution of emissivity for each element can be obtained quickly and accurately. This makes the distribution characteristics of different elements in plasma readily apparent, providing crucial data for studying the spatial distribution of elemental spectral intensity.

[0093] The optimization of the data acquisition process and data processing methods is specifically manifested in the following ways:

[0094] The standard formula for the limit of detection (LOD) is defined as: DLs = 3 × SDb / S, where SDb represents the standard deviation of the spectral intensity of the blank solution, and S represents the slope of the calibration curve obtained from the intensity measurements of different concentrations of the element. Calculating the LOD using this method requires knowledge of the intensity values ​​at different concentrations at each position, as well as the calibration curve, making the process relatively complex and time-consuming. However, the experimental objective of this invention is to compare the distribution of LODs at different positions. To achieve this goal, this invention calculated the LODs at approximately 80 positions across eight elements. Using the standard LOD calculation method would require a significant amount of work and a long computation time, and may introduce errors.

[0095] In contrast, the present invention uses a formula This formula estimates the detection limit using a single concentration of the element. The method is relatively simple, reducing computational burden. The formula is easy to operate and can facilitate rapid and efficient calculation of the detection limit distribution at plasma spatial locations.

[0096] The detection limit optimization and comparison module is used to calculate the detection limit at the location of the extreme point of the radial distribution curve of the emissivity, and compare it with the detection limit at the center of the plasma. The acquisition location corresponding to the spectral intensity data value with the lower detection limit is taken as the optimal acquisition area, thereby improving the element detection limit of the solution cathode glow discharge spectrum.

[0097] The detection limit optimization and comparison module focuses on comparing the detection limits at the transverse midpoint of the plasma and at the extreme point position after the inverse Abel transform. Through experimental data analysis, the intrinsic relationship between the extreme point position and the optimal detection limit was determined. Identifying these extreme point positions allows for spatial location of the optimal region for improving the detection limit, and further, by adjusting the detection position and other methods, significantly enhances the measurement sensitivity, providing a practical optimization strategy for real-world detection applications.

[0098] More specifically, an inverse Abel transform is first performed on the unilateral spectral intensity to obtain the radial distribution of radiance, and the locations of radiance extrema are recorded. The detection limits at these locations are then calculated compared to those at the locations with the maximum spectral intensity. It is found that the detection limits at the extrema locations are better than those at the locations with the maximum spectral intensity (the lower the detection limit at a given location, the higher the sensitivity of the detected element; therefore, the detection limit can be understood as the ratio of the stability of the blank signal to the detection sensitivity). Thus, by comparing the locations of the extrema locations with those at the conventional maximum spectral intensity, the detection limit is improved, i.e., the sensitivity of element measurement is enhanced.

[0099] In some embodiments, the data preprocessing module, the Abel inverse transform module, and the detection limit optimization comparison module are located within the computing terminal.

[0100] It should be noted that before performing the experimental method of Example 1 using the system of Example 2, the spectral acquisition equipment was checked to ensure the accuracy of the acquired spectral signals in terms of wavelength and intensity. For the three-dimensional light-receiving platform used for positioning and movement, the position was moved by a motor to ensure the accuracy of acquiring spectral signals at different positions and to avoid spectral signal deviations caused by platform positioning errors. At the same time, it was ensured that the experimental conditions could achieve stable discharge of the device to minimize errors.

[0101] It should be noted that the three-dimensional optical receiving platform is used to control the movement of the optical receiving fiber structure in order to locate the specific position of the optical receiving fiber structure.

[0102] like Figure 2 The diagram shows the experimental setup for acquiring the spatial distribution characteristics of solution cathode glow discharge plasma based on inverse Abel transform. A peristaltic pump pumps the sample solution (analyte solution) into a glass capillary (container) with an outer diameter of 1.0 mm and an inner diameter of 0.4 mm. The sample solution flows out from the top of the capillary at a flow rate of 2.92 mL / min, contacting the auxiliary electrode. A 3.0 mm diameter tungsten rod is placed 4.3 mm directly above the vertical centerline of the glass capillary, serving as the anode. The electrolyte solution containing the analyte flows down from the top of the glass capillary and connects to the electrode, forming a glow discharge circuit with the tungsten rod as the anode. A 2.7 kΩ current-limiting resistor connects the positive terminal of a high-voltage power supply to the tungsten rod anode and the negative terminal to the auxiliary electrode. When sufficient DC high voltage is applied to both electrodes, a stable glow discharge plasma is spontaneously generated. Once the plasma discharge stabilizes, two plano-convex quartz lenses image the plasma spectral signal onto the fiber optic head at a 1:1 scale, transmitting the spectral signal to the end of the fiber. The optical fiber used has an aperture size of 600 μm. The other end of the fiber is connected to a spectrometer with a spectral range of 200-1100 nm. This spectrometer measures 149 × 109 × 47 mm and is equipped with a charge-coupled device (CCD) detector. By moving a three-dimensional light-receiving platform, the distribution of the elemental plasmonic spectral signal between the two poles, as well as the transverse spectral signal intensity distribution between the poles, are acquired. The acquisition range is as follows: Figure 3 As shown.

