Method of operating a mass spectrometer including an ion trap

Abstract

A method of operating a mass spectrometer including an ion trap is provided. The method comprises introducing an ion having a mass to charge ratio into the ion trap; measuring time series data corresp

Description

[0001]Method of operating a mass spectrometer including an ion trap Field of the disclosure The present disclosure relates to mass spectrometry. In particular, the present disclosure relates to mass spectrometry techniques involving an ion trap. Background Mass spectrometry measures the atomic and molecular masses of charged species in complex sample mixtures and allows the analysis of compounds at extremely low concentrations. This measurement technique's high precision enables many applications within both industry and research fields, ranging from protein characterisation and pharmacokinetics to isotopic dating and space exploration. Modern mass spectrometers can typically be described as one of six types; magnetic sector, quadrupole, Fourier-transform ion cyclotron resonance (FT ICR), Orbitrap analyser, time-of-flight and radiofrequency (RF) ion trap. Though each type of mass spectrometer exploits different physical principles to direct or confine the charged species under study, all designs rely on the existence of a well-defined relationship between the mass of a species and a measured experimental parameter. For example, time-of-flight mass spectrometers accelerate charged species within a fixed potential and measure the traversal time of the ion between pickup electrodes. As additional mass increases the traversal time of an ion in a predictable way, the mass of charged species can be recovered from traversal time. Similarly, FT ICR and Orbitrap mass spectrometers confine charged species to quasi-periodic trajectories within the device and measure the period of oscillation by image current. This common functional principle of mass spectrometers also means that each design shares the same weakness. Namely, if uncontrolled experimental variables affect the measured parameter of time-of-flight or oscillation period, then the accuracy of the predicted mass for the charged species is significantly impacted. Therefore, the difficulty in controlling the energy, initial momentum, and position of the charged species under study presents a limitation for the measurement accuracy within mass spectrometry. 15026845v1 This experimental challenge has been addressed within the fields of ion optics and ion trap mass spectrometry through the careful design and manufacture of ion optics, which produce trajectories with oscillation frequencies independent of the energy of charge species. Trapping fields constructed with this energy independence property are called energy isochronous. For mass spectrometers relying on this principle, the resolving power and accuracy of the device are determined by the extent to which the trapping field conforms to the ideal of energy isochronicity. To achieve high resolution and accuracy, the trapping field must satisfy strict tolerances since any perturbation can significantly decrease the devices’ resolving power and accuracy. Such precision in the trapping field can only be achieved through extreme manufacturing tolerances in the shape and alignment of electrodes and by restricting the intrusion of external fields. The construction of ion traps to such exacting tolerances is an extremely difficult technical challenge, and trapping fields never conform precisely to the ideal of energy isochronicity. Beyond the technical challenge of construction, the condition of energy isochronous trapping fields also imposes significant design constraints. If this requirement could be relaxed or eliminated, designers would be free to optimise ion traps for different objectives, such as confinement over a broader range of ion energies and initial insertion angles. The strict manufacturing tolerances of energy isochronous designs also presents a barrier to the miniaturisation of electrostatic ion traps since it is not possible to construct microscale structures with the same tolerances possible at the macroscale. Therefore, to realise the promises of microscale electrostatic ion traps, which include high throughput single ion analysis, it is essential to develop methods for operating ion traps without the property of energy isochronicity. Further, the resolution of a mass spectrometer and the mass accuracy of a mass spectrometer are important parameters for many applications. This invention is devoted to improvement of resolution and mass accuracy of mass spectrometer including electrostatic traps (EST), multi-reflection Time of Flight mass spectrometers and orbital trapping mass spectrometers. 15026845v1 US-B-5,880,466 is one example of an EST. Such ESTs measure ions accelerated by a specific acceleration voltage (i.e. having a specific energy per unit charge) which travel along the same trajectories constrained within the EST. The oscillatory frequencies of each ion are dependent on the ion’s sort, being inversely proportional to the square root of m / z. The frequency of oscillations f0 may be converted to m / z with a formula: m / z = C / f0^2 (1) where C is a conversion constant that depends on the EST design and applied voltages. Due to a spread of coordinates and velocities at which an ion enters an EST, the orbital parameters (e.g. oscillation amplitudes) may vary from ion to ion in an a priori unknown manner. This results in a difference δf between the measured frequency of oscillations fz and the nominal frequency f0 for ions with the same m / z and oscillating exactly on the optical axis with a nominal injection energy. The uncertainty of δf additionally limits precision of the m / z determination. Because of this, EST for Fourier Transform Mass Spectrometry (FTMS) are specially designed to be as isochronous as possible, which means that the oscillation frequency for same m / z ions is predominantly independent of the orbital parameters. In practice, non-ideal EST retain a certain dependence of the oscillation frequencies on orbital parameters which deteriorates the accuracy of the mass analysis. With sufficiently low capacitance of detection electrodes and input channels of a preamplifier, it is possible to detect individual ions over prolonged duration of detection, for example as is known from methods of Charge Detection Mass Spectrometry (CDMS). US- B-11,232,941 is one known example of CDMS. Detection of a single elementary charge is also known from [A.R.Todd et al J. Am. Soc. Mass Spectrom.2020, 31, 146−154]. Therefore, CDMS could be considered as an implementation of highly sensitive single-ion (or individual-ion) FTMS. Single-ion sensitivity may also be practically achieved via miniaturization of the ion trap, which reduces the pickup electrode’s electric capacitance. Alternatively, single ion sensitivity may be achieved by prolonging the ion trapping time so that the induced current generated on the pickup electrode(s) during multiple passages of the ions is effectively summed up by the Fourier Transformation until it exceeds a slower growing noise level. 15026845v1 It should be noted that the term ‘single-ion FTMS’ is related to a single ion of any particular ion sort trapped in an EST at a time. Multiple ions of different sorts may be co-trapped. As these ions oscillate on substantially different frequencies, the signal from each may be effectively separated by standard FT methods of processing and analyzed individually. Non-FT methods could also be used, such as wavelet transforms, etc. Where a single ion is injected and trapped, the ion’s initial coordinates and velocities cannot be set exactly, which leads to an uncertainty about the trajectory parameters of the trapped ion. The non-ideality of the EST isochronism is revealed here as an uncertainty of an oscillation frequency and, therefore, an uncertainty of a derived m / z. One proposal for addressing the uncertainty in oscillation frequency in WO-A-2023288179 is to optimize the tuning of an EST. WO-A-2020198332 proposes to use a ratio of amplitudes of fundamental and second harmonic frequencies from the Fourier transform to obtain energy per charge of ions and subsequently correct m / z. US-A-2023046906 proposes to implement on-the-fly adjustment of EST. US-B-11,367,602 proposes to control a duration of trapping. As such, the problem of ion energy uncertainty in ESTs with non-ideal energy isochronism has been approached in number of prior publications. Against this background, the present disclosure aims to provide an improved, or at least commercially relevant alternative, method of operating a mass spectrometer. Summary To overcome these limitations, aspects of this disclosure propose a new present measurement approach. This approach supplements conventional mass spectrometer measurements of a single time-of-flight or oscillation frequency for an ion species with additional measurements. The present measurement approach outlined, provides a framework for incorporating this additional information about charge species and enables accurate measurement of the mass-charge ratio of ions within general trapping fields. Crucially, this permits the precise characterisation of ions in trapping fields without the property of energy isochronicity and enables error correction to be performed for ion traps with manufacturing defects. 15026845v1 The present measurement approach has both time-of-flight and frequency formulations. To characterise an ion within the time-of-flight formulation, a time-of-flight is measured between a pair of pickup electrodes and the overall period of oscillation of the ion—the additional time-of-flight measurement functions as a proxy for the ion's energy. Using calibration ions with known mass-charge, a relationship can be developed between the time-of-flight measurement and the mass-charge ratio of the ion. This relationship (ion trap function) can then be used to predict the mass-charge ratio of ions in experiments accurately. Within the frequency formulation, an identical calibration process can be used to relate the amplitudes of frequency peaks to an ion's unknown mass-charge ratio, enabling the subsequent measurement of ions with unknown mass-charge ratios. This present measurement approach can be applied to e.g. image current detection mass spectrometers of any type and provides a framework for incorporating information from multiple sets of pickup electrodes to accurately predict the mass-charge ratio of ions within general trapping fields. The method allows for variation in the energy, initial position and momentum of ions and for the intrusion of external fields into the device. With this methodology, the manufacturing tolerances of ion traps can be reduced, and a wider variety of ion trap designs can be considered. In particular, this method enables accurate measurement of the mass-charge ratio of ions within microscale electrostatic ion traps. Thus, according to a first aspect of the disclosure a method of operating a mass spectrometer including an ion trap is provided. The method also comprises introducing an ion having a mass to charge ratio into the ion trap. The method comprises measuring time series data corresponding to the oscillation of the ion in the ion trap. The method also comprises extracting a first feature indicative of the oscillation of the ion in the ion trap and a second feature indicative of a trajectory of the oscillation of the ion from the time series data, and computing the mass to charge ratio using an ion trap function and the extracted first and second features. The method of the first aspect may, in some embodiments, be implemented using an ion trap having a first axis, wherein the ion trap causes an ion to oscillate in a first direction aligned with the first axis at a first frequency, and causes the ion oscillates in a second direction transverse to the first direction at a second frequency. In some embodiments, the method may be a method of FTMS. 15026845v1 The method of the first aspect computes the mass to charge ratio for an ion based on the oscillation and trajectory of an individual ion in the ion trap. As such, the method aims to account for the δf effect the trajectory of the ion (i.e. the oscillation of the ion in a second direction) has on the observed oscillation of the ion a principal (first) direction. Accordingly, the resulting determination of the mass to charge ratio of the ion may be implemented more accurately. As such, the detection of transverse oscillations of individual ions improves the determination of mass to charge ratio of the ion by adding a correction based on detected frequencies of ion motion in directions other than the direction of separation (i.e. the first direction). In particular, as the size of ion trap is reduced, in particular the length of the ion trap along the first axis, and spatial deviation of ions from the axis relatively increases, the effect of oscillations in a second direction transverse to a first axis (i.e. the ion trajectory) have an increasingly significant effect. As such, methods according to the first aspect may be particularly applicable to ion traps such a microscale Electrostatic Ion Traps (μESTs) designed to detect individual ions. For example, methods according to the first aspect may improve accuracy of mass and charge measurements in an ion trap such as an EST and may also utilize a wider volume of the ion trap, instead of only a paraxial region. This is especially important for microscale ESTs where the lateral uncertainty of coordinates of injected ions is comparable to the size of the EST along the second axis. According to this disclosure, a μEST is considered to be an ion trap, wherein a typical length of the ion trap in the first direction is no greater than 10 mm, and optionally no more than 5 mm, 2 mm, 1 mm or 0.5 mm. Additionally or alternatively, the capacitance of at least one of the electrodes of the ion trap (in particular, an electrode configured to act as a detector) to ground is no more than 10 pF, preferably no more than 5 pF, 2 pF, 1pF, 0.5 pF or 0.1 pF. In some embodiments, all of the electrodes of the μEST may each have a capacitance to ground of no more than 10 pF, preferably no more than 5 pF, 2 pF, 1pF, 0.5 pF or 0.1 pF. In such embodiments, a capacitance to ground of an electrode configured to act as a detector (e.g. an image current detector) may be no greater than 1 pF, 500 fF, 100 fF, 50 15026845v1 fF, 10 fF, 5 fF or 1 fF. Such a low capacitance improves the sensitivity of the detector for single-charge detection. A transistor (for instance a FET or JFET) which may be configured to act as an amplifier for the signal from the detector may be connected to the detection electrode or electrodes, which may also be formed lithographically. Due to its small size and use of electrostatic potentials for ion trapping, a μEST permits confinement of a small numbers of ions, generally no more than 100, 50, 30, 20, 10, 5 or even a single charged particle in a small space. Nevertheless, high-resolution accurate- mass analysis is possible. Such μESTs typically may operate with a measurement time of no more than 20 ms and / or an acceleration voltage of no more than 200V and / or a gas pressure within the electrostatic ion trap of no more than 10-7mbar may be achieved. Moreover, the μEST can be manufactured efficiently and cost-effectively, for example using lithographic techniques to pattern electrodes of the μEST on a wafer or similar substrate. In some embodiments, the μEST may be formed as part of an integrated circuit. Modern micro- and nano-lithographic technologies may allow nanometer tolerances to be achieved on planar wafers. According to this disclosure, the time series data may be analysed in various domains in order to extract first and second features from which a mass to charge ratio of the ion may subsequently be determined. In some embodiments, the first feature may be an oscillation period of the ion in the ion trap, and the second feature may be a time of flight of the ion in the ion trap. As such, in some embodiments, analysis of the time series data may be performed in the time domain. In some embodiments, the first feature may be an oscillation frequency of the ion along a first direction of the ion trap, and the second feature may be an oscillation frequency along a second direction of the ion trap, wherein the second direction is transverse to the first direction. As such, in some embodiments, analysis of the time series data may be performed in the frequency domain. In some embodiments, the first feature may be an amplitude of an oscillation of the ion along a first direction of the ion trap, and the second feature may be an amplitude of an oscillation of the ion along second direction of the ion trap, wherein the second direction is transverse to the first direction. Thus, in some embodiments further analytical techniques in the frequency domain may also be used. 15026845v1 In some embodiments, the mass to charge ratio of the ion may be computed based on a ratio of the first feature to the second feature. As such, the ratio of the second feature to the first feature may provide information about the trajectory of the ion as it oscillates in the ion trap. For example, the relationship between the oscillation frequency f0 and mass to charge ratio (m / z) assumes that the ion is oscillating in a single direction only. Thus, knowledge of the trajectory of the ion allows a relationship to be inferred between the observed frequency of oscillations in the first direction and the underlying energy of the ion. As such, the ratio of the second feature to the first feature may be used to correct the first feature to reflect the improve the accuracy of the determined m / z of the ion. For example, the mass to charge ratio of the ion may be determined (or corrected) based on a ratio of an amplitude of oscillations having the second frequency to an amplitude of the oscillations having the first frequency. Initial phases of these oscillations may also be taken into account. Thus, the present inventors have also realised that the trajectory of the ion in the ion trap may also be inferred from an analysis of the oscillations in the first and second directions. As such, the determined first frequency of oscillations in the first direction may be corrected in a variety of ways according to this disclosure. In some embodiments, the ion trap may have a first axis, wherein the ion oscillates in a first direction aligned with the first axis. In some embodiments, the ion may oscillate in the ion trap with a trajectory relative to the first axis such that the ion oscillates in a second direction transverse to the first direction at a second frequency. In some embodiments, the ion trap may comprise at least one detector located along the first axis and offset from the first axis in the second direction to detect first feature and the second feature, the detector configured to measure the time series data. In some embodiments, the oscillation of the ion in the first and second directions may be detected by a single detector located at a position along the first axis where the ion oscillates in the first direction and offset from the first axis in the second direction. By providing the detector offset from the first axis in the second direction, the detector may detect the oscillation of the ion in the first direction as it passes by the detector along the first axis. The detector may also detect oscillation in the second direction based on the strength of the signal as the ion passes the detector, wherein the strength of the signal may be indicative of distance from the detector as the ion passes by the detector. As such, a single detector may be 15026845v1 provided within an ion trap, for example an μEST, in order to implement a method of mass spectrometry in a simple and economic manner. In some embodiments, the ion trap may comprise a first detector and a second detector, wherein the first and second detectors may each be located a position along the first axis and spaced apart on opposing sides of the first axis in the second direction. As such, in some embodiments, a plurality of detectors may be provided in the ion trap. For example, each detector may be an image current detector, such as a pickup electrode. This takes advantage of the fact that the method of Fourier Transform mass spectrometry may analyse the mass to charge ratio of the ion in a non-destructive manner. In some embodiments, the first detector may generate first time series data indicative of the oscillation of the ion, and the second detector may generate second time series data indicative of the oscillation of the ion. In some embodiments, the first feature may be determined from a sum of the first and second time series data, and the second feature may be determined from a difference between the first and second time series data. For example, the first detector may generate a first signal indicative of the oscillation of the ion, and the second detector may generate a second signal indicative of the oscillation of the ion. In some embodiments, the first frequency may be determined from a sum of the first and second signals. In some embodiments, the second frequency may be determined from a difference between the first and second signals. For example, in some embodiments, the first and second signal(s) may be linearly superimposed to generate a summed signal comprising harmonics of the first frequency. In some embodiments, the first and second signal(s) may be linearly superimposed to generate a difference signal comprising harmonics of the second frequency. In some embodiments, the first frequency may be determined from the summed signal and the second frequency may be determined from the second signal. By using a pair of opposing detectors, the summed signal (i.e. the sum of the first and second signals) may be used to determine the first frequency which is insensitive to oscillation in the second direction. Furthermore, the difference signal (i.e. the difference of the first and second signals) is proportional to the location of the ion in the second direction as it passes by the detector. As such, the difference signal has increased sensitivity for detection of the second frequency. 