A parameter design method for a time-of-flight mass spectrometer

Abstract

This invention provides a parameter design method for a time-of-flight mass spectrometer, relating to the field of mass spectrometry instrument design. The parameter design method includes: substituting preset parameter values ​​of the time-of-flight mass spectrometer into a kinetic equation to calculate the ion flight time; constructing a discretized matrix based on the ion flight time; then constructing a two-dimensional probability density function of the ion beam and an intensity matrix of the ion beam to obtain a flight time-intensity peak curve; thereby calculating the time resolution of the time-of-flight mass spectrometer under preset parameter values. In this invention, a method for calculating the time resolution of an ion beam with a determined charge-to-mass ratio is obtained using kinetic equations and statistical principles. Simultaneously, a relatively simple calculation model is established using statistical simulation to address the role dispersion effect of the grid. Furthermore, the gradient descent method is optimized to address the sensitivity of the time-of-flight mass spectrometer resolution to parameters, overcoming the problem of excessively large or small step sizes during the exploration of optimal parameter solutions.

Description

Technical Field

[0001] This invention relates to the field of mass spectrometry instrument design technology, and specifically to a parameter design method for a time-of-flight mass spectrometer. Background Technology

[0002] Time-of-flight mass spectrometers (TOF-MS) possess numerous advantages, including simple structure, high resolution, and fast detection speed. They are rapidly developing towards miniaturization and portability, and have found widespread application in agriculture, environmental monitoring, and biopolymer detection. Currently, reflectance-type TOF-MS is widely used, and resolution is a crucial performance indicator. Many factors influence resolution, such as the initial position and energy distribution of the ion beam, the lattice spread effect of the grid, and the rise time of the pulse voltage. Extensive discussions have been held regarding the time broadening caused by the initial position and energy distribution of ions. Taylor series expansions are primarily used to study the impact of initial position and energy diffusion on the final flight time, thereby deriving the relationship between ion beam parameters and instrument resolution, and further determining focusing conditions. The lattice spread effect generated when the ion beam passes through the grid has also been theoretically studied. The ion optics simulation software SIMON3D is mainly used to simulate the electric field distribution generated by the grid, and Monte Carlo simulations can visually visualize the ion distribution upon reaching the detector.

[0003] The aforementioned research is relatively mature in both theory and simulation. However, for high-resolution time-of-flight mass spectrometers, a suitable set of voltage and distance parameters is fundamental to realizing their performance. Currently, the multi-stage focusing conditions for ion beams are mainly based on Taylor expansion and derivative analysis, which are not intuitive enough for guiding the parameter design of time-of-flight mass spectrometers.

[0004] Optimizing the overall parameters of a high-resolution time-of-flight mass spectrometer under the influence of multiple variables, taking into account the above factors, has become a core technical challenge. Based on this technical problem, the applicant has proposed the technical solution in this application. Summary of the Invention

[0005] The purpose of this invention is to provide a parameter design method for a time-of-flight mass spectrometer. It uses kinetic equations and statistical principles to obtain a method for calculating the time resolution of the charge-to-mass ratio ion beam. At the same time, it innovatively uses statistical simulation to establish a relatively simple calculation model for the role dispersion effect of the grid. Furthermore, it optimizes the gradient descent method to address the sensitivity of the resolution of the time-of-flight mass spectrometer to the parameters, overcoming the problem of excessively large or small step sizes in the process of exploring the optimal parameter solution.

[0006] To achieve the above objectives, this invention provides a parameter design method for a time-of-flight mass spectrometer, comprising: presetting various parameter values ​​of the time-of-flight mass spectrometer and the upper limit values ​​of the ion beam charge-to-mass ratio, ion beam width, and ion beam energy; introducing the ion beam into the time-of-flight mass spectrometer; calculating the ion flight time of the ion beam at different initial positions and kinetic energies based on the preset parameter values ​​of the time-of-flight mass spectrometer using a kinetic equation; constructing a discretization matrix based on the ion flight time; constructing a two-dimensional probability density function of the ion beam based on the initial position and kinetic energy of the ions; and constructing a [missing information - likely a specific mathematical expression or algorithm] based on the two-dimensional probability density function and the discretization matrix. The intensity matrix of the ion beam is used to obtain the time-of-flight-intensity peak curve. The time resolution of the time-of-flight mass spectrometer at preset parameter values ​​is calculated based on the time-of-flight-intensity peak curve. By changing any one or more of the parameter values, the discretization matrix, the two-dimensional probability density function, and the time-of-flight-intensity peak curve are reconstructed. The time resolution of the time-of-flight mass spectrometer at the changed parameter values ​​is recalculated so that the time resolution converges to reach the maximum time resolution. The changed parameter values ​​corresponding to the maximum time resolution are used as the optimal parameter design for the time-of-flight mass spectrometer.

