Multiple reflection mass analyzer

Abstract

We provide a multiple reflection time-of-flight mass spectrometer. [Solution] The compensating electrodes extend along the Y direction in or adjacent to the space between the mirrors. Each compensating electrode has a surface parallel to the YZ plane, shaped so that its separation from one of the mirrors varies along the Y direction. The compensating electrodes are biased to produce a composite voltage offset that varies as a function of distance along the Y direction. A first component compensates for intended aberrations arising from the mirror tilt, and a second component compensates for unintended aberrations arising from perturbations with respect to the ideal time of flight, ranging from maximum to minimum perturbation. The shape of the compensating electrodes is such that some or all of the compensating electrodes can be excited to produce a range of composite voltage offsets that compensate for a range of time-of-flight aberrations corresponding to the intended and unintended aberrations.

Description

[Technical Field]

[0001] This invention relates to the field of mass spectrometers, and more specifically to time-of-flight mass spectrometry and electrostatic trap mass spectrometry utilizing multiple reflection techniques for extending ion flight paths. [Background technology]

[0002] Various configurations are known that utilize multiple reflections to extend the flight paths of ions within a mass spectrometer. Extending the flight paths is desirable to increase the time-of-flight separation of ions in a time-of-flight (ToF) mass spectrometer because it enhances the ability to distinguish small mass differences between ions.

[0003] An example of a multiple reflection time-of-flight (MR-ToF) mass spectrometer can be found in International Publication No. 2013 / 110587. Two parallel, opposing mirror electrodes are elongated in the drift direction (Y direction). Ions are extracted from an ion trap and injected into the mirror electrodes, where they are reflected between the mirror electrodes (Z direction) while drifting relatively slowly along the extended length of the mirror electrodes in the drift direction. Thus, the ions follow a zigzag flight path through the mass spectrometer.

[0004] Furthermore, the mirror electrodes are tilted by an angle Θ such that their separation in the X direction decreases as they extend in the drift direction. Ions that begin to oscillate between opposing mirror electrodes also drift in the Y direction due to the initial tilt into which the ions were injected into the mirror electrodes. The mirror focusing tilt angle Θ reduces the trajectory tilt angle by 2Θ for each oscillation involving two reflections. As a result, the drift direction is eventually reversed so that the ions return through the mirror electrodes and are detected by an ion detector positioned adjacent to the ion trap.

[0005] However, tilted mirror electrodes introduce ToF aberrations because not all ions follow a common path through the mirror electrodes. The finite spread of the beam angle in which ions are injected into the mirror electrodes causes some ions to drift further down the mirror electrodes than others. Ions entering through the mirror electrodes at a shallow angle to the longitudinal axis drift further down the mirror electrodes than ions injected at a relatively steep angle. Advantageously, the ions are spatially focused again as they return to the ion detector. However, time aberrations are introduced because the ion oscillation period decreases as a function of distance along the drift direction as a result of the decreasing distance between the mirror electrodes.

[0006] These ToF aberrations are corrected by decelerating the ions as they traverse between the mirror electrodes using stripe electrodes. The stripe electrodes are shaped to generate a voltage that changes as a function of distance along the mirror electrodes. The electric field increases along the drift direction so that the ions are decelerated as they drift further along the mirror electrodes. This deceleration increases the period of the oscillation as a function of distance along the drift direction, thereby mitigating the decrease in period due to the focusing mirror electrodes.

[0007] The voltage applied to the stripe electrodes can be adjusted to generate an electric field that cancels out the ToF aberration resulting from the angular spread of ions injected into the mirror electrodes. This correction helps to generate substantially equal oscillation times for each oscillation of ions between opposing mirror electrodes at all positions along the drift length, even as the distance between the mirrors changes.

[0008] These striped electrodes are designed to compensate for the unavoidable ToF aberrations that occur even in perfect mirror electrodes due to the required gradient.

[0009] An alternative MR-ToF analyzer is described in U.S. Patent Application Publication No. 2020 / 0243322. The analyzer includes mirror electrodes that are parallel rather than inclined, so ions travel along the length of the mirror electrodes at a constant drift velocity and are detected at the end of the mirror electrode opposite the ion trap into which the ions are injected.

[0010] U.S. Patent Application Publication No. 2020 / 0243322 includes strip electrodes, but for reasons different from those of International Publication No. 2013 / 110587, there is no need to correct the ToF errors resulting from intentionally tilting the mirror electrodes. Instead, a first pair of curved strip electrodes is used to correct any curvature in the mirror electrodes. A second pair of strip electrodes is used to correct misalignment between the mirror electrodes.

Summary of the Invention

Means for Solving the Problems

[0011] According to a first aspect, a multi-reflection time-of-flight mass spectrometer is provided that includes two ion optical mirrors. Each mirror is elongated generally along a drift direction (Y direction) away from an ion injection point, and each mirror faces the other in the Z direction, where the Z direction is orthogonal to the Y direction. The two mirrors are tilted such that the separation between the mirrors in the Z direction decreases as the distance along the Z direction increases.

[0012] The mass spectrometer further comprises at least two correction electrodes extending along at least a portion of the Y direction within or adjacent to the space between the mirrors. Each correction electrode has a surface substantially parallel to the Y-Z plane and is shaped such that the surface is separated from one of the mirrors by a distance that varies along the Y direction. In use, the correction electrodes are electrically biased with a voltage so as to generate a combined voltage offset that varies as a function of the distance along the Y direction in at least a portion of the space extending between the opposing mirrors. The voltage includes a first component for correcting an intended aberration resulting from the intended tilt angle of the mirror, and / or a second component for correcting an unintended aberration resulting from the range of perturbations with respect to the ideal flight time extending from the maximum perturbation to the minimum perturbation (such as perturbations resulting from mechanical imperfections of the mirror), and the second component varies between a maximum value and a minimum value. The shapes of the at least two correction electrodes are selected such that some or all of the at least two correction electrodes can be biased with a voltage including the first component and the second component that varies between the maximum value and the minimum value to generate a range of combined voltage offsets. These offsets correct for the range of flight time aberrations corresponding to the intended aberration resulting from the intended tilt angle of the mirror and the unintended aberration resulting from the range of perturbations with respect to the ideal flight time extending from the maximum perturbation to the minimum perturbation.

[0013] The ideal flight time of ions passing through the mass spectrometer corresponds to the flight time of ions passing through the mirrors when the mirrors are perfectly flat, set to the intended tilt angle, and perfectly aligned. The correction electrodes provide both correction for the intended tilt angle between the mirrors via the first component and correction for errors in the actual configuration of the mirrors via the second component. For example, the mirrors may be misaligned and not at the precisely intended tilt angle. Also, the mirrors may not be perfectly straight and may have curvature due to sag (caused by both gravity and other factors such as stress relief within the mirrors and other machining imperfections).

[0014] The range of perturbations relative to the ideal time of flight can extend from the maximum perturbation due to the maximum positive misalignment error in the mirror to the minimum perturbation due to the maximum negative misalignment error in the mirror. The maximum positive and maximum negative misalignment errors may be the maximum and minimum misalignment errors expected to affect the mass spectrometer. The maximum positive and maximum negative misalignment errors may correspond to manufacturing tolerances. As a mere example, shims may be used to introduce an intended inclination to other parallel mirror pairs, in which case the maximum positive and maximum negative misalignment errors may correspond to manufacturing tolerances near the nominal thickness of the shims.

