Improvements in and relating to ion analysis

Abstract

A method of processing an image charge / current signal representative of one or more ions undergoing oscillatory motion within an ion analyzer. The method includes obtaining a recording of an image charge / current signal generated by an ion analyzer in the time domain. The method includes determining, by a signal processing unit, a value of a period of a periodic signal component in the recorded signal. The method then includes truncating the recorded signal to provide a truncated signal having a duration approximately equal to an integer multiple of the period. A step is performed of reconstructing a time domain signal based on one or more selected frequency domain harmonic components of the truncated signal. The method then includes determining a magnitude of the reconstructed time domain signal and using it to calculate a value representative of the charge of the ions undergoing oscillatory motion within the ion analyzer.

Description

[Technical field]

[0001] The present invention relates to a method and apparatus for ion analysis using image charge / current analysis and an ion analyzer therefor. In particular, but not exclusively, the present invention relates to analysis of an image charge / current signal to identify the charge of an ion. For example, the image charge / current signal may be generated by an ion mobility analyzer, a charge detection mass spectrometer (CDMS), or an ion trap such as an ion cyclotron, an Orbitrap®, an electrostatic linear ion trap (ELIT), a quadrupole ion trap, an Orbital Frequency Analyser (OFA), a Planar Electrostatic Ion Trap (PEIT), or other ion analyzer for generating oscillatory motion therein. [Background technology]

[0002] In general, ion trap mass analyzers function to trap ions and place the trapped ions in oscillatory motion, for example back and forth along a linear trajectory or in an orbital path. Ion trap mass analyzers can generate magnetic, current or electrostatic fields, or a combination of these fields, to trap the ions. When electrostatic fields are used to trap ions, the ion trap mass analyzer is commonly referred to as an "electrostatic" ion trap mass analyzer.

[0003] In general, the oscillation frequency of trapped ions in an ion trap mass spectrometer depends on the mass-to-charge ratio (m / z) of the ions, because ions with a large m / z ratio usually require a longer time to oscillate than ions with a small m / z ratio. An image charge / current detector can be used to non-destructively obtain an image charge / current signal representing the trapped ions undergoing oscillatory motion in the time domain. This image charge / current signal can be transformed into the frequency domain, for example, by Fourier transform (FT). Since the oscillation frequency of trapped ions depends on m / z, the image charge / current signal in the frequency domain can be regarded as mass spectrum data that provides information about the m / z distribution of the trapped ions.

[0004] In mass spectrometry, one or more ions undergoing oscillatory motion within an ion analyzer (e.g., an ion trap) induce an image charge / current signal that can be detected by a sensor electrode of the device configured for detection of the image charge / current signal. One well-established method for analyzing such an image charge / current signal is to transform this time domain signal into the frequency domain. The most widely used transform for this purpose is the Fourier transform (FT). The Fourier transform breaks down the time domain signal into sinusoidal components, each with a specific frequency (or period), amplitude and phase. These parameters are related to the frequency (or period), amplitude and phase of the periodic components (frequency components) present in the measured image charge / current signal. The frequency (or period) of those periodic components can be easily related to the m / z value or mass of each ion species if the charge state of that species is known. Mass analyzers that utilize these principles are called Fourier transform mass analyzers, and the field itself is called Fourier transform mass spectrometry (FTMS).

[0005] Two widely used FTMS ion traps are the Fourier Transform Ion Cyclotron Resonance (FTICR) trap and the Orbitrap®. The former traps ions using a magnetic field, while the latter traps ions using an electrostatic field. Both traps generate harmonic image charge / current signals. Other types of FTMS ion traps are configured to generate non-harmonic image charge / current signals. FTICRs typically use a superconducting magnetic field to trap ions, while in Orbitrap® ions are trapped by an electrostatic field and orbit around a central electrode in a helical trajectory. Another known example of an ion trap mass spectrometer is the Orbital Frequency Analyzer (OFA), described in Non-Patent Document 1. Yet another known example of an ion trap mass spectrometer is the Electrostatic Ion Beam Trap (EIBT), described in Patent Document 1 by Zajfman et al. In EIBT, ions oscillate back and forth along a generally linear trajectory, and therefore such ion traps are also called "electrostatic linear ion traps" (ELIT).

[0006] Analysis of non-harmonic image charge / current signals can also be performed using Fourier transformation, which results in multiple harmonics for each periodic / frequency component of the image charge / current signal, but harmonics of different orders can mix (overlap) with each other in the frequency spectrum of the Fourier transformed image charge / current signal, making it much more difficult to relate the frequency of each component to the mass-to-charge ratio (m / z) or mass of the ion species.

[0007] Charge detection mass spectrometry utilizes the signal from the ion motion in an ion trap to simultaneously measure the m / z and charge of individual ions. The ion trap can be in the form of an ion cyclotron resonance (ICR) cell, an Orbitrap, or other types of electrostatic ion traps, such as electrostatic linear traps, electrostatic planar traps (OFA), and Cassinian traps. After the ions are introduced into the ion trap, they orbit or fly repeatedly back and forth in the trapping volume, the frequency of their oscillation or orbit depending on the m / z of each ion. One or several electrodes in the ion trap serve to pick up the image charge signal from the ion motion. Such a signal can be harmonic with a sinusoidal waveform, or it can be non-harmonic, meaning that in addition to the fundamental component it has one or more other sizable frequency components (e.g., higher harmonic frequency components). In any case, the repetition frequency of the signal is the same as or a multiple of the oscillation or orbit frequency. On the other hand, the amplitude of the signal is proportional to the charge of the ion.

[0008] When multiply charged ions are involved, especially the highly charged bioions generated from an electrospray ion source and introduced into the ion trap, the signal from the individual oscillating ions can be detected, but some signal processing algorithm must be used to suppress the noise. One widely used method / algorithm is the Fourier transform, which is the basis of the so-called Fourier transform mass spectrometry (FTMS).

[0009] In FTMS, the frequency of ion motion can be measured very accurately if the recorded transient image charge / current signal is long enough (e.g., 1 second). Measuring the charge of an ion, on the other hand, is difficult: the amplitude of the signal is distorted by electronic noise in the signal, and the oscillation of the ions in the trap can be disturbed by collisions with residual gas molecules, space charge interactions between ions, or signal interference when several ions are flying together. To mitigate these problems, the number of ions injected in each cycle is limited (typically tens to hundreds) and the instrument is placed in an ultra-high vacuum (10 -10Torr or less), and it is necessary to increase the signal-to-noise ratio (S / N) of the system that picks up and amplifies the signal.

[0010] From a hardware point of view, currently with electrostatic ion traps with very good vacuum and transition times of about 1 second, the charge measurement error can reach 2e, where e is the electron charge. In the software used to process the recorded transient image charge / current signal, it is important to measure accurately each frequency in the signal, which indicates how many ions are present and the m / z of each ion associated with the signal. This is usually done by applying a Fast Fourier Transform (FFT). The lifetime of each ion must also be measured, i.e. the time that the ion's oscillations lasted undisturbed by collisions. Conventional STORI gradient methods can be used to try to determine the lifetime (LT) and charge of the ions after the fact.

[0011] The STORI method (Non-Patent Document 2) provides a means to find the lifetime of ion oscillations. This method calculates the following quantity from the image charge / current signal f(t):

number

number

[0012] However, the STORI method is mainly suitable for harmonic oscillations, more specifically when the image charge / current signal resulting from the ion motion has a sinusoidal waveform. For non-harmonic signals that contain multiple harmonic components, the method does not efficiently utilize those harmonic components, and therefore leads to a low signal-to-noise ratio and poor charge measurement accuracy. In addition, when calculating the value of the ion's charge, the method suffers from electronic noise embedded in the signal. If multiple ions coexist in the ion trap during data acquisition, if the frequencies of the ion oscillations are close enough, they will start to interfere with each other, further increasing the inaccuracy of the charge measurement.

[0013] To illustrate the problems associated with the STORI method, consider the following simulated test data shown in FIG. 1b. This figure shows two sets of STORI plots from the prior art. The first set (curve 1) shows STORI plots of the image charge vs. current signal for a single ion, which does not include noise or interference from other ions. The second set (curves 2, 3, and 4) shows STORI plots of the image charge vs. current signal for an ion of interest, which include realistic levels of noise or interference from other ions. Curve 1 was generated by a single ion oscillating at 170,000.00 Hz over the entire length of the signal. The total duration of the signal was 1,000 milliseconds. This curve is a pure straight line, an idealized result that is unlikely to occur in reality. Whether the line is a straight line depends on how the sampling frequency is related to the frequency and phase of the signal. A perfect straight line, like curve 1 in FIG. 1b, will only occur when the sampling period is an integer multiple of the signal period. Here, "sampling" refers to successive time instants (t n) is related to the distance between the ions. Much more realistic are curves 2, 3, and 4, which represent STORI plots for the vibration of three ions of the same charge. Curve 2 corresponds to an ion (Ion#1) oscillating at a frequency of 170,000.00 Hz, curve 3 corresponds to an ion (Ion#2) oscillating at a frequency of 170,010.95 Hz, and curve 4 corresponds to an ion (Ion#3) oscillating at a frequency of 170,006.57 Hz. Ion#2 lasts for 200 ms before changing its frequency to 170,050.11 Hz. Ion#3 lasts for 300 ms before changing its frequency to 170,008.76 Hz. The total signal duration for all three ions is 1,000 ms, and all three ions have the same charge of 50e after changing their frequency.

[0014] The slope of each STORI is assumed to be proportional to the charge of the ion that produces it. The slope of the idealized ion (curve 1) represents a charge of 50e. The proportionality coefficient (gradient) of this curve can be used as a calibration to estimate the charge of other ions. One problem is that without the idealized curve 1, the next best (nearly linear) curve, say curve 2, must be used as a calibration. Curve 2 is clearly modulated by oscillations that are clearly periodic, meaning that they are not caused by noise, making it problematic to estimate its slope.

[0015] Another problem with the STORI method is that it can only be used while the oscillations of an ion are present and are evident in the curve of the STORI plot corresponding to that ion as a continuously rising linear (or quasi-linear) plot. When the oscillations cease and the "lifetime" of the ion oscillation ends, the corresponding portion of the data on the STORI plot should, at least in theory, stop rising. Any portion of the STORI data that corresponds to a time after this "lifetime" has ended should not be used in a STORI analysis. However, it is often very difficult to accurately determine the "lifetime" of an ion oscillation from its STORI plot. This is important because, given the shape of the "lines" on the STORI plot, their slopes depend on which portion of the "lines" is used to estimate the value of the slope. As a concrete example, in the current simulation, the lifetimes of Ion#1, Ion#2 and Ion#3 are "known" (i.e., 1000 ms, 200 ms and 300 ms, respectively), and if we determine a fictitious linear "gradient" for each curve by linear regression analysis of the respective STORI curves (2, 3 and 4), the result is the following charges for those ions (in units of electron charge, e):

[0016] [Table 1]

[0017] The true charge is 50e. This STORI result is unacceptable. Even the estimate of the charge of Ion#1, which has an oscillatory "lifetime" across the STORI plot, is compromised by the periodic noise seen in curve 2, including contributions from other ion signals (Ion#2, Ion#3) whose oscillation frequencies are close to Ion#1. It is therefore important to reduce the contribution of charge measurement errors from electronic and other noise, and to minimize or account for contributions from other ion signals whose frequencies are close.

[0018] The present invention has been made in view of the above circumstances. [Prior art documents] [Patent documents]

[0019] [Patent Document 1] WO 02 / 103747 A1 [Patent Document 2] WO 2012 / 116765 A1 [Non-patent literature]

[0020] [Non-Patent Document 1] Li Ding and Aleksandr Rusinov, “High-Capacity Electrostatic Ion Trap with Mass Resolving Power Boosted by High-Order Harmonics”, Anal. Chem. 2019, 91, 12, 7595-7602 [Non-Patent Document 2] Jared O. Kafader, “STORI Plots Enable Accurate Tracking of Individual Ion Signals”; J.Am. Soc. Mass Spectrum (2019) 30: 2200-2203 [Non-Patent Document 3] W. Shockley: “Currents to Conductors Induced by a Moving Point Charge”, Journal of Applied Physics 9, 635 (1938) [Non-Patent Document 4] S. Ramo: “Currents Induced by Electron Motion”, Proceedings of the IRE, Volume 27, Issue 9, Sept. 1939 Summary of the Invention [Means for solving the problem]

[0021] The image charge / current signal can be obtained in a mass spectrometer that utilizes non-destructive detection of a signal containing a periodic component corresponding to the oscillations of some trapped ion species. However, the invention is applicable to any other field of ion analysis where a signal containing a periodic component needs to be analyzed. The frequency of ion motion depends on the mass-to-charge (m / z) ratio of the ions, and when there are multiple packets of ions in an ion analyzer (e.g. an ion trap), the motion of each packet of ions with the same m / z ratio may be synchronized, depending on the focusing characteristics of the ion analyzer.

