Time-frequency analysis

Abstract

Apparatus and method for processing an image-charge/current signal for an ion(s) undergoing oscillatory motion within an ion analyser apparatus. The method comprises: obtaining a recording of the image-charge/current signal (20a-20e) in the time domain. Then, by a signal processing unit, a value for the period (T) of a periodic signal component is determined within the recorded signal. Subsequently, the recorded signal is segmented into a number of successive time segments [0;T] of duration corresponding to the period (T). These lime segments are then co-registered in a first time dimension (t.sub.1) defining the period (T). The co-registered time segments are then separated along a second time dimension (t.sub.2) transverse to the first time dimension (t.sub.1). This generates a stack of time segments collectively defining a 2-dimensional (2D) function. The 2D function varies both across the stack in the first time dimension and along the stack in the second time dimension.

Claims

1. A method of processing an image-charge/current signal representative of one or more ions undergoing oscillatory motion within an ion analyser apparatus, the method comprising: obtaining a recording of the image-charge/current signal generated by the ion analyser apparatus in the time domain; by a signal processing unit: determining a value for the period of a periodic signal component within the recorded signal; segmenting the recorded signal into a number of separate successive time segments of duration corresponding to the determined period; co-registering the separate time segments in a first time dimension defining the determined period; and, separating the co-registered time segments along a second time dimension transverse to the first time dimension thereby to generate a stack of time segments collectively defining a 2-dimensional (2D) function which varies both across the stack in said first time dimension according to time within the determined period and along the stack in said second time dimension according to time between successive said time segments.

2. A method according to claim 1 comprising, on a display apparatus, plotting the 2D function on a plane comprising the first time dimension and the second time dimension and representing a fixed value of the function, or in 3-dimensional (3D) form further comprising third dimension transverse to said plane and representing variation in the function.

3. A method according to claim 1 comprising determining a change in said motion of an ion according to a corresponding change in the periodic signal component within the 2D function in the first time dimension and/or in the second time dimension.

4. A method according to claim 3 comprising determining, in the second dimension of time, a change in the position of said periodic signal component in the first dimension of time, thereby to identify a change in said oscillatory motion of an ion.

5. A method according to claim 3 comprising determining, in the second dimension of time, a change in the duration of said periodic signal component in the first dimension of time, thereby to identify a change in said oscillatory motion of an ion.

6. A method according to claim 3 comprising: identifying, from amongst said separate successive time segments, time segments containing two or more periodic signal components in successive time segments; and, resolving two or more different mass-to-charge ratios (m/q) of said ions according to the two or more different periodic signal components within the 2D function.

7. A method according to claim 6 comprising determining a fragmentation of a said ion according to a bifurcation, in the second dimension of time, of the periodic signal component within the first dimension of time.

8. A method according to claim 3 comprising determining a time at which said change occurs, and applying a subsequent analytical process only to parts of the recorded signal generated before the time at which said change occurs.

9. A method according to claim 3 comprising determining a time at which said change occurs, and applying a subsequent analytical process only to parts of the recorded signal generated after the time at which said change occurs.

10. A method according to claim 3 comprising identifying, in the second dimension of time, a change in the position and/or duration of said periodic signal component in the first dimension of time, thereby to identify an instability in an electric field and/or magnetic field of said ion analyser apparatus.

11. A method according to claim 10 comprising correcting the 2D function based on the identified change to render said position of said periodic signal component in the first dimension of time, substantially unchanging in the second dimension of time.

12. A method according to claim 1 in which the signal processing unit is configured to determine said value for the period of a periodic signal component by iteratively: segmenting the recorded signal into a number of separate successive time segments of duration corresponding to a trial period; co-registering the separate time segments in said first time dimension defining the trial period; separating the co-registered time segments along said second time dimension thereby to generate a said stack of time segments collectively defining a said 2-dimensional (2D) function; and, determining whether the position of the periodic component in the first time dimension changes along the second time dimension, the iterative process ending when it is determined that substantially no such change occurs.

13. A method according to claim 1 including: determining a sub-set of instances of the 2D function in which the value of the 2D function falls below a pre-set threshold value; from amongst said sub-set of instances, and within each separate time segment, determining an interval of time in the first time dimension during which the 2D function never falls below said pre-set threshold value; and, identifying the interval of time as the periodic signal component.

14. A method according to claim 13 comprising determining in the second dimension of time, a change in the duration of said interval of time in the first dimension of time, thereby to identify a change in said oscillatory motion of an ion.

15. A method according to claim 13 comprising determining in the second dimension of time, a change in the position of said interval of time in the first dimension of time, thereby to identify a change in said oscillatory motion of an ion.

16. A method according to claim 1 comprising identifying, from amongst said separate successive time segments, time segments containing multiple periodic signal components which occur between time segments containing only one periodic signal component, and excluding those identified segments from the stack, thereby leaving within the stack those time segments containing only one periodic signal component.

17. A method according to claim 1 wherein the step of obtaining a recording of the image-charge/current signal generated by the ion analyser apparatus in the time domain includes obtaining a plurality of image charge/current signals before processing the plurality of image charge/current signals by said signal processing unit, wherein obtaining the plurality of image charge/current signals includes: producing ions; trapping the ions such that the trapped ions undergo oscillatory motion; and obtaining a plurality of image charge/current signals representative of the trapped ions undergoing oscillatory motion using at least one image charge/current detector.