[0103] The inverse Abel transform algorithm is used to perform an inverse transform calculation on the acquired transverse spectral intensity to obtain the radial distribution of emissivity for each element. The sine integral projection of an axisymmetrically distributed physical quantity is called the Abel transform. Conversely, the process of solving for an axisymmetrically distributed physical quantity from the projection function is called the inverse Abel transform. This paper applies the Abel integral equation to plasma diagnostics. Due to the complex and non-uniform spatial distribution of plasma during discharge, the measurement of plasma characteristics is challenging. Figure 4 This is the geometric interpretation of the inverse Abel transform in cylindrical symmetric plasmas. For example... Figure 4 As shown in (a), the plasma radiation source is assumed to be a cylinder with cylindrical symmetry around the z-axis and to be optically thin. Figure 4 In (b), the detector moves along the y-direction to obtain the lateral distribution of the plasma spectral intensity. The unilateral variation of the plasma spectral intensity is obtained, and the radial distribution of the emissivity E(r) is obtained through an inverse Abel transform using a cubic spline function algorithm. The specific process is as follows:

[0104] Two adjacent data points (y) obtained from the experiment i ,I i ) and (y i+1 ,I i+1 Approximated by a cubic polynomial, i.e.: I i (y)=a i0 +a i1 y+a i2 y 2 +a i3 y 3 We can obtain the first-order differential and the second-order derivative using the inverse Abel transform formula. Substitute the values ​​into the solution.

[0105] By comparing the detection limits at the horizontal midpoint of the element and the extreme point after the inverse Abel transform, it was found that the detection limits of each element decreased at the extreme point of emissivity after the inverse Abel transform.

[0106] The specific process is as follows: At the center y=0 between the two electrodes of the plasma (cathode and anode), the detection limit of each element is calculated. At this location (usually the location of the maximum transverse spectral intensity of the element, designated as y=0), the transverse intensity of the plasma is collected (using this location as the center, n / 2 spectral intensity data are collected on each side to obtain a single-sided transverse spectral intensity curve), and an inverse Abel transform is performed. After the inverse transform, the detection limit of the element is calculated at the location where the emissivity reaches its extreme value, and the two detection limit values ​​are compared. The results show that the detection limit near the extreme value location obtained by the inverse Abel transform is significantly lower. This indicates that the extreme value location determined by the inverse Abel transform can more accurately measure the detection limit of elements. Identifying these extreme value locations helps to spatially locate the optimal region for improving the detection limit, thereby improving the measurement sensitivity. Future research can further explore the radiation characteristics of different elements and other detection methods to broaden their application range and improve detection accuracy.

[0107] In summary, the solution cathode glow discharge element detection limit improvement method and system based on Abel inverse transform constructed in this invention, through the coordinated work of various functional modules, forms a complete and efficient analytical system, from the precise acquisition of spectral signals to the in-depth analysis of the distribution characteristics of blank solutions and multiple elements, and then to the calculation of key parameters and optimization of detection limits. This system not only provides researchers with powerful technical means to conduct in-depth studies on the physicochemical properties of plasma, but also significantly improves detection accuracy and efficiency in practical applications such as industrial detection and environmental monitoring, demonstrating broad application prospects and significant practical value.

[0108] Example 3 also discloses an electronic device, including at least one processor and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform a solution cathode glow discharge spectral detection limit improvement method based on inverse Abel transform as described in Example 1.

[0109] Example 4 also discloses a storage medium storing a computer program, which, when executed by a processor, implements the method for improving the detection limit of solution cathode glow discharge spectrum based on inverse Abel transform as described in Example 1.

[0110] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for improving the detection limit of solution cathode glow discharge spectroscopy based on inverse Abel transform, characterized in that, include: The spectral signals of the analyte in the transverse space of the plasma and the spectral signals of the blank solution were collected respectively. The plasma center position of the spectral signal in the transverse space of the plasma is determined, and the single-sided transverse spectral intensity curve of the spectral signal in the transverse space of the plasma is determined; at the same time, the spectral signal in the blank solution corresponding to the plasma center position is obtained as the blank solution center position, and the single-sided transverse spectral intensity data of the blank solution center position is determined. The radial distribution curve of emissivity is obtained by fitting the single-sided transverse spectral intensity curve with a cubic spline function to obtain the inverse Abel transform. The detection limit is calculated at the location of the extreme point of the radial distribution curve of the emissivity and compared with the detection limit at the center of the plasma. The spectral signal acquisition location corresponding to the spectral intensity data value with the lower detection limit is taken as the optimal acquisition area, thereby improving the element detection limit of the solution cathode glow discharge spectrum.