[0007] In one embodiment, the discretization matrix refers to:

[0008]

[0009] Among them, ±w m w represents the upper and lower limits of the initial moment width distribution of the ion beam. m The value is taken as 1 / 2 of the ion beam width; ±E m E represents the upper and lower limits of the kinetic energy distribution of the ion beam at the initial moment. m The value is taken as the upper limit of the ion beam energy; T(.,.) represents the flight time of the ion;

[0010] The two-dimensional probability density function refers to:

[0011]

[0012] Where w represents the distance between the ion and the central axis of the ion beam, and E represents the initial kinetic energy of the ion;

[0013]

[0014]

[0015] The intensity matrix of the ion beam refers to:

[0016]

[0017] The intensity values ​​in the intensity matrix of the ion beams with the same ion flight time in the discretized matrix are algebraically summed to obtain the flight time-intensity peak curve.

[0018] In one embodiment, the time resolution of the time-of-flight mass spectrometer calculated based on the time-of-flight-intensity peak curve at the preset parameter values ​​of the time-of-flight mass spectrometer refers to:

[0019] The following formula is used for calculation:

[0020]

[0021] Among them, R t The time resolution is represented by t, which represents the flight time corresponding to the peak value in the time-intensity peak curve, and Δt is the half-peak width corresponding to the peak value in the time-intensity peak curve. R m Indicates quality resolution.

[0022] In one embodiment, changing any one or more of the parameter values, reconstructing the discretization matrix, the two-dimensional probability density function, and the time-of-flight intensity peak curve, and recalculating the time resolution of the time-of-flight mass spectrometer under the changed parameter values, such that the time resolution converges to reach its maximum value, and using the changed parameter values ​​corresponding to the maximum time resolution as the optimal parameter design of the time-of-flight mass spectrometer, includes: finding the possible optimal solutions for the parameter values ​​using a mass spectrometry-gradient descent algorithm; and using the possible optimal solutions as initial conditions to obtain the optimal parameter design using a Nesterov accelerated gradient algorithm.

[0023] In one embodiment, finding the possible optimal solution for each parameter value using the mass spectrometry-gradient descent algorithm involves first setting any one or more of the parameter values ​​as an independent variable vector, and treating the other parameter values ​​as invariants, and then calculating using the following formula:

[0024]

[0025] Where α is a parameter used to adjust the step size; ε is a constant introduced to prevent the denominator from being 0; |.| is the absolute value sign, corresponding to the function abs in MATLAB; sgn is the sign function, corresponding to the function sign in MATLAB;

[0026] θ n This represents a set of values ​​for the independent variable vector after the nth iteration;

[0027] θ n+1 This represents another set of values ​​for the independent variable vector after the (n+1)th iteration;

[0028] The gradient value at the given time resolution is taken as the objective function;

[0029] Until the other set of values ​​of the independent variable vector converges to the maximum value of the time resolution within the set range, the other set of values ​​of the independent variable vector and the invariant are used to form the changed parameter values ​​as the possible optimal solution of the parameter values.

[0030] In one embodiment, the Nesterov accelerated gradient algorithm first jumps θ-γV in a cumulative gradient direction. t-1 The gradient of the point after the jump is calculated and then weighted and summed with the previous jump amount, using the following formula:

[0031]

[0032] θ=θ+V t Equation (7)

[0033] Where γ represents the weighting coefficient, η represents the learning rate of the gradient descent algorithm, and V t V represents the step size after the nth iteration. t-1 This represents the step size after the (n-1)th iteration.

[0034] In one embodiment, the preset time-of-flight mass spectrometer has six electrode plates: a first positive electrode plate, a first negative electrode plate, a second electrode plate, a third electrode plate, a fourth electrode plate, and a fifth electrode plate. The first positive electrode plate and the first negative electrode plate form an ion beam entry region, the first negative electrode plate and the second electrode plate form an acceleration region, the second electrode plate and the third electrode plate form a drift region, the third electrode plate and the fourth electrode plate form a first reflection region, and the fourth electrode plate and the fifth electrode plate form a second reflection region. The movement of ions in the first reflection region and the second reflection region is symmetrical. The vertical distance d1 of the ion beam entry region, the vertical distance d2 of the acceleration region, the vertical distance d3 of the drift region, and the vertical distance of the reflection region are the sum of d4 and d5. The distance d6 between the detector and the reflection region is also specified. The electrode voltages are: V1 of the first positive electrode plate, -V1 of the first negative electrode plate, V2 of the second electrode plate, V3 of the third electrode plate, V4 of the fourth electrode plate, V5 of the fifth electrode plate, and V6 of the detector.

[0035] It should be noted that the following ion velocities refer to the velocity component of the ion in the direction parallel to the electric field; kinetic energy and energy refer to the kinetic energy constituted by the velocity component of the ion in the direction parallel to the electric field.