[0022] Ion detection using image charges is based on principles derived by Shockley (Non-Patent Document 3) and Ramo (Non-Patent Document 4), where it was shown that the image of a charge moving past an electrode induces a measurable current in the electrode. The image charge Q induced on a detector electrode by a charge q moving in free space with velocity vector (v(r)) depends only on the position r and velocity of the moving charge and the configuration of the detector electrodes. The image charge Q does not depend on the bias voltage applied to the electrode or on the space charge present, and is given by

number

[0023] where V(r) is the electrostatic field potential at the location of the charge given by vector r in the detector. The induced image charge / current I is given by the rate of change of this quantity as

number

[0024] where E(r) is the electric field (vector) known as the "weighting field". As a simple concrete example of how to implement this relationship, consider a detector with a pair of parallel planar plates spaced uniformly apart d, in which an ion of charge q moves between the plates with speed v0 along a circular path in a plane perpendicular to the faces of the plates. The "weighting field" is uniform and oriented perpendicular to the plates and parallel to the ion's trajectory (in practical terms, this is essentially true if the dimensions of the plates are much larger than their spacing, so that fringe effects can be neglected). Thus,

number

number

[0025] The amplitude of the induced image charge / current is proportional to the charge q of the ion. By measuring this amplitude the charge of the ion can be determined once the proportionality constant term v0 / d is taken into account. More generally, the above principle applies equally to more complex detector electrode structures in that the amplitude of the induced image charge / current is proportional to the charge q of the ion, with the proportionality constant term being different depending on the detector electrode structure.

[0026] The present invention relates to the analysis of image charge / current signals. The signal may contain one or more periodic components. The periodicity of a component means that it exhibits a change in signal magnitude or amplitude once in a given time period and repeats once for every successive such time period. Each periodic component is also called a frequency component of the signal. The overall signal is the sum of all periodic / frequency components. The period T (seconds) of a periodic component corresponds to the frequency f (Hz) of the corresponding frequency component through the relationship f=1 / T. In this specification, "periodic component" and "frequency component" are interpreted interchangeably in this sense. Image charge / current signals may be non-harmonic or harmonic in nature, and in either case may contain periodic components within them. For example, image charge / current signals may result from ion motions that are "simple harmonic" and thus the image charge / current signal may be sinusoidal. However, the invention is not limited to such signals and such ion motions. Thus, image charge / current signals may also result from other types of harmonic motions of ions that are not "simple harmonic" but are repetitive periodic motions. The invention is particularly, but not exclusively, relevant to ion traps in which the motion of ions is periodic or nearly periodic and detected by a pick-up (image charge / current) detector.

[0027] The invention most generally provides a method and apparatus for reconstructing a time domain image charge / current signal corresponding to ions undergoing oscillatory motion within an ion analyzer, the reconstruction being based on one or more selected frequency domain harmonic components of a selected sub-portion / time interval from a previously acquired time domain image charge / current signal. The magnitude or duration of the selected signal sub-portion / time interval is selected in proportion to (e.g. as a multiple of) the value / magnitude of a period of oscillatory motion of the ions within the ion analyzer. The invention may include determining the magnitude of the reconstructed image charge signal and using it to calculate a value representative of the charge of an ion undergoing oscillatory motion within the ion analyzer. It has been found that selection of an appropriate sub-portion / time interval improves the clarity of the reconstructed image charge signal, thereby enhancing its effective use in calculating a value representative of the charge of an ion undergoing oscillatory motion within the ion analyzer.

[0028] One advantage of the present invention is that it reduces the spectral leakage of the spectral energy of an ion of interest into adjacent frequency bins on the frequency spectrum of the time domain image charge / current signal obtained for the ion. Advantageously, a greater proportion of the spectral energy of the frequency spectrum associated with the ion of interest can be concentrated in fewer spectral frequency bins or even in as few as one spectral frequency bin. Spectral energy from other ions can "leak" into this bin, and the present invention can provide a means of estimating the contribution of such "leak" from adjacent spectral bins associated with other ions (i.e. not related to the ion of interest). In this way, the present invention can account for the contribution of the image charge signals of other ions (i.e. ions other than the ion of interest) that may have been present in the trap together when the image charge / current signal of the ion was obtained. The present invention also has the advantage of reducing the effect of noise when analyzing the time domain image charge / current signal obtained for the ion. Overall, these advantages increase the accuracy of the assessment of the charge of the ion of interest, among others.

[0029] In a first aspect, the present invention provides a method for processing an image charge / current signal representative of one or more ions undergoing oscillatory motion in an ion analysis device, comprising the steps of: obtaining a recording of the image charge / current signal generated by the ion analyzer in the time domain; The signal processing unit determining a period value of a periodic signal component in the recorded signal; truncating the recorded signal to provide a truncated signal having a duration approximately equal to an integer multiple of the period; reconstructing a time domain signal based on one or more selected frequency domain harmonic components of the truncated signal; determining a magnitude of the reconstructed time domain signal and using it to calculate a value representative of the charge of the ions undergoing oscillatory motion within the ion analyzer; A method can be provided that includes:

[0030] Thus, the present invention truncates the recorded signal with the proviso that the length of the truncated signal is approximately an integer multiple of the oscillation period (T=1 / f) of the recorded oscillation signal, which results in an increased signal-to-noise (S / N) ratio in the reconstructed time domain signal, as discussed below.

[0031] The truncation of the recorded signal can be performed, for example, so that the end of the truncated signal coincides with a time just before or just after the end of the life of a periodic signal component (i.e., ionic oscillatory motion) in the recorded signal. In other words, the periodic signal component can exhibit a series of multiple signal peaks arranged periodically in time (i.e., spaced in time with a period T) throughout the duration of the "life" of the ionic oscillatory motion that produced them. The "life" of this oscillatory motion can be considered to have ended when the amplitude of such signal peak falls below an amplitude threshold. For example, the life of an ionic oscillatory motion and the oscillatory signal component it produces can be considered to have ended when the amplitude of the signal peak of that component deviates (falls) from the value of the maximum peak value (e.g., magnitude) of that component in the recorded signal by more than about 20%. Preferably, this deviation is more than about 15% from the value of the maximum peak value (e.g., magnitude). The recorded signal may be truncated such that the truncated signal contains only those signal peaks of the signal components that have an amplitude greater than the amplitude threshold. This effectively means that the ion oscillatory motion was "alive" (i.e., did not end its life) throughout the entire truncated signal. For example, if a recorded signal S(t) has a period T seconds and a lifetime T LT If we assume that the truncated signal contains a periodic component with seconds in duration, then the duration of the truncated signal can be N×T, where N is an integer and N×T <T LT It is.

[0032] Alternatively, the recorded signal can be truncated such that the truncated signal includes, in addition to the signal peaks of the signal components having amplitudes greater than the amplitude threshold, one (or two) signal peaks with amplitudes less than the amplitude threshold immediately after the end of the "lifetime" of the ionic oscillatory motion. This truncation is acceptable when the ionic oscillatory motion initially starts to "die" relatively slowly, and the drop in amplitude of successive signal peaks is relatively slow, so that the "die time" falls, for example, between the last two successive signal peaks of the truncated signal. For example, if a recorded signal S(t) has a period T seconds and a lifetime T LT If we assume that the truncated signal contains a periodic component with seconds in duration, then the duration of the truncated signal can be (N+1)×T, where N is an integer and N×T <T LT < (N+1) × T.

[0033] Preferably, the method can include identifying the frequency (or period) of the ion oscillations from the recorded image charge / current signal. The method can include determining the lifetime of this oscillation in the signal. The invention can include truncating the length of the recorded image charge signal (in the time domain) to within the lifetime of the oscillations. Thus, most preferably, the duration of the truncated signal does not exceed the lifetime of the periodic signal component in the recorded signal.

[0034] The step of truncating the recorded image charge / current signal suitably selects a sub-portion / time interval such that the length of the truncated signal is an integer multiple of the period of the ion oscillation, the period being determined according to the frequency of the ion oscillation. The truncation may provide a sub-portion / time interval of the recorded image charge / current signal starting at approximately the recorded start time of the recorded image charge / current signal and ending at a recorded time prior to the recorded end time of the recorded image charge / current signal. This arrangement may be appropriate in the case where one or more ions are injected from an ion trap or ion guide into an ion analyzer and may undergo oscillatory motion upon entering the ion analyzer. The invention may include an apparatus comprising an ion analyzer as described herein and an ion trap or ion guide configured for this purpose to inject ions into the ion analyzer. Alternatively, the truncation may provide a sub-portion / time interval of the recorded image charge / current signal starting at a recorded time after the recorded start time of the recorded image charge / current signal and ending at a recorded time prior to the recorded end time of the recorded image charge / current signal. This alternative may be appropriate in cases where one or more ions are generated in the ion analyzer (e.g. by collision with other ions, atoms or molecules) and undergo oscillatory motion only once recording of the image charge / current signal has begun. Preferably, the truncation selects a sub-portion / time interval of the recorded image charge / current signal in which there is a series of repeating signal peaks, each having peak signal values ​​that are approximately equal to each other, or each having peak signal values ​​that deviate by no more than about 20% from the maximum peak value (e.g. magnitude). Preferably, the deviation is no more than about 15%, or no more than about 10%, or no more than about 5% from the maximum peak value (e.g. magnitude).

[0035] Thus, a suitable selection of the sub-portion / time interval can be such that the truncated signal consists mainly or almost entirely of that part of the recorded image charge / current signal which corresponds to a "stable" ion oscillation signal. In other words, the recorded image charge / current signal will contain a sub-portion / time interval in which there are "strong" and "stable" recurring signal peaks with substantially the same amplitude (and often substantially the same shape / structure) indicative of stable ion oscillations. However, the recorded image charge / current signal will also contain one or more sub-portions / time intervals, sometimes near the beginning and certainly near the end of the recorded image charge / current signal, in which there are successive signal peaks with different amplitudes and shapes, often with varying amplitudes (e.g. lowering) and widths (e.g. widening). These are indicative of unstable ion oscillations and are not suitable for use in the accurate calculation of a value representative of the charge of an ion undergoing oscillatory motion in an ion analyzer. This can be avoided in the present invention by a suitable selection of the sub-portion / time interval for providing the truncated signal.

[0036] The step of truncating the recorded signal comprises: generating a transformed recorded signal by transforming the recorded time domain signal into a frequency domain (e.g., by a Fourier transform); selecting a peak value of the converted record signal from within a signal peak of the converted record signal that corresponds to a frequency domain harmonic content of the recorded signal; selecting a first adjacent value of the transformed recorded signal that is within the signal peak and corresponds to a frequency that is lower than a frequency associated with the peak value; selecting a second adjacent value of the transformed recorded signal that is within the signal peak and corresponds to a frequency higher than the frequency associated with the peak value; reconstructing a time domain signal based on the selected peak value, the selected first neighboring value, and the selected second neighboring value; determining a threshold time at which the amplitude modulation falls below a signal threshold within the reconstructing the time domain signal; truncating said recorded signal according to the threshold time thus determined. It may include:

[0037] The signal threshold may be a signal value corresponding to at least 80% of the maximum amplitude modulation (e.g., the amplitude of the modulation envelope). Preferably, the signal threshold is at least 85%, or at least 90%, or at least 95% of the maximum amplitude modulation (e.g., the amplitude of the modulation envelope). A user may empirically determine a suitable signal threshold within these limits.

[0038] The frequency (ω Peak ) is preferably selected to be as close as possible to the frequency of the harmonic associated with a given signal peak of the converted recorded signal (i.e., ω1 is the fundamental frequency [first harmonic], N is an integer, and ω Peak =ω N=Nω1). It may be selected simply by selecting a signal maximum within a given signal peak of the converted recorded signal, since that maximum tends to be at the frequency of the harmonic of interest. It has been found that the third harmonic of the frequency domain harmonic components of the recorded signal is particularly suitable to be used as the harmonic from which the selected peak value, the selected first adjacent value and the selected second adjacent value are obtained. However, frequency domain signal peaks corresponding to harmonics other than the third harmonic may also be used if empirically found to be more suitable, since this may depend on the shape of the time domain signal, which may depend on the geometry of the ion analyzer. In addition, it has been found that the signal to noise ratio (S / N) of the frequency domain peak becomes increasingly worse (i.e., decreases) as the harmonic order increases. Ultimately, a practical and appropriate choice can be made by the user by balancing these cost / benefit factors. It has been found that the third harmonic (or other, e.g. adjacent, harmonics depending on the circumstances) has the combined advantage of having sufficient strength, a narrow spectral profile shape, being relatively free of interference from other harmonic components, and also corresponding to a frequency (ω3=3ω1, where ω1 is the fundamental frequency [first harmonic]) such that the rate of variation / slope / drop of the amplitude modulation shape is appropriate within the reconstructed time domain signal used to provide the threshold in the signal truncation process.