15026845v1 In some embodiments, the oscillation of the ion in the first and second direction may be detected by a plurality of pairs of first and second detectors, each pair of detectors being located along the first axis. By using a plurality of detectors, difference signals of combinations of different detectors may be used to generate harmonics of the second frequency, thereby allowing for accurate determination of the second frequency. In some embodiments, by providing a plurality of pairs of detectors, observation of the oscillation of the ion in a third direction transverse to the first and second directions may also be provided. As such, in some embodiments the method may correct for the oscillation of the ion in both the second and third directions. In some embodiments, each detector may comprise a planar electrode extending in a plane normal to the second direction. For example, each detector may be configured to detect an image current of the ion as it oscillates past the planar electrode. As such, the detector may be configured to detect the oscillation of the ion in a non-destructive manner. In some embodiments, a capacitance of each planar electrode to ground may be no more than: 0.1 pF, 0.5 pF 1 pF, or 2 pF. Thus, the planar electrode of the detector, in particular where the detector is provided as part of a μEST, may have a capacitance which allows the detector to detect an image current, in particular the image current associated with a single ion with a relatively high sensitivity. The ion trap of the first aspect causes an ion to oscillate in a first direction and a second direction. As such, in some embodiments, the ion trap causes an ion to be injected into the ion trap, where it oscillates in the first and second direction. At the point of injection into the ion trap, the ion may have a trajectory which is not aligned with the first axis, and / or a position which is not aligned with the first axis. Where the position and / or trajectory of the ion deviates from the first axis in the second direction, the ion trap may cause the ion to oscillate in the second direction as well as in the first direction. In some embodiments, the ion may be injected into the ion trap from an axial end of the ion trap aligned with the first axis. As such, the ion may be injected into the ion trap generally in the first direction. It will be appreciated that at the point of injection, the position of the ion may not be exactly aligned with the first axis. For example, a position of the ion may be spaced apart from the first axis in the second direction. Similarly, a trajectory of the ion at the point of injection may not be aligned with the first axis. For example the amplitude of a 15026845v1 trajectory of the ion in the plane defined by the first and second directions, relative to the first axis of the ion trap may be non-zero. Such non-zero trajectories may result in oscillation of the ion in the second direction as the ion oscillates in the first direction. In some embodiments, the ion may be injected into the ion trap having a non-zero deviation relative to the first axis. That is to say, the direction of ion injection into the ion trap may have a non-zero offset and / or angle relative to the first axis. As such, the ion may be injected into the ion trap in order to intentionally induce oscillations in the second direction. By injecting the ion into the ion trap at a non-zero angle and / or offset to the first axis, the trajectory (or likely range of possible trajectories) of the ion as it oscillates in the ion trap (and an associated first and second frequency) may be more accurately controlled. While the method of the first aspect corrects for oscillation in a second direction, it will be appreciated that the principles of the first aspect may also be applied to correct for oscillations of the ion in a third direction transverse to the first and second directions. As such, in some embodiments the ion trap may cause the ions to oscillate in a third direction transverse to the first direction and the second direction at a third frequency. By causing the ion to oscillate in a third direction, the divergence of the ion may be controlled over the duration of the observation of the ion oscillation in the ion trap. In some embodiments, the ion trap may comprise a first ion mirror and an opposing second ion mirror arranged along a first axis, wherein the ion oscillates between the first ion mirror and the second ion mirror. For example, the ion trap may be an μEST, wherein the μEST comprises first and second ion mirrors which are spaced apart by in the first direction. Where the ion trap is an μEST, the overall length of the ion trap along the first axis from a distal end of the first ion mirror to a distal end of the second ion mirror may be no greater than: 10 mm, 5 mm, 2 mm, 1 mm or 0.5 mm. In some embodiments, each of the first and second ion mirrors may comprise a first electrode assembly extending in a first plane normal to the second direction, and a second electrode assembly extending in a second plane normal to the second direction. In some embodiments, the first and second electrode assemblies may be spaced apart in the second direction on opposing sides of the first axis. As the method of the first aspect may account for oscillation of the ion in the second direction, the method of the first aspect may accurately determine the mass to charge ratio of ions, even when the ion has a trajectory 15026845v1 which deviates from a paraxial region of the ion trap. That is to say, methods according to the first aspect may utilise a larger portion of the volume of ion trap between the first and second electrode assemblies of each ion mirror. Where the ion trap is a μEST, the first and second ion mirrors may be spaced apart in the second direction by a distance which is generally no more than 100µm and typically may be about 80µm or 70µm. In some embodiments, each first electrode assembly may comprise a plurality of first planar electrodes distributed along the first axis. In some embodiments, each second electrode assembly may comprises a plurality of second planar electrodes distributed along the first axis. Where the ion trap is a μEST, the first planar electrodes of the first electrode assembly may be spaced apart from adjacent first planar electrodes other in the first direction by a distance of no greater than 100µm, preferably no more than 50µm and typically much smaller, for example no more (or less) than 20µm, 10µm or 5µm. First and second electrode assemblies may be mirror-symmetric relative to the first axis. In some embodiments, for at least one of the first and second ion mirrors: the plurality of first planar electrodes may each extend in the first plane in a third direction normal to the first and second directions. In addition, or as an alternative, in some embodiments the plurality of second electrodes may each extend in the second plane in a third direction normal to the first and second directions. In some embodiments, the arrangement of each set of planar electrodes of the first and second ion mirrors are substantially symmetrical between opposite sides of a center of the ion trap along the first axis. Additionally, or alternatively, one or both edges of at least some of the planar electrodes in the respective plane may have an arc shape centered on the first axis. For example, some of the electrodes may have a curved shape, an arc shape, a circular shape or an elliptical shape. The curved shape permits improved containment of ions in the third direction when using planar electrodes. For example, in some embodiments for at least one of the first and second ion mirrors: the plurality of first planar electrodes may each extend in the first plane along an arc, wherein a centre of each arc in the first plane is aligned with the first axis. In addition, or as an alternative, in some embodiments the plurality of second planar electrodes may each extend in the second 15026845v1 plane along an arc, wherein a centre of each arc in the second plane is aligned with the first axis. In some embodiments, the first electrode assembly may be aligned with the second electrode assembly in the first direction. As such, each of the first and second ion mirrors may have an arrangement of planar electrodes which is generally symmetrical about the first axis. Such implementations of the ion trap may provide a number of stable, non- resonant trajectories along which an ion may oscillate. In some embodiments, the first electrode assembly may be offset from the second electrode assembly of one of, or both of, the first and second ion mirrors in the first direction. Such an offset, or perturbation of one or more ion mirrors may introduce more complex ion trajectories into the ion trap, which may allow for more complex analysis or separation of ions within the ion trap. In some embodiments, computing the mass to charge ratio of the ion using the ion trap function and the extracted first and second features may comprise determining a trajectory correction factor for the ion based on the first and second features and the ion trap function, and determining a mass to charge ratio for the ion based on the first frequency and the trajectory correction factor. In some embodiments, the trajectory correction factor may be determined based on the oscillation of the ion in the first and second directions and a trajectory correction function, wherein the trajectory correction function is pre-determined based on a calibration measurement using the ion trap and an ion of a known mass to charge ratio. Such calibration measurements allow the trajectory correction function to be determined empirically for a mass analyser in a straightforward manner. In some embodiments, the trajectory correction function may be determined based on ion-modelling of the trajectory of ions oscillating in the ion trap using, for example, suitable computational simulation. In some embodiments, where an ion is determined to have a ratio of the second feature (e.g. second frequency) to the first feature (e.g. first frequency) which is about m / n, where n and m are integers, preferably n being between 3 and 8 and m being between 1 and n, the determined mass to charge ratio may be flagged as having low precision or rejected. Ion trajectories which have a ratio which is about m / n may be indicative of one or more resonant trajectories which may be challenging to distinguish between. 15026845v1 In some embodiments, a single ion of any particular ion sort is trapped in the ion trap at a time. As such, in some embodiments, the method of the first aspect may be a method of single-ion mass analysis (in particular single-ion Fourier Transform Mass Spectrometry). As such, in some embodiments, a plurality of ions, each ion having a different ion sort (i.e. a different m / z), may be co-trapped in the method of single-ion mass analysis. As the ions of different ion sorts oscillate on substantially different frequencies, the oscillation signal from each ion of a different sort may be effectively separated. In some embodiments, no more than: 100, 10, 5, 3, or 2 ions may be trapped in the ion trap at a time, wherein each ion has a different ion sort. In some embodiments, a single ion of any ion sort may be trapped in the ion trap and analysed at a time. In some embodiments, a plurality of ions are trapped in the ion trap concurrently, wherein the ion trap causes each ion to oscillate in the first direction and the second direction at respective first and second frequencies. Preferably, the plurality of ions trapped in the ion trap have the same mass to charge ratio. Where ions of the same m / z are co-trapped the frequency of oscillation in the first direction of each ion may be difficult to resolve, even when the ions oscillate on different trajectories. However, the frequency of oscillation of each ion in the second direction may be more accurately resolved for each ion. As such, embodiments according to the first aspect may analyse and resolve trajectories of individual ions injected into the ion trap as part of an ion packet (i.e. a plurality of ions). In some embodiments, each detector may be configured to detect an image current of the ion as it oscillates in the first and second directions. As such, each detector of the ion trap may be a non-destructive ion detector (e.g. an image current detector) which is configured to detect a plurality of oscillations of the ion in the ion trap. In some embodiments, each detector is coupled to an amplifier configured to amplify a signal indicative of the oscillation of the ion at the first and second frequencies. In particular, where the method is performed on using a μEST, the amplifier may be provided on the same substrate or wafer as the detector. For example, where the detector is provided as a pickup electrode on a surface of a wafer, an amplifier for the detector may also be integrated into the wafer. For example, the amplifier may comprise one or more transistor (e.g. a JFET or FET) provided on the wafer. 15026845v1 In some embodiments, a signal generated by each detector which is indicative of the oscillation in the first and second directions may be digitised by a digitiser. The digitiser may generate a digitised signal which is indicative of the oscillation in the first and second directions, wherein the trajectory correction factor is determined based on the digitised signal. For example, the digitiser may comprise an analogue to digital converter. In some embodiments, each detector may be connected to a, wherein the controller determines the trajectory correction factor; and / or determines the mass to charge ratio of the ion. In some embodiments, the ion trap may be characterised based on a calibration measurement using the ion trap and an ion of a known mass to charge ratio. In some embodiments, performing a calibration measurement for the ion trap may comprise: providing a calibration ion of a known mass to charge ratio; introducing the calibration ion of known mass charge ratio into the ion trap; measuring calibration time series data corresponding to an oscillation of the calibration ion in the ion trap; extracting a first calibration feature indicative of the oscillation of the calibration ion in the ion trap and a second calibration feature indicative of a trajectory of the oscillation of the calibration ion from the calibration time series data; and determining, based at least in part on the first and second calibration features, the ion trap function corresponding to the ion trap. In some embodiments, the first calibration feature may be an oscillation period of the ion in the ion trap, and the second feature may be a time of flight of the ion in the ion trap. In some embodiments, the first calibration feature may be an oscillation frequency of the ion along a first direction of the ion trap, and the second calibration feature may be an oscillation frequency along a second direction of the ion trap, wherein the second direction is transverse to the first direction. In some embodiments, the first calibration feature may be an amplitude of an oscillation frequency of the ion along a first direction of the ion trap, and the second calibration feature may be an amplitude of an oscillation frequency of the ion along second direction of the ion trap, wherein the second direction is transverse to the first direction. 15026845v1 In some embodiments, the ion trap function may be determined based at least in part on the first and second calibration features using a machine learning technique. In some embodiments, the method may further comprise performing a plurality of calibration measurements for the ion trap using calibration ions of different known mass to charge ratios to generate a set of first and second calibration features and associated known mass to charge ratios, and training a neural network using the set of a set of first and second calibration features and associated known mass to charge ratios to provide the ion trap function. As such, a set of calibrant ions may be used to provide training data for a neural network across a mass to charge range of interest. The trained neural network may then be utilised to generate an ion trap function for ions of unknown mass to charge across the mass range of interest. In some embodiments, the method may comprise providing the ion trap function for computing the mass to charge ratio, wherein the ion trap function corresponds to the ion trap. The ion trap function may be obtained from one or more calibration measurements performed previously using the ion trap. In some embodiments, the ion trap function may be obtained based on a previously performed machine learning technique. According to a second aspect of the disclosure, a mass analyser configured to determine a mass to charge ratio of an ion is provided. The mass analyser comprises: an ion trap; a detector configured to detect an oscillation of the ion in the ion trap; and a mass analyser controller configured to: cause the mass analyser to introduce an ion having a mass to charge ratio into the ion trap; cause the detector of the mass analyser to measure time series data corresponding to the oscillation of the ion in the ion trap; extract a first feature indicative of the oscillation of the ion in the ion trap and a second feature indicative of a trajectory of the oscillation of the ion from the time series data; and compute the mass to charge ratio using an ion trap function and the extracted first and second features. 15026845v1 As such, it will be appreciated that the mass analyser of the second aspect is configured to perform the method according to the first aspect. As such, it will be appreciated that the mass analyser of the second aspect may incorporate any optional features and associated advantages of the first aspect. In some embodiments, the mass analyser controller may be configured to provide the ion trap function for computing the mass to charge ratio, wherein the ion trap function corresponds to the ion trap According to a third aspect of the disclosure, a mass analyser controller for use with the mass analyser of the second aspect is provided. The mass analyser controller is configured to cause the mass analyser of the second aspect to perform the method of any of the first aspect. According to a fourth aspect of the disclosure, a computer program comprising instructions to cause the mass analyser of the second aspect or the mass analyser controller the third aspect to execute the steps of the method of the first aspect is provided. According to a fifth aspect of the disclosure, a computer-readable medium having stored thereon the computer program of the fourth aspect is provided. Further aspects of the disclosure are set out according to the following numbered clauses. 1. A method of Fourier transform mass spectrometry comprising trapping an ion in an ion trap having a first axis, wherein the ion trap causes: the ion to oscillate in a first direction aligned with the first axis at a first frequency, and the ion oscillates in a second direction transverse to the first direction at a second frequency; using a detector located along the first axis and offset from the first axis in the second direction to detect the oscillation of the ion in the first direction and the oscillation of the ion in the second direction; determining a trajectory correction factor for the ion based on the oscillation of the ion in the first and second directions; and 15026845v1 determining a mass to charge ratio for the ion based on the first frequency and the trajectory correction factor. 2. A method according to clause 1, wherein the trajectory correction factor is determined based on a ratio of the second frequency to the first frequency. 3. A method according to clause 1, wherein the trajectory correction factor is determined based on a ratio of an amplitude oscillations having the second frequency to an amplitude of the oscillations having the first frequency. 4. A method according to any preceding clause, wherein the oscillation of the ion in the first and second directions is detected by a single detector located at a position along the first axis and offset from the first axis in the second direction. 5. A method according to any of clauses 1 to 4, wherein the oscillation of the ion in the first and second directions is detected by a first detector and a second detector, wherein the first and second detectors are located at positions along the first axis and spaced apart on opposing sides of the first axis in the second direction. 6. A method according to clause 5, wherein the first detector generates a first signal indicative of the oscillation of the ion; and the second detector generates a second signal indicative of the oscillation of the ion, wherein the first frequency is determined from a sum of the first and second signals, and the second frequency is determined from a difference between the first and second signals. 