18. An ion analyser apparatus configured to generate an image charge/current signal representative of one or more ions undergoing oscillatory motion therein, wherein the ion analyser apparatus is configured to implement the method according to claim 1.

19. An ion analyser apparatus according to claim 18 comprising any one or more of: an ion cyclotron resonance trap; an Orbitrap® configured to use a hyper-logarithmic electric field for ion trapping; an electrostatic linear ion trap (ELIT); a quadrupole ion trap; an ion mobility analyser; a charge detection mass spectrometer (CDMS); Electrostatic Ion Beam Trap (EIBT); a Planar Orbital Frequency Analyser (POFA); or a Planar Electrostatic Ion Trap (PEIT), for generating said oscillatory motion therein.

20. An ion analyser apparatus configured for generating an image-charge/current signal representative of oscillatory motion of one or more ions received therein, the apparatus comprising: an ion analysis chamber configured for receiving said one or more ions and for generating said image charge/current signal in response to said oscillatory motion; a signal recording unit configured for recording the image charge/current signal as a recorded signal in the time domain; a signal processing unit for processing the recorded signal to: determine a value for the period of a periodic signal component within the recorded signal; segment the recorded signal into a number of separate successive time segments of duration corresponding to the determined period; co-register the separate time segments in a first time dimension defining the determined period; and, separate the co-registered time segments along a second time dimension transverse to the first time dimension thereby to generate a stack of time segments collectively defining a 2-dimensional (2D) function which varies both across the stack in said first time dimension according to time within the determined period and along the stack in said second time dimension according to time between successive said time segments.

21. An ion analyser apparatus according to claim 20 wherein the ion analyser apparatus is configured for producing ions, and the ion analysis chamber is configured for; trapping the ions such that the trapped ions undergo oscillatory motion; and obtaining a plurality of image charge/current signals representative of the trapped ions undergoing oscillatory motion using at least one image charge/current detector.

22. An ion analyser apparatus according to claim 20 comprising any one or more of: an ion cyclotron resonance trap; an Orbitrap® configured to use a hyper-logarithmic electric field for ion trapping; an electrostatic linear ion trap (ELIT); a quadrupole ion trap; an ion mobility analyser; a charge detection mass spectrometer (CDMS); Electrostatic Ion Beam Trap (EIBT); a Planar Orbital Frequency Analyser (POFA); or a Planar Electrostatic Ion Trap (PEIT), for generating said oscillatory motion therein.

23. A computer-readable medium having computer-executable instructions configured to cause a mass spectrometry apparatus to perform a method of processing a plurality of image charge/current signals representative of trapped ions undergoing oscillatory motion, the method being according to claim 1.

Description

SUMMARY OF THE FIGURES

(1) Embodiments and experiments illustrating the principles of the invention will now be discussed with reference to the accompanying figures in which:

(2) FIG. 1A shows a schematic diagram relating to the generation of a time-frequency distribution function;

(3) FIG. 1B shows an example of a 2D time-frequency distribution function;

(4) FIG. 2 shows a schematic representation of an ion analyser apparatus:

(5) FIG. 3A shows a schematic representation of an image-charge/current signal representative of oscillatory motion of one or more ions in an ion analyser apparatus;

(6) FIG. 3B shows a schematic representation of a 2D function comprising a stack of segmented portions of an image-charge/current signal representative of oscillatory motion of one or more ions in an ion analyser apparatus;

(7) FIG. 4 shows a schematic representation of an image-charge/current signal such as shown in FIG. 3A, in which a process of segmentation is being applied;

(8) FIG. 5 shows a flow chart of steps in a process of generating a 2D function such as shown in FIG. 3B;

(9) FIG. 6A shows a schematic representation of a 2D function of an image-charge/current signal such as shown in FIG. 3B, in which a process of segmentation has been applied and in which co-registration has been applied. The view shown is equivalent to the “view (a)” indicated in FIG. 3B whereby a view of a second dimension of time is suppressed, and a view of a first dimension of time is presented;

(10) FIG. 6B shows a schematic representation of a 2D function of an image-charge/current signal such as shown in FIG. 6A, in which a process of thresholding has been applied. The view shown is equivalent to the “view (b)” indicated in FIG. 3B whereby a view of both a second dimension of time and a view of a first dimension of time are presented;

(11) FIG. 7A shows a schematic representation of a 2D function of an image-charge/current signal such as shown in FIG. 3B, in which a process of segmentation has been applied and in which co-registration has been applied. The view shown is equivalent to the “view (a)” indicated in FIG. 3B whereby a view of a second dimension of time is suppressed, and a view of a first dimension of time is presented;

(12) FIG. 7B shows a schematic representation of a 2D function of an image-charge/current signal such as shown in FIG. 7A, in which a process of thresholding has been applied. The view shown is equivalent to the “view (b)” indicated in FIG. 3B whereby a view of both a second dimension of time and a view of a first dimension of time are presented;

(13) FIG. 8 shows a schematic representation of a 2D function of an image-charge/current signal such as shown in FIGS. 6B and 7B, in which a process of thresholding has been applied. The view shown is equivalent to the “view (b)” indicated in FIG. 3B whereby a view of both a second dimension of time and a view of a first dimension of time are presented:

(14) FIG. 9A shows a schematic representation of a 2D function of an image-charge/current signal such as shown in FIGS. 6B and 7B, in which a process of thresholding has been applied. The view shown is equivalent to the “view (b)” indicated in FIG. 3B whereby a view of both a second dimension of time and a view of a first dimension of time are presented. The periodic signal component changes in position due to field instabilities in the ion analyser apparatus used to generate the image-charge/current signal;

(15) FIG. 9B shows a schematic representation of a 2D function of an image-charge/current signal corresponding to a corrected version of the 2D function of FIG. 9A, in which changes in the position of the periodic signal component are corrected;

(16) FIG. 10 shows a Fourier transform frequency spectrum of the periodic signal component corresponding to the 2D function illustrated in FIGS. 9A and 9B, both before and after correction of the position of the periodic signal component.

(17) FIG. 11 shows a schematic representation of a 2D function comprising a stack of segmented portions of an image-charge/current signal representative of oscillatory motion of one or more ions in an ion analyser apparatus. Here, two periodic signal components are present, in which one component has half the frequency of the other component;

(18) FIGS. 12(a), 12(b) and 12(c) show a schematic representation of: (a) a 1D function composed of a series of measured values of an image-charge/current signal containing a periodic component generated by the oscillatory motion of an ion(s) within an ion trap or analyser; and (b) the 1D function after it has been segmented and the segments co-registered in a segmentation interval [0:T′] of length equal to the period T of the periodic component; and (c) representing the 1D function after it has been segmented and the segments co-registered in a segmentation interval [0:T′] of length equal to 0.75T;

(19) FIGS. 13A and 13B show a schematic representation of (A): an ‘accumulated’ function S(t); and, (B) periodic basis functions for use in the ‘accumulated’ function, in the form of a succession of equally-spaced Gaussian functions.

DETAILED DESCRIPTION OF THE INVENTION

(20) Aspects and embodiments of the present invention will now be discussed with reference to the accompanying figures. Further aspects and embodiments will be apparent to those skilled in the art. All documents mentioned in this text are incorporated herein by reference.

(21) The features disclosed in the foregoing description, or in the following claims, or in the accompanying drawings, expressed in their specific forms or in terms of a means for performing the disclosed function, or a method or process for obtaining the disclosed results, as appropriate, may, separately, or in any combination of such features, be utilised for realising the invention in diverse forms thereof.

(22) While the invention has been described in conjunction with the exemplary embodiments described above, many equivalent modifications and variations will be apparent to those skilled in the art when given this disclosure. Accordingly, the exemplary embodiments of the invention set forth above are considered to be illustrative and not limiting. Various changes to the described embodiments may be made without departing from the spirit and scope of the invention.

(23) For the avoidance of any doubt, any theoretical explanations provided herein are provided for the purposes of improving the understanding of a reader. The inventors do not wish to be bound by any of these theoretical explanations.

(24) Any section headings used herein are for organizational purposes only and are not to be construed as limiting the subject matter described.

(25) Throughout this specification, including the claims which follow, unless the context requires otherwise, the word “comprise” and “include”, and variations such as “comprises”, “comprising” and “including” will be understood to imply the inclusion of a stated integer or step or group of integers or steps but not the exclusion of any other integer or step or group of integers or steps.

(26) It must be noted that, as used in the specification and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Ranges may be expressed herein as from “about” one particular value, and/or to “about” another particular value. When such a range is expressed, another embodiment includes from the one particular value and/or to the other particular value. Similarly, when values are expressed as approximations, by the use of the antecedent “about,” it will be understood that the particular value forms another embodiment. The term “about” in relation to a numerical value is optional and means for example +/−10%.

(27) In the drawings, like items are assigned like reference symbols, for consistency.

(28) FIG. 2 shows a schematic representation of an ion analyser apparatus in the form of an electrostatic ion trap 80 for mass analysis. The electrostatic ion trap includes an ion analysis chamber (81, 82, 83, 84) configured for receiving one or more ions 85A and for generating an image charge/current signal in response to oscillatory motion 86B of the received ions 85B when within the ion analysis chamber. The ion analysis chamber comprises a first array of electrodes 81 and a second array of electrodes 82, spaced from the first array of electrodes by a substantially constant separation distance.

(29) A voltage supply unit (not shown) is arranged to supply voltages, in use, to electrodes of the first and second arrays of electrodes 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, from the voltage supply unit, with substantially the same pattern of voltage, whereby the distribution of electrical potential in the space between the first and second electrode arrays (81, 82) is such as to reflect ions 85B in a flight direction 86B causing them to undergo periodic, oscillatory motion in that space. The electrostatic ion trap 80 may be configured, for example, as is describe in WO2012/116765 (A1) (Ding et al.), the entirety of which is incorporated herein by reference. Other arrangements are possible, as will be readily appreciated by the skilled person.

(30) The periodic, oscillatory motion of ions 85B within the space between the first and second arrays of electrodes may be arranged, by application of appropriate voltages to the first and second arrays of electrodes, to be focused substantially mid-way between the first and second electrode arrays for example, as is describe in WO2012/116765 (A1) (Ding et al.). Other arrangements are possible, as will be readily appreciated by the skilled person.