[0015] The compensation electrode can be shaped so that the combined voltage offset acts to shorten or lengthen the average drift length of the ion in the +Y direction through the mirror before the ion is reflected and drifts back in the -Y direction through the mirror. This configuration allows for compensation of smaller misalignment errors. For larger misalignment errors, a larger combined voltage offset may be used, which increases or decreases the number of vibrations the ion makes as it drifts through the mirror.

[0016] The range of perturbations relative to the ideal time of flight can extend from the maximum perturbation due to the maximum positive curvature error in the mirror to the minimum perturbation due to the maximum negative curvature error in the mirror. The maximum positive curvature error and the maximum negative curvature error may be the maximum and minimum curvature errors expected to affect the mass spectrometer. The maximum positive curvature error and the maximum negative curvature error in the mirror may correspond to the curvature of the mirror due to sag.

[0017] At least one compensating electrode may be shaped to compensate for both misalignment and curvature errors. Alternatively, the shape of one of at least two compensating electrodes may compensate for misalignment independently of curvature, and the shape of the other of at least two compensating electrodes may compensate for curvature independently of misalignment.

[0018] Optionally, at least two correction electrodes include one or more pairs of correction electrodes. A pair or each pair of correction electrodes may include a first correction electrode shaped to produce a voltage offset that compensates for intended aberrations resulting from the intended tilt angle of the mirror and unintended aberrations resulting from the maximum perturbation when a voltage equal to the maximum value of the first component + the second component is applied. A pair or each pair of correction electrodes may include a second correction electrode shaped to produce a voltage offset that compensates for intended aberrations resulting from the intended tilt angle of the mirror and unintended aberrations resulting from the minimum perturbation when a voltage equal to the minimum value of the first component + the second component is applied. The first and second correction electrodes may be shaped to produce different average drift lengths of ions passing through the mirror. The physical lengths of the first and second correction electrodes in the Y direction may be different. When correction for the maximum perturbation is required, the first correction electrode is subjected to a voltage equal to the maximum value of the first component plus the second component, while the second correction electrode is grounded. When correction for the minimum perturbation is required, the second correction electrode is subjected to a voltage equal to the minimum value of the first component plus the second component, while the first correction electrode is grounded. When correction for perturbations between the maximum and minimum perturbations is required, the first and second correction electrodes are subjected to a voltage equal to half of the first component plus a value between a predetermined minimum and maximum value of the second component. Each correction electrode then contributes half of the required first component, which are then added together to provide correction for the mirror tilt, and are then adjusted as needed by the second component to correct for unintended perturbations. If the mirror is precisely as intended, no correction for unintended aberrations is necessary, and the first and second corrective electrodes offset the corrections given for maximum and minimum perturbations by being energized with equal voltages having half the value of the first component plus the same value of the second component. The value of the second component may be zero. In such a configuration, each corrective electrode compensates for both intended and unintended time-of-flight aberrations, so the shape of the corrective electrode must be a composite shape that reflects both functions.

[0019] Alternatively, different compensating electrodes can be used to compensate for intended and unintended time-of-flight aberrations. For example, at least two compensating electrodes may include at least a first compensating electrode having a shape for compensating intended time-of-flight aberrations, and a second compensating electrode having a shape corresponding to the difference between the required shapes, wherein when a voltage equal to the maximum value of the first component + the second component is applied, the second compensating electrode generates a voltage offset that compensates for the maximum perturbation, and when a voltage equal to the minimum value of the first component + the second component is applied, the second compensating electrode generates a voltage offset that compensates for the minimum perturbation. If the mirror is precisely intended, no compensation for unintended aberrations is required, and therefore the second compensating electrode is grounded, and at least the first compensating electrode is used to compensate for the intended aberrations. If correction of unintended aberrations is required, the second electrode is biased with a voltage between the maximum and minimum values ​​of the second component to provide the necessary correction, where the maximum value corrects the maximum perturbation, the minimum value corrects the minimum perturbation, and the value of the second component between the maximum and minimum values ​​corrects the perturbation between the maximum and minimum perturbations. At least the first correction electrode may be a pair of electrodes flanking the second correction electrode. Each of the electrode pair may be subjected to a voltage equal to half of the first component.

[0020] A second aspect provides a method for operating a multiple reflection time-of-flight mass spectrometer. The spectrometer comprises two ion optical mirrors, each mirror being elongated generally along the drift direction (Y direction) away from the ion implantation point, each mirror facing the other in the Z direction, and the Z direction being perpendicular to the Y direction. The two mirrors are tilted such that the separation between the mirrors in the Z direction decreases as the distance along the Y direction increases. The spectrometer further comprises at least two correction electrodes extending along at least a portion of the Y direction in the space between the mirrors or adjacent to that space. Each correction electrode has a surface substantially parallel to the YZ plane and is shaped such that the surface is separated from one of the mirrors by a distance that changes along the Y direction. When in use, the compensating electrodes are electrically biased with a voltage to produce a composite voltage offset that varies as a function of distance along the Y direction in at least a portion of the space extending between the opposing mirrors, the voltage comprising a first component for compensating for intended aberrations arising from the intended tilt angle of the mirrors and a second component for compensating for unintended aberrations arising from a range of perturbations relative to the ideal time of flight, ranging from maximum to minimum perturbation (such as aberrations arising from mechanical imperfections of the mirrors), the second component varying between a maximum and minimum value. The shapes of at least two compensating electrodes are selected such that some or all of the at least two compensating electrodes are subjected to a voltage having a value including the first component and the second component varying between a maximum and minimum value, to produce a composite voltage offset that compensates for a range of time-of-flight aberrations corresponding to a range of perturbations relative to the ideal time of flight, ranging from maximum to minimum perturbation.

[0021] The method includes exciting the mirror to provide an electric field that causes ions to follow a zigzag path through the mirror. The method also includes applying a voltage having a value including a first component and / or a second component to each of at least two compensating electrodes so that the at least two compensating electrodes produce a combined voltage offset that compensates for time-of-flight aberrations within the range of perturbations relative to the ideal time of flight, spreading from maximum to minimum perturbation. The method further includes implanting ions from an ion source into the mirror and detecting the ions with an ion detector located at the same end of the mirror as the ion source.

[0022] Optionally, at least two correction electrodes include one or more pairs of correction electrodes. A correction electrode or each pair of correction electrodes may include at least a first correction electrode shaped to produce a voltage offset that compensates for the maximum perturbation when a voltage equal to the maximum value of the first component + the second component is applied to the first correction electrode. A correction electrode or each pair of correction electrodes may further include a second correction electrode shaped to produce a voltage offset that compensates for the minimum perturbation when a voltage equal to the minimum value of the first component + the second component is applied to the second correction electrode. Next, the method may include (i) compensating for the maximum perturbation by applying a voltage equal to the maximum value of the first component plus the second component to the first corrector electrode and not to the second corrector electrode; (ii) compensating for the minimum perturbation by applying a voltage equal to the minimum values ​​of the first and second components to the second corrector electrode and not to the first corrector electrode; or (iii) compensating for the perturbation between the maximum and minimum perturbation by applying a voltage equal to half of the first component plus the value between the maximum and minimum values ​​of the second component to the first corrector electrode and applying a voltage equal to half of the first component plus the value between the maximum and minimum values ​​of the second component to the second electrode.