7. A method according to clause 5 or clause 6, wherein the oscillation of the ion in the first and second direction is detected by a plurality of pairs of first and second detectors, each pair of detectors located along the first axis. 15026845v1 8. A method according to any of clauses 5 to 7, wherein the first and second signal(s) from the first and second detectors are linearly superimposed to generate a summed signal comprising harmonics of the first frequency; and the first and second signal(s) are linearly superimposed to generate a difference signal comprising harmonics of the second frequency, wherein the first frequency is determined from the summed signal and the second frequency is generated from the second signal. 9. A method according to any of clauses 4 to 8, wherein each detector comprises a planar electrode extending in a plane normal to the second direction. 10. A method according to clause 9, wherein a capacitance of each planar electrode to ground is no more than: 0.1 pF, 0.5 pF, 1 pF, or 2 pF. 11. A method according to any preceding clause, wherein the ion trap causes the ions to oscillate in a third direction transverse to the first direction and the second direction at a third frequency. 12. A method according to any preceding clause, wherein the ion trap comprises a first ion mirror and an opposing second ion mirror arranged along the first axis, wherein the ion oscillates between the first and second ion mirror. 13. A method according to clause 12, wherein each of the first and second ion mirrors comprise: a first electrode assembly extending in a first plane normal to the second direction; a second electrode assembly extending in a second plane normal to the second direction, wherein the first and second electrode assemblies are spaced apart in the second direction on opposing sides of the first axis. 14. A method according to clause 13, wherein 15026845v1 the first electrode assembly comprises a plurality of first planar electrodes distributed along the first axis; and the second electrode assembly comprises a plurality of second planar electrodes distributed along the first axis. 15. A method according to clause 14, wherein the plurality of first planar electrodes each extend in the first plane in a third direction normal to the first and second directions; and / or the plurality of second electrodes each extend in the second plane in a third direction normal to the first and second directions. 16. A method according to clause 14 or clause 15, wherein the plurality of first planar electrodes each extend in the first plane along an arc, wherein a centre of each arc in the first plane is aligned with the first axis; and / or the plurality of second planar electrodes each extend in the second plane along an arc, wherein a centre of each arc in the second plane is aligned with the first axis. 17. A method according to any of clauses 13 to 16, wherein the first electrode assembly is aligned with the second electrode assembly in the first direction. 18. A method according to any of clauses 13 to 16, wherein the first electrode assembly is offset from the second electrode assembly in the first direction. 19. A method according to any of clauses 12 to 18, wherein a length of the ion trap along the first axis from a distal end of the first ion mirror to a distal end of the second ion mirror may be no greater than: 10 mm, 5 mm, 2 mm, 1 mm or 0.5 mm. 20. A method according to any preceding clause, wherein the trajectory correction factor is determined based on the oscillation of the ion in the first and second directions and a trajectory correction function, wherein the trajectory correction function is pre-determined based on a calibration measurement using the ion trap and an ion of a known mass to charge ratio. 15026845v1 21. A method according to any preceding clause, wherein where an ion is determined to have a ratio of the second frequency to the first frequency which is about 1 / n, where n is an integer, preferably n being between 3 and 8, the determined mass to charge ratio is flagged as having low precision or rejected. 22. A method according to any preceding clause, wherein a single ion is trapped in the ion trap at a time. 23. A method according to any of clauses 1 to 22, wherein a plurality of ions are trapped in the ion trap concurrently, wherein the ion trap causes each ion to oscillate in the first direction and the second direction at respective first and second frequencies. 24. A method according to clause 23, wherein the plurality of ions trapped in the ion trap have the same mass to charge ratio. 25. A method according to any preceding clause, wherein the detector is configured to detect an image current of the ion as it oscillates in the first and second directions. 26. A method according to any preceding clause, wherein each detector is coupled to an amplifier configured to amplify a signal indicative of the oscillation of the ion at the first and second frequencies. 27. A method according to any preceding clause, wherein the ion trap is an electrostatic ion trap, preferably a microscale electrostatic ion trap (μEST). 28. A method according to any preceding clause, wherein a signal generated by the detector which is indicative of the oscillation in the first and second directions is digitized by a digitiser to generate a digitised signal which is indicative of the oscillation in the first and second directions, wherein the trajectory correction factor is determined based on the digitised signal. 15026845v1 29. A method according to any preceding clause, wherein a controller determines the trajectory correction factor; and / or the controller determined the mass to charge ratio. 30. A Fourier Transform Mass Analyser (FTMA) configured to determine a mass to charge ratio of an ion, the Fourier transform mass analyser comprising: an ion trap arranged along a first axis, wherein the ion trap is configured to: cause the ion to oscillate in a first direction aligned with the first axis at a first frequency, and cause the ion to oscillate in a second direction transverse to the first direction at a second frequency; a detector located along the first axis and offset from the first axis in the second direction, the detector configured to detect the oscillation of the ion in the first direction and the oscillation of the ion in the second direction; and a controller configured to: receive a signal indicative of the oscillation of the ion in the first and second directions from the detector; determine a trajectory correction factor for the ion based on the oscillation of the ion in the first and second directions; and determine a mass to charge ratio for the ion based on the first frequency and the trajectory correction factor. 31. A FTMA according to clause 30, wherein the controller is configured to determine the trajectory correction factor based on a ratio of the second frequency to the first frequency. 32. A FTMA according to clause 30, wherein the controller is configured to determine the trajectory correction factor based on a ratio of an amplitude oscillations having the second frequency to an amplitude of the oscillations having the first frequency. 33. A FTMA according to any of clauses 30 to 32, wherein the FTMA comprises a single detector configured to detect the oscillation of the ion in the first and second directions. 15026845v1 34. A FTMA according to any of clauses 30 to 32, wherein the FTMA comprises a first detector and a second detector, each configured to detect the oscillation of the ion in the first and second directions, wherein the first and second detectors are provided at a location along the first axis where the ion oscillates and spaced apart on opposing sides of the first axis in the second direction. 35. A FTMA according to clause 34, wherein the first detector generates a first signal indicative of the oscillation of the ion; and the second detector generates a second signal indicative of the oscillation of the ion, wherein the first frequency is determined from a sum of the first and second signals, and the second frequency is determined from a difference between the first and second signals. 36. A FTMA according to any of clauses 34 to 35, wherein the FTMA comprises a plurality of pairs of first and second detectors, each pair of detectors located along the first axis. 37. A FTMA according to any of clauses 35 to 36, wherein the controller is configured to linearly superimpose the first and second signals to generate a summed signal comprising harmonics of the first frequency; and the controller is configured to linearly superimpose the first and second signal(s) to generate a difference signal comprising harmonics of the second frequency, wherein the first frequency is determined from the summed signal and the second frequency is generated from the second signal. 38. A FTMA according to any of clauses 33 to 37, wherein each detector comprises a planar electrode extending in a plane normal to the second direction. 39. A FTMA according to clause 38, wherein a capacitance of each planar electrode to ground is no more than 1 pF. 40. A FTMA according to any of clauses 30 to 39, wherein 15026845v1 the ion trap is configured to cause the ions to oscillate in a third direction transverse to the first direction and the second direction at a third frequency. 41. A FTMA according to any of clauses 30 to 40, wherein the ion trap comprises a first ion mirror and an opposing second ion mirror arranged along the first axis, wherein the ion oscillates between the first and second ion mirror. 42. A FTMA according to clause 41, wherein each of the first and second ion mirrors comprise: a first electrode assembly extending in a first plane normal to the second direction; a second electrode assembly extending in a second plane normal to the second direction, wherein the first and second electrode assemblies are spaced apart in the second direction on opposing sides of the first axis. 43. A FTMA according to clause 42, wherein the first electrode assembly comprises a plurality of first planar electrodes distributed along the first axis; and the second electrode assembly comprises a plurality of second planar electrodes distributed along the first axis. 44. A FTMA according to clause 43, wherein the plurality of first planar electrodes each extend in the first plane in a third direction normal to the first and second directions; and / or the plurality of second electrodes each extend in the second plane in a third direction normal to the first and second directions. 45. A FTMA according to clause 43 or clause 44, wherein the plurality of first planar electrodes each extend in the first plane along an arc, wherein a centre of each arc in the first plane is aligned with the first axis; and / or the plurality of second planar electrodes each extend in the second plane along an arc, wherein a centre of each arc in the second plane is aligned with the first axis. 46. A FTMA according to any of clauses 42 to 45, wherein 15026845v1 the first electrode assembly is aligned with the second electrode assembly in the first direction. 47. A FTMA according to any of clauses 42 to 45, wherein the first electrode assembly is offset from the second electrode assembly in the first direction. 48. A FTMA according to any of clauses 41 to 47, wherein a length of the ion trap along the first axis from a distal end of the first ion mirror to a distal end of the second ion mirror is no greater than: 10 mm, 5 mm, 2 mm, 1 mm or 0.5 mm. 49. A FTMA according to any of clauses 30 to 48, wherein the controller is configured to determine the trajectory correction factor based on the oscillation of the ion in the first and second directions and a trajectory correction function, wherein the controller is configured to predetermine the trajectory correction function based on a calibration measurement using the ion trap and an ion of a known mass to charge ratio. 50. A FTMA according to any of clauses 30 to 49, wherein where the controller determines an ion to have a ratio of the second frequency to the first frequency of about 1 / n, where n is an integer, preferably n being between 3 and 8, the controller is configured to flag the determination as having low precision or to reject the determination. 51. A FTMA according to any of clauses 30 to 50, wherein a single ion is trapped in the ion trap at a time. 52. A FTMA according to any of clauses 30 to 51, wherein the ion trap is configured to trap a plurality of ions concurrently, wherein the ion trap causes each ion to oscillate in the first direction and the second direction at respective first and second frequencies. 53. A FTMA according to clause 52, wherein the plurality of ions trapped in the ion trap have the same mass to charge ratio. 15026845v1 54. A FTMA according to any of clauses 30 to 53, wherein the detector is configured to detect an image current of the ion as it oscillates in the first and second directions. 55. A FTMA according to any of clauses 30 to 54, wherein each detector is coupled to an amplifier configured to amplify a signal indicative of the oscillation of the ion at the first and second frequencies. 56. A FTMA according to any of clauses 30 to 55, wherein the ion trap is an electrostatic ion trap, preferably a microscale electrostatic ion trap (μEST). 57. A FTMA according to any of clauses 30 to 56, further comprising a digitiser configured to receive a signal from the detector which is indicative of the oscillation in the first and second directions, wherein the digitiser is configured to generate a digitised signal which is indicative of the oscillation in the first and second directions, wherein the controller is configured to determine the trajectory correction factor based on the digitised signal. 58. A FTMA controller for use with an FTMA of any of clauses 30 to 57, wherein the FTMA controller is configured to cause the FTMA to perform the method of any of clauses 1 to 29. 59. A computer program comprising instructions to cause the FTMA of any of clauses 30 to 57 or the FTMA controller of clause 58 to execute the steps of the method of any of clauses 1 to 29. 60. A computer-readable medium having stored thereon the computer program of clause 59. 61. A method comprising: providing ions of known mass-charge; introducing the ions of known mass-charge into an ion trap including image charge electrodes; measuring first time series data corresponding to the image charge electrodes; 15026845v1 extracting one or more calibration features from the first time series data; determining, based at least in part on the one or more calibration features, an ion trap function corresponding to the ion trap; introducing ions of unknown mass-charge into the ion trap; measuring second time series data corresponding to the image charge electrodes; extracting one or more measurement features corresponding to the image charge electrodes; and computing the unknown mass-charge using the ion trap function and the one or more measurement features. 62. The method of clause 61 wherein the first time series data comprises a first time-of- flight for the ions of known mass-charge and a first oscillation period for the ions of known mass-charge. 63. The method of clause 61 wherein the one or more calibration features comprises a ratio of time-of flight to oscillation period. 64. The method of clause 61 wherein the one or more calibration features or the one or more measurement features comprise dimensionless quantities. 65. The method of clause 61 wherein the ions of known mass-charge comprise a plurality of sets of ions, each of the plurality of sets of ions being characterized by a different mass-charge. 66. The method of clause 61 wherein the ions of known mass-charge comprise ions of a same mass- charge. 67. The method of clause 61 further comprising, concurrently with introducing the ions of known mass- charge into the ion trap varying an energy of the ions of known mass- charge. 68. The method of clause 61 further comprising, concurrently with introducing the ions of known mass- charge into the ion trap varying at least one of an insertion position or insertion angle of the ions of known mass-charge. 15026845v1 69. The method of clause 61 further comprising, concurrently with introducing the ions of known mass- charge into the ion trap varying electrode voltages corresponding to the ion trap. 70. The method of clause 69 wherein the electrode voltages are varied uniformly as a function of voltage. 71. The method of clause 61 wherein the ion trap comprises an element of a mass spectrometer. 72. The method of clause 61 wherein the ion trap function is a multi-dimensional function. 73. A method of operating a mass spectrometer including an ion trap, the method comprising: providing an ion trap function corresponding to the ion trap; introducing an analyte into the ion trap, wherein the analyte includes ions having a mass- charge; measuring time series data corresponding to the ion trap; extracting features from the time series data; and computing the mass-charge using the ion trap function and the extracted features. 74. The method of clause 73 wherein the time series data comprises time-of-flight data and oscillation period data. 75. The method of clause 74 wherein the features comprise a ratio of time-of flight to oscillation period. 76. The method of clause 74 wherein the features comprise a ratio of oscillation frequency to traversal frequency. 77. The method of clause 73 further comprising converting the time series data to frequency data including oscillation frequency data and traversal frequency data. 78. The method of clause 73 wherein the features are dimensionless quantities. 15026845v1 79. The method of clause 73 wherein the time series data corresponds to voltages measured at image charge electrodes. 80. The method of clause 73 wherein introducing the analyte comprises introducing the analyte at a predetermined energy. 21. The method of clause 13 wherein introducing the analyte comprises introducing the analyte at an insertion position or insertion angle. 22. The method of clause 13 wherein the ion trap function is a multi-dimensional function. Aspects of the present disclosure enable one or more of the following: 1. A computationally enhanced measurement method for mass spectrometry (CEMS) for accurately predicting the mass-charge ratio of ions within general trapping fields where oscillation frequency depends on ion energy, initial momentum and position. 2. A computationally enhanced measurement method for accurately predicting the mass-charge ratio of ions within time-of-flight mass spectrometers where time- of-flight depends on ion energy, initial momentum, and position. 3. A computationally enhanced measurement method that enables error correction for mass spectrometers subject to the intrusion of external fields. 4. A computationally enhanced measurement method that provides error correction for existing mass spectrometer designs through changed analysis and / or introduction of additional pickup electrodes for measuring image charge current. 5. A computationally enhanced measurement method that relaxes the manufacturing tolerances on the geometry of mass spectrometers which are required for accurate measurement. 15026845v1 6. A computationally enhanced measurement method that enables accurate measurement of the mass-charge ratio of ions within microscale traps. Brief description of the figures Embodiments of the disclosure will now be described with reference to the following non- limiting figures in which: - Fig.1 is an Outline of measurement protocol for computationally enhanced mass spectrometry (CEMS). In the calibration phase, ions of known mass-charge are injected into a non-ideal electrostatic trap and time-series records of image charge are captured. The ion energy and / or insertion angle / position and / or any other variables affecting ion trajectories can be varied. Features are extracted from each time-series record and are then combined into dimensionless arguments for the g- function which relates features to the mass-charge ratio of ions. The known inputs and outputs of the calibration phase can be used to estimate the g-function. In a subsequent measurement phase, an analyte ion of unknown mass-charge ratio is inserted into the non-ideal ^^EST and features are extracted from the resulting time- series record. The g-function estimate from the calibration phase can then be used to deduce the unknown mass-charge ratio of the analyte. - Fig.2 is an outline of the method for CEMS method using multiple features. - Fig.3a relates to the properties of a model electrostatic ion trap. Fig.3a shows a graph of the potential of the 1-dimensional electrostatic ion trap given by equation (3.1) with pickup electrodes located at ^^ / ^^ = ± ^^ / ^^. - Fig.3b shows a graph of the scaled oscillation period ^^ ^^^^of ions within the trap as a function of scaled energy ^^ / is the characteristic angular frequency. - Fig.4a relates to calibration and relative prediction error for 1-dimensional trap shows a log-log plot of a trap function ^^ with cubic interpolant between discrete samples; - Fig.4b is a graph showing the relative prediction error in the recovered mass- charge ratio(^^ / ^^)predict; 15026845v1 - Fig.5a relates to calibration phase and relative measurement error and shows the discrete samples of the calibration step, a fit using kernel regression, and the true trap-function ^^. - Fig.5b shows the relative measurement error using the trap-function estimate ^^̂ from the linear fit; - Fig.6 shows a schematic drawing of planar microscale electrostatic ion trap (μEST). An electrostatic trapping field is established between two opposing plates of electrodes held at carefully chosen potentials. Ions oscillating within the trapping field are detected through the induced charge on pairs of image charge electrodes (ICE) on each electrode plate, shown in orange. The substrates supporting each electrode plate are not shown. - Fig.7 shows an illustration of time-scale measurement from the induced image charge current signal produced by an ion within the μEST. Due to the large number of oscillations of an ion, the measurement can be performed repeatedly. - Fig.8a relates to calibration and measurement phases applied to ^^EST in an ideal configuration. The calibration phase is conducted with 100 ions at equispaced energy and a graph of the ^^-function estimate is shown. - Fig.8b shows the relative error in the predicted mass in the measurement phase is shown as a function of energy for the conventional uncorrected approach using equation (2.4) is compared with the proposed computationally enhanced (error- corrected) approach. - Fig.9 shows the relative error in the mass-charge predicted by the CEMS approach given in parts-per-billion (ppb). Due to the absence of noise in the measurement process, the predictions are accurate to the level of numerical precision. - Fig.10 shows an example of a fabrication error in ^^EST construction where the displacement between electrode plates increased 33% from design. - Fig.11a and Fig.11b show a comparison of trapping potential (Fig.11a) and oscillation period of the ions (Fig.11b) along the axis of the trap for the ^^EST in ideal and non-ideal configurations. The oscillation period of ions, ^^, is normalised by the characteristic angular frequency of the ion trap, ^^^^. - Fig.12a relates to an application of a method of this disclosure to a ^^EST in non- ideal configuration. Fig.12a shows a calibration phase of methodology using 100 ions of known mass-charge at equispaced energies and a ^^-function is estimated. The estimate of the ^^-function for the ^^EST in the ideal configuration is shown for comparison. 