[0036] In one embodiment, the kinetic equation is:

[0037] T(w,E)=t1+t2+t3+2t4+2t5+t6

[0038] The flight time t1, the regional electric field strength E1, and the ion velocity u2 when the ions enter the ion beam entry region and reach the first negative electrode plate are respectively:

[0039]

[0040] The flight time t2, the regional electric field strength E2, and the ion velocity u3 when the ion enters the acceleration region and reaches the second electrode are respectively:

[0041]

[0042] The flight time t3, the regional electric field strength E3, and the ion velocity u4 when the ion enters the drift region and reaches the third electrode are respectively:

[0043]

[0044] u4 = u3

[0045] E3 = 0

[0046] The flight time t4, the regional electric field strength E4, and the ion velocity u5 when the ion enters the first reflection region and reaches the fourth electrode are respectively:

[0047]

[0048] The flight time t5 and the regional electric field intensity E5 when the ions enter the second reflection region are respectively:

[0049]

[0050] The flight time t6, the regional electric field strength E6, and the ion velocity u7 when the ion leaves the reflection region and arrives at the detector are respectively:

[0051]

[0052] Among them, the ion velocity when the ion just enters the electric field of the time-of-flight mass spectrometer. m represents the ion mass, E represents the kinetic energy at the initial moment, w represents the distance between the ion and the central axis of the ion beam, and q represents the charge in the charge-to-mass ratio of the ion beam.

[0053] In one embodiment, the spacing between the grid and the corresponding wire in each electrode of the time-of-flight mass spectrometer is d.

[0054] The dynamic equation is:

[0055] T(w,E)=t1+t2+t3+2t4+2t5+t6

[0056] The flight time t1, the regional electric field strength E1, and the ion velocity u2 when the ions enter the ion beam entry region and reach the first negative electrode plate are respectively:

[0057]

[0058]

[0059] The flight time t2, the regional electric field strength E2, and the ion velocity u3 when the ion enters the acceleration region and reaches the second electrode are respectively:

[0060]

[0061]

[0062]

[0063]

[0064] The flight time t3, the regional electric field strength E3, and the ion velocity u4 when the ion enters the drift region and reaches the third electrode are respectively:

[0065]

[0066] u4=u3'

[0067]

[0068]

[0069] The flight time t4, the regional electric field strength E4, and the ion velocity u5 when the ion enters the first reflection region and reaches the fourth electrode are respectively:

[0070]

[0071]

[0072]

[0073]

[0074] u′4=u4+Δu4=u3+Δu3+Δu4

[0075] The flight time t5 and the regional electric field intensity E5 when the ions enter the second reflection region are respectively:

[0076]

[0077]

[0078]

[0079]

[0080] The flight time t6, the regional electric field strength E6, and the ion velocity u7 when the ion leaves the reflection region and arrives at the detector are respectively:

[0081]

[0082]

[0083] u6 = u4

[0084]

[0085] Among them, the ion velocity when the ion just enters the electric field of the time-of-flight mass spectrometer. m represents the ion mass, E represents the kinetic energy at the initial moment, w represents the distance between the ion and the central axis of the ion beam, and q represents the charge quantity in the charge-to-mass ratio of the ion beam. This represents the set value, which ranges from 0.8897 to 0.88976.

[0086] In one embodiment, the spacing between the grid and the corresponding wire in each electrode of the time-of-flight mass spectrometer is d. Assuming that it takes time t0 for the voltage of the first positive electrode to rise from 0 to the electrode voltage V1 of the first positive electrode, the time t0 is added to the ion flight time. Attached Figure Description

[0087] Figure 1 This is a detailed flowchart of the parameter design method for the time-of-flight mass spectrometer according to the first embodiment of the present invention;

[0088] Figure 2 This is a schematic diagram of a time-of-flight mass spectrometer according to the first embodiment of the present invention;

[0089] Figure 3 This is a schematic diagram of the flight time-intensity peak curve in the first implementation method;

[0090] Figure 4 This is a partial schematic diagram of the grid arrangement in the second embodiment;

[0091] Figure 5 The electric field component U near a grid composed of uniformly distributed conductors. x - The change curve (where =0.5);

[0092] Figure 6 This is a schematic diagram of the general electric field situation in the second implementation method;

[0093] Figure 7 This is a comparison chart of three optimized gradient descent algorithms. Detailed Implementation

[0094] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings to provide a clearer understanding of the purpose, features, and advantages of the present invention. It should be understood that the embodiments shown in the drawings are not intended to limit the scope of the present invention, but are merely illustrative of the essential spirit of the technical solution of the present invention.

[0095] In the following description, certain specific details are set forth for the purpose of illustrating various disclosed embodiments in order to provide a thorough understanding of the various disclosed embodiments. However, those skilled in the art will recognize that embodiments may be practiced without one or more of these specific details. In other instances, well-known apparatuses, structures, and techniques associated with this application may not have been shown or described in detail to avoid unnecessarily obscuring the description of the embodiments.