[0023] Optionally, at least two correction electrodes include at least a first correction electrode having a shape that compensates for time-of-flight aberration corresponding to the intended tilt angle of the mirror along the Y direction when a voltage equal to the first component is applied. The at least two correction electrodes may further include a second correction electrode having a shape corresponding to the difference between the required shapes, wherein when a voltage equal to the maximum value of the second component is applied, the second correction electrode generates a voltage offset that compensates for the maximum perturbation, and when a voltage equal to the minimum value of the second component is applied, the second correction electrode generates a voltage offset that compensates for the minimum perturbation. Next, the method may include (i) compensating for the maximum perturbation by applying a voltage equal to the first component to at least a first corrective electrode and a voltage having the maximum value of the second component to a second electrode in order to compensate for the intended time-of-flight aberration; (ii) compensating for the minimum perturbation by applying a voltage equal to the first component to at least a first corrective electrode and a voltage having the minimum value of the second component to a second electrode in order to compensate for the intended time-of-flight aberration; or (iii) compensating for the perturbation between the maximum and minimum perturbation by applying a voltage equal to the first component to at least a first corrective electrode and a voltage having a value between the maximum and minimum values ​​of the second component to a second electrode in order to compensate for the intended time-of-flight aberration. The at least first corrective electrode may be a pair of electrodes flanking the second corrective electrode. Each of the electrode pair may be to which a voltage equal to half of the first component is applied.

[0024] A third aspect provides a method for designing a multiple reflection time-of-flight mass spectrometer. The method involves configuring an ideal arrangement of an ion source, an ion detector, and two ion optical mirrors, each of which is elongated along the drift direction (Y direction) away from the ion implantation point, and each of which faces the other in the Z direction perpendicular to the Y direction, thereby configuring ions supplied from the ion source to enter the mirrors at the ion implantation point and then follow a zigzag path through the mirrors when the mirrors are excited to provide an electric field. The method also includes configuring at least two compensating electrodes extending in or adjacent to the space between mirrors along at least a portion of the Y-direction, each of which has a surface substantially parallel to the YZ plane and is shaped such that it is separated from one of the mirrors by a distance that varies along the Y-direction, and the compensating electrodes are electrically biased with a voltage to produce a combined voltage offset that, when in use, varies as a function of distance along the Y-direction in at least a portion of the space extending between opposing mirrors, wherein the voltage comprises a first component for compensating for intended aberrations arising from the intended tilt angle of the mirrors and a second component for compensating for unintended aberrations arising from a range of perturbations with respect to the ideal time of flight from maximum to minimum perturbation (such as aberrations arising from mechanical imperfections of the mirrors), the second component varying between a maximum and a minimum value. The method also includes determining the maximum and minimum perturbations away from the ideal arrangement of the mirrors, and the resulting maximum and minimum aberrations in the time of flight of ions passing through the mirrors. The method may also include determining the shape of at least two compensating electrodes such that some or all of the two compensating electrodes are subjected to a voltage having a value comprising a first component and a second component varying between a maximum and a minimum value, thereby generating a range of combined voltage offsets that compensate for a range of time-of-flight aberrations extending from the maximum perturbation to the minimum perturbation.

[0025] This method may include determining the shapes of at least two correction electrodes to compensate for the range of time-of-flight aberrations corresponding to perturbations ranging from the maximum perturbation due to the maximum positive displacement value in the mirror to the minimum perturbation due to the maximum negative displacement value in the mirror, relative to the ideal time of flight.

[0026] The combined voltage offset can act to shorten or lengthen the average drift length of an ion in the +Y direction through the mirror before the ion is reflected and drifts back through the mirror in the -Y direction. The combined voltage offset can also act to increase or decrease the number of vibrations an ion makes as it drifts through the mirror.

[0027] This method may include determining the shapes of at least two correction electrodes to compensate for the range of time-of-flight aberrations corresponding to perturbations ranging from the maximum perturbation due to the maximum positive curvature error in the mirror to the minimum perturbation due to the maximum negative curvature error in the mirror, relative to the ideal time of flight. The maximum positive curvature error and the maximum negative curvature error in the mirror correspond to the curvature of the mirror due to sag.

[0028] This method may include determining the shape of one of at least two correction electrodes so as to compensate for misalignment error independently of curvature error, and determining the shape of the other of at least two correction electrodes so as to compensate for curvature error independently of misalignment error.

[0029] Optionally, at least two correction electrodes include one or more pairs of correction electrodes. The method may then include determining the shape of the first correction electrode or each pair of correction electrodes such that when a voltage equal to the maximum value of the first component + the second component is applied, the first correction electrode produces a voltage offset that compensates for the maximum perturbation. The method may also include determining the shape of the second correction electrode such that when a voltage equal to the minimum value of the first component + the second component is applied, the second correction electrode produces a voltage offset that compensates for the minimum perturbation. The first and second correction electrodes may be shaped to produce different average drift lengths of ions passing through the mirror. The lengths of the first and second correction electrodes in the Y direction may be different.

[0030] Optionally, the method includes determining the shape of at least a first compensating electrode that compensates for time-of-flight aberration corresponding to the intended tilt angle of the mirror along the Y direction when a voltage equal to the first component is applied. The method may also include determining the shape of a second compensating electrode to correspond to the difference between the required shapes such that when a voltage having the maximum value of the second component is applied, the second compensating electrode generates a voltage offset that compensates for the maximum perturbation, and when a voltage having the minimum value of the second component is applied, the second compensating electrode generates a voltage offset that compensates for the minimum perturbation.

[0031] To facilitate understanding of the present invention, the accompanying drawings are provided for illustrative purposes only. [Brief explanation of the drawing]

[0032] [Figure 1] This is a schematic diagram of a conventional multiple reflection time-of-flight mass spectrometer. [Figure 2] This is a schematic diagram of a mirror assembly design that provides a focusing angle via shims. [Figure 3A] The normalized shape function for the correction electrode is shown. [Figure 3B]This shows the time-of-flight correction obtained when the correction electrode and mirror tilt work together. [Figure 4] This is a schematic diagram of a first embodiment of a multiple reflection time-of-flight mass spectrometer having correction electrodes of unequal physical length. [Figure 5A] The correction electrode shape is shown as a function of the drift coordinate "y" normalized to different drift lengths L1 and L2. [Figure 5B] It provides a variable effective drift length L of 300mm to 400mm, thereby exhibiting an array with two pairs of correction electrodes having different shapes and different electrical biases to compensate for mirror misalignment. [Figure 6A] The shape function represents the shape function of the differential correction electrode, which is equal to the difference between the shape functions normalized to the corresponding effective drift lengths of 375 mm and 325 mm. [Figure 6B] This configuration shows a configuration having three pairs of correction electrodes, including one pair of differential correction electrodes that are biased by voltage U1. [Figure 7A] This shows the shape function of the correction electrode that achieves the optimal solution for a mirror with a sag parameter of ±0.01 mm. [Figure 7B] Its shape is estimated from the difference between the shapes in Figure 7A, and it shows a configuration having a pair of correction electrodes that are biased to compensate for slack. [Figure 8] The correction electrodes include a pair of differential correction electrodes that correct both curves. [Modes for carrying out the invention]

[0033] As described above, mass spectrometers typically utilize multiple reflections to extend the flight path of ions, which is desirable because it increases the time-of-flight separation of ions and therefore increases the resolution within the time-of-flight (ToF) mass spectrometer. Figure 1 shows an example of a multiple reflection time-of-flight (MR-ToF) mass spectrometer 10. A pair of ion optical mirrors are provided by two elongated, parallel, opposing mirror electrodes 12 in the drift direction (y-direction). Ions 20 are extracted from an ion trap 14 and injected into the mirror electrodes 12. The ions 20 are beam-shaped by a lens / deflector 18 before being reflected from the first mirror electrode 12. The expanding ion beam then strikes a second deflector and drift focusing lens 19, which set the final injection angle and parallelize the ion beam 20 as much as possible. Ion 20 is then subjected to multiple reflections (in the z direction) between the mirror electrodes 12, while drifting relatively slowly along the extended length of the mirror electrodes 12 in the drift (y) direction. Thus, ion 20 follows a zigzag flight path through the mass spectrometer 10.