15026845v1 - Fig.12b shows the relative error in the predicted mass-charge in the measurement phase for the conventional uncorrected approach using (2.4) and the computationally enhanced (error-corrected) approach. - Fig.13a shows a comparison of the induced image current signal (ICC) for ions moving along the canonical trajectory with different energies, 100eV and 160eV. The different energy ions oscillate with different frequencies, and a single period of each ICC signal is shown to directly compare of the duty-cycle. - Fig.13 b shows the power spectral densities (PSD) of the ICC signals of Fig.13a for each ion energy are shown. - Fig.14 shows a graph of induced image charge current signals detected by two independent pickup electrodes. These are shown for a fixed ion trajectory over several oscillation cycles. - Fig.15 shows a schematic diagram of a FTMA according to an embodiment of the disclosure; - Fig.16 is an illustration of a plurality of a Poincare orbits for the FTMA of Fig.15. - Fig.17 is a graph showing the dependency of the relative frequency error on the x-amplitude of a Poincare orbit; - Fig.18 is a graph showing the dependence of the frequency ratio ^^ = ^^^^ / ^^^^on the transversal amplitude (represented by initial ion trajectory ^^0; - Fig.19 is a graph showing the relationship between the frequency error ^^ ^^ / ^^0and the frequency ratio ^^ = ^^^^ / ^^^^; - Fig.20 is a block diagram of a method of FTMS according to an embodiment of the disclosure; - Fig.21 is a further schematic diagram of the FTMA of Fig.15; - Fig.22 shows graphs of simulated sum and difference signals generated by a FTMA according to this disclosure; - Fig.23A shows a plan view of a y-z plane of an ion trap according to an embodiment of the disclosure; - Fig.23B shows a cross-sectional view of a x-z plane of the ion trap of Fig.23A; - Fig.24A shows a plan view of an ion trap in the y-z plane according to another embodiment of the disclosure; - Fig.24B shows a cross-sectional view of a x-z plane along the of the of the ion trap of Fig.24A; - Fig.25A shows a graph of a peak in the frequency spectrum associated with the oscillation frequency fz in the first direction of a plurality of ions; 15026845v1 - Fig.25B shows a graph of a peak in the frequency spectrum associated with the oscillation frequency fx in the second direction of the plurality of ions of Fig.25A; - Fig.26 shows a schematic diagram of a FTMA 1 comprising an ion trap wherein an electrode assembly is perturbed along the z-axis; - Fig.27 shows an illustration of a plurality of Poincare orbits for the ion trap of Fig. 26; - Fig.28 shows a graph of the relationship between the frequency error δ ^^ / ^^ ^^ and the initial ion trajectory for the ion trap of Fig.26; - Fig.29 shows a graph of the relationship between the frequency ratio r and the initial ion trajectory varies for the ion trap of Fig.26; and - Fig.30 shows a schematic diagram of an orbital trapping mass analyser. Detailed description Consider the trajectory of an ion oscillating within the potential of an electrostatic trap. By considering the fundamental physical variables of the system, a simple formula for the mass-charge ratio of the ion can be developed by using the Buckingham-Π theorem of dimensional analysis.9–11The relevant physical parameters influencing the trajectory of the ion within the trap are; the length of the ion trap, ^^, the characteristic potential of the electrodes, ϕ0, and the mass, charge and energy of the ion, which are denoted by ^^, ^^ and ^^, respectively. In addition, the initial position, ^^0, and momentum direction, ^^ , are also necessary to define the ion's trajectory. If the potential of the electrostatic trap is known precisely, then these physical parameters can be used to determine the period of oscillation of the ion, where ℎ is a dimensionless function depending on the ion trap potential. The dimensionless groups of this system are; the scaled energy of the ion, ^^ / ( ^^ϕ0), the scaled initial position, ^^0 / ^^, and the initial momentum direction of the ion, ^^ . The dimensionless group, ^^ / ( ^^ϕ0) gives the ratio of ion-ion and ion-electrode forces, 15026845v1 The conventional approach used in mass-spectrometry is to engineer the trap so that the period of oscillation is independent of the energy and trajectory of an ion within the trap. If such conditions can be achieved the function ℎ in (2.1) is constant, This allows recovery of the mass-charge ratio by measurement of the period of oscillation as, ^^2=^^0^^22. (2.4) ^^ ^^ ℎ0In practice, however, manufacturing defects, misalignment of electrodes, variations in ion injection angles, or variation in the voltages of electrodes can give rise to nonidealities, obfuscating the measurement of ^^ / ^^. This is because manufacturing defects or intrusions by external fields perturb the potential of the ion trap from the ideal energy isochronous configuration. A further difficulty is that the precise nature of the manufacturing defects are unknown. This prevents the computation of the dimensionless functio ^^ ℎ by reference to a theoretical model and crucially introduces a dependence on energy. To overcome this challenge, we introduce a time-of-flight measurement, Δ ^^, between a pair of pickup electrodes within the ion trap. This time-of-flight is taken over a subset of the ion trajectory and does not correspond with the full period of oscillation. Using the same dimensional considerations used in (2.1) we can express the time of flight as, where ℎΔis a unknown function of dimensionless variables. By dividing (2.5) by (2.1) we obtain, 15026845v1 Keeping all other dimensionless variables fixed, (2.6) allows us to directly relate the time- scale ratio Δ ^^ / ^^ and the dimensionless energy parameter, ^^ / ( ^^ ^^0). This relationship can also be understood intuitively, since time-of-flight provides a proxy measurement of ion energy using, where ^^pickupis the distance between the pickup electrodes. We now substitute the unmeasured ion energy for our proxy time-of-flight measurement. Application of dimensional analysis provides an expression for the mass-charge ratio of the ion as, where ^^ is a function of dimensionless variables dependent on the perturbed potential of the ion trap. For convenience we refer to ^^ as the trap function as it describes the parameters of trapped ions within the trap. A formal justification for using time-of-flight as a proxy measurement for energy is provided below in the section titled "Relationship between a time-of-flight measurement and the energy of an ion“. Consider now a typical experimental scenario where the trajectories of ions are dominated by their interactions with the electrode potentials. Under these conditions the dependence on the dimensionless group, ^^ / ( ^^ϕ0), can be neglected. Suppose also that the time-of- flight and period of oscillation are to a first approximation independent of the initial position and momentum direction of an ion; or equivalently, only a single ion direction and initial position are considered. With these assumptions the expression for the mass-charge ratio (2.8) simplifies to, By measuring the period of oscillation, ^^, and time-of-flight, Δ ^^, for ions with known mass charge ^^ / ^^ a sample of the unknown trap function can be obtained by rearranging (2.7) This suggests the following algorithm for measuring the mass-charge ratio of ions within ion traps which lack the property of energy isochronicity due to manufacturing defects. 15026845v1 The proposed CEMS method enables deduction of the mass-charge ratio of ions in electrostatic ion traps with non-ideal configurations and consists of successive calibration and measurement phases. Fig.1 shows an overview of the method. As shown in Fig.1, in the calibration phase, ions of known mass-charge ratio are inserted into the non-ideal ^^EST and the time-series records of image charge are captured. The ion energy and / or insertion angle / position and / or any other variables affecting ion trajectories can be varied. To sample different trajectories within the trap, one (or all of) the ion energy, insertion position, or insertion angle is varied in this calibration set of ions. Alternatively, the voltages of the trapping electrodes can also varied uniformly, in place of varying the ion energy. For example the potential of each electrode can be increased by 1-10%. Features may then be extracted from each time-series record and may then be combined into dimensionless arguments for the g-function which relates features to the mass-charge ratio of ions. Features may be extracted from each time-series record in either the time or frequency domain. These features can be, but are not limited to, the amplitudes and peaks of the time-series in the frequency domain or the characteristics of the pulsed waveforms in the time-domain. These features are then combined into dimensionless groups and, motivated by dimensional considerations, are the arguments to an a priori unknown g-function providing the mass-charge ratio of an ion. The known inputs and outputs in the calibration phase can be used to estimate the unknown g-function. As shown in Fig.1, in the measurement phase, the time-series record for an analyte ion with unknown mass-charge is measured and the same features are extracted. The g- function estimate from the calibration phase can then be used to measure the mass-charge of the analyte ion. By way of example, the above general formulation can be applied use the time-scale ratio shown in equations (2.9) and (2.10) as a second algorithm (Algorithm 2). Algorithm 2 – Time-scale formulation 15026845v1 In the time-scale formulation of this embodiment, the calibration phase comprises: measuring the oscillation period, ^^ and time-of-flight Δ ^^ for ions of known mass-charge ^^ / ^^ to sample the unknown trap-function ^^(Δ ^^ / ^^) using equation (2.10). In the time-scale formulation, the measurement phases uses the calibration set to develop an estimate ^^̂ of the trap function. This can be done using standard regression approaches or machine learning (neural networks) for better results. Then, given an ion of unknown mass-charge, the oscillation period and time-of-flight could be measured to recover the mass-charge ratio using equation (2.9). It is of course to be understood that the invention is not intended to be restricted to the details of the above embodiment (Algorithm 2) which is described by way of example only. Thus, further embodiments of this disclosure are set out below. Multiple Time-of-flight measurements The embodiment of the present measurement method outlined above, enables the accurate measurement of the mass charge ratio of ions for scenarios where the period of oscillation varies as a function of energy. The present measurement method, however, is not limited to a single time-of-flight measurement and multiple time-of-flight measurements, Δ ^^1, Δ ^^2, … , Δ ^^^^, can be used in a similar fashion to account for experimental variation in the initial position, momentum direction and ion-ion charge interactions. For properly positioned pickup electrodes these additional time-of-flight measurements can distinguish between different ion trajectories which are defined by the initial conditions of the ion and the strength of ion-ion Coulomb interactions. Consequently, these time-of-flight measurements act as a proxy measure of the unknown and uncontrolled ion parameters in an identical fashion to the proxy energy measurement discussed above. These considerations yield the expression for the mass-charge ratio of the ion as, where ^^ is the period of oscillation as before and Δ ^^1, Δ ^^2, … , Δ ^^^^are the time-of-flight measurements from a set of properly positioned electrodes. Accordingly, Algorithm 3 below provides a further embodiment of the disclosure. 15026845v1 time-of-flight measurements According to an embodiment of the disclosure (Algorithm 3), multiple time-of-flight measurements may provide computationally enhanced mass-charge measurement for ion traps. According to this embodiment, the calibration phase comprises: measuring the oscillation period, ^^ and time-of-flights Δ ^^1, Δ ^^2, … , Δ ^^^^for ions of known mass-charge ^^ / ^^ to sample the unknown trap-function ^^ by rearranging equation (2.9). According to this embodiment, the measurement phase comprises: using the calibration set to develop an estimate ^^̂ of the trap function in equation (2.9). Then, given an ion of unknown mass-charge, measuring the oscillation period and time-of-flights to recover the mass-charge ratio using equation (2.9). In some cases, the image charge current signal produced by pickup electrodes may contain additional information beyond a single time-of-flight value, Δ ^^. For example, the proximity of the ion trajectory to the surface of the pickup electrode modulates the shape of the peak in the image charge current. Consequently, the shape of the image charge current peak can be used to make inferences about the position, momentum, and ion-ion interactions of the trajectory. The present measurement method can naturally include such information. If the image charge current signal from a set of ^^ pickup electrodes are denoted the natural generalisation of (2.9) is given by, where‖⋅‖is a function norm, ^^, denotes the characteristic timescale of the signals, and the trap function has been extended to a real functional on the Banach space of image charge current signals, ^^: ^^^^→ ℝ. Through discrete time-sampling of the image-charge current signals the functional ^^ simplies to a real function on a finite-dimensional vector space, ^^: ℝ^^⋅ ^^→ ℝ where ^^, is the number of samples in each signal. A natural extension of Algorithm 2 provides a method for measuring the mass-charge ratio using (2.10) and applying widely available regression or machine learning methods. For the practical 15026845v1 application of this approach, it is advantageous to use wavelet methods, or similar, to reduce the dimensionality of the image charge current information input into method. Frequency Formulation The time-of-flight formulation discussed so far is just one embodiment of the present measurement method. Since time-of-flight and frequency of oscillation are related as the reciprocal, the present measurement method has a natural expression in terms of frequencies. Denote the frequency of oscillation as, ^^ = 1 / ^^, and the traversal frequency as = 1 / Δ ^^, measured as the reciprocal of the traversal time between a set of pickup electrodes. The trap function can then be written in terms of a ratio of frequencies as, Equation (2.11) leads to a modification of Algorithm 1, for measuring mass-charge ratio of an ion using frequencies. As such, Equation 2.11 my be considered to be an ion trap function corresponding to an ion trap. A more general frequency formulation will now be outlined. For ions undergoing periodic oscillation within the trapping field of a device, the image charge current produced by a set of electrodes produces a stationary periodic current signal, ^^(^^). Since measurement occurs over a finite period, the signal recorded is the product of the current signal, ^^( ^^), and a windowing function, ^^( ^^), as ^^(^^)= ^^(^^)⋅ ^^(^^).(2.12)If the passage of an ion past a pickup electrode produces a signal, ^^(^^), ^^n elementary analysis shows that the Fourier spectrum of the signal, ^^( ^^), is given by, where ^^ (ω) denotes the Fourier transform of a function, ^^( ^^), the fundamental angular frequency of oscillation is denoted by, ^^0= and ^^(ω) is a function determined by the time-of-flights between the pickup electrodes. The spectrum of (2.13) consists of a 15026845v1 fundamental peak at ω0with peaks at higher harmonics 2ω0, 3ω0, …. In the limit of long sample times the complex amplitudes of the peaks are given by, ^^^^= ^^ ( ^^ ^^0) ⋅ ^^( ^^ ^^0), (2.14) where ^^ ∈ ℤ, and a constant multiplicative factor has been neglected. Expression (2.14) demonstrates that the time-of-flight and frequency formulations of the present measurement method are essentially equivalent methods for extracting the same information from a periodically oscillating ion. We can use dimensional considerations to express the mass charge ratio as, An equivalent expression, better suited to regression or machine learning approaches, is given by defining a vector of complex frequency peak amplitudes as ^^ = ( ^^1, ^^2, … , AM) ∈ ℂMand writing, The application of the frequency formulation of the present measurement method follows the same process of calibration and measurement outlined for the time-of-flight formulation. Multisensor The method is not limited to a time series generated by a single image charge electrode (ICE) or a single time-of-flight measurement. By obtaining time series records from a single or multiple ICE’s, one (or several) dimensionless features can be extracted from the time or frequency domain. In this analysis step, features may also be obtained through the comparison or combination of the time series records from different ICE’s. The set of dimensionless features for each ion measurement are provided as arguments to the a priori unknown g-function. The calibration and measurement phases as outline in Algorithm 1 proceed as before with minimal modification. Fig.2 shows and outline of the method for CEMS using multiple features. Different Types of Mass Spectrometers 15026845v1 This disclosure has so far primarily discussed electrostatic ion traps and the dynamics of ions in these devices however this is only to provide an example for explaining the disclosure. It will be appreciated that the present measurement method can readily be applied to other forms of mass spectrometer. This can be done through collecting multiple time-of-flight measurements or frequency information as described above. The types of devices the present measurement method applies to include, but are not limited to; magnetic sector, quadrupole, multi-reflection time-of-flight, FT ICR and electrostatic ion trap mass spectrometers. It is of course to be understood that the invention is not intended to be restricted to the details of the above embodiment which is described by way of example only. Non-ideal Electrostatic Ion One application of the mass-charge measurement algorithm is now demonstrated according to the following simulated experiment. A canonical model of a non-ideal ion trap is considered for which the oscillation period is strongly dependent on ion energy, a regime for which conventional measurement methods are not applicable. We demonstrate that the algorithm can accurately recover the mass-charge ratio of ions and is robust in the presence of noise. To capture the key features of a type of ion trap commonly used in mass-spectrometry, referred to as a multi-reflecting electrostatic trap, the 1-dimensional potential is considered, ϕ(^^)= ^^4− 2 ^^2.(3.1)where ^^ is the Cartesian coordinate along which the ion traverses. The trap potential is shown in Fig.3a with pickup electrodes for charge detection located at ^^ / ^^ = ±3 / 5. To apply the present measurement method, a time-of-flight, Δ ^^, is measured between two nominal points ^^ / ^^ = ±3 / 5 (these can be varied) and the oscillation period ^^ for a range of different ion energies. Though complex 3-dimensional orbits are possible within linear multi-reflecting ion traps in practice, confined orbits are often closely aligned with the axis of the trap. As a result, this 1-dimensional model characterises key features of confined trajectories. 