[0096] Unless the context requires otherwise, throughout the specification and claims, the word “comprising” and its variations, such as “including” and “having”, shall be understood to have an open, inclusive meaning, that is, to be interpreted as “including, but not limited to”.

[0097] Throughout this specification, references to "an embodiment" or "an embodiment" indicate that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Therefore, the appearance of "in an embodiment" or "an embodiment" in various places throughout the specification does not necessarily refer to the same embodiment. Furthermore, a particular feature, structure, or characteristic may be combined in any manner in one or more embodiments.

[0098] The singular forms “a” and “the” used in this specification and the appended claims include plural references unless otherwise expressly stated herein. It should be noted that the term “or” is generally used to include the meaning of “or / and” unless otherwise expressly stated herein.

[0099] In the following description, in order to clearly demonstrate the structure and working method of the present invention, a number of directional terms will be used. However, terms such as "front", "back", "left", "right", "outside", "inside", "outward", "inward", "up", and "down" should be understood as convenient terms and not as limiting terms.

[0100] The first embodiment of the present invention relates to a parameter design method for a time-of-flight mass spectrometer, which uses kinetic equations and statistical principles to obtain a method for calculating the time resolution of an ion beam with a charge-to-mass ratio.

[0101] The specific process of the parameter design method for the time-of-flight mass spectrometer in this embodiment is as follows: Figure 1 As shown.

[0102] Step 101: Preset the parameter values ​​of the time-of-flight mass spectrometer, the charge-to-mass ratio of the ion beam, the upper limit of the ion beam width, and the upper limit of the ion beam energy. Introduce the ion beam into the time-of-flight mass spectrometer. Substitute the preset parameter values ​​of the time-of-flight mass spectrometer into the kinetic equation to calculate the ion flight time in the ion beam at different initial positions and different initial kinetic energies. Construct a discretized matrix based on the ion flight time.

[0103] Step 102: Based on the initial position and initial kinetic energy of the ion beam, construct the two-dimensional probability density function of the ion beam; based on the two-dimensional probability density function and the discretization matrix, construct the intensity matrix of the ion beam; and obtain the time-of-flight-intensity peak curve based on the intensity matrix.

[0104] Specifically, the discretization matrix refers to:

[0105]

[0106] Among them, ±w m w represents the upper and lower limits of the initial moment width distribution of the ion beam. m The value is taken as 1 / 2 of the ion beam width; ±E m E represents the upper and lower limits of the kinetic energy distribution of the ion beam at the initial moment. m The value is taken as the upper limit of the ion beam energy; T(.,.) represents the flight time of the ion;

[0107] The two-dimensional probability density function refers to:

[0108]

[0109] Where w represents the distance between the ion and the central axis of the ion beam, and E represents the initial kinetic energy of the ion;

[0110]

[0111]

[0112] The intensity matrix of the ion beam refers to:

[0113]

[0114] The intensity values ​​in the intensity matrix of the ion beams with the same ion flight time in the discretized matrix are algebraically summed to obtain the flight time-intensity peak curve.

[0115] Step 103: Calculate the time resolution of the time-of-flight mass spectrometer at the preset parameter values ​​of the time-of-flight mass spectrometer based on the time-of-flight-intensity peak curve.

[0116] Specifically, the following formula is used for calculation:

[0117]

[0118] Among them, R t The time resolution is represented by t, which represents the flight time corresponding to the peak value in the time-intensity peak curve, and Δt is the half-peak width corresponding to the peak value in the time-intensity peak curve. R m Indicates quality resolution, specifically as follows: Figure 3 As shown.

[0119] Step 104: Change any one or more of the parameter values, reconstruct the discretization matrix, the two-dimensional probability density function, and the time-of-flight intensity peak curve, recalculate the time resolution of the time-of-flight mass spectrometer under the changed parameter values, so that the time resolution converges to reach the maximum time resolution value, and use the changed parameter values ​​corresponding to the maximum time resolution value as the optimal parameter design of the time-of-flight mass spectrometer.

[0120] Specifically, step 104 includes the following sub-steps:

[0121] Sub-step 1041: Use the gradient descent algorithm to find the possible optimal solutions for the values ​​of the parameters;

[0122] Specifically, the method of finding the possible optimal solutions for each parameter value using the mass spectrometry-gradient descent algorithm involves first setting any one or more of the parameter values ​​as an independent variable vector, and treating the other parameter values ​​as invariants, and then calculating using the following formula:

[0123]

[0124] Where α is a parameter used to adjust the step size; ε is a constant introduced to prevent the denominator from being 0; |.| is the absolute value sign, corresponding to the function abs in MATLAB; sgn is the sign function, corresponding to the function sign in MATLAB;

[0125] θ n This represents a set of values ​​for the independent variable vector after the nth iteration;

[0126] θ n+1 This represents another set of values ​​for the independent variable vector after the (n+1)th iteration;

[0127] The gradient value at the given time resolution is taken as the objective function;

[0128] Until the other set of values ​​of the independent variable vector converges to the maximum value of the time resolution within the set range, the other set of values ​​of the independent variable vector and the invariant are used to form the changed parameter values ​​as the possible optimal solution of the parameter values.