[0034] Furthermore, the mirror electrodes 12 are tilted by an angle Θ (typically about 0.05 degrees) such that their separation in the z-direction decreases as they extend in the drift direction. The focusing angle Θ reduces the orbital tilt angle of the ions 20 by 2Θ for each vibration (each vibration involves two reflections). As a result, the drift of the ions 20 is eventually reversed, and the ions 20 return through the mirror electrodes 12 and are detected by the ion detector 16 positioned adjacent to the ion trap 14.

[0035] Because the ion beam 20 has a small spread at the injection angle, it spreads as it drifts along the mirror electrode 12. Therefore, the drift length of the ion along the mirror electrode 12 varies depending on the injection angle of the ion. Ions 20 injected at a relatively steep angle have a lower velocity component in the y direction and therefore drift a shorter distance along the mirror electrode 12 than ions injected at a relatively shallow angle, which have a higher velocity component in the y direction. A small inclination angle Θ acts to spread the time of flight of the ion 20 because ions 20 that drift further along the mirror electrode 12 pass through a narrower gap between the mirror electrodes 12 than ions 20 that do not drift as far. This results in different times of flight for ions 20 with the same m / z ratio but different injection angles, and consequently, a loss of resolution.

[0036] The error introduced by the tilted mirror electrode 12 is addressed by adding a pair of correction electrodes 24 along the length of the drift dimension, with one correction electrode 24 positioned above the ion beam 20 and the other below the ion beam 20. The edge of each correction electrode 24 has a shape determined by a shape function S(y) corresponding to the error to be corrected. The shape function can define the width (z direction) of the correction electrode 24 as a function of position along the drift (y) direction. The correction electrodes 24 modify the electric field in the region through which the ions 20 propagate, thus causing additional drift deflection and time-of-flight perturbations in the ions 20. Furthermore, the correction to the electric field can be configured so that the correction electrodes 24 counteract the focusing effect of the mirror electrode, ensuring that all ions 20 have the same time-of-flight from the ion trap 14 to the ion detector 16, regardless of any variations in the starting point y0 and initial drift velocity v0 = dy0 / dt.

[0037] This correction can be achieved by changing the value of the focusing angle Θ of the mirror electrode by adopting a specific shape of the correction electrode 24. This shape can be defined by a shape function S(y), which is a polynomial that describes the width of the correction electrode 24 in the z direction at each value y along the drift direction y.

[0038]

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[0039]

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[0040] Optimizing the coefficient c[n] minimizes the variance of the time of flight for ion 20 with the same m / z ratio. The function s(y / l) can take negative values, but the shape function S(y) is kept positive by selecting c0, which ensures that the stripe width S(y) is positive for all values ​​of y.

[0041] An example of the normalized function s(y) is shown in Figure 3A. Figure 3B shows the obtained time-of-flight error versus the ion injection angle, and in particular, a very reduced time-of-flight error plateau achieved within 30% of the injection angle. This reduction in time-of-flight dispersion minimizes the width of the detected ion peak caused by the thermal dispersion of the initial ion velocity.

[0042] Ion drift is due to voltage U sAnd two pseudo-potentials Φ generated from the correction electrode 24 biased at the focusing angle Θ. s (y) and Φ m This can be explained by the adiabatic approximation using (y).

[0043]

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[0044]

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[0045]

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[0046]

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[0047] To ensure that ions 20 are incident on the ion detector 16, the total drift time from y=0 to y=L and back to y=0 is set to the time per vibration K0T. oscill It must be a multiple of , where K0 is the number of oscillations (in the z direction) per drift (in the y direction). This requirement, along with the requirement for correcting time-of-flight errors, can be satisfied when the mirror focusing angle Θ takes a specific value using a correction electrode 24 of the shape shown in Figure 3A in normalized coordinate y / L.

[0048] The dimensionless function s(y / L) is strictly defined for the optimal solution, but the drift length L is a free parameter to be selected. The drift length L is related to the mirror focusing angle Θ by the following equation.

[0049]

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[0050] The above describes a time-of-flight mass spectrometer 10 having a predetermined focusing angle Θ of the mirror electrode 12. However, mechanical imperfections may act to counteract the time-of-flight correction provided by the correction electrode 24. For example, mechanical imperfections may include displacement of the mirror electrode 12 from the predetermined focusing angle Θ, and curvature of the mirror electrode 12, such as slack. These defects directly affect the resolution.

[0051] Figure 2 shows a typical configuration for holding the mirror electrode 12 in place. Two parallel rods 26 hold the mirror electrode 12, and the focusing angle Θ is defined by a shim 28 of a certain thickness placed between one end of the mirror electrode 12. The shim 28 is held in place by one of the two parallel rods 26, thereby moving the mirror electrode 12 from parallel alignment. The rods 26 are manufactured from Invar and have exactly equal lengths to maintain a stable focusing angle Θ of the mirror electrode. Figure 2 also shows potential mechanical defects, namely misalignment 30 and slack 32.

[0052] The mass spectrometer 10 is highly sensitive to mechanical imperfections in the mirrors because the ionic energy component of the drift is typically only 1 / 1000 of the total kinetic energy (e.g., the former is 5 eV per charge, and the latter is 4000 eV per charge). The mirror tilt and correction electrode 24 work together to generate a drift-reversal effective potential, which is only a few volts. Any perturbation of the mirror shape affects this effective potential by coupling the vibration direction with the drift direction, disrupting the otherwise precisely balanced compensation for ionic optical aberrations. Both spatial focusing of the drift and ToF aberration compensation are problematic.

[0053] One way to counteract aberrations in ToF is to impose extremely tight tolerances on the mass spectrometer 10, for example, by machining components to an accuracy of less than 10 microns. However, for complex systems with typical dimensions of 0.5m to 3m, such accuracy is virtually impossible to achieve and / or prohibitively expensive, making it unsuitable for mass production.