15026845v1 To model the presence of large manufacturing defects, the potential of the ion trap (3.1) is strongly anharmonic, resulting in a period of oscillation sensitively dependent on ion energy, as shown in Fig.3b. This sensitive dependence on energy means that traditional mass-charge recovery methods cannot be applied. As such, Fig.3a shows the properties of a model electrostatic ion trap. The potential of the 1-dimensional electrostatic ion trap given by (3.1) with pickup electrodes located at ^^ / ^^ = ± ^^ / ^^. Fig.3b shows the scaled oscillation period ^^ ^^^^of ions within the trap as a function of scaled energy ^^ / ( ^^ϕ0)where ^^^^= characteristic angular frequency. Ideal Conditions To demonstrate the method, the calibration step may be performed without introducing experimental noise. This reflects an ideal experimental scenario for which noise is negligible and the time-of-flight, period of oscillation and the mass-charge ratio of ions in the calibration step are known / measured to a high degree of accuracy. Introducing noise does not alter the essential performance of the method; see next section. In the calibration step the time-of-flight and oscillation period of ions with known mass- charge ratios are recorded for the scaled energies ^^ / (^^ϕ0)= 0.01, … ,  20. Then, using (8), a discrete set of samples for the trap-function ^^ are obtained and cubic interpolation is used to estimate the trap-function ^^, shown in Figure 4 (left). The trap function estimate, ^^, is then used to predict the mass charge ratio of ions in simulated experiments over a range of energies, shown Figure 4 (right), which demonstrates that the mass-charge ratio can be recovered to the level of computer precision, i.e., better than one part in 1 quadrillion. Noisy conditions To demonstrate that the mass-charge recovery method is robust in the presence of noise, noise (uncertainty) is now introduced within the calibration step of the algorithm. The values of the mass-charge ratio of the analyte, the time-of-flight and period of oscillation used for calibration are 15026845v1 where Θ is a log-normal random variate with zero mean and standard deviation 0.005. This models an experiment with a relative measurement error of around 0.5%. Currently, instrumentation used in mass-spectrometry can often reach much higher levels of accuracy in time-of-flight measurements. As result, level of noise (uncertainty) considered in the calibration step represents a worst-case scenario. Kernel regression is used to estimate the trap-function from the noisy calibration data. The results of the kernel regression fit and resulting prediction error for 4000 noisy calibration samples are shown in Figure 6. The error in the predicted mass-charge ratio is commensurate with the level of error in the calibration data. Crucially, this example demonstrates that sensitive dependence oscillation period on ion energy does not pose a limitation on the accuracy of this method. Alternate regression methods, such as machine learning, can also be used. An Microscale Electrostatic Ion The CEMS method may be applied to a planar microscale electrostatic ion trap (μEST). This demonstrates the wide applicability of the methodology which is independent of the scale or configuration of the electrostatic ion trap. The application of the method to a specific electrostatic ion trap is provided as an example, and it should be understood that the method is in no way limited to a specific trap configuration. The microscale electrostatic ion trap (μEST) comprises two opposing plates of electrodes held a fixed distance apart by manufacturing the electrodes on a substrate. An electrostatic trapping field is established between the electrodes and ions are focused and confined within the trap through carefully choosing the electrode potentials and shape. Ions are inserted into the μEST along the principal z-axis of the device by lowering the potential applied to one of the outer electrodes. The electrode geometry and plate alignment is shown in Figure 6. Ions oscillating within the μEST are detected by the induced charge on pairs of image charge electrodes (ICE) on each electrode plate and the induced charge over time is recorded. Due to the limitations of manufacturing microscale structures, even perfectly constructed microscale electrostatic ion traps (μESTs) that conform precisely to the intended design do not adhere to the ideal of an energy isochronous trapping potential. Consequently, the 15026845v1 oscillation period of trapped ions will vary as a function of ion energy. If the conventional measurement method given in (2.4) is used, this variation with respect to energy restricts the precision and resolution of the instrument. In this way, even perfectly fabricated μESTs exhibit non-ideal behaviour and CEMS method is required to overcome the limitations of these devices. Ideal The application of the CEMS to perfectly fabricated μESTs, dubbed the ideal configuration is considered first. For simplicity of presentation, consider the case of ions inserted exactly on axis. Under these conditions the trapped ions undergo periodic linear orbits along the axis of the ion trap, which we refer to as canonical trajectories. In the calibration phase the trajectories and image charge time-series of 100 ions at equispaced energies are simulated. For each simulation, a nominal mass-charge is used and a time-of-flight, Δ ^^, and period of oscillation, ^^, are extracted from the image charge time-series. An illustration of the time-scale extraction is shown in Figure 7. The results from this calibration set of ions forms a collection known data points for the unknown ^^-function using (2.10). Cubic interpolation is then used to estimate the ^^-function and results are shown in Figure 8. Such an estimate may be used to formulate an ion trap function according to this disclsoure. Due to the absence of noise in the measurement process the CEMS predictions are accurate to numerical precision, shown in Figure 9. In a subsequent measurement phase, the CEMS is validated by simulating ion trajectories over a broad range of energies and computing the relative error in the mass-charge predicted for each ion, shown in Figure 5. Comparing against the results obtained for the conventional method using (2.4), it can be seen that the proposed method yields accurate predictions across a broad range of energies. The conventional approach, in contrast, is accurate only within an extremely narrow energy band. Non-Ideal A manufacturing defect that readily occurs in the fabrication of μESTs is the misalignment of electrode plates. Figure 10 illustrates a misalignment defect where the separation of the electrode plates deviates from the nominal design value. This defect is dubbed the non- ideal configuration. The trapping potentials along the centerline are compared in Figure 11 15026845v1 for μESTs in the ideal and non-ideal configurations. Though this minor change to the μEST configuration varies the trapping field only slightly, large changes are observed in ion dynamics. Figure 11 compares the oscillation period of ions with respect to energy for the ideal and non-ideal configurations. This reveals that the defect introduces significant variation in the oscillation period with respect to energy. It must be concluded that even minor microscale fabrication defects can disrupt energy isochronous trapping potentials. Figure 12 demonstrates the application of the CEMS method to a μEST in a non-ideal configuration. During the calibration phase, the time-of-flight and period of oscillation are extracted from the time-series generated by simulating the trajectories of 100 ions of nominal mass-charge. Using (2.10), the g-function is estimated and the g-function estimates for the ideal and non-ideal μEST configurations are compared. During the measurement phase, the validity of the CEMS is verified by computing the relative error in mass-charge prediction across a range of ion energies. The results indicate that the CEMS provides accurate predictions at the numerical precision level, while the predictions from conventional methods are so inaccurate that they are unusable. The frequency-domain formulation of the CEMS is also readily applicable to the ^^EST. To demonstrate the validity of the frequency-domain approach, the trajectories of two ions are simulated on the canonical trajectory with different energies, 100eV and 160eV, and the same mass-charge ratio, 1000 Thompsons. This change in energy results in radically different oscillation frequencies for the ions of 1.3967 MHz and 1.4272 MHz, respectively. The conventional approach, using just the fundamental oscillation frequency, would erroneously produce a different mass-charge ratio prediction for each ion. However, Figure 13, shows changing energy of the ions is clearly evident in the altered duty-cycle of the induced image charge current (ICC). An equivalent variation is observed in the changing amplitudes of the harmonics in the frequency-domain. This variation in the frequency-domain provides a rich set of features which the identification of different trajectories with the ^^EST. Application of CEMS of Multisensor Formulation to ^^EST 15026845v1 By recording the time-series of the ICC for individual pickup electrodes in the ^^EST simulation it can be seen that each pickup electrode provides an independent time-series and feature set for the CEMS approach. Several oscillation periods of an ICC signals due to two independent pickup electrodes is shown in Figure 14. Relationship between a time-of-flight measurement and the energy of an ion In this section a relationship between a time-of-flight measurement and the energy of an ion is derived. This relation provides a one-to-one mapping between the time-of-flight and ion energy in 1-dimensional systems. This implies that a time-of-flight measurement uniquely specifies the energy of an ion in a 1-dimensional ion trap and justifies using time- of-flight as a proxy measurement for ion energy. This section concludes with an extension of the argument to 3-dimensional systems. By conservation of energy in a 1-dimensional electrostatic trap we have where ^^( ^^) is the position of the ion at time ^^. By integrating (A.1) over distance, we can express the time-of-flight, Δ ^^, between points ^^1and ^^2as, where ^^ = ^^ / ( ^^ϕ0) is the scaled ion energy. If the oscillation of the ion occurs between the extremes of ^^−∗and ^^+∗we can use (A.2) to write, If the potential is a bounded continuous function of finite variation, (A.3) shows that Δ ^^ / ^^ is a continuous monotonic function of ^^ . Consequently, a one-to-one mapping exists between Δ ^^ / ^^ and the energy of the ion ^^ in 1-dimensional ion traps. 15026845v1 To extend our argument to ion traps with 3-dimensinal orbits we appeal to the theory of initial value problems. For an ion trajectory ^^( ^^) the initial conditions are a continuous- differentiable function of ^^ . If the potential is at least Lipschitz continuous (which is guaranteed for electrostatic fields) then trajectory will be a continuous-differentiable function of the initial conditions and hence ^^ . Further, any time-of-flight measurement is a continuous differentiable function of the trajectory. Suppose all other initial conditions of the ion trajectory are fixed, except for energy. In that case, the time-of-flight is a continuous-differentiable function of the single variable, ion energy, For an open neighbourhood of time-of-flight, assuming, 0, the inverse function theorem can be applied to obtain a one-to-one mapping of time-of-flight and ion energy. This justifies the usage of a time-of-flight as a proxy for ion energy for general 3-dimensional orbits. Next embodiments of this disclosure will be discussed with respect to a Fourier Transform Mass Analyser (FTMA). It will be appreciated that the following discussion may be applicable to various types of mass analyser. The following discussion of embodiments of the disclosure assumes that the ion charge is positive. Accordingly, discussion of reflective potential for such an ion are also assumed to be positive. It will be appreciated that embodiments of this disclosure are also applicable to negatively charged ions, wherein the signs of voltages and potentials discussed herein should be changed to the opposite. According to an embodiment of the disclosure, a Fourier Transform Mass Analyser (FTMA) 1 is provided. Fig.15 shows a schematic diagram of a FTMA 1 according to an embodiment of the disclosure. The FTMA 1 of Fig.15 comprises an ion trap 10, a first detector 12 and a second detector 14. As shown in Fig.15, the ion trap 10 is an electrostatic ion trap (EST). The ion trap 10 comprises a first ion mirror 20 and a second ion mirror 30. The first and second ion mirrors 20, 30 are arranged along a first axis (z-axis shown in Fig.15). As will be appreciated from Fig.15, an ion trapped in the ion trap 10 oscillates between the first and second ion mirrors 20, 30 in a first direction aligned with the z-axis of the ion trap 10. The operation of the ion trap 10 and the first and second detectors 12, 14, along with any associated signal may be 15026845v1 controlled by a suitable controller (not shown in Fig.15) of the FTMA 1. As such, it will be appreciated that the controller may cause the FTMA 1 to perform a method of Fourier Transform Mass Spectrometry (FTMS) as further explained below. ESTs used for FTMS aim to determine an ion’s mass to charge ratio (m / z) based on are specially designed to minimize the uncertainty of the ion oscillation frequency. As such, the FTMA of Fig. 1 aims to determine a frequency of oscillation f0 of an ion along the z axis with no oscillation in a direction transverse to the z-axis. Ideally, the frequency with which an ion oscillates in the first direction (fz) should have little or no dependence on the ion’s parameters such as energy, an injection coordinate, and an injection angle. In practice, EST are not ideal such that the oscillation frequency fz is affected by these a priori unknown parameters. This in turn leads to an uncertainty of in the determination of the ion’s mass- to-charge ratio (m / z). As such, the observation of the frequency with which an ion oscillates in the first direction fz may be perturbed by an unknown frequency component δf due to oscillation in a direction transverse to the z-axis, where: fz= f0+ δf According to embodiments of this disclosure, a trajectory correction factor is determined which aims determine a mass-to-charge ratio (m / z) of an ion which corrects or reduces the effects of the a priori unknown off-axis coordinate and angle of an ion as it is injected into the ion trap. As will be appreciated from Fig.15, the first and second detectors 12, 14 are image current detectors. Each image current detector 12, 14 is aligned with the z-axis and spaced apart from the z-axis in a second direction. In Fig.15, the second direction is aligned with the x- axis which extends from a centre of the ion trap 10. A current is induced in each detector 12, 14 as the ion oscillates past the detectors 12, 14. In some embodiments, each detector may be a pickup electrode. Each detector may be positioned at a location along the z-axis between the first and second ion mirrors 20, 30. Every time as an ion passes by a pickup electrode, an induced current is generated in the pickup electrode. The induced current may be amplified by an amplifier connected to the detector 15 and detected by an appropriate electronic circuit. For example, amplified signals from the pickup electrodes may be digitised by a digitiser (not shown in Fig.15), 15026845v1 stored in a memory (not shown in Fig.15). The digitised signals may be analysed by a controller (not shown in Fig.15) in order to determine a m / z of the ion. While in some embodiments, a single detector 12 may be sufficient to detect oscillation of the ion in both the first and second direction, in the embodiment of Fig.15 specific linear combinations of the signals from each detector may be analysed to determine the amplitude and / or frequency of ion’s motion in both the first direction (z direction) and the second direction (x-direction). A correction factor is then calculated to in order to correct the measured frequency of oscillations (fz) to account for the trajectory of the ion (which is a priori unknown). In some embodiments, the trajectory correction factor may be defined as a function of ratio of the frequency of oscillation in the second direction (fx) to the frequency of oscillation in between the ion mirrors along the z-axis (fz). The trajectory correction factor may be determined from ion-optical modelling. More practically, a trajectory correction function for determining the trajectory correction factor may be calibrated by performing a number of measurements using the FTMA with ions of known m / z and having different random injection parameters. Once the trajectory correction function is calibrated, it may then be applied to obtain more accurate measurements of the m / z of unknown ionic species with the uncertainty of injection coordinate and angle being accounted for. The principle of invention could be exemplified first on a two-dimensional example of EST with electrodes that extend in the direction Y. In more detail, each ion mirror 20, 30 of Fig.15 comprises a first electrode assembly 22, 32 extending in a first plane normal to the second direction (x-axis) and a second electrode assembly 24, 34 extending in a second plane normal to the x-axis. As such, the first and second planes are parallel to each other. As shown in Fig.15, the first and second electrode assemblies 22, 24; 32, 34 are spaced apart in the second direction on opposing sides of the first axis. For example, each electrode assembly 22, 24, 32, 34 may be spaced apart from the z-axis by a distance of h in the second direction. As such, the first and second electrode assemblies 22, 24; 32, 34 may be spaced apart from each other by a distance of 2h. As shown in Fig.15, the first and second electrode assemblies may be mirror images of each other relative to the y-z plane. 15026845v1 Each electrode assembly 22, 24; 32, 34 comprises a plurality of planar electrodes. As shown in Fig.15, the first electrode assembly of the first ion mirror 20 comprises a plurality of first planar electrodes 23a, 23b, 23c distributed along the z axis. The second electrode assembly 24 of the first ion mirror 20 comprises a plurality of second planar electrodes 25a, 25b, 25c distributed along the z axis. Each of the plurality of first planar electrodes 23a, 23b, 23c extend in the first plane in the third direction (aligned with the y axis) normal to the first and second directions. As such, each of the first planar electrodes 23a, 23b, 23c may have a generally rectangular shape in the first plane. In the embodiment of Fig.15, the plurality of second planar electrodes 25a, 25b, 25c of the second electrode assembly 24 of the first ion mirror 20 extend in the second plane in the third direction. In the embodiment of Fig.15, each of the planar electrodes 23a, 23b, 23c, 25a, 25b, 25c has a uniform width in the first direction. Each of the first planar electrodes 23a, 23b, 23c is aligned in the second direction with a corresponding second planar electrode 25a, 25b, 25c such that the first and second electrode assemblies 22, 24 are arranged symmetrically about the z-axis. Each planar electrode 23a, 23b,23c, 25a, 25b, 25c of the first and second electrode assemblies 22, 24 are configured to receive a voltage from a voltage supply (not shown in Fig.15) connected to each electrode. Each planar electrode 23a, 23b,23c, 25a, 25b, 25c may be configured to receive a different voltage from the voltage supply. To ensure stability of the ion motion in the third direction aligned with the y axis, each ion mirror may be provided with a pair (or pairs) of guarding electrodes (not shown in Fig.15). Each pair of guarding electrodes may extend along the z-axis of the ion trap 10, wherein the pair of guarding electrodes are spaced apart from each other in the y direction. As such, the ion oscillates in the region of the ion trap 10 bounded by the first and second ion mirrors 20, 30 and the guarding electrodes. A small positive bias may be applied to each guarding electrode to bias the ion towards the z-axis. Confinement of the ion motion in the y direction may also be provided by the first and second electrode assemblies 22, 24; 32, 24 of each ion mirror 20, 30. For example as discussed further below in respect of the embodiment of Fig.23A, the planar electrodes 23a, 23b,23c, 25a, 25b, 25c may be provided in a curved manner in order to provide a confining potential in the y-direction. For example, one or both ion mirrors 20, 30 may be provided with planar electrodes which extend in the plane of the respective electrode assembly 22, 24; 32, 34 along an arc, wherein a centre of each arc in the plane is aligned with the first axis. Such curved 15026845v1 electrodes may provide a confining potential in the y-direction in addition to, or as an alternative to, the provision of guarding electrodes. The second ion mirror 30 may be provided in a similar manner to the first ion mirror 20. As such, the first and second electrode assemblies 32, 34 of the second ion mirror 30 may also comprise a plurality of first planar electrodes 33a, 33b, 33c and a plurality of second planar electrodes respectively 35a, 35b, 35c. As shown in Fig.15, the first and second ion mirrors 20, 30 may each be operated in an ion trapping mode. For example, when the first ion mirror 20 is biased with a set of voltages in the ion trapping mode, the planar electrodes 23a, 23b,23c, 25a, 25b, 25c generate a reflecting potential distribution which is configured to reflect ions moving from the centre of the ion trap 10 towards the first ion mirror 20 