[0129] This section optimizes the gradient descent algorithm, such as... Figure 7 As shown in the comparison diagram of the three optimized methods, gradient descent has a larger step size when the function gradient is large, and a smaller step size near the extreme values ​​where the gradient is small. Therefore, it can converge to the maximum and minimum values ​​more quickly, thus improving the time efficiency of finding the optimal solution. For the case of seeking the maximum value, gradient descent has the following expression:

[0130]

[0131] Where θ n θ represents the position after the nth iteration. n+1 Let f be the position after the (n+1)th iteration, f be the objective function, and η be the learning rate, used to control the step size. However, when studying the impact of a single variable on temporal resolution, the resolution is extremely sensitive to the response of a single variable, which means that traditional gradient descent methods may not achieve good results. Therefore, the gradient term is moved to the denominator:

[0132]

[0133] To further improve the step size, a square root term is introduced:

[0134]

[0135] Sub-step 1042: Using the possible optimal solution as the initial condition, the optimal parameter design is obtained using the Nesterov accelerated gradient algorithm.

[0136] Specifically, the Nesterov accelerated gradient algorithm first jumps θ-γV in a cumulative gradient direction. t-1 The gradient of the point after the jump is calculated and then weighted and summed with the previous jump amount, using the following formula:

[0137]

[0138] θ=θ+V t Equation (7)

[0139] Where γ represents the weighting coefficient, η represents the learning rate of the gradient descent algorithm, and V t V represents the step size after the nth iteration. t-1 This represents the step size after the (n-1)th iteration.

[0140] In this embodiment, as Figure 2 As shown, the preset time-of-flight mass spectrometer has six electrode stages: a first positive electrode, a first negative electrode, a second electrode, a third electrode, a fourth electrode, and a fifth electrode. The first positive electrode and the first negative electrode form an ion beam entry region; the first negative electrode and the second electrode form an acceleration region; the second electrode and the third electrode form a drift region; the third electrode and the fourth electrode form a first reflection region; and the fourth electrode and the fifth electrode form a second reflection region. The movement of ions in the first and second reflection regions is symmetrical. The vertical distance d1 of the ion beam entry region, the vertical distance d2 of the acceleration region, the vertical distance d3 of the drift region, and the vertical distance of the reflection region are the sum of d4 and d5. The distance d6 between the detector and the reflection region is also specified. The electrode voltages are: V1 of the first positive electrode, -V1 of the first negative electrode, V2 of the second electrode, V3 of the third electrode, V4 of the fourth electrode, V5 of the fifth electrode, and V6 of the detector.

[0141] The following describes three different implementation methods in detail.

[0142] The first implementation is based on an ideal scenario, assuming that the movement of ions in the first and second reflection regions is symmetrical, and that the field strength E3 in the drift region is 0, i.e., V2 = V3.

[0143] The dynamic equation is:

[0144] T(w,E)=t1+t2+t3+2t4+2t5+t6

[0145] The flight time t1, the regional electric field strength E1, and the ion velocity u2 when the ions enter the ion beam entry region and reach the first negative electrode plate are respectively:

[0146]

[0147] The flight time t2, the regional electric field strength E2, and the ion velocity u3 when the ion enters the acceleration region and reaches the second electrode are respectively:

[0148]

[0149] The flight time t3, the regional electric field strength E3, and the ion velocity u4 when the ion enters the drift region and reaches the third electrode are respectively:

[0150]

[0151] u4 = u3

[0152] E3 = 0

[0153] The flight time t4, the regional electric field strength E4, and the ion velocity u5 when the ion enters the first reflection region and reaches the fourth electrode are respectively:

[0154]

[0155] The flight time t5 and the regional electric field intensity E5 when the ions enter the second reflection region are respectively:

[0156]

[0157] The flight time t6, the regional electric field strength E6, and the ion velocity u7 when the ion leaves the reflection region and arrives at the detector are respectively:

[0158]

[0159] Among them, the ion velocity when the ion just enters the electric field of the time-of-flight mass spectrometer. m represents the ion mass, E represents the kinetic energy at the initial moment, w represents the distance between the ion and the central axis of the ion beam, and q represents the charge in the charge-to-mass ratio of the ion beam.

[0160] The second implementation considers the effect of the grid's dispersion effect on ion movement, and presupposes that the spacing between the grid wires in each electrode of the time-of-flight mass spectrometer is d, such as... Figure 4 As shown.

