Multi-reflection mass spectrometer

Abstract

To provide a multi-reflection time-of-flight mass spectrometer.SOLUTION: Correction electrodes extend along the Y direction in or near a space between mirrors. Each correction electrode has a surface parallel to the Y-Z plane shaped such that its separation from one of the mirrors varies along the Y direction. The correction electrodes are biased to produce a combined voltage offset which varies as a function of distance along the Y direction. A first component corrects an intended aberration arising from a mirror tilt, and a second component corrects unintended aberrations arising from perturbations to the ideal time of flight extending from maximum to minimum perturbations. The shapes of the correction electrodes are such that some or all of the correction electrodes may be energized to generate a range of combined voltage offsets that compensate for a range of time-of-flight aberrations corresponding to the intended and unintended aberrations.SELECTED DRAWING: Figure 4

Description

[Technical field]

[0001] The present invention relates to the field of mass spectrometry, and in particular to time-of-flight mass spectrometry and electrostatic trap mass spectrometry utilizing a multiple reflection technique to extend the ion flight path. [Background technology]

[0002] Various arrangements are known that utilize multiple reflections to extend the flight path of ions in a mass spectrometer. An extended flight path is desirable for increasing the time-of-flight separation of ions in a time-of-flight (ToF) mass spectrometer, as it enhances the ability to distinguish small mass differences between ions.

[0003] An example of a multi-reflecting time-of-flight (MR-ToF) mass analyzer can be found in WO 2013 / 110587. Two parallel opposing mirror electrodes are elongated in the drift direction (Y direction). Ions are extracted from the ion trap and injected into the mirror electrodes, and then the ions 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 analyzer.

[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 oscillating between the opposing mirror electrodes also drift in the Y direction due to the initial tilt at which the ions were injected into the mirror electrodes. The mirror focusing tilt angle Θ reduces the trajectory tilt angle by 2Θ for every oscillation that includes two reflections. As a result, the drift direction is eventually reversed as the ions travel back through the mirror electrodes and are detected by an ion detector located adjacent to the ion trap.

[0005] However, tilted mirror electrodes cause ToF aberrations because not all ions follow a common path through the mirror electrodes. The finite spread of the beam angle at which ions are injected into the mirror electrodes causes some ions to drift further down the mirror electrode than other ions. Ions entering through the mirror electrode at a shallow angle to the longitudinal axis drift further down the mirror electrode than ions injected at a steeper angle. Advantageously, the ions are once again spatially focused on their return to the ion detector. However, time aberrations are introduced because the oscillation period of the ions decreases as a function of distance along the drift direction as a result of the reduced spacing between the mirror electrodes.

[0006] These ToF aberrations are corrected by slowing down the ions as they cross between the mirror electrodes using stripe electrodes. The stripe electrodes are shaped to generate an electric field with a voltage that varies as a function of distance along the mirror electrodes. The electric field increases along the drift direction such that the ions are slowed down the further they drift along the mirror electrodes. This slowing increases the period of the oscillations as a function of distance along the drift direction, thereby mitigating the reduction in period caused by the focusing mirror electrodes.

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

[0008] These stripe electrodes are designed to compensate for the unavoidable ToF aberrations caused even in perfect mirror electrodes by the required tilt.

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

[0010] US2020 / 0243322 includes stripe electrodes, but for a different reason than WO2013 / 110587, there is no need to correct ToF aberrations resulting from intentionally tilting the mirror electrodes. Instead, a first pair of curved stripe electrodes is used to correct for any curvature in the mirror electrodes. A second pair of stripe electrodes is used to correct for misalignment between the mirror electrodes. Summary of the Invention [Means for solving the problem]

[0011] According to a first aspect, there is provided a multi-reflecting time-of-flight mass spectrometer comprising two ion-optical mirrors, each elongated generally along a drift direction (Y direction) away from an ion implantation point, and each mirror facing the other in a Z direction, which 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 YZ 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 to generate a resultant 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 includes a first component for correcting intended aberrations resulting from an intended tilt angle of the mirrors, and / or a second component for correcting unintended aberrations resulting from a range of perturbations to the ideal flight time ranging from a maximum to a minimum perturbation (such as perturbations resulting from mechanical imperfections of the mirrors), the second component varying between a maximum and a minimum value. The shape of the at least two correction electrodes is selected such that some or all of the at least two correction electrodes can be biased with a voltage including the first component and a second component that varies between a maximum and a minimum value to generate a range of resultant voltage offsets. These offsets correct a range of time-of-flight aberrations corresponding to intended aberrations resulting from the intended tilt angles of the mirrors, and unintended aberrations resulting from a range of perturbations to the ideal time-of-flight extending from maximum to minimum perturbations.

[0013] The ideal flight time of an ion through a mass spectrometer corresponds to the flight time of an ion through the mirror when it is perfectly flat and perfectly aligned at its intended tilt angle. The correction electrodes provide both a correction for the intended tilt angle between the mirrors via a first component, and a correction for errors in the actual configuration of the mirrors via a second component. For example, the mirrors may be misaligned and not exactly at the intended tilt angle. Also, the mirrors may not be perfectly straight, but have curvature due to sagging (caused by both gravity and other factors such as stress relief in the mirrors and other machining imperfections).

[0014] The range of perturbations to the ideal time of flight may extend from a maximum perturbation due to a maximum positive misalignment error in the mirror to a minimum perturbation due to a maximum negative misalignment error in the mirror. The maximum positive and negative misalignment errors may be the maximum and minimum misalignment errors expected to affect the mass spectrometer. The maximum positive and negative misalignment errors may correspond to manufacturing tolerances. By way of example only, shims may be used to introduce an intended tilt in an otherwise parallel mirror pair, in which case the maximum positive and negative misalignment errors may correspond to manufacturing tolerances around the nominal thickness of the shim.

[0015] The correction electrodes may be shaped such that the resultant voltage offset acts to shorten or lengthen the average drift length of the ions in the +Y direction through the mirror before they are reflected and drift back through the mirror in the -Y direction. This configuration allows smaller misalignment errors to be compensated. For larger misalignment errors, a larger resultant voltage offset may be used that increases or decreases the number of oscillations the ions make as they drift through the mirror.