in the first direction (i.e. in a direction of increasingly negative z co-ordinate) and back towards the centre of the ion trap 10 (i.e. in a direction of increasingly positive z co-ordinate). Similarly, the second ion mirror 30 may be biased with a set of voltages to reflect ions travelling towards the second ion mirror 30 in the z direction back towards the first ion mirror 20. To enter the ion trap, ions may be injected into the ion trap from a suitable ion source (not shown in Fig.15). The ion source may be another form of ion trap, such as the C-trap disclosed in WO-A-02078046, in which ions have been stored or any other source of ions known in the art. Ions may be injected from the ion source into the ion trap at an axial end of the ion trap 10 (i.e. an end of the ion trap aligned with the z-axis). As shown in Fig.15, in an injection mode the voltages on one of the ion mirrors (e.g. first ion mirror 20) are lowered below the ion’s energy, so that the ion may enter the space between the ion mirrors 20, 30. The voltages may then be raised before the ion is able to return back, such that the ion mirror 20 operates in the ion trapping mode once more to make the ions oscillate along the z direction. The first and second ion mirrors may be configured in such way that the ion’s oscillations are stable in the x-direction. For this purpose, each ion mirror 20, 30 may comprise at least one negatively biased electrode and an interval of accelerated motion is formed to serve as an ion-optical lens. 15026845v1 Once an ion is trapped within the ion trap 10, the ion oscillates between the first and second ion mirrors. The frequency ^^^^of the oscillations in the first direction (z-direction) is defined as the number of oscillations per second, each oscillation comprising two subsequent reflections. The nominal oscillation frequency ^^0is defined as the frequency of oscillation exactly on the optical axis Z and with a certain nominal energy. The oscillatory frequency ^^^^in an EST with non-ideal isochronism slightly depends on the amplitudes of motion in a transversal direction X orthogonal to Z. The frequency difference δf is small to compare to ^^0, but cannot be neglected if an accurate value of m / z is to be obtained. In some embodiments, induced current signals of a trapped ion may be collected from more than one detector 12, 14. As such, the first detector 12 may generate a first signal indicative of the ion oscillation and the second detector 14 may generate a second signal indicative of the ion oscillation. A certain linear combination of these signals may be Fourier transformed to obtain a frequency ^^^^and an amplitude ^^^^of ion oscillation in the x- direction. The parameters ^^^^and ^^^^are then used to assess the x-amplitude of the ion orbit, and a corresponding correction is applied to the measured frequency ^^^^of the principal oscillations. The correction helps to determine the true m / z of the trapped ion. As such, the action of a pair of ion mirrors 20, 30 facing each other may be described by a mapping ^^: ( ^^0, ^^0) ^ ( ^^1, ^^1) of the ion coordinate ^^0and the inclination ^^0of the ion trajectory towards the axis Z in the plane Z=0 to the corresponding pair of coordinates ^^1and angle ^^1in the same plane after one reflection. The coordinate transformation after an integer number ^^ of oscillations is given by the mapping ^^^^, accordingly. The mapping ^^ is symplectic, in particular, the determinant of the paraxial transfer 2x2 matrix is unity. The confinement criterion for oscillations is that the eigenvalues of the matrix ^^0both lie on the unit circle of the complex plane. This condition comes down to the inequality 15026845v1 which, if satisfied, guaranties the stability of ion motion within a certain domain around the optical axis.When mapped multiple times on the ( ^^, ^^) plane, a point of initial phase coordinates( ^^0, ^^0) describes a Poincare orbit as illustrated in Fig.16. The phase-space points on a setof sequential reflections are separated by an angle as illustrated with a broken line in Figure 2, so that the point rotates around the centre of the diagram a certain amount. The average number of rotations performed in the course of one oscillation gives the ratio r = fx / fzof the transversal frequency and the oscillatory frequency. Due to symmetries inherit to ion mirrors, the paraxial transfer matrix ^^0has the following structure where ^^ is a focal length of a mirrors and ^^ = acos( ^^ ^^1 / ^^ ^^0) is an angle of phase-space revolution on one reflection. In the paraxial domain characterized by small amplitudes of transversal oscillations, the ratio of frequencies is ^^0= ^^^^0 / ^^^^= 2 ^^ / 2 ^^ = ^^ / ^^ (as the phase-space revolution by ^^ happens during the axial phase increment by ^^). Beyond the paraxial domain, where the amplitude of transversal oscillations is comparable with the EST size, the ratio of frequencies ^^ = ^^^^ / ^^^^differ from this value and is usually smaller. This ratio may be calculated by ion-optical modelling during a large number of oscillations ^^^^as a number of circles around the center of the Poincare diagram divided by ^^^^. Generally, the ratio of frequencies ^^ depends on the Poincare orbit, and every stable Poincare orbit may be ascribed a certain value of ^^. Vice versa, knowing the frequency ratio ^^ allows to judge on which Poincare orbit an ion oscillates. Another characteristic of the EST is the half-oscillation time ^^(^^, ^^, ^^), which is a function of the ion’s x-coordinate, inclination, and energy. There is a class of energy-isochronous EST in which the function ^^(0,0, ^^) = ^^0is constant with a high degree of precision within a sufficient interval of energies. Yet, the ions oscillating beyond the optical axis have a substantial divergence of the oscillation periods form the nominal period 1 / f0. The average half-oscillation time per many ^^ >> 1 reflection is given by the formula 15026845v1 ^^(^^0, ^^0)= ^ l^i→m∞ where = ^^^^(^^0, ^^0). The averaged oscillation frequency fz = 1 / (2T) is the same for all points of a Poincare orbit but may be different on different orbits. An example of dependency of the relative frequency error ( ^^ ^^ / ^^0) on the x-amplitude of a Poincare orbit is presented in Fig.17. In Fig.17, the x-amplitude of a Poincare orbit is characterized by the initial injection angle ^^0. Due to symmetry, the frequency error ^^ ^^ / ^^0= ( ^^^^− ^^0) / ^^0may be expanded into a series with even powers of the amplitude ^^0. If an EST is specially optimized as in this example, the expansion starts from the power ^^04. In the general case, the term proportional to ^^02is also present. The frequency ^^^^of transversal oscillations in the x direction is a fraction of the frequency of oscillations in the longitudinal direction ^^^^. The ratio of these frequencies is a mean number of loops which a phase point(^^^^, ^^^^)makes around the center of the Poincare map in the course of one oscillation (two subsequent reflections). An arrow line in Fig.16 shows an example of a phase point moving around the Poincare map. The ratio ^^ = ^^^^ / ^^^^depends, usually monotonously, on the transversal amplitude, as illustrated in Fig.18. Though the transversal amplitude is not directly observed, it may be estimated from the observed frequency ^^^^. Furthermore, the longitudinal frequency error ^^ ^^ / ^^0is a function of the frequency ratio ^^ = ^^^^ / ^^^^^^ ^^ =^^ (^^ ^^) ^^0^^^^as illustrated in Fig.19 via exclusion of the unobservable orbit transversal amplitude. In some embodiments, the function G may be calculated for an EST geometry and electrode voltages via ion-optical modelling. Alternatively, the function G may be obtained via calibration measurements performed on the ion trap 10 as described further below. The function G may be used to formulate an ion trap function in accordance with this disclosure. In order to calibrate the correction function ^^(^^^^ / ^^^^), the calibration measurements using the FTMA 1 may be performed a number of times with ions of known ( ^^ / ^^)0. In each calibration measurement, an ion is injected into the ion trap 10 with random coordinates and at random angle, covering a wide range of stable Poincare orbits. The frequencies ^^^^15026845v1 and ^^^^may be detected separately through FT transformation of induced-current signals from one or more detectors 12, 14 (e.g. pickup electrodes). The frequency ^^^^should be determined with a sufficient precision, preferably with a relative precision of several parts- per-million (ppm). The pairs of values(^^^^; ^^ = ^^^^ / ^^^^)are then used to fit a function ^^^^(^^). The function may be normally represented in the form of a power series ^^^^( ^^) = ^^0× {1 + ^^1( ^^0− ^^) + ^^2( ^^0− ^^)2+ ⋯ } where ^^0is the maximum observed frequency ratio with corresponds to ions on mostly on- axis orbits. The coefficients ^^0and ^^^^may be found by, e.g., a polynomial regression method. In some embodiments, a second order approximation may be used, while in other embodiments higher order polynomials may also be used. As discussed above, the frequency ^^0is the frequency of oscillation on the axial orbit. The coefficient ^^ in formula (1) is estimated as: ^^ = ^^02( ^^ / ^^)0The dimensionless trajectory correction function ^^ for frequency correction may then be estimated as ^^( ^^) = ^^1( ^^0− ^^) + ^^2( ^^0− ^^)2+ ⋯ After calibration, the constant C and the trajectory correction function GI may then be applicable to the entire m / z range of interest or, at least a portion of it. In some embodiments, the calibration ions of known m / z used for calibration may be multiply-charged calibration ions. For example, the calibration ions may be small, denatured proteins like ubiquitin or myoglobin. Use of such ions for calibration may be preferable as they will provide significantly increased signal-to-noise ratio compared to performing calibration with singly charged ions. Thus, it follows that a method 100 of FTMS may be performed to determine a m / z of an unknown analyte ion. The method 100 may be performed using the FTMA 1 of Fig.15 which is controlled by a suitable controller (not shown in Fig.15). Fig.20 shows a block diagram of method 100. In step 101 of the method 100, the unknown analyte ion is trapped in the ion trap 10 where it oscillates along the z-axis between the first and second ion mirrors. The unknown 15026845v1 analyte ion may be injected axially into the ion trap 10. As the trajectory and x-axis position of the unknown analyte ion are a priori unknown, the ion will oscillate in the ion trap with an unknown Poincare orbit. In step 102 of the method 100, the oscillation of the ion in the z-direction and the x-direction is detected using the detectors 12, 14. From the detected signals, the frequencies of oscillation in the z- and x- directions, ^^^^and ^^^^respectively may be determined. For example, Fourier analysis of the detected signals may be used to determine the frequencies. In step 103, a trajectory correction factor is estimated as ^^∗= ^^( ^^^^ / ^^^^), where ^^( ^^) is a pre-calibrated function (a trajectory correction function). As further discussed below, other methods for determining a trajectory correction factor may also be used as part of method 100. In step 104, the trajectory correction factor may then be used to account for the effect of the ion trajectory on the observed frequency fz. As such, a corrected frequency is then estimated as ^^0= ^^^^ / (1 + ^^∗). From this corrected frequency, the m / z ratio of the unknown analyte ion is determined as^^^^ = where the coefficient C is pre-calibrated. Combining the calculations of steps 103 and 104, we arrive at the formula (ion trap function): Thus, according to method 100 it is possible to correct for deviation of ions in the transversal direction in a FTMS measurement. By way of further explanation, Fig.21 shows a further schematic diagram of ion trap 10 of Fig.15. In this embodiment, the frequencies ^^^^and ^^^^are measured using first and second signals detected from respective first and second detectors 12, 14 (pickup) electrodes. As shown in Fig.21, the first and second detectors 12, 14 are located at ^^ = ±ℎ on opposing sides of the z-axis. Each of the first and second detectors 12, 14 has a length ^^ which is aligned with the z-axis. As such, each of the first and second detector is a planar pickup electrode which extends in a plane normal to the x-direction. 15026845v1 When an ion of charge + ^^ passes a pair of pickup electrodes at a distance ^^( ^^) from the axis, the induced charges on the detectors 12 and 14 are In the above equations, the sensitivity function Θ( ^^) is determined by the pickup electrode length ^^. In a simplified model the sensitivity function is The first and second signals which are indicative of the induced charges on the detectors 12, 14 may be amplified by amplifiers 15. These amplified signals may then be processed as shown schematically in Fig.21 to determine sum and difference signals. As such, two combinations of the signals which may be stored by the memory are the sum ^^( ^^) = ^^1+ ^^2= − ^^Θ( ^^( ^^)) and the difference It will be appreciated that the sum signal is insensitive to the transversal coordinate ^^. As such, this signal may be used to determine the frequency of oscillations fz. By contrast, the difference signal ^^(^^)is proportional to the x-coordinate of an ion that crosses the pickup assembly. Fig.22 shows simulated examples of the sum and difference signals (normalized to a unitcharge of ions). The sum signal s(t) contains comb-like oscillations with the repetition rate2 ^^ ^^ (because the signal is picked up on the ion passed in both directions) and containsharmonics at frequencies 2 ^^ ^^^^where ^^ is an integer. The lowest harmonic of s(t) is observed at the double frequency of z-oscillations, from which ^^^^is determined. The difference signal d(t) Is modulated by the factor ^^ / ℎ and therefore contains harmonics at the frequencies 2 ^^ ^^^^+ ^^ ^^^^where ^^ and ^^ are integers. The strongest harmonic appears at ^^ = 0, ^^ = 1 and its spectral position gives the frequency ^^^^. Fig.22 depicts two different graphs of the difference signal d(t) for ion trajectories on different Poincare orbits with ^^0= 5 ^^ ^^ ^^ ^^ and ^^0= 10 ^^ ^^ ^^ ^^. The amplitudes and frequencies for different Poincare orbits apparently differ, which offers the opportunity to 15026845v1 determine the ion’s transversal amplitude of the orbit and, consequently, calibrate the axial frequency. In the example of Fig.22, the axial frequency ^^^^should be corrected by approximately 2e-6 for the smaller transversal amplitude ^^0= 5 ^^ ^^ ^^ ^^ and by 1.8e-5 for the larger amplitude ^^0= 10 ^^ ^^ ^^ ^^ according to the calibration curves in Fig.17. It will be appreciated that the amplitude of the signal ^^( ^^) is proportional to the amplitude of transversal motion of a confined ion. Thus, in a further embodiment an alternative way to assess the trajectory of the trapped ion utilises the ratio of amplitudes of the strongest harmonics of ^^( ^^) and ^^( ^^). Such an assessment may, however, be more susceptible to noise as the amplitude of a signal may be likely to be affected by noise to a greater extent than the frequency position. In this embodiment, a number of calibration measurements may be performed and the ratios ^^ = ^^^^ / ^^^^, where ^^^^is the amplitude of the ^^^^harmonic and ^^^^is the amplitude of the ^^^^harmonic, may be recorded for a number of calibration ions of known m / z oscillating on arbitrary orbits. The frequency of oscillations ^^^^is supposed to be a function of this ratio, e.g. a polynomial: ^^^^( ^^) = ^^0× {1 + ^^1^^ + ^^2^^2+ ⋯ } The unknown coefficients ^^^^are assessed by means of fitting the polynomial function to the pairs { ^^, ^^^^}. When the calibration is completed, the m / z ratio of unknown ionic species may be obtained as As such, in some embodiments of the disclosure the trajectory correction factor may be determined based on a ratio of an amplitude oscillations having the second frequency (Af) to an amplitude of the oscillations having the first frequency (Az). While the embodiments of Figs.15 and 21 included a single detector, or a pair of detectors 12, 14 at a single axial location of the ion trap, in other embodiments, the ion detection principle may be extended to a larger number of detectors and / or detector locations. 15026845v1 For example, Figs.23A and 23B provide schematic diagrams of a FTMA 1 according to a further embodiment of the disclosure, with different view at FTMA 1. The FTMA 1 of Figs. 23A and 23B is similar to the FTMA of Fig.15, at least in that it comprises an ion trap 10 comprising opposing first and second ion mirrors 20, 30 arranged about a z-axis. The ion mirrors 20, 30 are spaced apart in the direction of the x-axis, such that the x, y, z co- ordinate system discussed above applies similarly to the ion trap 10 of this embodiment. Fig.23A shows a plan view of a y-z plane of the ion trap 10, which shows in plan view the layout of the planar electrodes of the first electrode assemblies 22, 32 of each of the first and second Ion mirrors 20, 30 and the detector electrodes D1, D2. While the ion trap 10 shown in Figs.23A and 23B may be formed of any size, preferably the ion trap 10 in Figs.23A and 23B is provided as a microscale Electrostatic Ion Trap (μEST). As such, a total length of the ion trap in the z-direction (from a distal end 27 of the first ion mirror 20 to the opposing distal end 37 of the ion mirror 30) may be no greater than 10 mm. As shown in Fig.23A, the first electrode assembly 22 of the first ion mirror 20 may comprise a plurality of first planar electrodes 23a, 23b, 23c, 23d, 23e. Similar to the embodiment of Fig.15, the first planar electrodes 23a, 23b, 23c, 23d, 23e are aligned in the z-direction of the ion trap 10 and extend in a first plane (a y-z plane) of the ion trap. By contrast to the embodiment of Fig.15, the first planar electrodes 23a, 23b, 23c, 23d, 23e each extend in the first plane along an arc. A centre of each arc in the first plane is aligned with the first axis. It will also be appreciated that the each of the first planar electrodes 23a, 23b, 23c, 23d, 23e has a different width in the z-direction. The curvature of the first planar electrodes 23a, 23b, 23c, 23d, 23e may provide a means of reducing or eliminating oscillation of the ions in a y-direction of the ion trap. As shown in Fig.23A, the first electrode assembly 32 of the second ion mirror 30 comprises a plurality of first planar electrodes 33a, 33b, 33c, 33d, 33e. Similar to the embodiment of Fig.15 these electrodes 33a, 33b, 33c, 33d, 33e extend in a direction generally aligned with the y-direction (i.e. the electrodes are generally rectangular). As shown in the cross section of Fig.23B, the first and second ion mirrors 20, 30 are aligned such that the z-axis pass through a centre of each ion mirror 20, 30. The first and second planar electrodes of each ion mirror 20, 30 are spaced apart an equal distance in 15026845v1 the x-direction from the z-axis. To increase sensitivity by reducing EST size, the first planar electrodes of the first electrode assemblies 22, 24 may be spaced apart from adjacent first planar electrodes in the z-direction by a distance of no greater than 100µm, preferably no more than 50µm and typically much smaller, for example no more (or less) than 20µm, 10µm or 5µm. The second planar electrodes and pickup electrodes D1u, D1d, Du, D2d may also be spaced apart from adjacent electrodes by a similar distance. As shown in Fig.23A, one or more detection electrodes D1, D2 may be provided in the first plane. In the embodiment of Fig.23A, a first upper detection electrode D1u and a second upper detection electrode D2u are located between the first and second ion mirrors 20, 30. The detection electrodes D1u, D2u may be planar electrodes which have a length which is aligned with the z axis as shown in Fig.23A. In order to provide a μEST, the first electrode assemblies 22, 32 of the first and second ion mirrors and the detectors D1u, D2u may all be formed on a single wafer 40, wherein the various electrodes are patterned on using a suitable lithographic technique. Similarly, the second electrode assemblies 24, 34 of the first and second ion mirrors and the detectors D1dand D2dmay also be formed on a single wafer 40. Accordingly, the μEST may be formed by two parallel flat wafers 40 with electrodes patterned on a surface of the wafer 40 them using lithographic methods. Preferably, the lithographic method used to define the electrodes has an alignment tolerance of no greater than ±0.01*h, preferably ±0.001*h, or more preferably ±0.0001*h (where h is the spacing between the electrode assemblies as shown in e.g. Fig.23B) in order to ensure high mass accuracy and resolving power of the resulting electrodes. As such, the edges of each electrode of each of the electrode assemblies may be defined with a relatively high degree of precision in order to allow the ion trap to be assembled with electrodes which can be aligned with a relatively high degree of precision. As shown in the side view of Fig.23B (a cross section in a x-z plane of the ion trap 10), there is a pair of detection electrodes D1u, D2uon the top wafer 40 (u for up) and a pair D1d, D2don the bottom wafer 40 (d for down). The individual up and down detection electrodes may be connected to individual preamplifiers fabricated on the corresponding wafers. This allows the detection of four signals independently. In particular, even singly charged ions may be detected if the noise and capacitance of amplifiers are designed to be 15026845v1 sufficiently