[0039] The first neighboring value is the frequency (ω Peak ) by an amount not exceeding half the full width at half maximum (FWHM) of a given signal peak of the converted recording signal (Δω FA ) lower frequency (ω FA ) (i.e., Δω FA Let ω be the frequency difference. FA =ω Peak -Δω FA The second adjacent value is the frequency (ω Peak ) by an amount not exceeding half the full width at half maximum (FWHM) of a given signal peak of the converted recording signal (Δω SA) higher frequency (ω SA ) (i.e., Δω SA Let ω be the frequency difference. SA =ω Peak +Δω SA ). This of course assumes that a given signal peak in the transformed recorded signal can be resolved into a peak structure with a recognizable width within the frequency resolution (bin size) of the frequency domain representation being used.

[0040] Preferably, Δω FA = Δω SA It is.

[0041] Reconstructing a time domain signal based on one or more selected frequency domain harmonic components of the truncated signal may include computing a time domain signal using an inverse transform (e.g., an inverse Fourier transform) of a frequency domain transform applied to the truncated time domain signal to generate the frequency domain harmonic components of the truncated signal. For example, the method may include computing a Fourier transform of a truncated time domain signal to generate the frequency domain harmonic components of the truncated signal, and then applying the inverse Fourier transform in reconstructing a time domain signal based on one or more selected frequency domain harmonic components of the truncated signal.

[0042] For example, the method may include calculating a Fourier transform of the truncated time domain signal and selecting at least one value (e.g., a single point) of the signal present at each of a plurality of (e.g., each of) the harmonic peaks in the transformed truncated time domain signal. The invention may include reconstructing the time domain signal in the time domain (i.e., representing a "cleaned" version of the image charge signal) using the selected values ​​of the transformed truncated time domain signal. As described above, by appropriately selecting a sub-portion / time interval for providing the truncated signal, the invention may thus provide a "cleaner" time domain signal (e.g., in the Fourier spectrum) that is better representative of ions in oscillatory motion, is less contaminated by other harmonic components resulting from the presence and interference of other ions in the ion analyzer, and is less corrupted by noise (i.e., has a higher signal-to-noise ratio).

[0043] In the method, the step of selecting one or more values ​​of the frequency domain signal comprises: N distinct values ​​(OP n , where n=1 to N, and N≧M) from a plurality of distinct adjacent signal peaks of the frequency domain signal that include a signal peak corresponding to an ion of interest; and α nm is the coefficient, TP m where M is the correction value among the selected N distinct values ​​of the frequency domain signal.

number

number

number

number

[0044] For example, more than one signal value can be selected within any signal "peak" (i.e., multiple distinct values ​​from within the same given "peak" structure). This results in a greater number of signal values ​​than there are signal "peak" structures, i.e., the number of ions that give rise to those "peak" structures. As an example, consider a spectrum that shows two adjacent "peaks" in the spectrum. Two distinct signal values ​​(OP1 and OP2) can be selected from different locations within the same peak for one of the two peaks, and a third signal value (OP3) can be selected from the second "peak".

[0045] This is a 3-by-3 matrix like this:

number

number

[0046] As a further example, situations can arise where there are more signal "peaks" present than there are ions that produce them. As an example, consider the case where a spectrum shows three adjacent "peaks" in the spectrum, but there are only two ions (ion#1 and ion#2) present in the instrument. The first peak (OP1) is produced by ion#1, the second peak (OP2) by ion#2, but an apparent third peak (OP3) may simply be produced by the superposition of a sidelobe of peak OP1 with a sidelobe of peak OP2. This may be "mistaken" for a peak due to ion#3, which does not exist.

[0047] This is a 3-by-3 matrix like this:

number

number

[0048] For example, several selections / points (OP n ) can be performed for any number of two or more peaks that may be present in the signal spectrum, but most preferably for a selection / point (OP n ) should be taken from two or more peaks in the spectrum.

[0049] Preferably, the value of N in the matrix equation should be greater than the value of M. It has been found that in this way, the solution of the matrix equation becomes more stable due to the greater number of equations than unknowns. Preferably, at least one or more of the selected N distinct values ​​of the frequency domain signal correspond to adjacent signal peaks at frequencies that are not harmonic frequencies of the ions of interest (i.e., ions whose charge is to be measured). For example, at least one of the selected N distinct values ​​of the frequency domain signal corresponds to a spectral peak at a frequency that is a harmonic frequency of a non-target ion that may, for example, spectrally interfere with the spectral peak of the ions of interest. This may occur due to partial overlap of the spectral peak of the ions of interest with a portion of the frequency domain signal components (e.g., side lobes, etc.) associated with the adjacent spectral peak of the non-target ion. Thus, the selected N distinct values ​​of the frequency domain signal most preferably include values ​​associated with adjacent spectral peaks that may (e.g., are highly likely to) interfere with (e.g., have spectral leakage) the spectral peak of the ions of interest.

[0050] For example, OP1 can be the value of the frequency domain signal that corresponds to a frequency that is a harmonic of the motion of the ion of interest (e.g., the value "observed" as the maximum value within the shape of a signal "peak" that corresponds to a certain harmonic, where "OP" stands for "Observed Peak"). For example, OP mEach of m>1 may be a value of the frequency domain signal corresponding to a frequency that is a harmonic of the motion of another respective ion that is not the ion of interest (e.g., a value "observed" as the maximum value within the signal "peak" shape corresponding to a certain harmonic, where "OP" stands for "Observed Peak"). In this way, the motions of all ions contributing to the signal associated with a given harmonic of the ion of interest result in said selected distinct values ​​of the frequency domain signal (OP n ) contributions made to each of the nm ) is prepared. By solving this set of equations, a corrected value (TP1) of the frequency domain signal associated with a given harmonic of the target ion can be obtained (e.g., a value corrected to be considered as the "true" value for the "peak" shape caused by the target ion, where "TP" stands for "True Peak"), where the contributions from the motion of all other ions contributing to the signal have been removed. Also, a corrected value TP1 of the frequency domain signal associated with a given harmonic of a non-target ion can be obtained. m (where m>1), in which the contributions from the motion of all other ions contributing to the signal (including the motion of the ion of interest) have been removed.

[0051] As an example, if three (or more) distinct values ​​of the frequency domain signal are selected, each corresponding to one of three (N=3) adjacent signal peaks at each frequency that is a harmonic frequency of one ion that contributes to the overall signal (i.e., the ion of interest and two other non-target ions), the equation can be expressed as follows:

number

number

[0052] By solving this set of simultaneous equations for TP1, TP2, TP3, a correction value (e.g., TP1 for the ion of interest) for any one of the values ​​of the frequency domain signal used in the step of reconstructing the time domain signal is obtained based on one or more selected frequency domain harmonic components of the truncated signal (e.g., the "true peak" of the ion of interest), as described above. The same procedure can be applied to each value of the frequency domain signal used in the step of reconstructing the time domain signal, so that the correction value is used in the step of reconstructing the time domain signal.

[0053] A frequency domain signal can be derived from a time domain signal by applying a frequency domain transform (e.g. a Fourier transform), where the transformed signal is represented as a complex number. A complex number has a magnitude and a phase that are expressed in the complex (Argand) plane. A complex number has real and imaginary components. The magnitude is given by the sum of the squares of the real component and the imaginary component. The phase is given by the arctangent of the ratio of the real and imaginary components.

[0054] The values ​​of the frequency domain signal used in the step of reconstructing the time domain signal may be complex numbers representing the transformed signal. For example, the selected N distinct values ​​(OP n ) may each be a complex number. For example, the corrected M distinct values ​​of the frequency domain signal (TP m ) can each be a complex number. nm ) can be complex numbers. By considering the phase of these complex coefficients, the corrected M distinct values ​​of the frequency domain signal (TP m ) can be made more accurate. Once the solution TP (a complex number) is found, the "magnitude" = √({Re[TP]} 2+{Im[TP]} 2 ) can be calculated. This calculation can be done at several points for each harmonic of each peak.

[0055] The ion analysis device may be configured to generate ions, the ion analysis chamber may be configured to trap ions, cause the trapped ions to undergo oscillatory motion, and acquire a plurality of image charge / current signals representative of the trapped ions in oscillatory motion with at least one image charge / current detector.

[0056] The ion analysis chamber may include any one or more of an ion cyclotron resonance trap, an Orbitrap® configured to use a hyper-logarithmic electric field to trap ions, an electrostatic linear ion trap (ELIT), a quadrupole ion trap, an ion mobility analyzer, a charge detection mass spectrometer (CDMS), an electrostatic ion beam trap (EIBT), an orbital frequency analyzer (OFA), and a planar electrostatic ion trap (PEIT) to generate the oscillatory motion therein.

[0057] In another aspect, the invention may provide a computer readable medium comprising computer executable instructions configured to cause a mass spectrometer to perform a method as described above, the method comprising processing a plurality of image charge / current signals representative of trapped ions undergoing oscillatory motion, wherein the signal processing unit may comprise a processor or computer programmed or programmable (e.g. comprising a computer readable medium containing a computer program) to execute the computer executable instructions.

[0058] As used herein, the term "peak" as a noun may be understood to include a reference to a prominent, pointed portion, shape or structure (e.g., in a signal), or the highest area, point, value or level (e.g., in a signal).

[0059] As used herein, the term "recording" as a verb may be understood to include a reference to contemporaneously recording a signal as it is generated, and may also be understood to include a reference to recording data representative of a signal, for example by recording / making a copy of such pre-recorded data, or to obtaining such a recording. As a noun, the term "recording" may be understood to include a reference to the result of the act of "recording."

[0060] As used herein, the term "time domain" may be considered to include reference to time being considered as an independent variable in the analysis or measurement of time-dependent phenomena. As used herein, the term "frequency domain" may be considered to include reference to frequency being considered as an independent variable in the analysis or measurement of time-dependent phenomena.

[0061] As used herein, the term "periodic" may be considered to include a reference to a phenomenon that appears or occurs at intervals (e.g., a transient or peak or pulse in a signal). The term "period" includes a reference to a time interval during which successive identical or nearly identical events or conditions occur in an oscillatory or periodic phenomenon.

[0062] The term "segmenting" as a gerund can be understood to include a reference to dividing something into separate parts or intervals. The term "segment" as a noun can include a reference to each of multiple parts into which something is or could be divided.

[0063] The term "co-registering" as a gerund may be considered to include a reference to the process of lining up two or more items together within a domain (e.g., the time domain) in which both items are represented or defined. This process may involve designating one item as a reference item and applying a geometric transformation, coordinate transformation, or local translation, or a numerical / mathematical constraint within the domain, to the other item so that it aligns with the reference item.

[0064] Combinations of the described aspects and preferred features are encompassed by the invention unless such combinations are expressly impermissible or explicitly avoided. [Brief description of the drawings]

[0065] BRIEF DESCRIPTION OF THE DRAWINGS Embodiments and experiments illustrating the principles of the present invention are discussed below with reference to the accompanying drawings.