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

[0017] At least one correction electrode may be shaped to compensate for both the misregistration error and the curvature error. Alternatively, the shape of one electrode of the at least two correction electrodes may correct the misregistration value independent of the curvature value, and the shape of another electrode of the at least two correction electrodes may correct the curvature value independent of the misregistration value.

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

[0019] Alternatively, different correction electrodes can be used to compensate for the intended and unintended time-of-flight aberrations. For example, the at least two correction electrodes may include at least a first correction electrode having a shape for compensating the intended time-of-flight aberrations and a second correction electrode having a shape corresponding to the difference between the shapes required, such that when a voltage having a value equal to the maximum value of the first component plus the second component is applied to the second correction electrode, the second correction electrode generates a voltage offset that compensates for the maximum perturbation, and when a voltage having a value equal to the minimum value of the first component plus the second component is applied to the second correction electrode, the second correction electrode generates a voltage offset that compensates for the minimum perturbation. If the mirror is exactly the intended one, no correction of the unintended aberrations is required, and therefore the second correction electrode is grounded and at least the first correction electrode is used to compensate for the intended aberrations. When correction of unintended aberrations is required, the second electrode is energized with a voltage between a maximum and minimum value of the second component to provide the necessary correction, the maximum correcting the maximum perturbation and the minimum correcting the minimum perturbation, and a value of the second component between the maximum and minimum corrects the perturbation between the maximum and minimum. The at least first correction electrode may be a pair of electrodes sandwiching the second correction electrode. Each of the electrode pair may be energized with a voltage equal to half the first component.

[0020] According to a second aspect, there is provided a method of operating a multi-reflecting time-of-flight mass spectrometer. The spectrometer comprises two ion-optical mirrors, each elongated generally along a drift direction (Y direction) away from the ion injection point, each mirror facing the other in a Z direction, which 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 Y direction increases. The spectrometer further comprises at least two correction electrodes extending along at least a portion of the Y direction in or adjacent to the space between the mirrors. 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 varies along the Y direction. In use, the correction electrodes are electrically biased with a voltage in at least a portion of the space extending between the opposing mirrors to generate a resultant voltage offset that varies as a function of distance along the Y direction, the voltage including a first component for correcting intended aberrations resulting from an intended tilt angle of the mirrors and a second component for correcting unintended aberrations (such as aberrations caused by mechanical imperfections in the mirrors) resulting from a range of perturbations to the ideal time-of-flight extending from a maximum perturbation to a minimum perturbation, the second component varying between a maximum and a minimum value. The geometry of the at least two correction electrodes is selected such that some or all of the at least two correction electrodes are energized with a voltage having a value that includes the first component and a second component that varies between a maximum and a minimum value to generate a resultant voltage offset that compensates for a range of time-of-flight aberrations corresponding to a range of perturbations to the ideal time-of-flight extending from a maximum perturbation to a 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 the at least two correction electrodes such that the at least two correction electrodes produce a resultant voltage offset that compensates for time-of-flight aberrations within a range of perturbations to an ideal time-of-flight spanning from a maximum perturbation to a minimum perturbation. The method further includes injecting 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, the at least two correction electrodes include one or more pairs of correction electrodes. The correction electrodes, or each pair of correction electrodes, may include at least a first correction electrode shaped such that when the first correction electrode is applied with a voltage having a value equal to the maximum value of the first component plus the second component, the first correction electrode generates a voltage offset that compensates for a maximum perturbation. The correction electrodes, or each pair of correction electrodes, may further include a second correction electrode shaped such that when the second correction electrode is applied with a voltage having a value equal to the minimum value of the first component plus the second component, the second correction electrode generates a voltage offset that compensates for a minimum perturbation. The method may then include (i) compensating for a maximum perturbation by applying a voltage having a value equal to the maximum of the first component plus the second component to the first correction electrode and not to the second correction electrode, (ii) compensating for a minimum perturbation by applying a voltage having a value equal to the minimum of the first and second components to the second correction electrode and not to the first correction electrode, or (iii) compensating for a perturbation between the maximum and minimum perturbations by applying a voltage having a value equal to half the first component plus a value between the maximum and minimum values ​​of the second component to the first correction electrode and applying a voltage having a value equal to half the first component plus a value between the maximum and minimum values ​​of the second component to the second correction electrode.

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

[0024] According to a third aspect, there is provided a method of designing a multi-reflecting time-of-flight mass spectrometer, the method comprising configuring an ideal arrangement of an ion source, an ion detector, and two ion optical mirrors, each of the mirrors being elongated generally along a drift direction (Y direction) away from an ion injection point, and each of the mirrors facing each other in a Z direction orthogonal to the Y direction, such that ions provided from the ion source enter the mirror at the ion injection point and then follow a zigzag path through the mirror when the mirror is excited to provide an electric field. The method also includes configuring at least two correction electrodes extending along at least a portion of the Y direction in or adjacent to the space between the mirrors, each of the correction electrodes having a surface substantially parallel to the YZ plane and shaped such that the surface is separated from one of the mirrors by a distance that varies along the Y direction, the correction electrodes being electrically biased with a voltage to generate, in use, a resultant 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 including a first component for correcting intended aberrations resulting from an intended tilt angle of the mirrors and a second component for correcting unintended aberrations (such as aberrations caused by mechanical imperfections in the mirrors) resulting from a range of perturbations to the ideal flight time spanning from a maximum perturbation to a minimum perturbation, 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 flight time of ions through the mirrors. The method may also include shaping the at least two correction electrodes such that some or all of the at least two correction electrodes are applied with voltages having values ​​that include a first component and a second component that varies between a maximum and a minimum value to produce a range of resultant voltage offsets that compensate for a range of time-of-flight aberrations extending from a maximum perturbation to a minimum perturbation.

[0025] The method may include determining a shape of the at least two correction electrodes to compensate for a range of time-of-flight aberrations corresponding to perturbations ranging from a maximum perturbation due to a maximum positive misalignment value on the mirror to a minimum perturbation due to a maximum negative misalignment value on the mirror, relative to an ideal time-of-flight.