[0054] Existing correction electrodes 24 have the drawback of being unable to maintain resolution even when small mechanical misalignments of about 10 microns exist. This is because the tilt shifts the focal plane of the ion beam away from the ion detector 16, causing defocusing. Adjusting the voltage of the stripe electrodes 24 to position the voltage of the stripe electrodes 24 moves them away from the voltage required for optimal resolution. The correction electrodes 24 have conflicting requirements for providing beam focus and counteracting time-of-flight errors. Furthermore, existing correction electrodes 24 cannot adequately provide drift focusing when curvature is present in the mirror electrode 12. An additional correction electrode with the function of accommodating the mechanical error of the mirror, as described in U.S. Patent Application Publication No. 2020 / 0243322, can compensate for ToF aberration but does not improve the spatial focusing of ion drift. Therefore, the mass spectrometer 10 with the tilted mirror electrode 12 loses the ability to focus ions 20 onto the ion detector 16.

[0055] Instead of simple compensation of ToF aberration at each Y position of the drift axis (by the correction electrode in U.S. Patent Application Publication No. 2020 / 0243322), the ToF aberration is compensated more effectively on average for the entire number of ion vibrations. While these conditions are not entirely precise, they are still sufficient to maintain the high mass resolution of the mass spectrometer 10. At the same time, the correction electrode 24 should also restore the spatial focusing of ions 20 onto the ion detector 16.

[0056] Precise optimization of the shape function S(y) of the correction electrode 24 is only possible for a specific shape of the mirror electrode 12 and a specific focusing angle Θ of the mirror electrode. In practice, the mirror electrode 12 is linear with an accuracy of ±0.01 mm. The shim thickness has a similar accuracy and results in a residual loss of time-of-flight resolution.

[0057] If the focus angle Θ of the mirror electrode is incorrectly set or changes over time, adjusting the focus angle Θ requires disassembling and reassembling the mirror electrode unit. While this is generally possible during manufacturing, it requires additional manufacturing and testing time. If the focus angle Θ of the mirror electrode changes accidentally during use of the mass spectrometer, a difficult and time-consuming inspection becomes necessary. Such a significant reliance on mirror manufacturing and positioning accuracy is a major drawback of mass spectrometer design.

[0058] It is recognized that further improvements to the shape function S(y) of the correction electrode 24 and the voltage applied to the correction electrode 24 can be used to compensate for various mechanical deviations within the tilt mirror MR-ToF analyzer 10. This allows the ion flight time between the mirror electrodes 12 to be adjusted overall or as a function of the ion implantation angle, enabling specific corrections for errors in the tilt angle Θ of the mirror electrodes or the curvature of the mirror electrodes, acceptance of a wider range of ion implantation angles, or even adjustment of the focal plane position of the ion beam.

[0059] A solution to the mechanical imperfection problem in the mirror electrode 12 involves adding some flexibility to how the compensating electrode 24 is designed and operates. This makes it possible to compensate for time-of-flight errors even if the mirror electrode 12 is not perfectly linear, or if the focusing angle Θ of the mirror electrode deviates from the intended value. Advantageously, during operation, only small adjustments around the voltage set on the compensating electrode 24 are required, and no mechanical adjustments are necessary.

[0060] In the conventional mass spectrometer 10 shown in Figure 1, there are two degrees of freedom available to assist in correcting time-of-flight errors due to mechanical imperfections. Specifically, the correction electrode 24 can be set to any voltage up to 100V, and the initial angle of ion incidence can be corrected by applying a specific voltage to the ion deflector 18. However, this is insufficient to compensate for the adverse effects caused by mechanical imperfections in the mirror electrode 12, as these two parameters alone cannot compensate for the continuity of all possible variations in the shape of the mirror electrode.

[0061] It is recognized that mechanical imperfections require any modification of the function s(y), which cannot be achieved by electrical means alone and necessitate changing the compensating electrode 24 to another compensating electrode 24 having a different shape. Therefore, one or more additional compensating electrodes 24 are introduced to supplement the existing (main) compensating electrode 24. A voltage can be set for the set of compensating electrodes 24, and in some cases, this includes holding one or more of the compensating electrodes 24 to a 0 voltage bias in order to compensate for any mechanical defects. The compensating electrodes 24 are not 0 biased u n It can be activated by applying a certain force, where n=1...N. The effective shape function obtained as a result of the combined correction electrodes is given by linear superposition.

[0062]

number

[0063] Any shape function S * (y) is not to be emulated, but rather, using a finite number of parameters u n to find the shape S that compensates for the most common mechanical imperfections, namely, the misalignment of the mirror electrode 12 (e.g., caused by the imperfection in the thickness of the shim 28) and the relaxation of the mirror electrode 12 (i.e., any curvature of the mirror electrode 12 centered at the center of the support rod 26). n (y) can be found. These are shown in FIG. 2 as an additional angular error 30 and curvature 32 in one of the mirror electrodes 12. Note that since only the sum of the curvatures of the two mirror electrodes 12 is effective in the motion of the ions, the relaxation of both mirror electrodes 12 can be corrected with only one parameter.

[0064] FIG. 4 shows a mass spectrometer 10 that can be used to correct an error in the focusing angle Θ of the mirror electrode, for example, caused by an incorrect shim thickness. The imperfection in the focusing angle Θ of the mirror electrode does not eliminate the correction problem from the class of optimal solutions for the perfectly aligned mirror electrodes 12. The optimal angle given by the above equation (3) is Θ, and when the angle is set imperfectly as Θ * the correction can be made by adjusting the average drift length L of the ions 20 passing through the mirror electrode 12 accordingly so that the imperfect angle Θ * satisfies equation (3). The required average drift length L * is given by the following equation.

[0065] [Number]

[0066] [[ID=,32]]The length is limited only by the physical length of the mirror electrode and can be increased until the ions 20 get too close to the fringe in the electric field of the mirror electrode. Therefore, usually, the average drift length L *There is a certain margin of error. Therefore, using the maximum and minimum predicted errors away from the desired focusing angle Θ, the average drift length L is obtained. * The required maximum and minimum values ​​for can be calculated.

[0067] Another approach is to switch to a different number of ion vibrations during the drift, i.e.,

[0068]

number

[0069] Average drift length L * The technical difficulty in measuring this is that the shape of the correction electrode 24, given by the dimensionless function s(y), is normalized to a specific (nominal) drift length L. However, a correction electrode 24 with a nominal drift length L can be emulated (at a specific interval of L) by electrically biasing two correction electrodes 24 with different drift lengths with individual voltages.

[0070] Figure 4 shows a mass spectrometer 10 equipped with two pairs of correction electrodes 24. Space 25 separates adjacent correction electrodes 24 and is effectively grounded. In this case, the intended mirror electrode focusing angle Θ = 0.05° and the nominal average drift length is 350 mm. However, the electrode focusing angle Θ is expected to vary by ±15%. To accommodate this, the pair of main correction electrodes 24 is effectively divided into two corresponding pairs of correction electrodes 241 and 242, and furthermore, the minimum average drift length L resulting from the expected ±15% variation in the intended mirror electrode focusing angle Θ is further reduced. * and maximum average drift length L * It is adapted to provide.

[0071] Figure 4 shows a shortened pair of additional correction electrodes 241 designed for an average drift length of 300 mm and an extended pair of additional correction electrodes 242 designed for an average drift length of 400 mm. The physical lengths of the correction electrodes 241 and 242 are set to ensure that the ions 20 do not experience the fringe electric field generated near the ends of the correction electrodes 241 and 242, and the average drift length L * Note that it is larger than. Applying voltage to the shortened correction electrode 241 rather than the extended correction electrode 242 results in an average drift length L * =300mm is set, therefore, Θ * This corrects the actual focusing angle of =0.05° × 300 / 350 = 0.04285°. Applying voltage to the extended correction electrode 242 instead of the shortened correction electrode 241 corrects the average drift length L * =400mm is set, therefore, Θ * The actual focusing angle is corrected to 0.05° × 400 / 350 = 0.05714°. Therefore, even if the mirror electrode 12 has an imperfection of ±15% in the focusing angle Θ, time-of-flight correction is achieved.