[0161] The dynamic equation is:

[0162] T(w,E)=t1+t2+t3+2t4+2t5+t6

[0163] The flight time t1, the regional electric field strength E1, and the ion velocity u2 when the ions enter the ion beam entry region and reach the first negative electrode plate are respectively:

[0164]

[0165]

[0166] The flight time t2, the regional electric field strength E2, and the ion velocity u3 when the ion enters the acceleration region and reaches the second electrode are respectively:

[0167]

[0168]

[0169]

[0170]

[0171] The flight time t3, the regional electric field strength E3, and the ion velocity u4 when the ion enters the drift region and reaches the third electrode are respectively:

[0172]

[0173] u4=u3'

[0174]

[0175]

[0176] The flight time t4, the regional electric field strength E4, and the ion velocity u5 when the ion enters the first reflection region and reaches the fourth electrode are respectively:

[0177]

[0178]

[0179]

[0180]

[0181] u′4=u4+Δu4=u3+Δu3+Δu4

[0182] The flight time t5, the regional electric field strength E5, and the ion velocity u5 when the ion enters the second reflection region are respectively:

[0183]

[0184]

[0185]

[0186]

[0187] The flight time t6, the regional electric field strength E6, and the ion velocity u7 when the ion leaves the reflection region and arrives at the detector are respectively:

[0188]

[0189]

[0190] u6 = u4

[0191]

[0192] Among them, the ion velocity when the ion just enters the electric field of the time-of-flight mass spectrometer. m represents the ion mass, E represents the kinetic energy at the initial moment, w represents the distance between the ion and the central axis of the ion beam, and q represents the charge quantity in the charge-to-mass ratio of the ion beam. This represents the set value, which ranges from 0.8897 to 0.88976.

[0193] In this embodiment, for simplicity, it is assumed that the electric field strength is 0 when x→-∞ and constant at E when x→+∞ for the grid composed of parallel wires, and the spacing between adjacent wires is d. The expression for the electric field components near the grid composed of uniformly distributed wires is:

[0194]

[0195] In the formula, Analyzing the graph of the above function can The entire region is treated as a uniform electric field, and the main consideration is the flight of ions from the negative x-axis to... The velocity change produced at that point, specifically as follows: Figure 5 As shown.

[0196] The flight path of ions can be determined using the energy conservation equation and small-scale processing. The velocity change produced at:

[0197]

[0198] Rewritten as:

[0199]

[0200] in

[0201]

[0202] Consider it from a statistical perspective Regarding the impact on the final result, random numbers were used to select the ions when passing through each grid. The values ​​of are determined by obtaining a sufficient number of samples through a large number of ion inputs, thereby obtaining statistical regularities.

[0203] Numerical simulation results show that This is a good empirical value. For high-resolution time-of-flight mass spectrometry, the error between the result obtained using the above empirical value and the result obtained from random number simulation is less than 1%. Figure 6 As shown, for the general electric field case, the following calculation results are obtained:

[0204]

[0205] The third implementation considers the effect of the rise time of the electrode voltage on the ion flight time. The electrode potential needs a certain amount of time to rise from 0 to V1. During this time, the voltage rises rapidly, but it still differs from the rectangular signal. We use a ramp signal to linearly approximate the rising voltage and classify the ions entering the acceleration zone at different times. We then use similar steps from the first two implementations to calculate the corresponding flight time.

[0206] In the time-of-flight mass spectrometer, the spacing between the grid and the corresponding wire in each electrode is d. Assuming that it takes time t0 for the voltage of the first positive electrode to rise from 0 to the electrode voltage V1, this time t0 is added to the ion flight time, specifically in two cases:

[0207] Assuming that it takes time t0 for the plate voltage to rise from 0 to a predetermined value V1, for the sake of simplifying the calculation, the voltage can be considered to rise linearly, that is:

[0208]

[0209] At time t = 0, the plate voltage is 0. Since the initial positions and energies of the ions differ, the time it takes for them to reach the acceleration region will also differ. Based on the voltage rise curve, we can divide the situation into two cases: Case 1, the ions reach the acceleration region before t0; Case 2, the ions reach the acceleration region after t0.

[0210] Let the initial position and velocity (z, u1) of a certain ion be set, where,

[0211] electric field strength at steady state

[0212]

[0213] If the ion has not entered the acceleration region by time t, then its position at time t is...

[0214] Therefore, at time t0 we have:

[0215]

[0216] The following classifications exist:

[0217] z t0 When <0, condition 1 is met;

[0218] z t0 When the value is greater than 0, condition 2 is met.

[0219] Let t1 be the time required for an ion to reach the acceleration region, and u2 be its velocity in the direction parallel to the electric field upon arrival. (Here, t1 and u2 are defined the same as in the previous two implementations.)

[0220] In scenario 1,

[0221] time:

[0222]

[0223] This is a cubic equation. The non-negative real roots t1 can be found by directly calling the MATLAB polynomial root finder function roots().