[0026] The resultant voltage offset may act to shorten or lengthen the average drift length of the ions in the +Y direction through the mirror before they are reflected back through the mirror in the -Y direction, and the resultant voltage offset may act to increase or decrease the number of oscillations that the ions make as they drift through the mirror.

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

[0028] The method may include determining a shape of one electrode of the at least two correction electrodes to compensate for the misregistration error independent of the curvature error and a shape of another electrode of the at least two correction electrodes to compensate for the curvature error independent of the misregistration error.

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

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

[0031] In order that the invention may be more readily understood, reference will now be made, by way of example only, to the accompanying drawings, in which: [Brief description of the drawings]

[0032] [Figure 1] FIG. 1 is a schematic diagram of a prior art multi-reflecting time-of-flight mass spectrometer. [Diagram 2] FIG. 13 is a schematic diagram of a mirror assembly design that provides a focusing angle via shims. [Figure 3A] 1 shows the normalized shape function for the correction electrode. [Figure 3B]1 shows the time-of-flight correction obtained when the correction electrodes and mirror tilt work together. [Figure 4] FIG. 1 is a schematic diagram of a first embodiment of a multi-reflecting time-of-flight mass spectrometer having correction electrodes of unequal physical lengths. [Figure 5A] 1 shows the corrected electrode shape as a function of drift coordinate "y" normalized to different drift lengths L1 and L2. [Figure 5B] An array with two pairs of correction electrodes with different shapes and different electrical biases is shown to provide a variable effective drift length L between 300 mm and 400 mm, thereby correcting for mirror misalignment. [Figure 6A] 4 shows the shape function of a differential correction electrode, which shape function is equal to the difference between the shape functions normalized to effective drift lengths of 375 mm and 325 mm, respectively. [Figure 6B] A configuration is shown having three pairs of correction electrodes, including one pair of differential correction electrodes energized with voltage U1. [Figure 7A] The shape function of the correction electrodes that achieves the optimum solution for a mirror with sag parameters of ±0.01 mm is shown. [Figure 7B] 7B shows a configuration having a pair of compensation electrodes whose shape is inferred from the difference between the shapes of FIG. 7A and which are biased to compensate for sagging. [Figure 8] A correction electrode is shown that includes a differential correction electrode pair that corrects both curves. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0033] As mentioned above, mass spectrometers typically utilize multiple reflections to extend the flight path of ions, which is desirable as it increases the time-of-flight separation of ions and therefore the resolution in a time-of-flight (ToF) mass spectrometer. Figure 1 shows an example of a multi-reflection time-of-flight (MR-ToF) mass analyzer 10. A pair of ion-optical mirrors is provided by two parallel opposing mirror electrodes 12 that are elongated 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 sets the final injection angle and collimates the ion beam 20 as much as achievable. The ions 20 are then multiple-reflected (in the z-direction) between the mirror electrodes 12 while drifting relatively slowly in the drift (y) direction along the extended length of the mirror electrodes 12. The ions 20 therefore follow a zig-zag flight path through the mass analyzer 10.

[0034] Furthermore, the mirror electrodes 12 are tilted by an angle Θ (typically about 0.05 degrees) so that their separation in the z-direction decreases as they extend in the drift direction. The focusing angle Θ reduces the trajectory tilt angle of the ions 20 by 2Θ per oscillation (each oscillation includes 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 located adjacent to the ion trap 14.

[0035] Because the ions 20 have a smaller spread for the injection angle, the ion beam 20 spreads as it drifts along the mirror electrodes 12. Thus, the drift length of an ion along the mirror electrodes 12 varies with the injection angle of that ion, with ions 20 injected at a steeper angle having a lower velocity component in the y direction and therefore drifting a shorter distance along the mirror electrodes 12 than ions injected at a shallower angle having a higher velocity component in the y direction. A smaller tilt angle Θ acts to cause a spread in the flight time of the ions 20 because ions 20 that drift further along the mirror electrodes 12 experience a narrower gap between the mirror electrodes 12 than ions 20 that do not drift as far. This results in different flight times for ions 20 with the same m / z ratio but with different injection angles, and thus a loss of resolution.

[0036] The errors introduced by the tilted mirror electrodes 12 are addressed by adding a pair of correction electrodes 24 along the length of the drift dimension, one correction electrode 24 positioned above the ion beam 20 and the other correction electrode 24 positioned below the ion beam 20. The edges of each correction electrode 24 have a shape determined by a shape function S(y) corresponding to the error to be corrected. The shape function may 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 where the ions 20 propagate, thus causing additional drift deflection and flight time perturbation to the ions 20. Furthermore, the correction to the electric field can be set to counter the focusing effect of the mirror electrodes such that the correction electrodes 24 ensure that all ions 20 have the same flight time 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 to change the value of the focusing angle Θ of the mirror electrodes by adopting a particular 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]

number

[0039]

number

[0040] The coefficient c[n] is optimized to minimize the dispersion of flight times for ions 20 with the same m / z ratio. Although the function s(y / l) can take negative values, the shape function S(y) is kept positive by choosing 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 resulting time-of-flight error versus the injection angle of the ions, and in particular shows the greatly 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 thermal dispersion of the initial ion velocity.

[0042] The drift of the ions is governed by the voltage U sand two pseudo-potentials Φ resulting from the correction electrode 24 biased at the focusing angle Θ. s (y) and Φ m This can be explained in the adiabatic approximation by (y).

[0043]

number

[0044]

number

[0045]

number

[0046]

number

[0047] To ensure that the 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 the time K0T oscill where K0 is the number of oscillations (in the z direction) per drift (in the y direction). This requirement, together with the requirement for correction of time-of-flight errors, can be met for specific values ​​of the mirror focusing angle Θ using a correction electrode 24 shaped as shown in Figure 3A in the normalized coordinate y / L.