[0072] Furthermore, providing two pairs of correction electrodes 241, 242 having different average drift lengths L1 and L2 allows for any effective drift length L between the value of L1 and the value of L2. *However, this can be achieved by applying appropriate voltages to both pairs of correction electrodes 241 and 242. Since both correction electrodes 241 and 242 contribute to the correction provided by a single main correction electrode 24, each correction electrode 241 and 242 is provided with a fixed voltage of 1 / 2U0 plus or minus adjustment Δu to compensate for mechanical imperfections. The two contributions of 1 / 2U0 together provide the correction required for the slope, but adding the correction offset Δu to one of the correction electrodes 241 and 242 and subtracting it from the other correction electrode 241 and 242 results in an effective average drift length L of one of the correction electrodes. eff This is superior to the other, and as a result, the effective average drift length L eff The nominal value L * This means moving away from something.

[0073] Therefore, the correction electrodes 241 and 242 can be biased with different voltages U1 = 1 / 2U0 + Δu and U2 = 1 / 2U0 - Δu. Effective average drift length L eff This is given by the following assumptions.

[0074]

number

[0075] As expected, when Δu=U0, only the shortened correction electrode 241 is excited, and the effective drift length L eff When =L1 and Δu=-U0, only the extended correction electrode 242 is excited, and the effective drift length L eff = L2. However, when both the shortened electrode 241 and the extended electrode 242 are biased with the same voltage U1=U2=U0 (i.e., Δu=0), the effective drift length L eff = 1 / 2 × (L1 + L2), that is, the average of the average drift lengths is equal to the nominal drift length L required for a mirror electrode 12 without mechanical defects. * Therefore, by adjusting the value of Δu to a finite value between U1 and U2, it becomes possible to set any average drift length between 0 mm and 40 mm.

[0076] As explained above, the effective drift length L eff The correction electrode 24 having the average drift length L1 and L2 can be emulated by electrically biasing two correction electrodes 241 and 242 having different average drift lengths L1 and L2 with different voltages. Furthermore, the physical lengths of the correction electrodes 241 and 242 are determined by the average drift length L1 to ensure that the ions 20 do not experience the fringe field generated near the ends of the correction electrodes 241 and 242. * Note that this is greater than [the specified value]. Therefore, although Figure 4 shows additional correction electrodes 241 and 242 having different physical lengths L1 and L2, this is not necessarily required. The additional correction electrodes 241 and 242 may have the same physical length, provided that their shape function S(y) produces different average drift lengths L1 and L2.

[0077] Figure 5A shows an example where additional correction electrodes 241 and 242 of the same physical length have different average drift lengths L1=300 and L2=400 mm. Figure 5B shows the resulting correction electrodes 241 and 242 having the same physical length but different drift lengths L1 and L2, positioned on either side of the central axis Z=0. A variable power supply provides the required voltages U1=1 / 2U0+Δu and U2=1 / 2U0-Δu.

[0078] In the above embodiment, a pair of correction electrodes 241 and 242 are used to correct the time-of-flight dispersion arising from the inclined mirror electrode 12 and also to correct mechanical imperfections (i.e., the correction electrodes 241 and 242 serve as the main and additional correction electrodes). In an alternative embodiment, two pairs of main correction electrodes 24 are used to correct the time-of-flight dispersion arising from the inclined mirror electrode 12, and a pair of additional correction electrodes 243 are added to correct mechanical imperfections. The pair of additional correction electrodes 243 have edges having a shape given by the difference between a shortened correction electrode 241 having a drift length L1 = L0 + ΔL and an extended electrode 242 having a drift length L2 = L0 - ΔL.

[0079]

number

[0080] Effective drift length L eff It is given by the following equation.

[0081]

number

[0082] Figure 6A shows the shape function S(y) of such a differential compensation electrode 243, and Figure 6B shows such a differential compensation electrode 243 in a fixed position between two main compensation electrodes 24 that operate to compensate for the tilt of the mirror electrode. The main compensation electrodes 24 have a nominal effective drift length L0 and different effective drift lengths L to compensate for mechanical imperfections. eff If required, a voltage of a specific value and polarity is applied to the differential correction electrode 243. The voltage U applied to the main correction electrode 24 S=1 / 2U0 ensures that the main correction electrode 24 is combined to provide the necessary correction for the tilt angle Θ. The advantage of the correction electrode arrangement in Figure 6B over the correction electrode arrangement in Figure 5B is that it maintains symmetry around the y-axis regardless of what correction voltage u1 is applied to the differential correction electrode 243.

[0083] In addition to compensating for mechanical imperfections in the focusing angle Θ of the mirror electrode 12, the correction electrode 24 can be used to correct any curvature in the mirror electrode 12. The most common mechanical imperfection in the shape of the mirror electrode is the slack between the support rods 26, which can be approximated by the slack parameter h, and the quadratic function of the shape of the mirror electrode is given by:

[0084]

number

[0085] Figure 7A shows the optimized shape function for a predicted error range h = ±0.01 mm compared to the optimal shape function for a perfectly straight mirror electrode 12 (i.e., h = 0). When the differential compensation electrode 243 is used, the difference between the shape functions for the determined maximum error values ​​of h (h = +0.01 mm and h = -0.01 mm) defines the shape function of the differential compensation electrode 243, as shown in Figure 7B. During operation, the differential compensation electrode 243 adjusts the voltage u s ∈[-0.5U s ,0.5U s It is biased by ]. When the curvature of the actual mirror electrode reaches h=0.01mm, the difference correction electrode 243 is 0.5U s It should be biased with a voltage equal to , and thus emulate the shape optimized for the actual curvature of the mirror electrode 12. In the case of the opposite maximum predicted negative sag h = -0.01 mm, the differential correction electrode 243 is -0.5 U to compensate for mechanical imperfections. s It is biased by the voltage.

[0086] Figure 8 shows a further embodiment including a pair of main correction electrodes 24 for correcting mechanical imperfections at the focusing angle Θ of the mirror electrode 12, and additional differential correction electrodes 243 for correcting mechanical imperfections. A separate pair of differential correction electrodes 243 correct the inclination and curvature individually.

[0087] While the embodiments described above are primarily intended to correct mechanical errors in slope and curvature, they can also at least partially correct other mechanical imperfections that cause time-of-flight aberrations. Specifically, the voltage applied to the correction electrode 24 can be adjusted to provide optimal resolution, which essentially compensates for other imperfections.

[0088] Those skilled in the art will understand that the above embodiments can be modified in many different ways without departing from the scope of the invention as defined by the appended claims.

[0089] For example, the error in the focusing angle Θ of the mirror electrode 12 will be explained by referring to an example in which focusing is performed using a shim 28, but other configurations are also possible. The focusing angle Θ can be set by the size of the mounting, such as by cutting into the mirror electrode 12, setting the length of the mounting rod 26, or positioning the mounting point within the support frame. The mirror can have an angle incorporated into its structure by changing the thickness of the electrodes or their separators (the mirror of the present invention is constructed as a stack of aluminum electrodes and ceramic spacers).