[0066] [Figure 1a] FIG. 1 shows the theoretical shape of a STORI plot according to the prior art. [Figure 1b] Figure 1 shows several STORI plots from simulations. [Figure 2a] FIG. 1 illustrates an ion analyzer according to an embodiment of the present invention. [Figure 2b] FIG. 2 shows an image charge / current signal generated by an ion analysis device, including a number of pulses in the image charge / current signal forming a periodic succession of repetitive signal pulses having a repetition period T. [Figure 2c] FIG. 2 shows a schematic representation of a two-dimensional function comprising a stack of segmented portions of an image charge / current signal representing the oscillatory motion of one or more ions within an ion analyzer. [Figure 2d] FIG. 2c shows a schematic representation of an image charge / current signal as shown in FIG. 2c, where a segmentation process has been applied. [Figure 2e](1) and (2) an image charge / current signal generated by an ion analyzer corresponding to FIG. 2a, including multiple portions of the same image charge / current signal of duration T (seconds) comprising a periodic succession of repetitive signal pulses with repetition period T, the multiple portions being superimposed so as to be aligned with each other at the same interval on the time axis (from t=0 to t=T) when viewed from the perspective of FIG. 2b, and stacked in alignment along the dimension perpendicular to the time axis so as to be aligned with each other when viewed from the perspective of FIG. 2c. [Diagram 3] FIG. 13 shows the frequency spectrum of the recorded image charge / current signal, which contains a series of spectral peaks located at frequency harmonics. [Figure 4] FIG. 4 shows an image charge / current signal reconstructed using three values ​​selected from within the third harmonic (H3) peak in the frequency spectrum of FIG. 3, and an estimate from the reconstructed signal of the lifetime of the ion that gave rise to the original signal. [Diagram 5] FIG. 5 shows the image charge / current signal being truncated based on the lifetime estimates of the ions shown in FIG. 4. [Figure 6] FIG. 6 shows the frequency spectrum of the truncated recorded image charge / current signal, which has been truncated as shown in FIG. 5 and which includes a series of spectral peaks located at frequency harmonics. [Figure 7] FIG. 7 shows an image charge / current signal reconstructed using values ​​selected from among a number of spectral peaks located at frequency harmonics (H1', H2', H3') in the frequency spectrum of FIG. 6, which includes a periodic series of repetitive signal pulses having a repetition period T. Also shown is the (non-reconstructed) image charge / current signal from which the reconstructed signal is derived. [Figure 8] A diagram showing the frequency spectrum of a recorded image charge / current signal containing a series of spectral peaks located at frequency harmonics (H1, ..., Hi) caused by the vibrational motion of a target ion, each peak surrounded by a number of adjacent lower harmonic spectral peaks caused by the vibrational motion of other non-target ions. [Figure 9] 1 shows a section of the frequency spectrum of a recorded image charge / current signal containing a cluster of three spectral peaks located at frequency harmonics among a series of further spectral peaks (not shown) caused by the vibrational motion of the ion of interest. The cluster includes the main (target) harmonic spectral peak and two lower adjacent spectral peaks located at frequency harmonics caused by the vibrational motion of other non-target ions. Three simultaneous equations relating the three spectral peaks are also shown. [Figure 10] FIG. 2b illustrates a method according to an embodiment of the invention that can be performed on an ion analyzer according to FIG. 2a. [Figure 11] Schematic of a recorded image charge / current signal of complete duration TR, consisting of a pure sinusoidal oscillatory signal of lifetime LT. [Figure 12] Schematic diagram of frequency bins in the Fourier transform spectrum of the recorded image charge / current signal, before and after signal truncation. [Figure 13] Schematic of three different recorded image charge / current signals of different durations associated with different ions. [Figure 14] A diagram showing the actual recorded image charge / current signal. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0067] BRIEF DESCRIPTION OF THE DRAWINGS Aspects and embodiments of the present invention are discussed below with reference to the accompanying drawings. Further aspects and embodiments will be apparent to those skilled in the art. All documents mentioned in this document are incorporated herein by reference.

[0068] Each feature disclosed in the foregoing description, the following claims, or the accompanying drawings may, where appropriate, be expressed in its specific form or in terms of a means for performing a disclosed function or a method or process for obtaining a disclosed result, but the features may be utilized individually or in any combination of several features to realize the invention in various of its forms.

[0069] Although the present invention has been described in connection with exemplary embodiments, many equivalent modifications and variations will be apparent to those skilled in the art in view of the present disclosure. Accordingly, the exemplary embodiments of the present invention described above should be considered as illustrative and not restrictive. Various changes can be made to the embodiments without departing from the spirit and scope of the present invention.

[0070] For the avoidance of doubt, any theoretical explanations provided herein are intended to enhance the understanding of the reader, and the inventors do not wish to be bound by any of these theoretical explanations.

[0071] The headings used herein are for organizational purposes only and should not be construed as limiting the subject matter described.

[0072] Throughout this specification, including the claims which follow, the words "comprise" and "include", and variations thereof (such as "comprises", "comprising", "including", etc.), unless the context otherwise requires, shall be interpreted as meaning the inclusion of stated integers or steps or groups of integers or steps, but not the exclusion of other integers or steps or groups of integers or steps.

[0073] As used herein and in the appended claims, the singular forms "a," "an," and "the" include the plural referents unless the context clearly dictates otherwise. When expressing a range in this specification, a particular value as the beginning and / or another particular value as the end may be used as the beginning and / or the other particular value as the end, respectively. When such a range is expressed, the range in which the particular value is the very beginning and / or the other particular value is the very end is another embodiment. Similarly, when values ​​are expressed as approximations by use of the antecedent "about," it should be understood that the particular values ​​form another embodiment. The relationship between the term "about" and the numerical values ​​is arbitrary, and may mean, for example, ±10%.

[0074] For consistency, the same reference numerals are used in each figure to refer to the same parts.

[0075] Figure 2a shows a schematic of an ion analysis apparatus in the form of an electrostatic ion trap 80 for mass spectrometry. The electrostatic ion trap includes an ion analysis chamber (81, 82, 83, 84) configured to receive one or more ions 85A and generate an image charge / current signal in response to the vibrational motion 86B of the received ions 85B while in the ion analysis chamber. The ion analysis chamber comprises a first electrode array 81 and a second electrode array 82 spaced a substantially fixed distance from the first electrode array.

[0076] A voltage supply unit (not shown) is arranged to supply a voltage to each of the electrodes of the first and second electrode arrays in use to create an electrostatic field in the space between the electrode arrays. The electrodes of the first array and the electrodes of the second array are supplied with substantially the same pattern of voltages from the voltage supply unit, such that the potential distribution in the space between the first and second electrode arrays (81, 82) is such as to reflect ions 85B in the flight direction 86B and cause the ions to undergo a periodic oscillatory motion in the space. The electrostatic ion trap 80 can be constructed, for example, as described in US Pat. No. 5,399,363 (Ding et al.), which is incorporated herein by reference in its entirety. Other arrangements are possible and will be readily apparent to those skilled in the art.

[0077] The periodic oscillatory motion of ion 85B in the space between the first and second electrode arrays can be focused, for example, approximately midway between the first and second electrode arrays, as described in U.S. Patent No. 5,399,993 (Ding et al.) by application of appropriate voltages to the first and second electrode arrays. Other arrangements are possible and would be readily apparent to one skilled in the art.

[0078] One or more electrodes of each of the first and second electrode arrays are configured as image charge / current sensor electrodes 87 and as such are connected to a signal recording unit 89 configured to receive an image charge / current signal 88 from the sensor electrodes and record the received image charge / current signal in the time domain. The signal recording unit 89 may comprise amplification circuitry as required for detection of an image charge / current having a periodic / frequency component related to the mass-to-charge ratio of ions 85B undergoing said periodic oscillatory motion 86B in the space between the first and second electrode arrays (81, 82).

[0079] The first and second electrode arrays may be, for example, as described in U.S. Patent No. 5,399,933 (Ding et al.) (a) parallel strip electrodes, and / or (b) Concentric, circular, or part-circular conductive rings The electrostatic ion trap may comprise a planar array formed by a first and second electrode array. Other arrangements are possible and will be readily apparent to one skilled in the art. Each of the first and second electrode arrays extends in the direction of the periodic oscillatory motion 86B of the ions 85B. The ion analysis chamber comprises a main segment defined by the first and second electrode arrays and a space therebetween, and two end electrodes (83, 84). A voltage difference applied between the main segment and each end segment forms a potential barrier to reflect the ions 85B in the direction of the oscillatory motion 86B, thereby trapping the ions in the space between the first and second electrode arrays. The electrostatic ion trap may include an ion source (not shown, e.g., an ion trap) configured to temporarily store ions 85A outside the ion analysis chamber and then inject the stored ions 80A into the space between the first and second electrode arrays through an ion injection aperture formed in one 83 of the two end electrodes (83, 84). For example, the ion source may include a pulser (not shown) for injecting ions into a space between first and second electrode arrays, as described in U.S. Patent No. 5,399,323 (Ding et al.). Other arrangements are possible and would be readily apparent to one skilled in the art.

[0080] The ion analyzer 80 further includes a signal processing unit 91 which receives the recorded image charge / current signal 90 from the signal recording unit 89 and processes the recorded signal to: (a) determining a period (T) of a periodic signal component in the recorded signal; (b) providing a truncated signal having a duration approximately equal to an integer multiple of said period; (c) reconstructing a time domain signal based on the frequency domain harmonic components of the truncated signal; (d) determining the magnitude of the reconstructed time domain signal and using it to calculate the charge of ions undergoing oscillatory motion within the ion analyzer;

[0081] The time domain magnitude values, which represent the charge of the ions of interest, are multiplied by a normalization or calibration constant or term according to a normalization / calibration procedure readily understood by one of skill in the art, e.g., which characterizes the proportional relationship between the magnitude values ​​and their corresponding ion charge q in terms of the "weight field" described above, and then multiplied by a selected correction value for the frequency domain peak (TP m ) as a magnitude value derived using the signal processing steps performed by a signal processing unit 91 and described in more detail below. The signal processing unit 91 comprises a processor or computer programmed to execute computer program instructions to perform the above signal processing steps on the image charge / current signal representative of the trapped ions undergoing oscillatory motion. The result is a value representative of the charge of the ions. The ion analyzer 80 further comprises a storage and / or display unit 93 configured to receive data 92 corresponding to the charge of the ions and to indicate the measured charge value to a user and / or store the value in a storage unit.

[0082] FIG. 2b shows a schematic diagram of a recorded image charge / current signal generated by the ion analyzer of FIG. 2a. This signal consists of a "transient" of the acquired signal that can be observed to be present typically for about 1 second or less. This occurs when ions undergo oscillatory motion within the ion analyzer (e.g. an ion trap) and, in so doing, induce an image charge / current signal that is detectable by a sensor electrode of the apparatus configured for detection of the image charge / current signal. The recorded image charge / current signal comprises a number of pulses in the image charge / current signal that constitute a periodic succession of repetitive signal pulses with a repetition period T. This one-dimensional time-domain image charge / current signal is generated by the ion analyzer 80 of FIG. 2a. It corresponds to the recorded image charge / current signal that the signal processor 91 receives from the signal recording unit 89 and is representative of the oscillatory motion of one or more ions within the ion analyzer. This signal is a regularly spaced sequence of short but intense image charge / current signal pulses (such as "7", including 7a, 7b, 7c, 7d, 7e, 7f, 7g, ... and "8") separated from each other by noise-only intermediate intervals in which there are no discernible transient signal pulses. Each signal pulse corresponds to a brief period during which an ion 85B or group of ions passes momentarily between two opposing image charge / current sensor electrodes 87 of the electrostatic ion trap 80 during the ion's oscillatory motion within the ion.

[0083] The period of an oscillation is by definition the time interval between two reflections, i.e. the two states where the ion's kinetic energy is a minimum and its potential energy is a maximum. In a symmetric system the period of the ion's oscillation can be considered as the signal period.

[0084] A first pulse (7a) is generated as ion 85B passes sensor electrode 87 from left to right during the first half of one cycle of its oscillatory motion within the electrostatic trap, and a second pulse (7b) is generated as the ion passes sensor electrode 87 again during the second half of the same cycle, this time from right to left. Subsequent signal pulses (7c, 7d) are generated during the second cycle of the oscillatory motion. A next signal pulse (7e) is generated during the first half of a third cycle of the oscillatory motion, followed by further pulses as the cycles of oscillatory motion continue one after the other.

[0085] Each successive signal pulse is separated in the time domain (i.e., along the time axis (t) of the signal) from its nearest neighbor by a common time period T. T corresponds to the period of a virtually periodic signal that persists as long as the oscillatory motion of the ions persists within the electrostatic ion trap. Thus, the periodicity of the periodic signal is related to the period of the periodic, cyclical motion of the ions within the electrostatic ion trap 80, as described above. Thus, the existence of this common time period (T) identifies the succession of pulses (7, 8) as a "periodic component" of the image charge / current signal. Given that the common time period T necessarily corresponds to a frequency (i.e., the reciprocal of the common time period), this "periodic component" can also be referred to as a "frequency component." The signal can be harmonic or non-harmonic, depending on the nature of the periodic oscillatory motion of the ions. Such a signal can be harmonic in the sense that it has a sinusoidal waveform. Otherwise it is non-harmonic, which means that it has one or more sizable frequency components (eg, other higher harmonic frequency components, or non-harmonic frequency components) in addition to the fundamental component.

[0086] The following method calculates the period T and lifetime T of the periodic component in the recorded image charge signal. LT is an example of one possible way to determine the lifetime of the vibrational motion of an ion. However, other methods readily apparent to those skilled in the art may be used to determine the lifetime of the vibrational motion of an ion, such as, for example, the Short-Time Fourier Transform (STFT) or the STORI method described above.

[0087] Fig. 2c is a schematic representation of a two-dimensional function F2(t1,t2) including a stack of segmented portions of the image charge / current signal F1(t) as shown diagrammatically in Fig. 2b. This is an example of a two-dimensional function defined by data 92 generated by a signal processor 91 and output to a display unit 93. The signal processor 91 is configured to determine a period value (T) of the periodic components (7a, 7b, 7c, 7d, 7e, etc.) in the image charge / current signal F1(t) and to divide the image charge / current signal F1(t) into a number of distinct and consecutive time segments of duration corresponding to the determined period. The signal processor is then configured to align the distinct time segments in a first time dimension t1 that defines the determined period (T). The signal processor 91 then separates the aligned time segments along a second time dimension t2 that intersects (e.g. is orthogonal to) the first time dimension. The result is a stack of distinct and consecutive time segments aligned along the second time dimension. Collectively, this sequence of aligned time segments defines a two-dimensional function F2(t1,t2) that varies with time within the determined period T across the width of the stack in a first time dimension t1, and varies with time between successive time segments along the length of the stack in a second time dimension t2.