[0048] While the dimensionless function s(y / L) is precisely defined for the optimum solution, the drift length L is a free parameter to be chosen. The drift length L is related to the mirror focusing angle Θ by the following equation:

[0049]

number

[0050] The above describes a time-of-flight mass analyzer 10 having a predetermined focusing angle Θ of the mirror electrodes 12. However, mechanical imperfections can act to counter the time-of-flight correction provided by the correction electrodes 24. For example, mechanical imperfections can be deviations of the mirror electrodes 12 from the predetermined focusing angle Θ, and curvature of the mirror electrodes 12, such as sagging. These imperfections directly affect the resolution.

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

[0052] The mass analyzer 10 is very sensitive to mechanical imperfections in the mirrors because the ion 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 electrodes 24 act 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 oscillation direction to the drift direction, upsetting the otherwise precisely balanced compensation of the ion optical aberrations. Both spatial focusing of the drift and ToF aberration compensation become problematic.

[0053] One way to combat aberrations in ToF is to impose extremely tight tolerances on the mass analyzer 10, for example by machining components to an accuracy of less than 10 microns. However, for complex systems with typical dimensions of 0.5 m to 3 m, such accuracy is nearly unachievable and / or prohibitively expensive and not suitable for mass production.

[0054] Existing correction electrodes 24 have the disadvantage of being unable to maintain resolution even in the presence of mechanical misalignments as small as 10 microns. This is because the tilt shifts the focal plane of the ion beam away from the ion detector 16, causing it to be defocused. Adjusting the voltages on the stripe electrodes 24 to position them moves them away from the voltages required for optimal resolution. The correction electrodes 24 have the conflicting requirements of providing beam focus and combating time-of-flight errors. Furthermore, existing correction electrodes 24 cannot adequately provide drift focusing when curvature is present in the mirror electrodes 12. Additional correction electrodes with the ability to accommodate mechanical errors in the mirror as described in US Patent Application Publication No. 2020 / 0243322 can compensate for ToF aberrations, but do not improve spatial focusing of ion drift. Thus, a mass analyzer 10 with a tilted mirror electrode 12 loses the ability to focus ions 20 onto the ion detector 16.

[0055] Instead of simple compensation of the ToF aberrations at each Y position of the drift axis (by the correction electrodes of US Patent Application Publication No. 2020 / 0243322), the ToF aberrations are better compensated on average for the total number of ion oscillations. These conditions are less precise but still sufficient to maintain the high mass resolution of the mass analyzer 10. At the same time, the correction electrodes 24 should also restore the spatial focusing of the ions 20 onto the ion detector 16.

[0056] An exact 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 mirror electrode focusing angle Θ. In practice, the mirror electrodes 12 are straight with an accuracy of ±0.01 mm. The thickness of the shims has a similar accuracy, resulting in a residual loss of time-of-flight resolution.

[0057] If the focusing angle Θ of the mirror electrodes is set incorrectly or changes over time, adjustment of the focusing angle Θ of the mirror electrodes requires disassembly and reassembly of the mirror electrode unit. In principle, this is possible during manufacturing, but requires additional manufacturing and testing time. If the focusing angle Θ of the mirror electrodes is accidentally changed during use of the mass analyzer, difficult and time-consuming inspections will be required. Such a critical dependency on mirror manufacturing and positioning accuracy is a significant drawback of mass analyzer design.

[0058] It is recognized that further refinements of 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 tilted mirror MR-ToF analyzer 10. This allows the ion flight time between the mirror electrodes 12 to be adjusted globally or as a function of the ion injection angle, allowing specific correction for errors in the mirror electrode tilt angle Θ or the mirror electrode curvature, accommodating a wider range of ion injection angles, or even adjusting the focal plane position of the ion beam.

[0059] The solution to the problem of mechanical imperfections in the mirror electrodes 12 involves adding some flexibility in how the correction electrodes 24 are designed and operated. This allows time-of-flight errors to be corrected even if the mirror electrodes 12 are not exactly straight and if the focusing angle Θ of the mirror electrodes deviates from the intended value. Advantageously, during operation, only small corrections around the voltage set on the correction electrodes 24 are required, and no mechanical corrections are required.

[0060] In a prior art mass analyzer 10 such as that of Figure 1, there are two degrees of freedom available to assist in the correction of time-of-flight errors due to mechanical imperfections: the correction electrode 24 can be set to any voltage up to 100V, and the initial angle of ion incidence can be modified via application of 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 electrodes 12, since only two parameters cannot compensate for the full continuum of possible variations in the shape of the mirror electrodes.

[0061] It is recognized that mechanical imperfections require any correction of the function s(y), which cannot be achieved by electrical means alone, but requires changing the correction electrode 24 to another correction electrode 24 having a different shape. Therefore, one or several additional correction electrodes 24 are introduced to supplement the existing (main) correction electrode 24. A voltage can be set on the set of correction electrodes 24, possibly including holding one or more of the correction electrodes 24 at a zero voltage bias to correct any mechanical imperfections. The correction electrodes 24 are connected to a non-zero bias u n where n=1...N. The resulting effective shape function of the combined correction electrodes is given by a linear superposition:

[0062]

number

[0063] Any shape function S * Rather than trying to emulate (y), we use a finite number of parameters, u n 2. Using the shape S to compensate for the most common mechanical imperfections, i.e., misalignment of the mirror electrode 12 (e.g., caused by imperfections in the thickness of the shim 28) and sagging of the mirror electrode 12 (i.e., any curvature of the mirror electrode 12 centered at the middle of the support rod 26). n 2 as an additional angular error 30 and curvature 32 in one of the mirror electrodes 12. Note that only the sum of the curvatures of the two mirror electrodes 12 is effective for the ion motion, so that the sagging of both mirror electrodes 12 can be corrected with only one parameter.