low. In practice, this means r.m.s. noise below 50 nV / sqrt(Hz) and input capacitance no greater than: 10 pF, 5 pF, 1 pF, 0.5 pF or 0.1 pF. Such capacitances may be achieved by implementing amplifiers as a set of transistors (preferably FET or JFET) directly on the wafer with minimum wiring to the detection electrodes D1u, D2u, D1d, D2d. Low capacitance may be achieved by reduction of μEST dimensions, with h preferably being in the range of no greater than: 200 µm, 100 µm, 50 µm, 30 µm, 20 µm or 10 µm. Four signals S1u, S2u, S1d, S2d may be generated by the detectors D1u, D2u, D1d, D2d respectively. As shown in Fig.23B, detector may be connected to an amplifier 15, which may be provided on the same wafer as the respective detector. These signals may be further processed in different combinations as shown in Table 1 below. Combination 1 2 3 4 Signal S1u+ + + + S1d + + - - S2u+ - + - S2d + - - + Output harmonics 2 ^^^^, ^^ ^^, ^^ ^^, ^^ ^^ ± ^^ ^^4^^ ^^ 3 ^^ ^^ 2 ^^ ^^ ± ^^ ^^ 3 ^^ ^^ ± ^^ ^^… … … …. Table 1 As shown in Table 1, combination 1 (all signals summed up) generates a summed signal having harmonics similar to the signal s(t) discussed above. Combination 3 generates a difference signal having harmonics similar to difference signal d(t) discussed above. As such, signal combinations 1 and 3 may allow for the trajectory of the ion to be determined according to embodiments of this disclosure and as discussed above. While Table 1 sets out linear combinations of the two pairs of detectors D1, D2 in order to determine the frequencies ^^^^and ^^^^, in another embodiment the two pairs of detectors may be utilised independently. As such, in one embodiment, the spectral components on the frequencies ^^^^and ^^^^may be determined by a Fourier Transform of signals acquired from different detectors separated laterally both sides of the optical axis (e.g. Detectors D1u and D2u). Alternatively, different pairs of detectors may be used to determine ^^^^and ^^^^15026845v1 respectively. Specific linear superpositions of these signals may be constructed in such manner that one superposition contains solely the harmonic of oscillations ^^^^, 2 ^^^^, 3 ^^^^… and the other(s) contain a harmonic(s) on the frequencies related to ^^^^Embodiments of this disclosure have discussed the correction of the frequency fz to account for oscillation of the ion in a single transverse direction fx. It will be appreciated that this concept may also be extended to all three (x, y, z) dimensions as shown in Figs. 24A and 24B. In this embodiment, an ion trap 10, which may be an μEST, similar to the ion trap 10 of Figs.23A and 23B is provided. As such, the first and second ion mirrors 20, 30 may be provided by a pair of opposing wafers on which a plurality of electrodes are patterned. Fig.24A is a plan view of one wafer 40 in the y-z plane, while Fig.24B is a cross section of the ion trap 10 in the x-z plane. In the embodiment of Figs.24 and 24B, each of detection electrodes is further split into a central I section and an outer (O) one. As such, each outer detection electrode D1O, D2Opartially, or fully encircles the central detection electrode D1C, D2C. The outer detection electrode D1O, D2Omay be provided such that it extends beyond the central detection electrode D1C, D2Cin the third direction (y-direction) in order to distinguish the motion of the ion in the y direction (relative to the signal detected by the central detection electrode). As will be appreciated from the cross-sectional view of Fig.24B, the arrangement of the detection electrodes may be mirrored on a second wafer such that a total of eight detection electrodes are provided. Said outer and central detection electrodes for both first and second detector location, on upper and lower wafers results in eight signals being generated. These signals may be linearly combined to generate harmonics of the various oscillation frequencies fx, fy, and fz. Table 2 indicates the resulting combinations and associated harmonics, with the minimum set of signal combination numbers 1, 3, 5 providing all three major frequencies of an ion. Combination 1 2 3 4 5 … Signal S1u-c+ + + + + S1d-c + + - - + S1u-o+ + + + - 15026845v1 S1d-o+ + - - - S2u-c + - + - + S2d-c+ - - + + S2u-o + - + - - S2d-o+ - - + - Output 2*fz,4*fz fz, 3fz fx fx, 3fx 2*fy Table 2 Embodiments of the disclosure have so far provided a discussion of the correction of a trajectory of a single ion trapped within an ion trap 10. As such, the present disclosure is particularly applicable to single-ion FTMS. Embodiments of this disclosure may also be applicable to the simultaneous analysis of a plurality of ions (i.e. an ion packet). In particular, embodiments of this disclosure may be particularly applicable to ion packets that contain more than one ion of the same sort. For such ions the frequencies ^^^^are close and may barely be unresolved. However, provided that the ions move on different Poincare orbits, the frequencies ^^^^are still substantially different and a number of corresponding peaks are observed in the FT spectrum of d(t). This number gives an estimation of the actual number of co-trapped ions and may be used to assess the amplitude of the signal in s(t) that comes from an Individual ion. This aspect is similar to the multiplexed charge detection developed in WO2020198332 with the following substantial difference. In WO2020198332, the signals from co-trapped ions are separated due to the energy differences of these ions and non-exact energy isochronism of an EST. This approach is not applicable to EST highly optimized for energy isochronism because the ^^^^of the ions may be challenging or impossible to resolve. Instead, the current invention capitalizes on the fact that the co-trapped ions generate peaks in the auxiliary d(t) signal which are significantly easier to resolve. Figs.25A and 25B demonstrate schematically the usage of the auxiliary spectrum of d(t) in which individual ions of the same sort (same m / z) present as a single peak in the frequency spectrum of the summed signal s(t). As such, resolution of the individual ions from the summed signal as shown in Fig.25A is difficult, if not impossible, due to the overlapping 15026845v1 nature of the peaks associated with each ion. However, as shown in Fig.25B, the ions are easily distinguished by different frequencies ^^^^provided that the ions in question oscillate on different Poincare orbits due to random injection parameters. This approach allows also to distinguish ions that lock in coalescence on axial frequency but remain apart on transversal frequencies. It will be appreciated that the signal processing required to amplify the signal from each detector 12, 14, digitise the signal and generate the desired sum and difference signals may be implemented in a variety of manners. For example, buffered outputs from each detector 12, 14 could be combined into all possible combinations using analogue electronics, in particular in a summing or differential configuration, followed by digitisation of the resulting signals. Alternatively, the individual signals from each detector may be digitised, from which the sum and difference signals are calculated using a suitable controller (e.g. a computer processor). In the latter case, signal from a preamplifier on each electrode may be sent to its own analogue to digital converter channel and only after that different combinations are implemented and processed in parallel. In some embodiments, the resulting peaks from the frequency domain could be used as a part of input string into machine learning for the development of a suitable trajectory correction function, or for further analysis of experimental data and the like. In some embodiments where all signals are summed (e.g. combination 1 of Tables 1-2), common mode rejection may be implemented by utilising a measurement on a virtual ground of the ion trap 10. For example in the embodiments of Figs.23A and 24A, a virtual ground may be provided by a virtual ground electrode 36 surrounding the detector electrodes D1, D2. By differentially subtracting a signal acquired by connecting an additional amplifier to the virtual ground electrode 36 (Figs.21-22) surrounding detection electrodes, the sum signal s(t) may have improved resilience to common-mode noise and noise coming from surrounding sources such as power supplies, pumping, vibrations, ground loops, and the like. While the above embodiments of this disclosure have referred to ion traps with a plurality of detectors, it will be appreciated that in some embodiments a FTMA may be provided which comprises a single detector 12 (e.g. a single pickup electrode). In such embodiments, for example referring to the embodiment of Fig.15, the oscillation of the ion in the ion trap 10 15026845v1 may be detected from only one of detector 12 and14. Said single detector is located along the z-axis of the ion trap 10 and offset from the z-axis in the second direction (x-direction). Such a unilateral signal (e.g. signal q1(t) or q2(t) as discussed above) contains both the oscillatory harmonic at the frequency fz and the auxiliary harmonic of transversal oscillations at the frequency fx. These harmonics may be separated by a Fourier Transform as used as described above. This approach suffers, however, from lower sensitivity as only 50% of the signal intensity is used. Having both harmonics present in the signal may also give rise to errors in the interpretation of the signals. As such, it will be appreciated that embodiments involving a plurality of detectors 12, 14 to detect the oscillation of the ion may provide improved signal to noise ratio. In the above-described embodiments, the first and second electrode assemblies 22, 24; 32, 34 of each ion mirror 20, 30 have been arranged in a symmetrical manner about the z-axis. As such, the first planar electrodes 23a, 23b, 23c are generally identical to the second planar electrodes 25a, 25b, 25c, such that the first electrode assembly 22, 32 has a similar arrangement of planar electrodes as the second electrode assembly 24, 34. Furthermore, the first electrode assembly 22, 32 have been aligned such that the each first planar electrode 23a, 33a of the first electrode assembly 22, 32 is aligned in the y-direction with a corresponding second planar electrode 25a, 35a of the second electrode assembly 24, 34. It will be appreciated that in other embodiments, the arrangements of the electrodes in each ion mirror may be varied from the generally symmetrical arrangements described above. For example, Fig.26 shows a schematic diagram of a FTMA 1 comprising an ion trap 10. The ion trap 10 comprises first and second ion mirrors 20, 30, similar to the embodiments described above. Each ion mirror 20, 30 comprises a first and second electrode assembly 22, 24; 32, 34. Each electrode assembly 22, 24; 32, 34 may be provided with planar electrodes generally in accordance with the above-described embodiments, or any other arrangement of planar electrodes. In the embodiment of Fig.26, the alignment of the first and second electrode assemblies 22, 24; 32, 34 in the z-direction is perturbed by a relatively small distance (e.g. h / 25 in Fig.26). As such, the first and second electrode assemblies 22, 24; 32, 34 still overlap in order to provide a reflecting potential when operated in the ion trapping mode. However, the alignment of each first planar electrode 23a, 33a with a corresponding second planar electrode 25a, 35a in the y-direction is now offset in the z-direction by a small perturbation. The small perturbation may be, for example 15026845v1 a distance which is much smaller than the distance h / 2, where h is the distance between the first and second electrode assemblies 22, 24. In some embodiments, the perturbation may be no greater than h / 8, h / 16, h / 20, h / 50 or h / 100. Results of ion modelling in perturbed fields, such as the perturbed reflecting potentials of Fig.26, reveal high heterogeneity and resonances of ion trajectories caused even by simple perturbations. As indicated in Fig.26, a drastic change of ion trajectory results from with a small perturbation of the electrode assemblies by h / 25. As such, the principal loop trajectory (around which the diagram of Fig.26 is centred) is in fact not straight anymore and could follow a complicated shape dictated by perturbations. The perturbations and related resonances reduce the acceptance of the ion trap 10 and shift the centre of stability zone from the origin of the phase plane. Nevertheless, the phase volume domain in the vicinity of the principal loop trajectory reveals a prominent dependence of the frequency ratio ^^ = ^^^^ / ^^^^in the interval of about 0.4 to about 0.333. This ratio unambiguously characterizes the amplitude of the transversal oscillations around the principal trajectory, as shown in the Poincare diagram of Fig.27 for the FTMA of Fig.26. Accordingly, it will be appreciated that the trajectory correction principles of this disclosure may be fully applicable to construct a trajectory calibration function ^^: ^^−> ^^ ^^ and therefore to adjust the reported m / z ratio based on the measured auxiliary frequency ^^^^. In the perturbed embodiment of Figs.26 and 27, it will be appreciated that the Poincare diagram comprises three resonant regions. In the vicinity of the resonances, however, the transversal oscillations are phase-locked with the oscillations along the z-axis and the frequency ratio is 1 / 3 exactly. Figs.28 and 29 show graphs of the frequency error δ ^^ / ^^^^and the frequency ratio r as the initial ion trajectory varies for the ion trap of Fig.26. Though the perturbation of oscillation frequency near the resonances ^^ ^^ is quite significant, it cannot be accurately accounted for judging on the frequency ratio alone because this ratio is the same (1 / 3) for all three of the phase-locked orbits. As such, in some embodiments (e.g. where such phase-locked orbits may occur), where an ion is determined to have a frequency ratio r = fx / fz which is about m / n, where n and m are integers, preferably n being between 3 and 8 and m being between 1 and n, the determined mass to charge ratio may be flagged as having low precision or even rejected. 15026845v1 Such measurements may be flagged as being indicative of that ion trajectory is affected by some form of phase-locked resonance. As such, embodiments of this disclosure may attempt to flag observations of ions which may be indicative of a resonance even where detailed ion modelling of the ion trap 10 is not available. While the above-described calibration of the FTMA according to embodiments of this disclosure contemplated calibration measurements performed using single ion FTMS, in some embodiments the FTMA 1 may be calibrated using a plurality of calibration ions (i.e. calibration using an ion packet). In such circumstances, the FTMS measurement may be perturbed due to space-charge effects when several ions co-exist in the ion trap 10. This perturbation may also be corrected for by extending the previous calibration on individual ions to cases where a plurality of ions e.g.2, 3, 4… ions are co-injected into the ion trap 10. It such embodiments, the calibrant ions may preferably be provided by relatively lower charge calibrant compounds / ions, e.g. peptide (ions) with 2-4 elementary charges. For example, calibrant ions formed from such compounds may have a charge state of no more than 10+, preferably no more than: 5+, 4+, 3+, or 2+ or a singly charged ion. Similarly, for negatively charged calibrant ions, the calibrant ion may have a charge state of no more than 10-, preferably no more than 5- and so on. Such calibrant ions may be used to more accurately represent the expected behaviour of unknown analytes ions. Accordingly, the calibration methods according to this disclosure may be provided in order to account for perturbations resulting from local and global space charge-effects. Such local and global space charge effects are further described in DOI: 10.1142 / S0217751X19420077 (D. Grinfeld et al. Int.J. Modern Phys. A, 34, No.36, 1942007 (2019)). While embodiments of the disclosure have thus far described the invention in relation to an ion trap 10 comprising generally planar first and second ion mirrors 20, 30, it will be appreciated that embodiments of this disclosure may include other ion trap architectures. For example, in some embodiments the ion trap 10 may be an orbital trapping mass analyser. A schematic diagram of an orbital trapping mass analyser 80 is shown in Fig.16. The orbital trapping mass analyser of Fig.30 is further described in at least US5,886,346 and US-B-7,714,283, the contents of which is incorporated by reference. As shown in Fig.30, the orbital trapping mass analyser 80 comprises split outer electrodes 400, 410 and an inner electrode 90. As shown in Fig.30, the electrodes are shaped, so far 15026845v1 as is possible within manufacturing tolerances, to have a hyper-logarithmic shape defined by the equation: where the equation is expressed in terms of a cylindrical co-ordinate system (r, z). Within the outer electrode 410 is a deflector 420. Ions may be introduced into the trapping volume defined between the inner electrode 90 and outer electrodes 400, 410 through a slot 425 between the outer electrodes 400, 410. End cap electrodes 440, 450 are provided to contain ions within the trapping volume. An image current may be obtained which is representative of the oscillation of an ion using a differential amplifier 430 connected between the two outer electrodes 400, 410. A summed signal may also be obtained from the sum of the signals generated by outer electrodes 400, 410. In accordance with this disclosure, it will be appreciated that the outer electrodes 400, 410 are spaced apart from the z-axis in a direction transverse to the z-direction such that the outer electrodes 400, 410 may detect a signal indicative of oscillations in both the x-direction and the z-direction. The orbital trapping mass analyser 80 may be operated in a single-ion mode. When operated in a single-ion mode, e.g. for multiply charged ions and / or transients of many seconds long, the sum and difference signals of the outer electrodes 400, 410 may comprise harmonics which are indicative of the radial frequency fr, axial fz, and optionally rotational fφ. Such frequencies may be used to correct for the trajectory of the ion as it oscillates about the orbital trapping analyser in the z-direction in accordance with the techniques described above. Building on the above-described embodiments, in some embodiments, the method of FTMA may utilise an initial period of the ion measurement (i.e. the first few oscillations of the ion in the ion trap following injection) for on-the-fly detection. As such, the initial transient signal following injection of the ion for the first N oscillations may be detected, where N is no greater than: 50, 20, or 10. This transient signal may be used to make an initial estimation of the m / z of the ion in accordance with embodiments of the disclosure. The transient signal may also be used to adjust parameters of the FTMA 1 based on the initial estimation of the m / z of the ion, or the initially determined frequency ratio r, or other parameter which may be indicative of the trajectory of the ion within the ion trap 10. As such, the initial estimation may be used to apply a dynamic compensation to the FTMA 1 15026845v1 based on an observation of the initial transient signal. For example, the dynamic compensation may comprise active feedback control of voltages applied to one or more electrodes of the ion mirrors 20, 30 in order to improve parameters (e.g. reduce disbalance of certain outputs, minimize certain harmonics, etc.). Such techniques are further described in at least US-B-7,714,283, the contents of which are incorporated by reference. The FTMA dynamic compensation may be trained on multiply charged calibration ions of small, denatured proteins and applied then to lower-charged analyte compounds with lower signal-to-noise. Following an initial observation and any dynamic compensation, the FTMA 1 may then make a further determination of the m / z of the ion including a correction to account for the trajectory of the ion as described above. For embodiments comprising a plurality of pairs of detectors, such as the embodiment of Figs.9A and 10A, the initial observation of the transient may utilise all detectors (e.g. D1u, D1d, D2u, D2d in Fig.23A) present in the ion trap 10 in order to increase the number of data points available. Usage of multiple detection electrodes (e.g. four in Fig.23A, eight in Fig.24A), as well as dynamic on-the-fly detection, is further described in at least US-B-7,399,962 and US-B-9,520,280, the contents of which are incorporated by reference. The subsequent higher accuracy measurements following dynamic compensation may then utilise a lower number of detectors (e.g. D1u,D1donly in Fig.23A). For example, the higher accuracy measurement may be performed using a single pair of detectors D1u,D1dor even a single detector D1uin order to improve the signal-to-noise ratio of the detected signal. The resulting higher accuracy signal may then be used for mass determination- and determined ion parameters could be used to improve mass accuracy, following the principles set out in at least US-B-8,853,620, the contents of which are incorporated by reference. Thus, embodiments of this disclosure provide a FTMA and methods of FTMS which can account for the oscillation of an ion in direction transverse to the direction of principle oscillation (fz) in order to improve the accuracy of determining the m / z of the oscillating ion. 15026845v1