(31) One or more electrodes of each of the first and second arrays of electrodes, are configured as image-charge/current sensing electrodes 87 and, as such, are connected to a signal recording unit 89 which is configured for receiving an image-charge/current signal 88 from the sensing electrodes, and for recording the received image charge/current signal in the time domain. The signal recording unit 89 may comprise amplifier circuitry as appropriate for detection of an image-charge/current having periodic/frequency components related to the mass-to-charge ratio of the ions 85B undergoing said periodic oscillatory motion 86B in the space between the first and second arrays of electrodes (81, 82).

(32) The first and second arrays of electrodes may comprise, for example, planar arrays formed by: (a) parallel strip electrodes; and/or, (b) concentric, circular, or part-circular electrically conductive rings,
as is described in WO2012/116765 (A1) (Ding et al.). Other arrangements are possible, as will be readily appreciated by the skilled person. Each array of the first and second arrays of electrodes extends in a direction of the periodic oscillatory motion 86B of the ion(s) 85B. The ion analysis chamber comprises a main part defined by the first and second arrays of electrodes and the space between them, and two end electrodes (83, 84). A voltage difference applied between the main segment and the respective end segments creates a potential barrier for reflecting ions 85B in the oscillatory motion direction 86B, thereby to trap the ions within the space between the first and second arrays of electrodes. The electrostatic ion trap may include an ion source (not shown, e.g. an ion trap) configured for temporarily storing ions 85A externally from the ion analysis chamber, and then injecting stored ions 80A into the space between the first and second arrays of electrodes, via 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 the space between the first and second arrays of electrodes, as is described in WO2012/116765 (A1) (Ding et al.). Other arrangements are possible, as will be readily appreciated by the skilled person.

(33) The ion analyser 80 further incudes a signal processing unit 91 configured for receiving a recorded image-charge/current signal 90 from the signal recording unit 89, and for processing the recorded signal to: (a) determine a value for the period of a periodic signal component within the recorded signal; (b) segment the recorded signal into a number of separate successive time segments of duration corresponding to the determined period; (c) co-register the separate time segments in a first time dimension defining the determined period; and, (d) separate the co-registered time segments along a second time dimension transverse to the first time dimension thereby to generate a stack of time segments collectively defining a 2-dimensional (2D) function which varies both across the stack in said first time dimension according to time within the determined period and along the stack in said second time dimension according to time between successive said time segments.

(34) These signal processing steps are implemented by the signal processing unit 91, and will be 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 upon image charge/current signals representative of trapped ions undergoing oscillatory motion. The result is the 2D function. The ion analyser 80 further incudes a display unit 93 configured to receive data 92 corresponding to the 2D function, and to display the 2D function to a user.

(35) FIG. 3A shows a schematic representation of a one-dimensional time-domain image-charge/current signal, F.sub.1(t), generated by an ion analyser 80 of FIG. 2. The signal corresponds to the recorded image-charge/current signal 90 received by the signal processor 91 from the signal recording unit 89, and is representative of the oscillatory motion of one or more ions in the ion analyser apparatus. The signal consists of a sequence of regularly-spaced sequence of brief (or transient), but intense, image-charge/current signal pulses (20a, 20b, 20c, 20d, 20e . . . ) each being separated, one from another, by intermediate intervals of mere noise in which no discernible transient signal pulse is present. Each transient signal pulse corresponds to the brief duration of time when an ion 85B, or a group of ions, momentarily passes between the two opposing image-charge/current sensing electrodes 87 of the electrostatic ion trap 80 during the oscillatory motion of the ion(s) within the ion trap.

(36) The period of oscillations by definition is the time distance between two reflections (e g states where ion kinetic energy is minimal and its potential energy is maximal. In symmetric systems, one can consider that an ion's oscillation period is the signal period.

(37) A first transient pulse 20a is generated when the ion(s) 85B passes the sensing electrodes 87, moving from left-to-right, during the first half of one cycle of oscillatory motion within the electrostatic trap, and a second transient pulse 20b is generated when the ion(s) passes the sensing electrodes 87 again, this time moving from right to left during the second half of the oscillatory cycle. A subsequent, second cycle of oscillatory motion generates subsequent transient signal pulses 20c and 20d. The first half of the third cycle of oscillatory motion generates subsequent transient signal pulse 20e, and additional transient pulses (not shown) follow as the oscillatory motion continues, one cycle after another.

(38) Successive transient signal pulses are each separated, each one from its nearest neighbours, in the time-domain (i.e. along the time axis (t) of the function F.sub.1(t)), by a common period of time, T, corresponding to a period of what is, in effect, one periodic signal that endures for as long as the ion oscillatory motion endures within the electrostatic ion trap. In this way, the periodicity of the periodic signal is related to the period of the periodic, cyclic motion of the ion(s) within the electrostatic ion trap 80, described above. Thus, the existence of this common period of time (T) identifies the sequence of transient pulses (20a, 20b, 20c, 20d, 20e, . . . ) as being a “periodic component” of the image-charge/current signal, F.sub.1(t). Given that the common period of time, T, necessarily corresponds to a frequency (i.e. the inverse of the common time period), then this “periodic component” can also be described as a “frequency component”. The signal, F.sub.1(t), may be harmonic or may be non-harmonic, depending on the nature of the periodic oscillatory motion of the ion(s).