[0064] 4 shows a mass analyzer 10 that can be used to correct errors in the focusing angle Θ of the mirror electrodes, caused for example by an incorrect shim thickness. Imperfections in the focusing angle Θ of the mirror electrodes do not remove the correction problem from the class of optimal solutions for perfectly aligned mirror electrodes 12. If the optimal angle given by equation (3) above is Θ, and the angle is Θ * If the incomplete angle Θ is set as * Correction can be made by adjusting the average drift length L of the ions 20 through the mirror electrodes 12 accordingly, so that satisfies equation (3). The required average drift length L * is given by the following formula:

[0065]

number

[0066] The average drift length L is usually increased until the ion 20 approaches too close to the fringes in the electric field of the mirror electrode, which is limited only by the physical length of the mirror electrode. *Therefore, the maximum and minimum predicted errors away from the desired focusing angle Θ are used to determine the average drift length L * We can calculate the required maximum and minimum values ​​for

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

[0068]

number

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

[0070] 4 shows a mass analyzer 10 with two pairs of correction electrodes 24. A 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, it is expected that the electrode focusing angle Θ may vary by ±15%. To accommodate this, the pair of primary correction electrodes 24 is effectively split into two corresponding pairs of correction electrodes 241 and 242, and furthermore, the minimum average drift length L resulting from an expected ±15% variation in the intended mirror electrode focusing angle Θ is calculated. * and the maximum average drift length L * The method is adapted to provide:

[0071] 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 adjusted to be equal to or less than the average drift length L to ensure that the ions 20 do not experience fringe fields near the ends of the correction electrodes 241 and 242. * Note that applying a voltage to the shortened correction electrode 241 rather than the extended correction electrode 242 reduces the average drift length L * = 300 mm, and therefore, Θ * = 0.05° × 300 / 350 = 0.04285°. Applying a voltage to the extended correction electrode 242 instead of the shortened correction electrode 241 reduces the average drift length L * = 400 mm, and therefore, Θ * = 0.05° × 400 / 350 = 0.05714°. Thus, time-of-flight correction is achieved even for mirror electrodes 12 with imperfections in the focusing angle Θ of ±15%.

[0072] Furthermore, providing two pairs of correction electrodes 241, 242 with different average drift lengths L1 and L2 allows for any effective drift length L between the values ​​of L1 and L2. *can be achieved by applying appropriate voltages to both pairs of correction electrodes 241, 242. Because both correction electrodes 241, 242 contribute to the correction provided by the single main correction electrode 24, each correction electrode 241, 242 is provided with a fixed voltage of ½U0 plus or minus an adjustment Δu to correct for mechanical imperfections. While the two contributions of ½U0 add up to provide the correction needed for tilt, adding a correction offset Δu to one of the correction electrodes 241, 242 and subtracting it from the other of the correction electrodes 241, 242 reduces the effective average drift length L of one correction electrode. eff dominates over the other, thereby reducing the effective mean drift length L eff The nominal value L * means to move away from

[0073] Therefore, the correction electrodes 241, 242 can be biased with different voltages U1=1 / 2U0+Δu and U2=1 / 2U0-Δu. The effective average drift length L eff 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 Δu=−U0, only the extended correction electrode 242 is excited, and the effective drift length L eff However, if 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), i.e., the average of the average drift length is the nominal drift length L required for a mirror electrode 12 without mechanical defects. * 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 just explained, the effective drift length L eff A correction electrode 24 having a drift length L1 can be emulated by electrically biasing two correction electrodes 241 and 242 having different average drift lengths L1 and L2 at different voltages. Also, the physical lengths of the correction electrodes 241 and 242 are set to be equal to or smaller than the average drift length L1 to ensure that the ions 20 do not experience fringe fields that arise near the ends of the correction electrodes 241 and 242. * Note that the average drift lengths L1 and L2 are greater than . Thus, although Fig. 4 shows the additional correction electrodes 241 and 242 having different physical lengths L1 and L2, this does not necessarily have to be the case. The additional correction electrodes 241 and 242 may have the same physical length, provided that their shape functions S(y) produce 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, 242 with the same physical length but different drift lengths L1, L2 arranged on either side of the central axis Z = 0. The 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, 242 are used, which correct the time-of-flight dispersion arising from the tilted mirror electrodes 12 and also correct mechanical imperfections (i.e. the correction electrodes 241, 242 act as 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 tilted mirror electrodes 12, and one pair of additional correction electrodes 243 is added to correct mechanical imperfections. The pair of additional correction electrodes 243 has edges with a shape given by the difference between a shortened correction electrode 241 with drift length L1=L0+ΔL and an extended electrode 242 with drift length L2=L0-ΔL,

[0079]

number

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

[0081]

number

[0082] 6A shows the shape function S(y) of such a differential correction electrode 243, and FIG. 6B shows such a differential correction electrode 243 in a fixed position between two primary correction electrodes 24 that operate to correct for mirror electrode tilt. The primary correction electrodes 24 have a nominal effective drift length L0 and are configured to have different effective drift lengths L0 to correct for mechanical imperfections. eff When a voltage U is required, a voltage of a particular value and polarity is applied to the differential correction electrode 243. S= 1 / 2U0 ensures that the primary correction electrodes 24 combine to provide the necessary correction for tilt angle Θ. The advantage of the correction electrode arrangement of Figure 6B over that of Figure 5B is that it maintains symmetry about the y-axis no matter 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 for any curvature in the mirror electrode 12. The most common mechanical imperfection in the shape of the mirror electrode is sagging between the support rods 26 which can be approximated by a sagging parameter h, a quadratic function of the mirror electrode shape given by:

[0084]

number

[0085] 7A shows the shape function optimized for an expected error range h=±0.01 mm compared to the optimal shape function for a perfectly straight mirror electrode 12 (i.e., h=0). If a differential correction 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 correction electrode 243, as shown in FIG. 7B. In operation, the differential correction electrode 243 is driven by a voltage u s ∈[-0.5U s ,0.5U s When the curvature of the actual mirror electrode reaches h=0.01 mm, the differential correction electrode 243 is biased at 0.5U s , thus emulating a shape optimized for the actual curvature of the mirror electrode 12. For the opposite maximum predicted negative sag h=-0.01 mm, the differential correction electrode 243 should be biased with a voltage equal to -0.5U to compensate for mechanical imperfections. s The input is biased at a voltage of

[0086] 8 shows a further embodiment including a pair of primary correction electrodes 24 that correct for mechanical imperfections in the focusing angle Θ of the mirror electrodes 12, and a further differential correction electrode 243 that corrects for mechanical imperfections. The separate pair of differential correction electrodes 243 corrects for tilt and curvature individually.