2. The method for improving the detection limit of solution cathode glow discharge spectroscopy based on inverse Abel transform according to claim 1, characterized in that, The specific process for acquiring the spectral signal of the analyte in the transverse space of the plasma in the solution is as follows: Solution cathode glow discharge plasma is obtained between vertically spaced cathode and anode rods; The spectral signal of the plasma is obtained by acquiring the optical fiber structure, and the optical fiber structure is moved in the same vertical region between the cathode and the anode to obtain the spectral signal of the plasma in the lateral space between the cathode and the anode.

3. The method for improving the detection limit of solution cathode glow discharge spectroscopy based on inverse Abel transform according to claim 1, characterized in that, The specific process for determining the single-sided transverse spectral intensity curve of the spectral signal in the transverse space of the plasma is as follows: Starting from the plasma center position, obtain n / 2 spectral intensity data values ​​on the left and right sides of the plasma center position respectively; The average value of the sum of the two spectral intensity data values ​​symmetrical about the center position of the plasma is taken as the spectral intensity data value of the corresponding position on one side. Then, a curve is prepared based on the spectral intensity data value of one side and the spectral intensity data value of the center position of the plasma, thereby obtaining the one-sided transverse spectral intensity curve of the spectral signal of the transverse space of the plasma.

4. The method for improving the detection limit of solution cathode glow discharge spectroscopy based on inverse Abel transform according to claim 1, characterized in that, The specific process of fitting the single-sided transverse spectral intensity curve using the cubic spline function method to obtain the inverse Abel transform and thus the radial distribution curve of the radiance is as follows: The two adjacent spectral intensity data points (y) in the single-sided transverse spectral intensity curve i ,I i ) and (y i+1 ,I i+1 It can be approximated by a cubic polynomial, i.e., I i (y)=a i0 +a i1 y+a i2 y 2 +a i3 y 3 Thus, we obtain the first-order differential Ii′(y) and the second-order derivative I″. i (y), where I′ i (y)=b i +2c i y+3d i y 2 ;I″ i (y)=2c i +6d i y; a i0 a i1 a i2 a i3 b i c i d i For coefficients; The first-order differential I′ i (y) and the second derivative I″ I Substituting (y) into the inverse Abel transform formula The emissivity E(r) is obtained by solving the equation. A radial distribution curve is plotted based on the emissivity E(r).

5. A solution cathode glow discharge spectral detection limit enhancement system based on inverse Abel transform, used to execute the solution cathode glow discharge spectral detection limit enhancement method based on inverse Abel transform as described in any one of claims 1-5, characterized in that, include: The spectral signal acquisition module is used to acquire the spectral signals of the plasma transverse space of the analyte in the test solution and the spectral signals of the blank solution, respectively. The data preprocessing module is used to determine the plasma center position of the spectral signal in the transverse space of the plasma, and to determine the single-sided transverse spectral intensity curve of the spectral signal in the transverse space of the plasma; at the same time, it acquires the spectral signal in the blank solution corresponding to the plasma center position as the blank solution center position, and determines the single-sided transverse spectral intensity data with the blank solution center position as the blank solution center position. The Abel inverse transform module is used to perform a cubic spline function fit on the single-sided transverse spectral intensity curve to obtain the radial distribution curve of the emissivity. The detection limit optimization and comparison module is used to calculate the detection limit at the location of the extreme point of the radial distribution curve of the emissivity, and compare it with the detection limit at the center of the plasma. The acquisition location corresponding to the spectral intensity data value with the lower detection limit is taken as the optimal acquisition area, thereby improving the element detection limit of the solution cathode glow discharge spectrum.

6. The solution cathode glow discharge spectral detection limit enhancement system based on Abel inverse transform according to claim 5, characterized in that, The spectral signal acquisition module includes a peristaltic pump, a cathode rod, an anode rod, a power supply, a light-collecting fiber structure, and a spectrometer. The cathode rod and anode rod are electrically connected to the power supply, and the cathode rod is vertically arranged in a container. The container is connected to the peristaltic pump, so that the peristaltic pump draws the liquid to be tested or a blank solution into the container, bringing the cathode rod into contact with the liquid to be tested or the blank solution. The cathode rod and anode rod are vertically spaced facing each other. The light-collecting fiber structure is located on the side of the space between the cathode rod and the anode rod, and is used to collect the spectral signal of the plasma when plasma is generated between the cathode rod and the anode rod. The light-collecting fiber structure is connected to a computing terminal through the spectrometer.

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