[0088] Referring to FIG. 2c, the period T of the periodic component is determined to be T=4.5 μsec, and the continuous one-dimensional image charge / current signal is divided into a number of time segments (7A, 7B, 7C, 7D, 7E, etc.) each having a duration of 4.5 μsec. Each of the time segments of the plurality of time segments is aligned with each of the other time segments of the plurality of time segments. This means that the first time segment 7A is selected to be the reference time segment, with respect to which all other time segments are aligned. To achieve this alignment, a step is performed in which the recorded signal is divided into a number of separate time segments by subjecting the time coordinates of each signal data value / point in a given time segment other than the "reference" time segment (i.e., the first time dimension t1) to a one-dimensional time (t) to two-dimensional time (t1, t2) transformation as follows: The result is a transformation of a one-dimensional function F1(t) into a two-dimensional function F2(t1, t2) by the following relationship:

number

number

[0089] In other words, these constraints allow for segmentation such that every distinct value of the integer m defines a new segment and a step along the second time dimension t2. Each segment has a duration only in the range t1=0 to t1=T in the first time dimension t1. This also means that the start of each segment shares the same value of the continuous time variable t1 (i.e. t1=0) with the start of all other segments, but has a unique value of time t2 in the second time dimension. Similarly, this also means that the end of each segment shares the same value of the continuous time variable t1 (i.e. t1=T) with the end of all other segments, but has a unique value of t2 in the second time dimension. In this sense, the different segments are "aligned" (i.e. aligned in time) with each other in the two-dimensional space of the two-dimensional function F2(t1,t2). Of course, it should be understood that the values ​​of the image charge / current signal actually sampled are discrete values ​​sampled at a finite number of discrete time instants within the continuous time interval [0;T]. This means that the actual measured signal values ​​may or may not be present at the exact times t1=0, t1=T during each segment (depending on the sampling rate etc.).

[0090] For example, the step of dividing the recorded signal into a number of distinct time segments may include converting a one-dimensional function F1(t) into a two-dimensional function F2(t1, t2) by the following relationship:

number

number

[0091] The result is equivalent to a common time shift or translation (schematically represented by reference number 25 in FIG. 2c) in the negative time direction along the first time dimension, which is sufficient to ensure that the translated time segments start (21, 23, ... etc.) at time t1 = 0 and end (22, 24, ... etc.) at time t1 = T = 4.5 μs. As a result, each time segment (7A, 7B, 7C, 7D, 7E ... etc.) undergoes its own appropriate time translation (see reference number 25 in FIG. 2c), which is sufficient to ensure that all time segments extend only within the time interval [0; T] along the first time dimension.

[0092] It is important to note that this alignment process applies to the entire time segment, and not to the positions of the transient signal pulses (7a, 7b, 7c, 7d, 7e, ... etc.) appearing in successive time segments. However, if the time period T of the periodic signal components is accurately determined, the alignment of the time segments will result in the transient signal pulses being aligned as well, and the positions of successive transient pulses along the first time dimension will not change from one aligned time segment to the next. This is the case in the schematic diagram of Fig. 2c, where it can be seen that the transient signal pulses are aligned along straight paths parallel to the axis of the second time dimension.

[0093] Conversely, if the time period T of the periodic signal component is not accurately determined, alignment of the time segments will not result in the transient signal pulses being aligned as well, and the positions of successive transient pulses along the first time dimension will change / drift from one aligned time segment to the next.

[0094] The signal processor 91 then shifts or translates each of the aligned time segments along a second time dimension t2 that intersects (e.g., is orthogonal to) the first time dimension. Specifically, each signal data value / point in a given time segment other than the "reference" time segment is assigned an additional coordinate data value so that each signal data point has three numbers: a signal value, a time value in the first time dimension, and a value in the second time dimension. The values ​​of the first and second time dimensions define a coordinate in the two-dimensional time plane for a given signal data point, and the signal value associated with that data point defines the value of the signal at that coordinate. In the example shown in FIG. 2c, the signal value is represented by the "height" of the data point above the two-dimensional time plane.

[0095] The time shift or translation applied along the second time dimension is sufficient to ensure that each translated time segment is separated by the same shift / spacing from its two immediately adjacent aligned time segments, i.e., the previous and next time segments. This results in a stack of separate consecutive time segments aligned along the second time dimension, which collectively define a two-dimensional function F2(t1,t2) as shown in FIG. 2c. This function varies across the width of the stack in the first time dimension t1 to indicate the position and shape of the transient signal pulse in time [0;T], and along the length of the stack in the second time dimension t2 according to the time between consecutive time periods, or stack segment number. Since the time interval between the start of the nth and n+1th stacks, or between any two points with the same coordinate in the first time dimension, is necessarily equal to the time period T, consecutive time segments are inherently separated by a time interval of T seconds (e.g., 4.5 μsec in the example of FIG. 2c) along the second time dimension.

[0096] Fig. 2d shows a schematic representation of a procedure for determining the value T of the period of the periodic signal component in the image charge / current signal F1(t) in a manner that generates a two-dimensional function F(t1,t2). The first step of the method is to generate the image charge / current signal and to record it in the time domain.

[0097] The acquired one-dimensional time-domain image charge / current signal record, i.e. F1(t) in Fig. 2d, contains one or more periodic oscillations, which may correspond to frequency components f1=1 / T1, f2=1 / T2, ...

[0098] The next step of the method then consists in determining the period (T) of the periodic signal components in the recorded signal, which may comprise the following sub-steps: (1) The first sub-step is to sample the one-dimensional time-domain signal F1(t) of FIG. 2d with a sampling step of size δt. (2) The second sub-step is to calculate the time period T of each of the periodic / frequency components f1=1 / T1, f2=1 / T2, etc. i (i=1,2,...) values. This may be done using any suitable spectral decomposition method that will be readily apparent to one skilled in the art, or simply by first guessing their values ​​and applying the method iteratively until a consistent result is found. (3) The third sub-step divides the one-dimensional signal F1(t) into segments and extracts selected period (frequency) values ​​f i =1 / T i The goal of the method is to create a two-dimensional function F(t1,t2) by aligning the time segments according to. Specifically, the variable t1 starts at t1=0 (zero) and increases along the t1 axis by a step size δt for each subsequent sampling step. Initially, the variable t2=0 during this process. When a time is reached where t1 is equal to or greater than T, the variable t1 is reset to t1=0 (zero) and the variable t2 is increased by the step size T, i.e., t2=T. Thus, each sampling point of the measured signal is assigned a pair of values ​​(t1,t2). In this way, a two-dimensional mesh / plane (t1,t2) is formed. This constitutes a "separation" of the aligned time segments along the second time dimension t2 that intersects with the first time dimension, thereby creating a stack of time segments that together define a two-dimensional function. The resulting function F2(t1,t2) can be considered as a set of layers F(t1). Here, t1 always lies in the interval [0;T], and each layer corresponds to some t2 that has a constant value (an integer multiple of T) within that layer. (4) The first optional fourth sub-step is to produce a first 2D scatter plot of F(t1,t2 = fixed), i.e. F2(t1,t2) along "view (a)" of Fig. 2c ignoring the variation of t2 values, such that all layers are visible overlapping. For an appropriate choice of the segment period T, peaks become visible above the noise region, as shown in Fig. 2e(1). (5) The fourth sub-step by the second option is to create a second two-dimensional scatter plot corresponding to F2(t1, t2) as viewed along "View (b)" in FIG. 2c. This shows F2(t1, t2) under the condition that, with a predetermined threshold value (for example, a predetermined signal level) being C, if |F2(t1, t2)| < C, the point (t2; t1) is plotted, and otherwise it is skipped / omitted from the plot. For an appropriate selection of the segment period T, an empty channel of width Δt1 where there are substantially no data points in FIG. 2e(2) appears to be surrounded / bounded by points and extend along a path parallel to the t2 axis as shown in FIG. 2e(2). It should be understood that the condition |F2(t1, t2)| > C is also possible, and in this case, "clogged" channels surrounded by empty spaces are formed in the two-dimensional space.

[0099] Procedures (4) and / or (5) can be used to iteratively arrive at a value for the period T to determine whether the selected period value corresponds to a frequency component of the signal F1(t). This determination can be based on any criteria. For example, according to method step (4), if the plot of F2(t1,t2) contains peak-like dense regions, this is classified as a frequency component. An example is shown in FIG. 2e(1). Alternatively or additionally, according to method step (5), if, for a predefined signal threshold level C, the representation of F2(t1,t2) contains an almost straight empty channel (6 in FIG. 2e(2)) extending along a path parallel to the t2 axis, this is classified as a frequency component. An example is shown in FIG. 2e(2). Either method provides a means of identifying when the selected segment period T (i.e. the length of each time segment) exactly matches the actual time period of a periodic component in the signal F1(t). Only then will the transient peaks of the periodic components in successive time segments "align" linearly along paths parallel to the axis of the stacking dimension (t2). If the selected segment period T does not exactly match the actual time period of the periodic components in signal F1(t), then the transient peaks of the periodic components in successive time segments will not "align" linearly along paths parallel to the axis of the stacking dimension. Instead, the peaks will drift along paths that deviate toward or away from the axis of the stacking dimension.

[0100] Non-iterative methods of frequency determination are also possible. Such methods can be faster. For example, suppose that the period of the initially determined periodic component is slightly inaccurate (i.e., T' ≠ T, but not significantly different). As a result, a linear feature appears that extends through the two-dimensional space of the two-dimensional function in a direction tilted from the second time dimension (t2 axis). The period corresponding to this signal may be determined by repeatedly re-segmenting and restacking the original one-dimensional signal until the linear feature is parallel to the t2 axis, as described above iteratively. Alternatively, the angle of inclination that the linear path of the linear feature makes with respect to the axis of the first time dimension (e.g., with respect to the t1 axis) can be determined, and the correct stacked period (i.e., T' = T) can be obtained according to this angle (i.e., the angle between the t1 axis and the direction of the linear path). The advantage is that no iterative re-segmenting and restacking needs to be performed at all, which saves a lot of computation time. Because the signal array in memory is usually very large amount of data, and accessing such an array in PC memory takes a long time, which becomes a bottleneck in processing speed. Once the tilt angle is determined, the formula to determine the correct period using the "incorrect" stacking period (T') and the tilt angle is as follows:

number

[0101] Either method, i.e., method (4) or method (5), can be performed by either an image analysis algorithm or a numerical algorithm. In such an algorithm, it is preferable to consider the density or number of data points on each representation F2(t1,t2). For example, an algorithm can be used to obtain the number of points below a predetermined threshold |F2(t1,t2)| < C within a predetermined time interval Δt1 in the first time dimension. If the density or number of data points is smaller than the threshold C, it can be used to indicate that the frequency components are properly detected. Fig. 2e(2) illustrates this method. Here, the method includes obtaining a subset of cases of the two-dimensional function such that the value of the two-dimensional function is below a predetermined threshold C. From among the subset of cases, a time interval Δt1 in the first time dimension is obtained such that the two-dimensional function never falls below the predetermined threshold. And that time interval can be identified as the position / existence of the periodic signal component.

[0102] Machine learning techniques including neural networks trained to classify images having resolved peak structures (method (4)) and / or prominent channels (method (5)) can be used in the algorithm.

[0103] Once the value of the period T is reached iteratively, the method proceeds to divide the recorded signal into a number of separate consecutive time segments having a duration corresponding to the determined period. The procedure for doing this is the same as that described in sub-step (3). Note that according to the iterative method of determining the time period T, it will be understood that sub-step (3) of the method is actually executed when performing the last successful sub-step (4) or (5) described above.

[0104] The final step of the method is to create a stack of the time segments of the previous steps in a second time dimension t2, thereby generating a stacked image charge / current signal. The procedure for doing this is the same as described in sub-step (3) of aligning separate time segments in a first time dimension t1 that defines the determined period T, and separating the aligned time segments along a second time dimension t2 that intersects the first time dimension. Again, according to the iterative method of determining the time period T, this final step is performed in the first place when performing the last successful sub-step (4) or (5) of step S3 described above.

[0105] In the method, the signal processing unit can be programmed to iteratively determine the value T of the period of the periodic signal component in this way. It can first estimate a "tentative" value of T as described above, use the "tentative" value to divide the recorded signal F1(t) into a number of time segments with durations corresponding to the "tentative" periods, align them, and then separate the aligned time segments along the second time dimension t2 to create a stack of time segments. The signal processing unit can be configured to automatically determine whether the position of the periodic component (transient peak) in the first time dimension changes along the second time dimension. If a change is detected, a new "tentative" value T is selected by the signal processing unit and a new stack of time segments is created with the new "tentative" time period. The signal processing unit then re-evaluates whether the position of the periodic component (transient peak) in the first time dimension changes along the second time dimension, and the iterative process ends when it is determined that no such change has substantially occurred. This condition means that the latest "tentative" time period T is an accurate estimate of the true time period value.