[0087] Although the above-described embodiments are primarily intended to correct for tilt and curvature mechanical errors, they can also at least partially correct other mechanical imperfections that cause time-of-flight aberrations, i.e., the voltage applied to the correction electrodes 24 can be adjusted to provide optimal resolution, which inherently accounts for other imperfections.

[0088] Those skilled in the art will appreciate that the above embodiments can be modified in many different respects 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 electrodes 12 is described with reference to focusing using shims 28, but other configurations are possible. The focusing angle Θ can be set by the size of the attachment, such as by cutting into the mirror electrodes 12, or by setting the length of the attachment rods 26, or by locating the attachment points in the support frame. The mirror can have the angle built into its structure by varying the thickness of the electrodes or their separators (the mirrors of the present invention are constructed as a stack of aluminum electrodes and ceramic spacers).

[0090] Note that although we have described the sagging as curvature of the mirror electrode 12, this sagging is not necessarily due to gravity. The curvature can be any distortion that follows a curve that peaks in the center of the mirror electrode 12. This can result from the release of stress in the metal mirror electrode 12, distorting the mirror electrode 12 during and after machining. Other factors such as thermal shifts and assembly errors / insufficient force can also cause sagging.

Claims

1. 1. A multi-reflecting time-of-flight mass spectrometer, comprising: two ion optical mirrors, each of which is elongated generally along a drift direction (Y direction) away from the ion implantation point, each of which faces the other in a Z direction, the Z direction being orthogonal to the Y direction, and the two mirrors being tilted at a tilt angle such that the Z direction separation between the mirrors decreases as the distance along the Y direction increases; at least one pair of correction electrodes extending along at least a portion of the Y direction in or adjacent to a space between the mirrors, the at least one pair of correction electrodes facing each other across a gap between the ion optical mirrors; 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, the correction electrodes being electrically biased with a voltage so as to, in use, generate an electric field between the opposing mirrors in at least a portion of a space extending between the mirrors that varies as a function of distance along the Y direction, the voltage including a first component for correcting intended aberrations resulting from the intended tilt angles of the mirrors and a second component for correcting unintended aberrations resulting from a range of perturbations to an ideal time-of-flight ranging from a maximum perturbation to a minimum perturbation, the second component varying between a maximum value and a minimum value; the at least one pair of correction electrodes are shaped such that some or all of the at least one pair of correction electrodes apply the voltage including the first component and the second component varying between a maximum value and a minimum value to generate a range of resultant voltage offsets that compensate for a range of time-of-flight aberrations corresponding to the intended aberrations resulting from the intended tilt angle of the mirror and the unintended aberrations resulting from a range of perturbations relative to the ideal time-of-flight from the maximum perturbation to the minimum perturbation; A multi-reflecting time-of-flight mass spectrometer, wherein the range of perturbations relative to the ideal time-of-flight ranges from a maximum perturbation due to a maximum positive misalignment error in the mirror to a minimum perturbation due to a maximum negative misalignment error in the mirror.

2. 2. A multi-reflecting time-of-flight mass spectrometer as described in claim 1, wherein the resultant voltage offset acts to shorten or lengthen the average drift length of the ions in the +Y direction through the mirror before they are reflected and drift back through the mirror in the -Y direction.

3. 2. A multi-reflecting time-of-flight mass spectrometer as claimed in claim 1, wherein the resultant voltage offset acts to increase or decrease the number of oscillations that ions undergo as they drift past the mirror.

4. Each pair of the at least one correction electrode is a first correction electrode shaped to generate a voltage offset when subjected to a voltage having a value equal to the sum of the first component and the maximum value of the second component, the voltage offset compensating for the intended aberration resulting from the intended tilt angle of the mirror and the unintended aberration resulting from the maximum perturbation; a second correction 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 having a value equal to the sum of the first component and the minimum value of the second component is applied to the second correction electrode.

5. 5. The multi-reflecting time-of-flight mass spectrometer of claim 4, wherein the first and second correction electrodes are shaped to produce different average drift lengths of ions through the mirror, and optionally the first and second correction electrodes have different physical lengths in the Y direction.

6. The at least one pair of correction electrodes 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 to the correction electrode; a second correction electrode having a shape corresponding to the required difference between the shapes, wherein when a voltage having a value equal to the maximum value of the second component is applied to the second correction electrode, the second correction electrode generates a voltage offset that compensates for the maximum perturbation, and when a voltage having a value equal to the minimum value of the second component is applied to the second correction electrode, the second correction electrode generates a voltage offset that compensates for the minimum perturbation.

7. A multi-reflecting time-of-flight mass spectrometer, comprising: two ion optical mirrors, each of which is elongated generally along a drift direction (Y direction) away from the ion implantation point, each of which faces the other in a Z direction, the Z direction being orthogonal to the Y direction, and the two mirrors being tilted at a tilt angle such that the Z direction separation between the mirrors decreases as the distance along the Y direction increases; at least one pair of correction electrodes extending along at least a portion of the Y direction in or adjacent to a space between the mirrors, the at least one pair of correction electrodes facing each other across a gap between the ion optical mirrors; 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, the correction electrodes being electrically biased with a voltage so as to, in use, generate an electric field between the opposing mirrors in at least a portion of a space extending between the mirrors that varies as a function of distance along the Y direction, the voltage including a first component for correcting intended aberrations resulting from the intended tilt angles of the mirrors and a second component for correcting unintended aberrations resulting from a range of perturbations to an ideal time-of-flight ranging from a maximum perturbation to a minimum perturbation, the second component varying between a maximum value and a minimum value; the at least one pair of correction electrodes are shaped such that some or all of the at least one pair of correction electrodes apply the voltage including the first component and the second component varying between a maximum value and a minimum value to generate a range of resultant voltage offsets that compensate for a range of time-of-flight aberrations corresponding to the intended aberrations resulting from the intended tilt angle of the mirror and the unintended aberrations resulting from a range of perturbations relative to the ideal time-of-flight from the maximum perturbation to the minimum perturbation; A multi-reflecting time-of-flight mass spectrometer, wherein the range of perturbations relative to the ideal time-of-flight ranges from a maximum perturbation due to a maximum positive curvature error in the mirror to a minimum perturbation due to a maximum negative curvature error in the mirror.