[0224] Corresponding speed:

[0225]

[0226] In scenario 2,

[0227] The velocity of the ion in the direction parallel to the electric field at time t0:

[0228]

[0229]

[0230] time:

[0231]

[0232] The remaining calculation process is completely consistent with the second implementation method, and will not be described in detail here.

[0233] After obtaining the calculation results in the above three implementation methods, corresponding two-dimensional and three-dimensional display diagrams can be drawn by plotting. By simply inputting the value range of each variable, a distribution diagram of the time resolution as the variable changes can be obtained, thus intuitively displaying the relationship between each variable parameter and the time resolution to the user.

[0234] The preferred embodiments of the present invention have been described in detail above, but it should be understood that, if necessary, aspects of the embodiments can be modified to utilize aspects, features, and concepts from various patents, applications, and publications to provide other embodiments.

[0235] In light of the detailed description above, these and other changes can be made to the embodiments. Generally, the terminology used in the claims should not be considered limited to the specific embodiments disclosed in the specification and claims, but should be understood to include all possible embodiments together with the full scope of equivalents enjoyed by these claims.

Claims

1. A parameter design method for a time-of-flight mass spectrometer, characterized in that, include: The parameters of the time-of-flight mass spectrometer, the charge-to-mass ratio of the ion beam, the upper limit of the ion beam width, and the upper limit of the ion beam energy are preset. The ion beam is introduced into the time-of-flight mass spectrometer. The flight time of the ions in the ion beam at different initial positions and different initial kinetic energies is calculated by substituting the preset parameters of the time-of-flight mass spectrometer into the kinetic equation. A discretized matrix is ​​constructed based on the ion flight time. Based on the initial position and initial kinetic energy of the ions, a two-dimensional probability density function of the ion beam is constructed. Based on the two-dimensional probability density function and the discretization matrix, the intensity matrix of the ion beam is constructed. Based on the intensity matrix, the time-of-flight-intensity peak curve is obtained. The time resolution of the time-of-flight mass spectrometer at the preset parameter values ​​of the time-of-flight mass spectrometer is calculated based on the time-of-flight-intensity peak curve. By changing any one or more of the parameter values, the discretization matrix, the two-dimensional probability density function, and the time-of-flight intensity peak curve are reconstructed. The time resolution of the time-of-flight mass spectrometer under the changed parameter values ​​is recalculated so that the time resolution converges to the maximum time resolution. The changed parameter values ​​corresponding to the maximum time resolution are used as the optimal parameter design of the time-of-flight mass spectrometer. The discretization matrix refers to: Among them, ± w m This indicates the upper and lower limits of the initial moment width distribution of the ion beam. w m The value is taken as 1 / 2 of the ion beam width; ± E m This indicates the upper and lower limits of the kinetic energy distribution of the ion beam at the initial moment. E m The value is taken as the upper limit of the ion beam energy; T(.,.) represents the flight time of the ion; The two-dimensional probability density function refers to: in, w This indicates the distance between the ion and the central axis of the ion beam. E This represents the initial kinetic energy of the ion; ; ; The intensity matrix of the ion beam refers to: The intensity values ​​in the intensity matrix of the ion beams with the same ion flight time in the discretized matrix are algebraically summed to obtain the flight time-intensity peak curve.

2. The parameter design method for a time-of-flight mass spectrometer according to claim 1, characterized in that, The time resolution of the time-of-flight mass spectrometer calculated based on the time-of-flight-intensity peak curve at the preset parameter values ​​of the time-of-flight mass spectrometer refers to: The following formula is used for calculation: Among them, R t Indicates time resolution. t Δ represents the flight time corresponding to the peak value in the time-intensity peak curve. t R is the half-peak width corresponding to the peak value in the time-of-flight intensity peak curve. m Indicates quality resolution.

3. The parameter design method for a time-of-flight mass spectrometer according to claim 1, characterized in that, The process involves changing one or more of the parameter values, reconstructing the discretized matrix, the two-dimensional probability density function, and the time-of-flight-intensity peak curve, recalculating the time resolution of the time-of-flight mass spectrometer under the changed parameter values, such that the time resolution converges to its maximum value, and using the changed parameter values ​​corresponding to the maximum time resolution as the optimal parameter design for the time-of-flight mass spectrometer. This includes: The mass spectrometry-gradient descent algorithm is used to find the possible optimal solutions for the values ​​of the parameters. Using the possible optimal solution as initial conditions, the optimal parameter design is obtained by using the Nesterov accelerated gradient algorithm.