Claims

CLAIMS:

1. A method of operating a mass spectrometer including an ion trap, the method comprising: introducing an ion having a mass to charge ratio into the ion trap; measuring time series data corresponding to the oscillation of the ion in the ion trap; extracting a first feature indicative of the oscillation of the ion in the ion trap and a second feature indicative of a trajectory of the oscillation of the ion from the time series data; and computing the mass to charge ratio using an ion trap function and the extracted first and second features.

2. A method according to claim 1, wherein the first feature is an oscillation period of the ion in the ion trap; and the second feature is a time of flight of the ion in the ion trap.

3. A method according to claim 1, wherein the first feature is an oscillation frequency of the ion along a first direction of the ion trap, and the second feature is an oscillation frequency along a second direction of the ion trap, wherein the second direction is transverse to the first direction; or the first feature is an amplitude of an oscillation of the ion along a first direction of the ion trap, and the second feature is an amplitude of an oscillation of the ion along second direction of the ion trap, wherein the second direction is transverse to the first direction.

4. A method according to any preceding claim, wherein the mass to charge ratio of the ion is computed based on a ratio of the first feature to the second feature.

5. A method according to any preceding claim, wherein the ion trap has a first axis, wherein the ion oscillates in a first direction aligned with the first axis.

6. A method according to claim 5, wherein 15026845v1the ion oscillates in the ion trap with a trajectory relative to the first axis such that the ion oscillates in a second direction transverse to the first direction at a second frequency.

7. A method according to claim 5 or claim 6, wherein the ion trap comprises at least one detector located along the first axis and offset from the first axis in the second direction to detect the first feature and the second feature, the detector configured to measure the time series data.

8. A method according to claim 7, wherein The ion trap comprises a first detector and a second detector, wherein the first and second detectors are each located at the same position along the first axis and spaced apart on opposing sides of the first axis in the second direction.

9. A method according to claim 8, wherein the first detector generates first time series data indicative of the oscillation of the ion; and the second detector generates second time series data indicative of the oscillation of the ion, wherein the first feature is determined from a sum of the first and second time series data, and the second feature is determined from a difference between the first and second time series data.

10. A method according to claim 8 or claim 9, wherein the oscillation of the ion in the first and second direction is detected by a plurality of pairs of first and second detectors, each pair of detectors located along the first axis.

11. A method according to any of claims 7 to 10, wherein each detector comprises a planar electrode extending in a plane normal to the second direction.

12. A method according to any of claims 1 to 11, wherein 15026845v1the ion trap comprises a first ion mirror and an opposing second ion mirror arranged along a first axis, wherein the ion oscillates between the first ion mirror and the second ion mirror.

13. A method according to claim 12, wherein each of the first and second ion mirrors comprise: a first electrode assembly extending in a first plane normal to the second direction; a second electrode assembly extending in a second plane normal to the second direction, wherein the first and second electrode assemblies are spaced apart in the second direction on opposing sides of the first axis.

14. A method according to claim 13, wherein each first electrode assembly comprises a plurality of first planar electrodes distributed along the first axis; and each second electrode assembly comprises a plurality of second planar electrodes distributed along the first axis.

15. A method according to claim 14, wherein for at least one of the first and second ion mirrors: the plurality of first planar electrodes each extend in the first plane in a third direction normal to the first and second directions; and / or the plurality of second electrodes each extend in the second plane in a third direction normal to the first and second directions.

16. A method according to claim 14 or claim 15, wherein for at least one of the first and second ion mirrors: the plurality of first planar electrodes each extend in the first plane along an arc, wherein a centre of each arc in the first plane is aligned with the first axis; and / or the plurality of second planar electrodes each extend in the second plane along an arc, wherein a centre of each arc in the second plane is aligned with the first axis.

17. A method according to any of claims 12 to 16, wherein 15026845v1a length of the ion trap along the first axis from a distal end of the first ion mirror to a distal end of the second ion mirror may be no greater than: 10 mm, 5 mm, 2 mm, 1 mm or 0.5 mm.

18. A method according to any preceding claim, wherein computing the mass to charge ratio using the ion trap function and the extracted first and second features comprises determining a trajectory correction factor for the ion based on the first and second features and the ion trap function; and determining a mass to charge ratio for the ion based on the first frequency and the trajectory correction factor.

19. A method according to any preceding claim, wherein where an ion is determined to have a ratio of the second feature to the first feature which is about m / n, where n and m are integers, preferably n being between 3 and 8 and m being between 1 and n, the determined mass to charge ratio is flagged as having low precision or rejected.

20. A method according to any preceding claim, wherein the ion trap function is pre-determined based on a calibration measurement using the ion trap and an ion of a known mass to charge ratio.

21. A method according to any preceding claim, further comprising providing the ion trap function for computing the mass to charge ratio, wherein the ion trap function corresponds to the ion trap.

22. A method according to any preceding claim, further comprising: performing a calibration measurement for the ion trap comprising: providing a calibration ion of a known mass to charge ratio; introducing the calibration ion of known mass charge ratio into the ion trap; measuring calibration time series data corresponding to an oscillation of the calibration ion in the ion trap; extracting a first calibration feature indicative of the oscillation of the calibration ion in the ion trap and a second calibration feature indicative of a trajectory of the oscillation of the calibration ion from the calibration time series data; and 15026845v1determining, based at least in part on the first and second calibration features, the ion trap function corresponding to the ion trap.

23. A method according to claim 22, wherein the first calibration feature is an oscillation period of the ion in the ion trap, and the second feature is a time of flight of the ion in the ion trap; or the first calibration feature is an oscillation frequency of the ion along a first direction of the ion trap, and the second calibration feature is an oscillation frequency along a second direction of the ion trap, wherein the second direction is transverse to the first direction.; or the first calibration feature is an amplitude of an oscillation frequency of the ion along a first direction of the ion trap, and the second calibration feature is an amplitude of an oscillation frequency of the ion along second direction of the ion trap, wherein the second direction is transverse to the first direction.

24. A method according to claim 22 or claim 23, wherein the ion trap function is determined based at least in part on the first and second calibration features using a machine learning technique.

25. A method according to claim 24, further comprising performing a plurality of calibration measurements for the ion trap using calibration ions of different known mass to charge ratios to generate a set of first and second calibration features and associated known mass to charge ratios; training a neural network using the set of a set of first and second calibration features and associated known mass to charge ratios to provide the ion trap function.

26. A mass analyser configured to determine a mass to charge ratio of an ion, the mass analyser comprising: an ion trap; a detector configured to detect an oscillation of the ion in the ion trap; and a mass analyser controller configured to: cause the mass analyser to introduce an ion having a mass to charge ratio into the ion trap; cause the detector of the mass analyser to measure time series data corresponding to the oscillation of the ion in the ion trap; 15026845v1extract a first feature indicative of the oscillation of the ion in the ion trap and a second feature indicative of a trajectory of the oscillation of the ion from the time series data; and compute the mass to charge ratio using an ion trap function and the extracted first and second features.

27. A mass analyser according to claim 26, wherein the mass analyser controller is configured to obtain the ion trap function based on a plurality of calibration measurements of the ion trap.

26. A mass analyser controller for use with the mass analyser of claim 25, wherein the mass analyser controller is configured to cause the mass analyser of claim 25 to perform the method of any of claims 1 to 24. 15026845v1

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