[0106] Once we have the value of the period of the oscillatory motion of the ion of interest (T), we can go ahead and truncate the recorded signal F1(t) as follows:

[0107] 3, 4 and 5, a procedure is shown for truncating a recorded signal to obtain a truncated signal having a duration approximately equal to an integer multiple (N×T) of the value (T) of the period of the oscillatory motion of the ion of interest.

[0108] Specifically, Figure 3 shows a schematic diagram of a Fourier spectrum in the frequency domain resulting from applying a Fourier transform to the recorded signal F1(t). The Fourier spectrum has several distinct spectral peaks (H1, H2, H3) that rise clearly above the background spectral signal level 60. The first peak H1 is at a lower frequency than the location of the second and third spectral peaks (H2, H3). This peak corresponds to the frequency of the first (fundamental) harmonic of the vibrational motion of the ion of interest and encompasses a narrow range of frequencies including the fundamental frequency of the vibrational motion of the ion of interest (f0 = 1 / T Hertz).

[0109] The second spectral peak H2 is intermediate in frequency between the first and third spectral peaks (H1, H3), and corresponds to the second harmonic (first overtone) frequency (2f0=2 / T Hertz) of the vibrational motion of the ion of interest, and encompasses a narrow range of frequencies including the fundamental frequency of the vibrational motion of the ion of interest.

[0110] The third spectral peak H3 is at a higher frequency beyond the location of the first and second spectral peaks (H1, H2). This peak corresponds to the third harmonic (second overtone) frequency (3f0=3 / T Hertz) of the vibrational motion of the ion of interest and encompasses a narrow range of frequencies including the fundamental frequency of the vibrational motion of the ion of interest. Other spectral peaks (not shown) are present at even higher harmonic frequencies in the Fourier spectrum. The higher harmonics are responsible for the peak shape in the time domain in the recorded signal F1(t). The decay of the signal in the time domain is characterized by the peak shape in the frequency domain.

[0111] For example, the shape of the decay of signal peak 8 in the recorded signal shown in Figure 4 or 5 is characterized by the shape of the peak in the frequency domain signal shown in Figure 3. This decay of the signal peak begins when the regular oscillatory motion of the ion of interest begins to cease and the oscillatory motion becomes more complex and corrupted with significant spectral (frequency) content that is not pure harmonics such as H1, H2, H3, etc. The "life" of the regular oscillatory motion of the ion is essentially over at that point.

[0112] The procedure of truncating the recorded signal to obtain a truncated signal aims to "clean" the recorded signal prior to subsequent analysis by removing those parts of the recorded signal that do not fall within the "lifetime" of the ion of interest.

[0113] The end of the "lifetime" of the regular oscillatory motion of the ion of interest (T Life ), in order to estimate which portion of the recorded signal F1(t) should be removed by truncation. To make this estimate, a lower portion of the recorded signal can be selected as a truncated signal, beginning at a recording time that coincides with (or is later than) the recording start time of the recorded image charge / current signal and ending at a recording time that is earlier than the recording end time of the recorded image charge / current signal.

[0114] The truncated signal may be a subportion of the recorded signal in which there is a series of repeating signal peaks, each signal peak having a peak signal value that does not deviate by more than about 20% from the value of the largest peak value in the series of repeating signal peaks.

[0115] Alternatively, the truncation of the recorded signal may comprise the following steps, which are described with reference to Figures 3 and 4. (1) First, transform the recorded signal F1(t) into the frequency domain, such as by applying a Fourier transform to the signal. This results in a spectrum such as that shown in Figure 3, thereby producing the transformed recorded signal. (2) Select a harmonic spectrum peak (e.g., H3) from within the spectrum. From within the selected harmonic peak, a. The peak value (ω) of the converted recorded signal within the selected harmonic peak Peak , for example the maximum value 62). Then, b. Within the selected harmonic peak, Δω is greater than the frequency associated with that peak. FA The first adjacent value 61 (ω FA ), then c. Within the selected harmonic peak, Δω is less than the frequency associated with that peak. SA The first frequency of the converted recorded signal, which corresponds to a frequency that is only 2 The adjacent value of 63(ω SA ) (e.g., |Δω FA |=|Δω SA |). (3) Reconstructing a time domain signal (51, 53, 54) as shown in FIG. 4 based on the selected peak value 62, the selected first neighboring value 61, and the selected second neighboring value 63. The reconstruction produces an approximate version F of the recorded signal F1(t). 1Approx (t) is produced based on only a few samples selected from within the spectral harmonic peaks in the frequency spectrum of the recorded signal. (4) The threshold time (T Life ) is determined. This threshold can be set to approximately 80% of the maximum value of the first signal pulse 51 or the maximum value of the amplitude modulation envelope 50. For example, in the schematic diagram of FIG. 4, the first signal pulse 51 has an amplitude that approximately matches the amplitude modulation envelope 50, and the fourth signal pulse 53 is modulated by the amplitude modulation envelope 50 such that it has an amplitude smaller than the first signal pulse, but still above the threshold level. Meanwhile, the fifth signal pulse 54 is further modulated by the amplitude modulation envelope 50 such that it has an amplitude lower than the threshold level. As a result, the threshold time (T Life ) is at some point between the times of pulses 53 and 54. (5) The threshold time (T Life ) to truncate the recorded signal.

[0116] This method of reconstructing a version of the time domain signal using a small number (e.g., three) of frequency samples selected at and near the top of the harmonic peaks in the spectrum has been found to be effective in capturing sufficient spectral information to obtain an accurate estimate of when the "lifetime" of the regular oscillatory motion of the ion of interest has ended, and thus to estimate which parts of the recorded signal should be removed by truncation. This method results in spectral information that is more clearly related to the motional state of the ion of interest and is less corrupted by information about noise present in the recorded signal F1(t) or about the motional states of other interfering ions. It has been found that suitable spectral peaks are "strong" high-order harmonic peaks (the further away from the fundamental the better), in the sense that they are large enough (e.g., the signal-to-noise ratio is high enough) not to be overly affected by noise.

[0117] Once we have a value for the "lifetime" of an ion's oscillatory motion, along with the value of the period T of the ion's oscillatory motion, we can go ahead and calculate the "truncated lifetime" (T trunc ) the recorded signal F1(t) can be truncated. (1) The "truncated lifetime" is approximately equal to an integer (N) times the period (T) of the vibrational motion of the target ion. That is, T trunc =N×T. (2) The "truncated lifetime" is the "lifetime" (T Life ) shorter.

[0118] FIG. 5 shows this relationship diagrammatically.

[0119] Then, one or more frequency domain harmonic components (e.g., FIG. 1) selected from within the truncated time domain signal are 6The method can proceed to reconstruct a "cleaner" version of the time domain signal based on the truncated time domain signals H1', ​​H2', H3', ... etc. That is, the method proceeds to prepare a frequency domain spectrum of the truncated time domain signal by applying a transform of the truncated signal, such as a Fourier transform, from which one or more spectral signal values ​​are selected that respectively correspond to one or more harmonic peaks in the spectrum.

[0120] Based on these one or more values ​​of the spectral signal, a "cleaner" version of the time domain signal is now reconstructed in the time domain signal. Figures 5, 6 and 7 show aspects of this process diagrammatically.

[0121] The present method provides a means to estimate the value of the ion charge based on "cleaning" the frequency spectrum of the image charge / current signal and then reconstructing the signal from the "cleaned" frequency spectrum. Whereas in the prior art "cleaning" of a frequency spectrum is usually done by removing or modifying all frequency components in the spectrum that are considered to be noise or unimportant, the present invention implements a different approach. For example, in CDMS, once ion oscillations are identified in the Fourier spectrum, the magnitude of the spectral peaks is of interest. This means that the "useful" components of the spectrum are the frequency regions around the peak tops. The noise frequencies contained in those frequency regions cannot be removed during the prior art spectral "cleaning" methods.

[0122] However, the method illustrated in FIG. 5 reduces the size (truncate) of the input time domain image charge / current signal data set so that it covers a range that is, for example, slightly less than the “lifetime” of the ion oscillations, and the duration of the truncated data set is an integer number of periods (T=1 / F) of the fundamental of the oscillatory motion of the ion of interest. Double. This causes the time domain signal to approximately satisfy the boundary condition of an ideal period, and after applying a frequency transformation (e.g., a Fourier transform) to the truncated time domain signal, the spectral peak (harmonic peak) of the frequency of interest in the frequency domain spectrum will be much narrower (e.g., equivalent to a delta function) in the invention illustrated in FIG. 6. This allows for a much more precise selection of the spectral peak value within the spectral peak; that is, one will select a peak value with a very narrow peak shape as opposed to a much broader peak shape. The truncation of the recorded image charge signal to not exceed the "lifetime" of the ion's vibrational motion is a large part of the reason for the narrow spectral peak. Furthermore, the truncation of the recorded image charge signal to reduce its duration to an integer number of periods T. Double Equalizing ω reduces scalloping losses in the frequency domain signal.

[0123] Effect of signal truncation on Fourier spectrum values

[0124] While not wishing to be bound by theory, the following discussion is intended to provide a better understanding of the invention by considering illustrative theoretical principles and conceptual examples. To aid in a better understanding of the invention, the following discussion examines the effect of truncating a conceptual, idealized image charge current signal of total duration TR, comprising a pure sine wave (see FIG. 11) with period T0 and "lifetime" duration LT≦TR. The interest of the discussion herein is to illustrate the effect that truncating this signal has on the Fourier spectrum.

[0125] In what follows, we aim to show how truncating the length TR of a signal to an integer multiple of the period T0 affects its Fourier spectrum. Two cases of particular interest are: (1) When LT=TR (2)LT <TRのとき

[0126] A ω0The general formula for the spectral value A(ω) of the Fourier spectrum of a signal cos(ω0t+φ) at a frequency point ω, which will be derived later (see "Theoretical Background"), is

number

[0127] For simplicity, A ω0 =1, φ=0, T S =0, T E =LT. Then the above equation changes to the following equation.

number

number

number

[0128] As ω → ω0, y → 0 and M(ω) → LT / 2, and note that this value does not depend on TR. The discrete Fourier transform (DFT) of a signal of duration TR gives a series of spectral values ​​equally spaced along the frequency axis, with the distance between two adjacent points (frequency bins) given by

number

number

number

number

number

number

[0129] Note that strictly speaking, M and M' are different functions. Consider the following situation: (A) When m0 coincides with one of the frequency bins, TR is an integer number equal to T0. Double This occurs when a number is truncated to (B) When m0 is halfway between two adjacent frequency bins. This is the “worst case” situation where TR is not truncated, as shown diagrammatically in FIG.

[0130] Table 2 below shows the results for different values ​​of γ=LT / TR for the above situations A and B.

number

[0131] As can be seen from Table 2, the degree of benefit from truncating the signal depends on the LT / TR ratio. In particular, if the input signal is completely noise-free, there is no noise reduction benefit from truncating the signal. In that case, any two spectral values ​​selected from the frequency axis could be used to reconstruct the underlying sinc function.

[0132] However, in the presence of noise the situation is quite different. In this case it is important to have as high a signal-to-noise ratio (S / N) as possible in the input data, because the higher the S / N, the less noise will distort the input data and therefore the less useful information will be extracted from it. If we are interested in estimating the spectral values ​​at (or near) the top of each spectral peak in the Fourier spectrum, truncation will improve the S / N (see for example the values ​​in the "m" column in the table above).

[0133] Figure 7 shows the resulting reconstructed time domain image charge / current signal 11 after "cleaning", along with the original recorded image charge / current signal 10 for comparison. The reconstructed signal 11 has unwanted noise removed, making it easier to accurately measure the magnitude of the image charge signal.

[0134] If the vibrational motion of the ion of interest has a sufficiently well-defined period, and therefore very clearly defined and prominent harmonic frequency values ​​in the frequency spectrum, then in the method illustrated in FIG. 6, the frequency spectrum of the truncated signal can contain very "sharp" spectral components, allowing accurate identification of the appropriate peak spectral signal value at the apex of a given spectral peak. If the vibrational motion of the ion of interest is non-harmonic, such as that expected from an ELIT or orbital frequency analyzer, the spectral peaks will be broadened, and all spectral points, apart from those at harmonic frequencies (i.e. integer multiples of the fundamental frequency F0, e.g. F=nF0 for n=1, 2, 3, ...), will represent noise and will be unwanted signals to be removed by the above "cleaning" step. This maximizes the reduction of noise-related spectral power from the frequency spectrum of the image charge / current signal. After such "cleaning", a much smaller number of data points remain in the frequency spectrum, which the method uses to reconstruct the time domain signal and accurately measure the pulse magnitude of that signal to identify the charge of the ion of interest. The width (and shape) of the isolated spectral peaks defines the envelope of the respective time domain signal. It is not (generally speaking) noise or unwanted signals. It is not (generally speaking) noise or unwanted signals.