[0090] It should be noted that while this explanation describes the case where the curvature of the mirror electrode 12 results in slack, this slack is not necessarily due to gravity. The curvature can be any distortion that follows a curve with a peak in the center of the mirror electrode 12. This can result from the release of stress within the metal mirror electrode 12, causing distortion of the mirror electrode 12 during and after machining. Other factors such as thermal shift and assembly errors / insufficient force can also cause slack.

Claims

1. A multiple reflection time-of-flight mass spectrometer, Two ion optical mirrors, each of which is elongated along the drift direction (Y direction) away from the ion implantation point, each of which faces the other in the Z direction, the Z direction being perpendicular to the Y direction, and the two mirrors being inclined at an angle such that the separation between them in the Z direction decreases as the distance along the Y direction increases. The system comprises at least two correction electrodes extending in the space between the mirrors or adjacent to the space along at least a portion of the Y direction, Each of the correction electrodes has a surface substantially parallel to the Y-Z plane and is shaped such that the surface is separated from one of the mirrors by a distance that varies along the Y direction, and the correction electrode is electrically biased with a voltage to produce a composite voltage offset that varies as a function of the distance along the Y direction in at least a portion of the space extending between the opposing mirrors when in use, the voltage comprising a first component for correcting intended aberrations arising from the intended tilt angle of the mirrors, and a second component for correcting unintended aberrations arising from a range of perturbations with respect to the ideal time of flight from maximum to minimum perturbation, the second component varying between a maximum and a minimum value, Multiple reflection time-of-flight mass spectrometer, wherein the shapes of the at least two correction electrodes are such that some or all of the at least two correction electrodes are shaped to apply the voltage including a first component and a second component that varies between a maximum and a minimum value, thereby generating a range of composite voltage offsets that compensate for a range of time-of-flight aberrations corresponding to the intended aberration arising from the intended tilt angle of the mirror and the unintended aberration arising from the range of perturbations with respect to the ideal time-of-flight from the maximum perturbation to the minimum perturbation.

2. The multiple reflection time-of-flight mass spectrometer according to claim 1, wherein the range of the perturbation with respect to the ideal time of flight extends from the maximum perturbation due to the maximum positive misalignment error in the mirror to the minimum perturbation due to the maximum negative misalignment error in the mirror.

3. The multiple reflection time-of-flight mass spectrometer according to claim 2, wherein the combined voltage offset acts to shorten or lengthen the average drift length of the ions in the +Y direction through the mirror before the ions are reflected and drift back through the mirror in the -Y direction.

4. The multiple reflection time-of-flight mass spectrometer according to claim 2 or 3, wherein the combined voltage offset acts to increase or decrease the number of vibrations performed by the ions as they drift through the mirrors.

5. The multiple reflection time-of-flight mass spectrometer according to any one of claims 1 to 4, wherein the range of the perturbation with respect to the ideal time of flight extends from the maximum perturbation due to the maximum positive curvature error in the mirror to the minimum perturbation due to the maximum negative curvature error in the mirror.

6. The multiple reflection time-of-flight mass spectrometer according to claim 5, wherein the maximum positive curvature error and the maximum negative curvature error in the mirror correspond to the curvature in the mirror due to slack.

7. The multiple reflection time-of-flight mass spectrometer according to claim 5 or 6, as dependent on claim 2, wherein the shape of one of the at least two correction electrodes compensates for misalignment error independently of curvature error, and the shape of the other of the at least two correction electrodes compensates for curvature error independently of misalignment error.

8. The at least two correction electrodes include one or more pairs of correction electrodes, The correction electrode or each pair of correction electrodes is A first compensating electrode, shaped to generate a voltage offset that compensates for the intended aberration resulting from the intended tilt angle of the mirror and the unintended aberration resulting from the maximum perturbation, when a voltage equal to the sum of the first component and the maximum value of the second component is applied, A multiple reflection time-of-flight mass spectrometer according to any one of claims 1 to 7, comprising: a second compensating electrode shaped to produce a voltage offset that compensates for the intended aberration resulting from the intended tilt angle of the mirror and the unintended aberration resulting from the minimum perturbation when a voltage equal to the sum of the first component and the minimum value of the second component is applied.

9. The multiple reflection time-of-flight mass spectrometer according to claim 8, wherein the first and second correction electrodes are shaped to produce different average drift lengths of ions passing through the mirror, and optionally, the physical lengths of the first and second correction electrodes in the Y direction are different.

10. The at least two correction electrodes are, At least a first correction electrode having a shape that compensates for the intended time-of-flight aberration resulting from the intended tilt angle of the mirror when a voltage equal to the first component is applied, A multiple reflection time-of-flight mass spectrometer according to any one of claims 1 to 7, comprising: a second correction electrode having a shape corresponding to the difference between required shapes, wherein when a voltage equal to the maximum value of the second component is applied, the second correction electrode generates a voltage offset that compensates for the maximum perturbation, and when a voltage equal to the minimum value of the second component is applied, the second correction electrode generates a voltage offset that compensates for the minimum perturbation.

11. A method for operating a multiple reflection time-of-flight mass spectrometer, wherein the multiple reflection time-of-flight mass spectrometer is Two ion optical mirrors, each of which is elongated along the drift direction (Y direction) away from the ion implantation point, each of which faces the other in the Z direction, the Z direction being perpendicular to the Y direction, and the two mirrors being inclined such that the separation between them in the Z direction decreases as the distance along the Y direction increases. The system comprises at least two correction electrodes extending in the space between the mirrors or adjacent to the space along at least a portion of the Y direction, Each of the correction electrodes has a surface substantially parallel to the Y-Z plane and is shaped such that the surface is separated from one of the mirrors by a distance that varies along the Y direction, and the correction electrode is electrically biased with a voltage to produce a composite voltage offset that varies as a function of the distance along the Y direction in at least a portion of the space extending between the opposing mirrors when in use, the voltage comprising a first component for correcting intended aberrations arising from the intended tilt angle of the mirrors and a second component for correcting unintended aberrations arising from the range of perturbations with respect to the ideal time of flight from maximum perturbation to minimum perturbation, the second component varying between a maximum and a minimum value, The shape of the at least two correction electrodes is such that some or all of the at least two correction electrodes can apply the voltage including the first component and the second component which varies between a maximum and a minimum value, and generate a range of composite voltage offset that compensates for a range of time-of-flight aberrations corresponding to the intended aberration resulting from the intended tilt angle of the mirror and the unintended aberration resulting from the range of perturbation with respect to the ideal time of flight from the maximum perturbation to the minimum perturbation. The aforementioned method, Exciting the mirror to provide an electric field in order to cause the ions to follow a zigzag path through the mirror, Applying a voltage including the first component and / or the second component to each of the at least two correction electrodes such that the at least two correction electrodes generate a combined voltage offset that compensates for the intended time-of-flight aberration and the unintended time-of-flight aberration, Injecting ions from the ion source into the mirror, A method comprising detecting the ions using an ion detector positioned at the same end of the mirror as the ion source.