(39) FIG. 3B shows a schematic representation of a 2D function, F.sub.2(t.sub.1,t.sub.2), comprising a stack of segmented portions of the image-charge/current signal, F.sub.1(t), schematically shown in FIG. 3A. This is an example of the 2D function defined by the data 92 generated by the signal processor 91 and output to the display unit 93. The signal processor 91 is configured to determine a value (T) for the period of the periodic component (20a, 20b, 20c, 20d, 20e . . . etc.) within the image-charge/current signal, F.sub.1(t), and then to segment the image-charge/current signal, F.sub.1(t), into a number of separate successive time segments of duration corresponding to the determined period. The signal processor is configured to subsequently co-register the separate time segments in a first time dimension, t.sub.1, defining the determined period (T). Next, the signal processor 91 separates the co-registered time segments along a second time dimension, t.sub.2, transverse (e.g. orthogonal) to the first time dimension. The result is to generate a stack of separate, successive time segments arrayed along the second time dimension. Collectively, this array of co-registered time segments defines the 2D function, F.sub.2(t.sub.1,t.sub.2), which varies both across the width of the stack in the first time dimension, t.sub.1, according to time within the determined period, T, and also along the length of the stack in the second time dimension, t.sub.2, according to time between successive time segments. Referring to FIG. 3B, the period, T. of the periodic component has been determined to be T=4.5 μsec, and the continuous 1D image-charge/current signal has been segmented into a plurality of time segments (20A, 20B, 20C, 20D, 20E . . . etc.) each being 4.5 μsec in duration. Each one of the time segments of the plurality of time segments has been co-registered with each one of the other time segments of the plurality of time segments. This means that the first time segment 20A is selected to serve as a “reference” time segment against which al other time segments are co-registered. To achieve this co-registration, the time coordinate (i.e. the first time dimension t.sub.1) of each signal data value/point in a given time segment, other than the “reference” time segment, is subject to the following transformation of 1D time (t) into 2D time (t.sub.1, t.sub.2), in order to implement a step of segmenting the recorded signal into a number of separate time segments. The result is to convert the 1D function, F.sub.1(t), into the 2D function, F.sub.2(t.sub.1, t.sub.2), according to the relation:
t.fwdarw.t.sub.1+t.sub.2
F.sub.1(t).fwdarw.F.sub.2(t.sub.1,t.sub.2)˜F.sub.1(t.sub.1+t.sub.2).

(40) Here the variable t.sub.1 is a continuous variable with values restricted to be within the time segment, [0;T], ranging from 0 to T, where T is the period of the periodic component. The variable t.sub.2 is a discreet variable with values constrained such that t.sub.2=mT, where m is an integer (m=1, 2, 3 . . . , M). The upper value of m may be defined as: M=T.sub.acq/T, where T.sub.acq is the ‘acquisition time’, which is the total time duration over which all of the data points are acquired.

(41) The result is equivalent to a common time displacement or translation (schematically represented by item 25 of FIG. 3B) in a negative time direction along the first time dimension sufficient to ensure that the translated time segment starts (21, 23, . . . etc.) at time t.sub.1=0 and ends (22, 24, . . . etc.) at time t.sub.1=T=4.5 μsec. The result is that each time segment (20A, 20B, 20C, 20D, 20E . . . etc.) receives its own appropriate time translation (see item 25 of FIG. 3B) sufficient to ensure that all time segments extend only within the time interval [0;T] along the first time dimension.

(42) It is important to note that this registration process applies to time segments as a whole and does not apply to the location of transient signal pulses (20a, 20b, 20c, 20d, 20e, . . . etc.) appearing within successive time segments. However, if the time period, T, for the periodic signal component has been accurately determined, then the result of co-registering the time segments will be the consequential co-registration of the transient signal pulses, and the position of successive transient pulses along the first time dimension, will be static from one co-registered time segment to the next. This is the case in the schematic drawing of FIG. 3B, in which we see that the transient signal pulses align along a linear path parallel to the axis of the second time dimension.

(43) Conversely, if the time period, T, for the periodic signal component has not been accurately determined, then the result of co-registering the time segments will not result in a co-registration of the transient signal pulses, and the position of successive transient pulses along the first time dimension, will change/drift from one co-registered time segment to the next.

(44) The signal processor 91 subsequently displaces, or translates, each one of the co-registered time segments along a second time dimension, t.sub.2, which is transverse (e.g. orthogonal) to the first time dimension. In particular, each signal data value/point in a given time segment, other than the “reference” time segment, is assigned an additional coordinate data value such that each signal data point comprises three numbers: a value for the signal; a time value in the first time dimension and a value in the second time dimension. The first and second time dimension values, for a given signal data point, define a coordinate in a 2D time plane, and the signal value associated with that data point defines a value of the signal at that coordinate. In the example shown in FIG. 3B, the signal value is represented as a “height” of the data point above that 2D time plane.