[0135] Often, there are other ions present in the ion analyzer used to generate the image charge / current signal, and these other ions each have a different oscillation frequency and corresponding period (F other =1 / T other ) which may coexist in the ion analyzer and the oscillation frequency of each of them may be quite close to the oscillation frequency of the ion of interest. The signal is, according to the present method, divided by the period (T otherSince none of them were discarded according to any of them, these other signals exhibit spectral peaks in the frequency spectrum of the time-domain signal that do not appear as similar spectral peaks (e.g., not similar to a delta function), i.e., they have smaller amplitudes and wider widths. Therefore, the skirts, bases, or tails of these other peaks may extend to frequencies associated with the vibrational motion of the target ion, thereby interfering with the height and / or position of the sharp and high spectral peak associated with the target ion.

[0136] This method preferably includes the step of reducing / removing interference from each nearby peak. "Nearby" means that those peaks fall within a predetermined range (ΔF) from the target frequency. For example, with the fundamental frequency of ion vibration being F0, within the range of 0 < ΔF < F0, this range ΔF is selected by the user so that the adjacent harmonics of the vibration do not fall within it. Simultaneous equations can be set up for a plurality of components with nearby frequencies, and using the solution of the simultaneous equations, the contribution from the vibration frequencies of other ions that are spectral components close to the target frequency of the target ion can be calculated. These contributions can be subtracted from the spectrum of the signal, and the remaining target frequency components can be used to reconstruct the time-domain image charge / current signal of the target ion. The position and range (i.e., the upper and lower boundary values) of the predetermined range can be determined in advance by trial and error. Generally, it is not appropriate to give a strict way to set its position and range. However, as a guideline, the predetermined range extending from both sides of the target peak in the frequency domain can be determined according to the quantity HW = 2T Acq Here, T Acq is the acquisition time (total duration) of the recorded image charge signal. In this case, it is preferable to define the predetermined range as ±M × HW centered on the frequency of the target peak. Here, M is a positive integer from 1 to 20 (e.g., M = 10). As a result, the predetermined range includes all adjacent (interfering) frequency peaks within a maximum ±20 × HW interval (e.g., ±10 × HW interval) centered on the frequency of the target peak in question. For example, T AcqFor HW = 1 sec, 10 x HW = 20 Hz, so it is preferable to include all adjacent peaks within ±20 Hz of a given peak of interest. This width remains constant across harmonics of the peak of interest, but adjacent peaks (e.g. their harmonics) are further apart, i.e. in the present example it would be sufficient to consider only ±(20 / 3) Hz for H3. This is a parameter that can be established during tuning of the algorithm; it will be readily apparent to those skilled in the art.

[0137] The interference may be removed, for example, in step (E) below, in the context of a more general method of the invention described below with reference to FIG. (A) Acquire the recorded image charge / current signal (Figure 10, step S1). (B) Detecting a set of periodic / repeating pulses in the recorded image charge / current signal and determining the repetition period (T) of the set of periodic / repeating pulses for the detected set of periodic / repeating pulses (FIG. 10, step S2). (C) determining an estimate of the lifetime of the detected set of periodic / repeating pulses; (D) Adjusting / truncating the length of the recorded image charge / current signal comprising the detected set of periodic / repeating pulses to be shorter than (and within) the determined lifetime and such that the duration of the truncated signal is an integer multiple of the period of the periodic / repeating pulses, and then applying a frequency transformation (e.g. Fourier transform) to the signal (Figure 10, step S3). (E) Obtain the values ​​of the truncated signal at the frequency of interest (F=1 / T) and its higher harmonics; and a. Find other peaks and their harmonics within said predetermined range near the target frequency and determine their contributions at the target frequency and its harmonics. b. Magnitude-adjusting multiple (eg, up to 12 or more) harmonics of the target frequency by subtracting out interference contributions from nearby frequency peaks. (F) Using one or more real and imaginary spectral values ​​of those harmonics, an image charge / current signal is reconstructed in the time domain, for example by applying an inverse frequency (Fourier) transform to the adjusted harmonics (FIG. 10, step S4), the magnitude of one or more pulses in the reconstructed signal is identified, and the charge value of the target ion is calculated from the magnitude (FIG. 10, step S5).

[0138] As an example of the implementation of step (D) above, Fig. 2e(1) and (2) show experimentally acquired time domain image charge / current signals, stacked by dividing them by the signal period to form an F2(t1,t2) plot, which is described in detail below with reference to Fig. 2c. By excluding points that exceed a threshold ("Threshold C"), the 2D plot shows that the F2(t1,t2) plot is focused around t2=500 ms (i.e., the lifetime of the ion, T in Fig. 5). Life 5, the method clearly shows that the signal disappeared at T Life It is truncated to be just slightly shorter so that the signal length is an integer multiple of the period (T) of the ion motion of interest.

[0139] For the frequency-converted spectrum of image charge / current signals with normal non-harmonic waveforms, the number of high-order harmonic spectral components (Hi) is sufficient up to 12 (i.e., i=12), while for real image charge / current signals acquired with real detectors and bandwidth-limited signal amplifiers, the order is sufficient up to 5 or even 4 (i.e., i=4-5), which can effectively reduce the contribution from noise. The "cleaned" spectrum containing only a few lines can be used to reconstruct the time-domain signal.

[0140] However, if there are other ions with frequencies close to the target frequency, their frequency peaks can still affect the values ​​at the target frequency and its harmonics. This is important when one wants to move a large number of ions during one acquisition cycle to increase the measurement throughput. With hundreds of ions flying together, there is a high probability that some ions will fall in a frequency range near the target frequency. The other frequency peaks cannot be represented by sharp spectral peaks (e.g. delta functions) because the signal truncation was not aligned with those other frequencies. The leakage of such nearby peaks will cause significant interference with the target frequency.

[0141] Figure 8 shows an example of such interference, where a target frequency H1 and its harmonic Hi, both represented by delta functions, are surrounded by two other frequencies 12, 13. These two peaks have some side lobes 14 (or frequency leakage) that extend up to the target frequency (H1) and to each other. It is preferable to identify the contributions from such nearby frequencies and remove them before reconstructing the time domain image charge / current signal for charge measurement of the ions of interest. The method may then include such a correction step, as described above and in more detail below. In the correction step, a number of interfering frequencies are identified within a predetermined frequency range selected by the user around the target frequency and these interferences are removed.

[0142] In a frequency spectrum (such as in Figure 8), the observed peak value is actually a weighted combination of all components (with respect to their true peak values). It turns out that based on the known signal length used in the frequency (e.g. Fourier) transform, a mathematical description of the distribution (weights / coefficients) per frequency component can be derived. It turns out that a matrix of coupled equations can be created for the sum of contributions from all components (true peak value multiplied by weights / coefficients) equal to the observed peak value. The inventors have found that the solution of this simultaneous coupled equation gives the true peak value at the target frequency.

[0143] By removing interference of nearby frequencies to the target frequency (including interference at higher harmonics of the target frequency), reconstruction of the target frequency signal can be much more accurate, even if multiple ions of different frequencies are flying together and their signals are acquired together. Further filtering or smoothing of the reconstructed time domain signal may be used prior to measuring its magnitude, and this can be added as a common step in signal processing, as would be readily available within the general knowledge of signal processing.

[0144] In the method, the step of selecting one or more values ​​of the frequency domain signal comprises selecting N distinct values ​​(OP n , where n=1 to N, N≧M) are respectively selected from a plurality of distinct adjacent signal peaks of the frequency domain signal including a signal peak corresponding to an ion of interest; and nm is the coefficient, TP m where M is the correction value among the selected N distinct values ​​of the frequency domain signal.

number

[0145] That is, among the selected N distinct values ​​of the frequency domain signal, there is a value corresponding to each adjacent signal peak (e.g., Peak 2, Peak 3) that is at a frequency that is not a harmonic frequency of the ion of interest (i.e., Peak 1 in FIG. 9, the ion whose charge is to be determined). For example, OP1 can be the value of the frequency domain signal from within Peak 1 that corresponds to a frequency that is a harmonic of the motion of the ion of interest. This can be the value that is "observed" to be the highest value within the shape of signal Peak 1 that corresponds to a certain harmonic. Similarly, OP m (where m>1) may be values ​​of frequency domain signal peaks 2 and 3, etc., that each correspond to a frequency that is a harmonic of the motion of another ion that is not the ion of interest (i.e., a total of N-1 other ions). Again, these adjacent peak values ​​may each be "observed" to be the highest value within the range of the signal "peak" shape that corresponds to the harmonic.

[0146] These N selected values ​​(N=3 in FIG. 9) of the frequency domain signal are used to generate the selected distinct values ​​(OP n ) is made for each of the motional contributions (α nm ) is produced.

[0147] The method involves solving this set of equations to find a TP matrix such that the "difference" (e.g., the least squares difference value) between the left and right side of the matrix equation is minimized. n By finding a combination of these, the corrected (or "true") value of the frequency domain signal associated with a given harmonic of the ion of interest, i.e., a value (TP1) that has had the spectral energy resulting from the motion of all other ions contributing to the signal at that frequency removed. The method also finds the corrected (or "true") value of the frequency domain signal associated with adjacent harmonics of non-target ions, TP m (where m>1) are also obtained. These are other ions that contribute spectral energy to harmonics of the ion of interest.

[0148] In the example of Figure 9, three separate frequency domain signal values ​​are selected corresponding to each of the three (N=3) signal peaks (Peaks 1, 2, and 3), each at a frequency that is a harmonic frequency of an ion that contributes to the overall signal (i.e., the ion of interest and two other non-target ions).

[0149] The above equation can be expressed as follows:

number

[0150] In other words, rather than simply using the "observed" spectral peak value OP1 from each harmonic peak of the truncated signal (H1' in FIG. 6), the method can instead involve using the "true" spectral peak value TP1 (i.e., OP1 → TP1). By applying the same procedure to each of the values ​​of the frequency domain signal associated with the ion of interest (e.g., spectral peaks H1', ​​H2', and H3' in FIG. 6), (1) The "true" spectrum peak value TP1 relative to the peak value of the harmonic spectrum peak H1' (1) , (2) The "true" spectrum peak value TP1 relative to the peak value of the harmonic spectrum peak H2' (2) , (3) The "true" spectrum peak value TP1 relative to the peak value of the harmonic spectrum peak H3' (3) These three "true" spectral peak values ​​(TP1 (1) , TP1 (2) , TP1 (3) ) is used in the step of reconstructing the time domain signal.

[0151] The values ​​of the frequency domain signal used in the step of reconstructing the time domain signal may be complex numbers representing the transformed signal. For example, the selected N distinct values ​​(OP n ) may each be a complex number. For example, the corrected M distinct values ​​of the frequency domain signal (TP m ) can each be a complex number. nm ) can be complex numbers. By considering the phase of these complex coefficients, the corrected M distinct values ​​of the frequency domain signal (TP m ) can be made more accurate. Once the solution TP (a complex number) is found, the "magnitude" = √({Re[TP]} 2 +{Im[TP]} 2 ) can be calculated. This calculation can be done at several points for each harmonic of each peak.

[0152] theoretical background

[0153] Without wishing to be bound by theory, the following discussion is intended to provide a better understanding of the present invention, for example with respect to the use of the simultaneous equations defined above, through the consideration of illustrative theoretical principles and conceptual examples.

[0154] Problem to be solved

[0155] Consider an image charge current signal of known length caused by an oscillating ion of different charge. The ion is at any instant T S At any instant T E By definition, the lifetime of an ion is LT = T E -T S This is illustrated in Figure 13. What we need to do is determine the charge of each ion. T S and T Eare both unknown, as is the number of ions. In addition, in many practical experiments the noise level can exceed the useful signal level by nearly two orders of magnitude, so that the contributions of individual ions may not be visible in the time domain signal, as shown in Figure 14.

[0156] Fourier Transform

[0157] Time-Domain Image By taking the Fourier transform (FT) of the charge current signal, its frequency spectrum can be obtained. However, if these ions have oscillatory motions at very close frequencies, resulting in spectral interference, the charge estimation may be less accurate. The height of each peak in the frequency spectrum depends not only on the charge of the ion but also on its “lifetime” (LT). In addition, the width of these peaks depends on the “lifetime” (LT) of the ion, and adjacent peaks may interfere with each other as shown in Figure 9. Figure 9 shows a portion of the frequency spectrum of two ions, one of which, the ion associated with peak 2, has changed its oscillation frequency at some point during the acquisition of the recorded signal. It can be seen that the example spectrum has three spectral peaks at three different frequencies. Peak 1 is the frequency of interest for the ion of interest, and peaks 2 and 3 are interferences.