8. 8. The multi-reflecting time-of-flight mass spectrometer of claim 7, wherein the maximum positive curvature error and the maximum negative curvature error in the mirror correspond to curvature in the mirror due to sagging.

9. The range of perturbations relative to the ideal time-of-flight ranges from a maximum perturbation due to a maximum positive misalignment error in the mirror to a minimum perturbation due to a maximum negative misalignment error in the mirror; 9. The multi-reflecting time-of-flight mass spectrometer of claim 7, wherein the shape of one electrode of the at least one pair of correction electrodes compensates for positional error independently of curvature error, and the shape of another electrode of the at least one pair of correction electrodes compensates for curvature error independently of positional error.

10. 1. A method of operating a multi-reflecting time-of-flight mass spectrometer, the method comprising: two ion optical mirrors, each of which is elongated generally along a drift direction (Y direction) away from the ion implantation point, each of which mirrors faces the other in a Z direction, the Z direction being orthogonal to the Y direction, and the two mirrors being tilted such that the Z direction separation between the mirrors decreases as the distance along the Y direction increases; at least one pair of correction electrodes extending along at least a portion of the Y direction in or adjacent to a space between the mirrors, the at least one pair of correction electrodes facing each other across a gap between the ion optical mirrors; 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, the correction electrodes being electrically biased with a voltage so as to, in use, generate an electric field between the opposing mirrors in at least a portion of a space extending between the mirrors that varies as a function of distance along the Y direction, the voltage including a first component for correcting intended aberrations resulting from intended tilt angles of the mirrors and a second component for correcting unintended aberrations resulting from a range of perturbations to an ideal time-of-flight ranging from a maximum perturbation to a minimum perturbation, the second component varying between a maximum value and a minimum value; the at least one pair of correction electrodes are shaped such that some or all of the at least one pair of correction electrodes can apply the voltage comprising the first component and the second component varying between a maximum value and a minimum value to generate a range of resultant voltage offsets that compensate for a range of time-of-flight aberrations corresponding to the intended aberrations resulting from the intended tilt angle of the mirror and the unintended aberrations resulting from a range of perturbations to the ideal time-of-flight from the maximum perturbation to the minimum perturbation, the range of perturbations to the ideal time-of-flight ranging from a maximum perturbation due to a maximum positive misalignment error in the mirror to a minimum perturbation due to a maximum negative misalignment error in the mirror, and / or the range of perturbations to the ideal time-of-flight ranging from a maximum perturbation due to a maximum positive curvature error in the mirror to a minimum perturbation due to a maximum negative curvature error in the mirror; The method comprises: exciting the mirror to provide an electric field to cause 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 one pair of correction electrodes such that the at least one pair of correction electrodes generates a resultant voltage offset that compensates for the intended time-of-flight aberration and the unintended time-of-flight aberration; injecting ions into the mirror from an ion source; and detecting the ions with an ion detector located at the same end of the mirror as the ion source.

11. Each pair of the at least one correction electrode 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 subjected to a voltage having a value equal to the sum of the first component and the maximum value of the second component; a second correction electrode shaped to generate a voltage offset that compensates for the intended aberration and the unintended aberration resulting from the minimum perturbation when subjected to a voltage having a value equal to the sum of the first component and the minimum value of the second component; The method comprises: (i) compensating for the maximum perturbation by applying a voltage to the first correction electrode and not to the second correction electrode, the voltage having a value equal to the maximum of the first component and the second value; (ii) compensating for the minimum perturbation by applying a voltage to the second correction electrode and not to the first correction electrode, the voltage having a value equal to the minimum of the first and second components; or 11. The method of claim 10, comprising: (iii) compensating for perturbations between the maximum and minimum perturbations by applying to the first correction electrode a voltage having a value equal to the sum of half the first component and the second component having a value between the maximum and minimum values, and applying to the second correction electrode a voltage having a value equal to the sum of half the first component and the second component having a value between the maximum and minimum values.

12. The at least one pair of correction electrodes at least a first correction electrode having a shape that compensates for time-of-flight aberrations resulting from the intended tilt angle of the mirror when subjected to a voltage equal to the first component; a second correction electrode having a shape corresponding to the required difference between the shapes, such that when a voltage having the maximum value of the second component is applied to the second correction electrode, 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 to the second correction electrode, the second correction electrode generates a voltage offset that compensates for the minimum perturbation; The method comprises: (i) compensating the maximum perturbation by applying a voltage equal to the first component to the at least first correction electrode to compensate for the intended time-of-flight aberration, and applying a voltage having the maximum value of the second component to the second correction electrode to compensate for the unintended time-of-flight aberration; (ii) compensating for the minimum perturbation by applying a voltage equal to the first component to the at least a first correction electrode to compensate for the intended time-of-flight aberration, and applying a voltage having the minimum value of the second component to the second correction electrode to compensate for the unintended time-of-flight aberration; or 11. The method of claim 10, comprising: (iii) compensating for perturbations between the maximum perturbation and the minimum perturbation by applying a voltage to the at least a first correction electrode equal to the first component to compensate for the intended time-of-flight aberrations, and applying a voltage to the second correction electrode equal to the second component having a value between the maximum and minimum values ​​to compensate for the unintended time-of-flight aberrations.