(45) The time displacement or translation applied along the second time dimension is sufficient to ensure that each translated time segment is spaced from its two immediately neighbouring co-registered time segments. i.e. those immediately preceding and succeeding it, by the same displacement/spacing. The result is to generate a stack of separate, successive time segments arrayed along the second time dimension, which collectively defines the 2D function, F.sub.2(t.sub.1,t.sub.2), as shown in FIG. 3B. This function varies both across the width of the stack in the first time dimension, t.sub.1, so as to indicate the position and shape of the transient signal pulse within the time [0;T], and also along the length of the stack in the second time dimension, t.sub.2, according to time between successive time periods, or stack-segment number. Since the time interval between the beginning of the n.sup.th, and (n+1).sup.th stack, or between any two points with the same coordinate in the first time dimension, is necessarily equal to the time period, T, then the successive time segments are inherently spaced along the second time dimension by a time interval of T seconds (e.g. 4.5 μsec in the example of FIG. 3B).

(46) FIGS. 4 and 5 schematically represent the procedure for determining a value, T, for the period of the periodic signal component within the image-charge/current signal, F.sub.1(t), in the method for generating the 2D function F(t.sub.1,t.sub.2). FIG. 5 represents the steps S1 to S5 of the method, which are implemented at steps S2 to S5. The first step in the method is to generate an image charge/current signal (step S1), and then to record the image charge/current signal in the time domain (step S2).

(47) The acquired recording of the one-dimensional time domain image-charge/current signal, F.sub.1(t) of FIG. 4, contains one or more periodic oscillations. These periodic components may correspond to frequency components f.sub.1=1/T.sub.1, f.sub.2=1/T.sub.2 . . . etc.

(48) Subsequently, step S3 of the method determines a period (T) for a periodic signal component within the recorded signal, and this step may comprise the following sub-steps: (1) A first sub-step is to sample the one-dimensional time domain signal F.sub.1(t) of FIG. 4, with a sampling step of size “δt”. (2) A second sub-step is to estimate a value for the time period. T.sub.i (i=1, 2 . . . ), of each of the periodic/frequency components f.sub.1=1/T.sub.1, f.sub.2=1/T.sub.2 . . . etc. This may be done by means of any suitable spectral decomposition method as would be readily apparent the skilled person, or may be done purely by initially guessing those values and applying the present methods iteratively until a consistent result is found. (3) A third sub-step is to segment the one-dimensional signal, F.sub.1(t), and co-register the time segments according to a chosen period (frequency) value, f.sub.i=1/T.sub.i, so as to form the 2D function F(t.sub.1,t.sub.2). In particular, the argument t starts at t.sub.1=0 (zero) and every subsequent sampling step increases along the t.sub.1 axis by a step-size “δt”: initially the argument t.sub.2=0 (zero) during this process. After time t.sub.1 is equal to or greater than T has been reached, the argument t.sub.2 is reset to t.sub.1=0 (zero) and the argument t.sub.2 increases by a step size of T, i.e. t.sub.2=T. Thus, each sampling point of the measured signal is attributed to a pair of values, (t.sub.1, t.sub.2). In this way a 2D mesh/plane (t.sub.1, t.sub.2) is formed. This constitutes a “separating” of the co-registered time segments along a second time dimension, t.sub.2, transverse to the first time dimension thereby to generate a stack of time segments collectively defining a 2-dimensional (2D) function. The resulting function F.sub.2(t.sub.1,t.sub.2) can be thought of as a set of layers F(t.sub.1) where t.sub.1 is always within interval [0;T] and each layer corresponds to a certain t.sub.2 having a constant value (an integer multiple of T) within the layer. (4) A fourth sub-step, according to a first option, is to generate a first 2D scatter graph may be generated such that F(t.sub.1, t.sub.2=fixed), ignoring variation in t.sub.2 values, corresponds to viewing F.sub.2(t.sub.1,t.sub.2) along “View (a)” and will result in all layers been seen to overlap onto each other. For a proper choice of segment period, T, a peak can be seen above noise area, as shown in FIG. 6A and FIG. 7A. (5) A fourth sub-step, according to a second option, is to generate a second 2D scatter graph may be generated such showing F.sub.2(t.sub.1,t.sub.2) subject to the following condition: plot point (t2;t1) if |F.sub.2(t.sub.1,t.sub.2)|<C where C is predetermined threshold value (e.g. a pre-defined signal level), otherwise skip/omit it from the plot. For a proper choice of segment period, T, a clear channel, substantially free of data points, will appear to extend along a path parallel to the t.sub.2 axis, surrounded/bounded by points as shown in FIG. 6B and FIG. 7B. It is to be understood that the condition |F.sub.2(t.sub.1,t.sub.2)|>C is also possible, and this condition this will make a ‘filled’ channel with clear space around it in the 2D space.

(49) The value for the period, T, may be arrived at iteratively, using procedures (4) or/and (5) to decide whether the chosen period value corresponding to a frequency component of signal F.sub.1(t). This decision may be based on certain criteria. For example, according to method (4), if the representation of F.sub.2(t.sub.1,t.sub.2) contains a peak-shaped dense area then this is categorized as a frequency component. Examples are shown in FIG. 6A and FIG. 7A. Alternatively, or in addition, according to method (5), for a pre-defined signal threshold level, C, if the representation of F.sub.2(t.sub.1,t.sub.2) contains a clear and substantially straight channel extending along a path parallel to t.sub.2 axis, then this is categorized as a frequency component. Examples are shown in FIG. 6B and FIG. 7B. Both methods provide a means of identifying when the chosen segment period, T, (i.e. the length of each time segment) accurately matches the actual time period of the periodic component within the signal, F.sub.1(t). Only then will each transient peak of the periodic component in successive time segments ‘line-up’ in a linear fashion along a path parallel to the axis of the stacking dimension (t.sub.2). If the chosen segment period, T, does not accurately match the actual time period of the periodic component within the signal, F.sub.1(t), then the transient peak of the periodic component in successive time segments will not ‘line-up’ in a linear fashion along a path parallel to the axis of the stacking dimension. Instead, the peaks will drift along a path diverging either towards the axis of the stacking dimension, or away from it.