[0158] If peak 1 were the only spectral peak in the spectral interval shown in Figure 9, the power spectrum would be represented by a single "sinc function" and determining the magnitude of spectral peak 1 relative to its frequency components would be straightforward. However, as can be seen in Figure 9, when there are several frequency components (i.e., peaks 2 and 3), their individual spectra combine, making it more complicated to determine the true magnitude of peak of interest 1. In particular, the observed spectral magnitude OP1 of peak 1 is a combination of its "true" magnitude TP1 and contributions from peaks 2 and 3, which are proportional to the "true" magnitudes of each of the peaks.

[0159] From the peaks in the spectrum in Figure 9, the number of oscillating ions (3 types) and their frequencies can be determined. Each peak corresponds to a different ion, and the higher harmonics of the signal can be used to determine the frequencies of these ions with reasonable accuracy. Further analysis may be more desirable to improve the estimate of the charge of these ions, since the height of the peak depends on the charge, the LT of the image charge current signal of each ion, and some contribution / interference from neighboring peaks. For example, the three peaks in Figure 9 arise from ions with the same charge of 50e. For each peak, we can say that its observed height OP is a combination of its true peak height TP and the true heights of the neighboring peaks. The contribution of each peak can be expressed as αTP, where TP is the true (but unknown) height of the peak, and α is a coefficient that depends on the LT and charge of the ion. Thus, the following simultaneous equations can be created for N types of ions:

number

[0160] Useful Formulas

[0161] The following function

number

number

[0162] Δ ω =ω0-ω, LT=T E -T SIntroducing, the last equation can be rewritten as

number

number

number

number

[0163] For the frequency domain of interest,

number

number

number

[0164] The above formula is Aω0 *cos(ωt+φ) is a general approximation of the Fourier transform of the Fourier spectrum. From this formula, A at any given frequency ω in the Fourier spectrum ω0 *cos(ω0t+φ) is obtained, which in turn allows us to estimate the contribution from nearby peaks.

[0165] One simple example

[0166] There are N kinds of ions. The signal from each ion is ω k It is assumed that the ions are represented by a single harmonic and that all ions have the same phase (to simplify the equations, we assume that φ = 0, but this is not required, as long as the phase is the same for all ions), and that all ions are at the beginning of the transient (T S = 0) and do not disappear, all ions have the same T E All that follows is easily extended to the situation where the ion signal is represented by several harmonics. Then, ω k The frequency spectrum of an ion oscillating at

number

number

[0167] In reality, the input signal is noisy, so the OP in equation [1] k Since the estimate of will be inaccurate, we take the spectrum at a few points around the peak of each ion at a few harmonic frequencies and use the best fit (e.g., least squares fit) to equation [1], A ωk It may be preferable to explore combinations of

[0168] Another example

[0169] In some experiments, ions may be "born" during the transient of the image charge current signal. These so-called "secondary ions" are generated at different and unknown values ​​of T S , T E As can be seen from equation [2], the system of equations is not linear with respect to these new unknowns. The phase term in equation [2]

number

[0170] The inventors have found that a numerical approach, in which the unknown variables are varied within predetermined ranges and with predetermined step sizes, can be used particularly successfully.

[0171] For example, in general, the lifespan LT (LT = T E -T S) is the value of T E -45 ms ≤ T centered on the estimated value E The variation can be achieved by varying within a range of ≦+45 ms. The variation can be performed with a step size of about 1 ms. Of course, other ranges and / or step sizes may be used if desired.

[0172] For example, in general, the amplitude A ω0 is 0.80≦A ω0 The amplitude can be varied in the range ≦1.20. The variation can be performed with a step size of about 0.01. For example, an amplitude value of 1 can correspond to a charge of 50e. Of course, other ranges and / or step sizes can be used if desired.

[0173] At each step of the change, the sum of the squared differences between the measured and analytical (model) values ​​is calculated. The combination of unknowns that minimizes the sum of the squared differences is accepted as the solution to equation [1].

[0174] References

[0175] A number of publications have been cited above in order to more fully describe and disclose the invention and the state of the art to which it pertains. A complete list of the cited publications is set forth below. The entirety of each of these references is incorporated herein by reference. Jared O. Kafader, “STORI Plots Enable Accurate Tracking of Individual Ion Signals”; J.Am. Soc. Mass Spectrum (2019) 30: 2200-2203 “High-Capacity Electrostatic Ion Trap with Mass Resolving Power Boosted by High-Order Harmonics”: by Li Ding and Aleksandr Rusinov, Anal. Chem. 2019, 91, 12, 7595-7602. W. Shockley: “Currents to Conductors Induced by a Moving Point Charge”, Journal of Applied Physics 9, 635 (1938)] S. Ramo: “Currents Induced by Electron Motion”, Proceedings of the IRE, Volume 27, Issue 9, Sept. 1939 WO 02 / 103747 (A1) (Zajfman et al.) WO 2012 / 116765 (A1) (Ding et al.)

Claims

1. 1. A method for processing an image charge / current signal representative of one or more ions undergoing oscillatory motion within an ion analyzer, comprising the steps of: obtaining a recording of the image charge / current signal generated by the ion analyzer in the time domain; The signal processing unit determining a period value of a periodic signal component in the recorded signal; truncating the recorded signal to provide a truncated signal having a duration approximately equal to an integer multiple of the period; reconstructing a time domain signal based on one or more selected frequency domain harmonic components of the truncated signal; determining a magnitude of the reconstructed time domain signal and using it to calculate a value representative of the charge of the ions undergoing oscillatory motion within the ion analyzer; The method includes:

2. reconstructing the time domain signal applying a transformation of the recorded signal to prepare a frequency domain signal; selecting one or more values ​​of the frequency domain signal which respectively correspond to one or more harmonic peaks in the signal; and reconstructing a time domain signal based on the values ​​of the selected one or more frequency domain signals. The method of claim 1 , comprising:

3. Selecting one or more values ​​of the frequency domain signal N distinct values ​​(OP ｎ , where n=1 to N, N≧M), from a plurality of distinct adjacent signal peaks of the frequency domain signal that include a signal peak corresponding to an ion of interest; and ｎｍ is the coefficient, TP ｍ where M is the correction value among the selected N distinct values ​​of the frequency domain signal. [0048] To solve A correction value (TP) for the one or more values ​​of the frequency domain signal corresponding to a harmonic peak associated with the ion of interest. ｍ ) The method of claim 2 , comprising:

4. 4. The method of claim 3, wherein at least one of the selected M distinct values ​​of the frequency domain signal corresponds to a respective adjacent signal peak at a frequency that is not a harmonic frequency of an ion of interest.

5. A method according to any preceding claim, wherein said magnitude comprises the magnitude of the reconstructed time domain signal, and said value representing the charge of said ion is proportional to said magnitude.

6. 5. The method of claim 3, wherein the duration of the truncated signal is an integer multiple of the period of oscillation of the target ion.

7. 7. A method according to any preceding claim, wherein the truncated signal is a time section of the recorded signal starting at a recording time which coincides with (or is later than) the recording start time of the recorded image charge / current signal and ending at a recording time which is earlier than the recording stop time of the recorded image charge / current signal.

8. 8. A method according to any preceding claim, wherein the truncated signal is a time section of the recorded signal during which there is a series of repetitive signal peaks, each signal peak having a peak signal value that deviates by up to 22% from the value of the largest peak value in the series of repetitive signal peaks.

9. The recorded signal is a recorded time-domain signal, truncating the recorded signal generating a transformed recorded signal by transforming the recorded time domain signal into a frequency domain; selecting a peak value of the converted record signal from within a signal peak of the converted record signal that corresponds to a frequency domain harmonic content of the recorded signal; selecting a first adjacent value of the transformed recorded signal that is within the signal peak and corresponds to a frequency that is lower than the frequency associated with the peak value; selecting a second adjacent value of the transformed recorded signal that is within the signal peak and corresponds to a frequency higher than the frequency associated with the peak value; reconstructing a time domain signal based on the selected peak value, the selected first neighboring value, and the selected second neighboring value; determining a threshold time at which the amplitude modulation falls below a signal threshold within the reconstructing the time domain signal; providing a truncated time domain signal by truncating said recorded signal in accordance with the threshold time thus determined. The method according to any one of claims 1 to 8, comprising:

10. 10. The method of claim 9, wherein the signal threshold is a signal value corresponding to 72% of the maximum value of the amplitude modulation.

11. 11. A method according to claim 9 or claim 10, wherein the frequency associated with the selected peak value is approximately equal to the frequency of a harmonic associated with a given signal peak of the converted recorded signal.

12. 12. The method of any of claims 9 to 11, wherein the selected peak value, the selected first adjacent value and the selected second adjacent value are obtained from a spectral peak corresponding to an Nth harmonic of a frequency domain harmonic component of the recorded signal, where N is an integer greater than 1.

13. 13. The method of claim 12, wherein N=3.

14. 14. A method according to any one of claims 9 to 13, wherein the first adjacent value is selected to correspond to a frequency that is lower than the frequency of the selected peak value by an amount not exceeding half the full width at half maximum (FWHM) of a given signal peak of the transformed recorded signal.

15. 15. A method according to any one of claims 9 to 14, wherein the second adjacent value is selected to correspond to a frequency higher than the frequency of the selected peak value by an amount not exceeding half the full width at half maximum (FWHM) of a given signal peak of the transformed recorded signal.

16. 16. The method of claims 14 and 15, wherein the first adjacent value and the second adjacent value are selected to respectively correspond to frequencies that differ from the frequency of the selected peak value by the same amount.

17. 10. The method of claim 9, wherein the step of reconstructing a time domain signal based on one or more selected frequency domain harmonic components of the truncated signal comprises calculating a time domain signal using an inverse transform of a frequency domain transform applied to the truncated time domain signal to generate the frequency domain harmonic components of the truncated signal.

18. The step of acquiring a record of the image charge / current signals generated by the ion analyzer in the time domain comprises acquiring a plurality of image charge / current signals prior to processing the plurality of image charge / current signals by the signal processing unit, acquiring the plurality of image charge / current signals comprising: generating ions; trapping the ions and subjecting the trapped ions to oscillatory motion; and acquiring with at least one image charge / current detector a plurality of image charge / current signals representative of the trapped ions undergoing oscillatory motion; The method according to any one of claims 1 to 17, comprising:

19. 19. An ion analyser configured to generate an image charge / current signal representative of one or more ions undergoing oscillatory motion, the ion analyser being configured to carry out a method according to any one of claims 1 to 18.

20. 20. The ion analyzer of claim 19, comprising any one or more of an ion cyclotron resonance trap, an Orbitrap® configured to use a hyper-logarithmic electric field to trap ions, an electrostatic linear ion trap (ELIT), a quadrupole ion trap, an ion mobility analyzer, a charge detection mass spectrometer (CDMS), an electrostatic ion beam trap (EIBT), a planar orbital frequency analyzer (POFA) or a planar electrostatic ion trap (PEIT) to generate the oscillatory motion therein.

21. 1. An ion analyzer configured to generate an image charge / current signal representative of the vibrational motion of one or more ions received therein, comprising: an ion analysis chamber configured to receive the one or more ions and generate the image charge / current signal in response to the vibrational motion; a signal recording unit configured to record said image charge / current signal in the time domain as a recorded signal; Processing the recorded signal to determining a period value of a periodic signal component in the recorded signal; truncating the recorded signal to provide a truncated signal having a duration approximately equal to an integer multiple of the period; reconstructing a time domain signal based on one or more selected frequency domain harmonic components of the truncated signal; The magnitude of the reconstructed time domain signal is determined and used to calculate a value representative of the charge of the ions undergoing oscillatory motion within the ion analyzer. a signal processing unit for An ion analyzer comprising:

22. The ion analysis device is configured to generate ions, and the ion analysis chamber comprises: trapping ions and subjecting the trapped ions to oscillatory motion; A plurality of image charge / current signals representative of the trapped ions undergoing oscillatory motion are acquired with at least one image charge / current detector. The ion analyzing device according to claim 21 , configured as follows:

23. 22. The ion analyzer of claim 20 or 21, comprising any one or more of an ion cyclotron resonance trap, an Orbitrap® configured to use a hyper-logarithmic electric field to trap ions, an Electrostatic Linear Ion Trap (ELIT), a Quadrupole ion trap, an Ion Mobility Spectrometer, a Charge Detection Mass Spectrometer (CDMS), an Electrostatic Ion Beam Trap (EIBT), a Planar Orbital Frequency Analyzer (POFA) or a Planar Electrostatic Ion Trap (PEIT) to generate the oscillatory motion therein.

24. A computer readable medium comprising computer executable instructions configured to cause a mass spectrometer to perform the method of any of claims 1 to 18, comprising processing a plurality of image charge / current signals representative of trapped ions undergoing oscillatory motion.

Images