13. 1. A method for designing a multi-reflecting time-of-flight mass spectrometer, the method comprising: constructing an ideal arrangement of an ion source, an ion detector, and two ion optical mirrors, each of the mirrors being elongated generally along a drift direction (Y direction) away from an ion injection point, and each of the mirrors facing each other in a Z direction perpendicular to the Y direction, such that ions supplied from the ion source enter the mirrors at the ion injection point and then follow a zigzag path through the mirrors when the mirrors are excited to provide an electric field; configuring at least a pair of correction electrodes extending along at least a portion of the Y direction in or adjacent to a space between the mirrors, the at least a pair of correction electrodes facing each other across a gap between the ion optical mirrors, each of the correction electrodes having a surface substantially parallel to the Y-Z plane and shaped such that the surface is separated from one of the mirrors by a distance that varies along the Y direction, the correction electrodes being electrically biased with a voltage to, in use, generate an electric field between the mirrors in at least a portion of the space extending between the opposing mirrors that varies as a function of distance along the Y direction, the voltage including a first component for correcting intended aberrations resulting from intended tilt angles of the mirrors and a second component for correcting unintended aberrations resulting from a range of perturbations to ideal time-of-flight spanning from a maximum to a minimum perturbation, the second component varying between a maximum and a minimum value; determining maximum and minimum perturbations of the mirrors away from the ideal configuration and resulting maximum and minimum aberrations in the flight time of ions through the mirrors; determining the shape of the at least one pair of correction electrodes such that some or all of the at least one pair of correction electrodes can be applied with the voltage including the first component and the second component varying between a maximum value and a minimum value to produce a range of resultant voltage offsets that compensate for a range of time-of-flight aberrations corresponding to the intended aberrations resulting from the intended tilt angle of the mirror and the unintended aberrations resulting from a range of perturbations relative to the ideal time-of-flight from the maximum perturbation to the minimum perturbation; determining a shape of the at least one pair of correction electrodes to compensate for a range of time-of-flight aberrations corresponding to perturbations ranging from a maximum perturbation due to a maximum positive misalignment error in the mirror to a minimum perturbation due to a maximum negative misalignment error in the mirror relative to the ideal time-of-flight; A method wherein the resultant voltage offset acts to shorten or lengthen the average drift length of the ions in the +Y direction through the mirror before being reflected and drifting back through the mirror in the -Y direction.

14. 14. The method of flight mass spectrometry of claim 13, wherein the resultant voltage offset acts to increase or decrease the number of oscillations the ions undergo as they drift past the mirror.

15. A method for designing a multi-reflecting time-of-flight mass spectrometer, the multi-reflecting time-of-flight mass spectrometer comprising: constructing an ideal arrangement of an ion source, an ion detector, and two ion optical mirrors, each of the mirrors being elongated generally along a drift direction (Y direction) away from an ion injection point, and each of the mirrors facing each other in a Z direction perpendicular to the Y direction, such that ions supplied from the ion source enter the mirrors at the ion injection point and then follow a zigzag path through the mirrors when the mirrors are excited to provide an electric field; configuring at least a pair of correction electrodes extending along at least a portion of the Y direction in or adjacent to a space between the mirrors, the at least a pair of correction electrodes facing each other across a gap between the ion optical mirrors, each of the correction electrodes having a surface substantially parallel to the Y-Z plane and shaped such that the surface is separated from one of the mirrors by a distance that varies along the Y direction, the correction electrodes being electrically biased with a voltage to, in use, generate an electric field between the mirrors in at least a portion of the space extending between the opposing mirrors that varies as a function of distance along the Y direction, the voltage including a first component for correcting intended aberrations resulting from intended tilt angles of the mirrors and a second component for correcting unintended aberrations resulting from a range of perturbations to ideal time-of-flight spanning from a maximum to a minimum perturbation, the second component varying between a maximum and a minimum value; determining maximum and minimum perturbations of the mirrors away from the ideal configuration and resulting maximum and minimum aberrations in the flight time of ions through the mirrors; determining the shape of the at least one pair of correction electrodes such that some or all of the at least one pair of correction electrodes can be applied with the voltage including the first component and the second component varying between a maximum value and a minimum value to produce a range of resultant voltage offsets that compensate for a range of time-of-flight aberrations corresponding to the intended aberrations resulting from the intended tilt angle of the mirror and the unintended aberrations resulting from a range of perturbations relative to the ideal time-of-flight from the maximum perturbation to the minimum perturbation; determining a shape of the at least one pair of correction electrodes to compensate for a range of time-of-flight aberrations corresponding to perturbations ranging from a maximum perturbation due to a maximum positive curvature error in the mirror to a minimum perturbation due to a maximum negative curvature error in the mirror relative to the ideal time-of-flight.

16. The method of claim 15 , wherein the maximum positive curvature error and the maximum negative curvature error of the mirror correspond to curvature of the mirror due to sagging. determining the shape of said at least one pair of correction electrodes to compensate for a range of time-of-flight aberrations corresponding to perturbations ranging from a maximum perturbation due to a maximum positive misalignment error in said mirror to a minimum perturbation due to a maximum negative misalignment error in said mirror relative to said ideal time-of-flight; the resultant voltage offset acts to shorten or lengthen the average drift length of the ions in the +Y direction through the mirror before being reflected and drifting back through the mirror in the −Y direction; 17. The method of claim 15 or 16, comprising determining a shape of one electrode of the at least one pair of correction electrodes to compensate for misregistration errors independently of curvature errors, and a shape of another electrode of the at least one pair of correction electrodes to compensate for curvature errors independently of misregistration errors.

18. The method includes, for each pair of the at least one correction electrode: determining a shape of a first correction electrode such that, when a voltage equal to the sum of the first component and the maximum value of the second component is applied, the first correction electrode 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; and determining the shape of a second correction electrode such that, when subjected to a voltage equal to the sum of the first component and the minimum value of the second component, it produces 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.

19. 20. The method of claim 18, wherein the first correction electrode and the second correction electrode are shaped to produce different average drift lengths of ions through the mirror, and optionally the first correction electrode and the second correction electrode have different physical lengths in the Y direction.

20. determining a shape of at least a first correction electrode that, when subjected to a voltage having a value equal to the first component, compensates for time-of-flight aberrations corresponding to the intended tilt angle of the mirror along the Y direction; and determining a shape of the second correction 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 to the second correction electrode, 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 correction electrode is applied to the second correction electrode, the second correction electrode generates a voltage offset that compensates for the minimum perturbation.

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