(50) Non-iterative methods of determining the frequency are also possible. Such methods may be faster. For example, suppose that the period of the periodic component that is initially determined, is slightly incorrect (i.e. T′≠T, but not by much). The result is a linear feature extending through the 2D space of the 2D function in a direction inclined to the second time dimension (t.sub.2 axis). One may find the period corresponded to this signal iteratively as described above, by iteratively re-segmenting and re-stacking the original 1D signal again and again until the linear feature is made parallel to the t.sub.2 axis. Alternatively, one can determine an inclination angle which the linear path of the linear feature subtends to the axis of the first time dimension (e.g. with respect to t.sub.1 axis) and get correct stacking period (i.e. T′=T), according to that angle (i.e. the angle between the t.sub.1 axis and linear path direction). The advantage is one does do not need to perform iterative re-segmenting and re-stacking at all. This saves lots of computational time because usually a signal array in memory is a very large amount of data and accessing such arrays in a PC memory is a long process and is a bottleneck in processing speed. Once one has determined the inclination angle, the formula for the correct period, determined using the ‘incorrect’ stacking period (T′) and the inclination angle, is:

(51) $\frac{1}{T}=\frac{1}{T^{\prime }}\left(1+\frac{1}{\tan \left(\alpha \right)}\right)$

(52) The inclination angle, α, can be measured directly, and may be iteratively optimized by successive measurements of the inclination angle, α, made by successive versions of the linear feature for successive (improving) values of stacking period (T′). In this way, the inclination angle, α, can be used as an optimisation variable to find the condition T′=T. Optimization methods readily available to the skilled person (e.g. gradient descent) or by machine learning tools (e.g. neural networks) may be used to implement this.

(53) Either method, namely method (4) or method (5), may be performed either by image analysis algorithms or by numerical algorithms. Preferably, such algorithms would consider the density, or number, of data points on the respective representation of F.sub.2(t.sub.1,t.sub.2). For example, an algorithm may determine the number of points falling below a pre-defined threshold |F.sub.2(t.sub.1,t.sub.2)|<C within a pre-defined time interval Δt.sub.1 within the first time dimension. If the density, or number, of points is less than the threshold, C, then this may be used to indicate that the frequency component is suitably detected. FIGS. 6B, 7B and FIGS. 8, 9A and 9B, exemplify this method. Here the method includes determining a sub-set of instances of the 2D function in which the value of the 2D function falls below the pre-set threshold value, C. From amongst that sub-set of instances one determines the interval of time, Δt.sub.1, in the first time dimension during which the 2D function never falls below the pre-set threshold value. One may then identify that interval of time as being the location/presence of the periodic signal component.

(54) Algorithms may employ machine earning techniques including neural networks trained to classify images having resolved peak structures (method (4)) and/or noticeable channels (method (5)).

(55) Once a value for the period, T, has been arrived at iteratively, the method proceeds by segmenting the recorded signal into a number of separate successive time segments of duration corresponding to the determined period (step S4). The procedure for doing this is the same as that described in the sub-step (3) of step S3. It will be appreciated that, according to the iterative method of determining the time period, T, one inherently performs method step S3 when one implements the final, successful sub-step (4) or (5) of step S3, described above.

(56) The final step S5 of the method is to generating a stack of the time segments of step S4, in a second time domain, t.sub.2, to generate a stacked image charge/current signal. The procedure for doing this is the same as that described in the sub-step (3) for co-registering the separate time segments in a first time dimension, t.sub.1, defining the determined period, T, and of separating the co-registered time segments along the second time dimension, t.sub.2, transverse to the first time dimension. Once more, according to the iterative method of determining the time period, T, one inherently performs method step S5 when one implements the final, successful sub-step (4) or (5) of step S3, described above.

(57) In this method the signal processing unit may be programmed determine the value, T, for the period of a periodic signal component iteratively in this way. It may initially estimate a ‘trial’ value of T, as described above, and segment the recorded signal, F.sub.1(t), using that ‘trial’ value, into a number of time segments of duration corresponding to a ‘trial’ period, and co-registering them, then separate the co-registered time segments along the second time dimension, t.sub.2, to generate a stack of time segments. The signal processor unit may 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, then a new ‘trial’ time period, T, is chosen by the signal processor and a new stack of time segments is generated using the new ‘trial’ time period. The signal processor 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 substantially no such change occurs. This condition signifies that the latest ‘trial’ time period. T, is an accurate estimate of the true time period value.

(58) Analysis of F.sub.2(t.sub.1,t.sub.2) may provide information on existing frequency components (i.e. frequency spectrum), on frequency components behaviour in time (e.g. frequency stability), on interaction of frequency components with each other, on quality/property of a system which is responsible for the signal generation. Gathered information may be useful for further analysis or can be used to do some corrections on the measured signal in order to achieve certain improvements.