4. The parameter design method for a time-of-flight mass spectrometer according to claim 3, characterized in that, The method of finding the possible optimal solution for each parameter value using the mass spectrometry-gradient descent algorithm involves first setting any one or more of the parameter values ​​as an independent variable vector, and treating the other parameter values ​​as invariants, and then calculating using the following formula: in, α These are parameters used to adjust the step size; ε is a constant introduced to prevent the denominator from being 0; |.| is the absolute value sign, corresponding to the function abs in MATLAB; sgn is the sign function, corresponding to the function sign in MATLAB; θ n This represents a set of values ​​for the independent variable vector after the nth iteration; θ n+1 This represents another set of values ​​for the independent variable vector after the (n+1)th iteration; ▽f(θ) is taken as the gradient value of the time resolution as the objective function; Until the other set of values ​​of the independent variable vector converges to the maximum value of the time resolution within the set range, the other set of values ​​of the independent variable vector and the invariant are used to form the changed parameter values ​​as the possible optimal solution of the parameter values.

5. The parameter design method for a time-of-flight mass spectrometer according to claim 4, characterized in that, The Nesterov accelerated gradient algorithm first jumps in a cumulative gradient direction. The gradient of the point after the jump is calculated and then weighted and summed with the previous jump amount, using the following formula: Equation (6) Equation (7) in, γ Indicates the weighting coefficient. η This represents the learning rate of the gradient descent algorithm. V t This represents the step size after the nth iteration. V t-1 This represents the step size after the (n-1)th iteration.

6. The parameter design method for a time-of-flight mass spectrometer according to claim 1, characterized in that, The preset time-of-flight mass spectrometer has six electrode stages: a first positive electrode, a first negative electrode, a second electrode, a third electrode, a fourth electrode, and a fifth electrode. The first positive and first negative electrodes form the ion beam entry region; the first negative and second electrodes form the acceleration region; the second and third electrodes form the drift region; the third and fourth electrodes form the first reflection region; and the fourth and fifth electrodes form the second reflection region. The movement of ions in the first and second reflection regions is symmetrical. The vertical distances d1, d2, d3, and d4 of the ion beam entry region, the acceleration region, and the reflection region are the sum of d4 and d5. The distance d6 between the detector and the reflection region is also specified. The electrode voltage of the first positive electrode is... The voltage of the first negative plate - The voltage across the second plate The voltage across the third plate The voltage of the fourth plate The voltage of the fifth plate Detector voltage 6.

7. The parameter design method for a time-of-flight mass spectrometer according to claim 6, characterized in that, The dynamic equation is: The flight time of ions when they enter the ion beam entry region and reach the first negative electrode plate Regional electric field strength Ion velocity They are respectively: The flight time of ions when they enter the acceleration region and reach the second electrode plate Regional electric field strength Ion velocity They are respectively: The flight time of ions when they enter the drift region and reach the third electrode plate Regional electric field strength Ion velocity They are respectively: =0 The flight time of ions when they enter the first reflective region and reach the fourth electrode plate Regional electric field strength Ion velocity They are respectively: The flight time of ions entering the second reflective region Regional electric field strength They are respectively: The time of flight of ions from the reflector to the detector Regional electric field strength Ion velocity They are respectively: Among them, the ion velocity when the ion just enters the electric field of the time-of-flight mass spectrometer. , , Indicates the mass of the ion. This represents the kinetic energy at the initial moment. This indicates the distance between the ion and the central axis of the ion beam. This indicates the amount of charge in the charge-to-mass ratio of the ion beam.

8. The parameter design method for a time-of-flight mass spectrometer according to claim 6, characterized in that, In the time-of-flight mass spectrometer, the spacing between the grid and the corresponding wire in each electrode is d. The dynamic equation is: The flight time of ions when they enter the ion beam entry region and reach the first negative electrode plate Regional electric field strength Ion velocity They are respectively: The flight time of ions when they enter the acceleration region and reach the second electrode plate Regional electric field strength Ion velocity They are respectively: The flight time of ions when they enter the drift region and reach the third electrode plate Regional electric field strength Ion velocity They are respectively: The flight time of ions when they enter the first reflective region and reach the fourth electrode plate Regional electric field strength Ion velocity They are respectively: The flight time of ions entering the second reflective region Regional electric field strength They are respectively: The time of flight of ions from the reflector to the detector Regional electric field strength Ion velocity They are respectively: Among them, the ion velocity when the ion just enters the electric field of the time-of-flight mass spectrometer. , , Indicates ion mass. This represents the kinetic energy at the initial moment. This indicates the distance between the ion and the central axis of the ion beam. This represents the amount of charge in the charge-to-mass ratio of the ion beam. This represents the set value, which ranges from 0.8897 to 0.88976.

9. The parameter design method for a time-of-flight mass spectrometer according to claim 8, characterized in that, In the time-of-flight mass spectrometer, the spacing between the grid and the corresponding electrode is d. Assume the voltage of the first positive electrode increases from 0 to the electrode voltage of the first positive electrode. It takes time t 0, then the time will be... t 0 is added to the ion flight time.

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