12. The at least two correction electrodes include one or more pairs of correction electrodes, The correction electrode or each pair of correction electrodes is A first correction electrode, shaped to generate a voltage offset that compensates for the intended aberration and the unintended aberration resulting from the maximum perturbation when a voltage equal to the sum of the first component and the maximum value of the second component is applied, The system includes a second compensating electrode shaped to generate a voltage offset that compensates for the intended aberration and the unintended aberration resulting from the minimum perturbation when a voltage equal to the sum of the first component and the minimum value of the second component is applied, This method, (i) Compensating for the maximum perturbation by applying a voltage to the first correction electrode and not applying a voltage to the second correction electrode that has a value equal to the maximum value of the first component and the second value, (ii) Compensating for the minimum perturbation by applying a voltage to the second correction electrode, but not to the first correction electrode, that has a value equal to the minimum value of the first component and the second component, or (iii) The method of claim 11, comprising compensating for the perturbation between the maximum perturbation and the minimum perturbation by applying a voltage to the first correction electrode having a value equal to the sum of half of the first contribution and the second contribution having a value between the maximum and the minimum value, and applying a voltage to the second correction electrode having a value equal to the sum of half of the first component and the second component having a value between the maximum and the minimum value.

13. The at least two correction electrodes are, A first correction electrode having a shape that compensates for the time-of-flight aberration arising from the intended tilt angle of the mirror when a voltage equal to the first component is applied, The second correction electrode has a shape corresponding to the difference between the shapes required, such that when a voltage having the maximum value of the second component is applied, the second correction electrode generates a voltage offset that compensates for the maximum perturbation, and when a voltage having the minimum value of the second component is applied, the second correction electrode generates a voltage offset that compensates for the minimum perturbation. This method, (i) Compensating for the maximum perturbation by applying a voltage equal to the first component to at least the first correcting electrode in order to compensate for the intended time-of-flight aberration, and by applying a voltage having the maximum value of the second component to the second correcting electrode in order to compensate for the unintended time-of-flight aberration, (ii) Compensating for the minimum perturbation by applying a voltage equal to the first contribution to at least the first correcting electrode in order to compensate for the intended time-of-flight aberration, and by applying a voltage having the minimum value of the second component to the second correcting electrode in order to compensate for the unintended time-of-flight aberration, or (iii) The method of claim 11, comprising compensating for perturbations between the maximum perturbation and the minimum perturbation by applying a voltage equal to the first component to at least the first correcting electrode in order to compensate for the intended time-of-flight aberration, and by applying a voltage equal to the second component having a value between the maximum and the minimum value to the second correcting electrode in order to compensate for the unintended time-of-flight aberration.

14. A method for designing a multiple reflection time-of-flight mass spectrometer, wherein the multiple reflection time-of-flight mass spectrometer is The ideal configuration of an ion source, an ion detector, and two ion optical mirrors is such that each of the mirrors is elongated along the drift direction (Y direction) away from the ion implantation point, and each of the mirrors faces each other in the Z direction perpendicular to the Y direction, thereby constituting the ideal configuration in which ions supplied from the ion source enter the mirrors at the ion implantation point and then, when the mirrors are excited to provide an electric field, follow a zigzag path through the mirrors. The present invention comprises configuring at least two corrective electrodes extending in or along at least a portion of the Y-direction adjacent to the space between the mirrors, each of which has a surface substantially parallel to the Y-Z plane and is shaped such that the surface is separated from one of the mirrors by a distance that varies along the Y-direction, and the corrective electrodes are electrically biased with a voltage to produce a composite voltage offset that, when in use, varies as a function of the distance along the Y-direction in at least a portion of the space extending between the opposing mirrors, the voltage comprising a first component for correcting intended aberrations arising from the intended tilt angle of the mirrors and a second component for correcting unintended aberrations arising from a range of perturbations with respect to the ideal time of flight from maximum to minimum perturbation, wherein the second component varies between a maximum and a minimum value, and the corrective electrodes are configured accordingly. To determine the maximum and minimum perturbations of the mirrors from the ideal arrangement, and the resulting maximum and minimum aberrations in the time of flight of ions passing through the mirrors, A method comprising determining the shape of at least two compensating electrodes such that some or all of the at least two compensating electrodes are subjected to the voltage including a first component and a second component varying between a maximum and a minimum value to generate a range of composite voltage offsets that compensate for a range of time-of-flight aberrations corresponding to the intended aberration arising from the intended tilt angle of the mirror and the unintended aberration arising from the range of perturbation with respect to the ideal time of flight from the maximum perturbation to the minimum perturbation.

15. This includes determining the shapes of the at least two correction electrodes in order to compensate for the range of time-of-flight aberrations corresponding to perturbations ranging from the maximum perturbation due to the maximum positive misalignment error in the mirror to the minimum perturbation due to the maximum negative misalignment error in the mirror, relative to the ideal time of flight. The method according to claim 14, wherein the combined voltage offset acts to shorten or lengthen the average drift length of the ions in the +Y direction through the mirror before the ions are reflected and drift back through the mirror in the -Y direction.

16. The method for a flight mass spectrometer according to claim 15, wherein the combined voltage offset acts to increase or decrease the number of vibrations performed by the ions as they drift through the mirror.

17. The method according to claim 14, comprising determining the shapes of the at least two correction electrodes in order to compensate for the range of time-of-flight aberrations corresponding to perturbations ranging from the maximum perturbation due to the maximum positive curvature error in the mirror to the minimum perturbation due to the maximum negative curvature error in the mirror, with respect to the ideal time of flight.

18. The method according to claim 17, wherein the maximum positive curvature error and the maximum negative curvature error of the mirror correspond to the curvature of the mirror due to sagging.

19. The method according to claim 17 or 18, as dependent on claim 15, comprising determining the shape of one of the at least two correction electrodes so as to compensate for a misalignment error independently of a curvature error, and determining the shape of the other of the at least two correction electrodes so as to compensate for a curvature error independently of a misalignment error.

20. The at least two correction electrodes include one or more pairs of correction electrodes, The above method applies to the correction electrode or each pair of correction electrodes, The shape of the first correction electrode is determined such that, when a voltage equal to the sum of the first component and the maximum value of the second component is applied, it generates a voltage offset that compensates for the intended aberration resulting from the intended tilt angle of the mirror and the unintended aberration resulting from the maximum perturbation. The method according to any one of claims 14 to 19, comprising determining the shape of a second compensating electrode such that, when a voltage equal to the sum of the first component and the minimum value of the second component is applied, it generates a voltage offset that compensates for the intended aberration resulting from the intended tilt angle of the mirror and the unintended aberration resulting from the minimum perturbation.

21. The method according to claim 20, wherein the first and second correction electrodes are shaped to produce different average drift lengths of ions passing through the mirror, and optionally, the physical lengths of the first and second correction electrodes in the Y direction are different.

22. Determining the shape of at least a first correction electrode that compensates for the time-of-flight aberration corresponding to the intended tilt angle of the mirror along the Y direction when a voltage having a value equal to the first component is applied, The method according to any one of claims 14 to 19, comprising determining the shape of the second compensating electrode to correspond to the required difference between the shapes such that when a voltage having the maximum value of the second component is applied, the second compensating electrode generates a voltage offset that compensates for the maximum perturbation, and when a voltage having the minimum value of the second compensating electrode is applied, the second compensating electrode generates a voltage offset that compensates for the minimum perturbation.

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