(59) For example, one may identify, from amongst separate successive time segments, those time segments containing two or more periodic signal components, and one may resolve two or more different mass-to-charge ratios (m/q) of ions according to the two or more different periodic signal components within the 2D function. For example, in FIG. 8, the chosen segment period (i.e. the length of each time segment) initially accurately matches the actual time period of the periodic component within the signal, F.sub.1(t). The result is that the initial “channel #1” of the 2D function extends in a linear fashion along a path parallel to the axis of the stacking dimension, namely the second time dimension t.sub.2. However, subsequently, the “channel #1” bifurcates in to “channel #2” and “channel #3”, one of which drifts along a path diverging away from the axis of the stacking dimension (cf. “channel #3”). The other fork in the bifurcation (cf. “channel #2”) continues along a path parallel to the axis of the stacking dimension. This bifurcation indicates that an ion within the pack of ions 85B inside the electrostatic ion trap 80, after initially performing oscillatory motion possessing a periodic component of period T, has subsequently undergone a collision within the trap which has ionised it further and changed its m/z ratio. In addition, this picture also demonstrates fine isotopic structure elucidation. That is to say, two very close masses (different isotopes of the same species) may similarly bifurcate, or split, the channel #1 into channels #2 and #3.

(60) The consequence is a change in the orbital dynamics of the new ion so as to change its oscillatory motion relative to that of the ion pack it once resided within and, as a result, to add a new period of periodic component to the signal associated with the new ion. The new “channel #3” corresponds to the new ion, whereas the new “channel #2” is a continuation of “channel #1” which represents the remaining pack of ions, albeit now with one less ion in it. The remaining “channel #2” continues along a path parallel to the second time dimension, t.sub.2, because the stacking period, T, upon which the 2D function F.sub.2(t.sub.1,t.sub.2) is based, remains an accurate estimate of the period of the periodic component associated with the remaining ion pack. However, the stacking period, T, is not an accurate estimate of the period of the periodic component associated with the new ion and so “channel #3” diverges from the second time dimension. This divergence signals the creation of the new ion. Thus, the method may comprise determining a fragmentation of a said ion according to a bifurcation, in the second dimension of time, of the periodic signal component within the first dimension of time.

(61) The stacking period, T, may then be re-estimated to identify the period T.sub.new, of the new ion and this will be revealed when the 1D function, F.sub.1(t), is re-segmented and stacked according to a new estimate of the time period for the periodic signal component associated with the new ion, such that the path of “channel #3” extends along a linear path parallel to the second time dimension, t.sub.2. Of course, this will also cause the path of “channel #2” to diverge towards the second time dimension. In this way, one may determine, in the second dimension of time, a change in the position of the interval of time associated with a periodic component in the first dimension of time, thereby to identify a change in oscillatory motion of an ion. The signal processor unit may be configured to detect this type of change.

(62) Similarly, one may determine, in the second dimension of time, a change in the duration of the interval of time associated with a periodic component in the first dimension of time, thereby to identify a change in oscillatory motion of an ion. For example, FIGS. 3A, 6A and 6B show a 1D signal, F.sub.1(t), (cf. FIG. 3A), and alternative views of a corresponding 2D function, F.sub.2(t.sub.1,t.sub.2), in which the width of the transient signal peak associated with a periodic signal component, is seen to increase over successive cycles of oscillatory ion motion (cf. FIG. 6A, 6B). This increase in width is due to a spreading of the length of the ion pack along the trajectory of the ion pack within the electrostatic ion trap 80, from one oscillatory cycle to the next. By determining, in the second dimension of time, the change in the width of the channel (i.e. duration of the periodic signal component) as measured in the first dimension of time, one may identify a the occurrence of this change in the motion of the ions within the ion pack. The signal processor unit may be configured to detect this type of change.

(63) The method may comprise determining a time at which any change occurs in the position or duration of a transient structure in the 2D function, whether in the form of a signal peak structure or a channel derived from it as explained above, and applying a desired subsequent analytical process only to parts of the recorded signal generated before (or alternatively, only after) the time at which that change occurs. This allows one to identify periods of time during which a selected type of ion motion is taking place, and to exclude periods in which other types of ion motion are occurring, which may complicate analysis or be otherwise not necessary or of use.

(64) Desirably, the method may comprise identifying, from amongst said separate successive time segments, time segments containing multiple periodic signal components which occur between time segments containing only one periodic signal component, and excluding those identified segments from the stack, thereby leaving within the stack those time segments containing only one periodic signal component. FIG. 11 illustrates an example of this. In particular, a selection can be performed wherein certain undesired time segments are omitted from the stack defining the 2D function. This may be advantageous to exclude interference, for example to get rid of aliquoted frequency components. For example, with reference to FIG. 11, if we consider frequency component f.sub.0 and there is ½f.sub.0 component in the signal as well, there will be two transient peaks in half of the time segments (i.e. every alternate time segment) defining the 2D function, F(t.sub.1,t.sub.2).

(65) This would be revealed as two peaks in “View (a)” of the 2D function, and as two channels in “View (b)” of the 2D function after the threshold, C, has been applied to it. However, if we consider segment by segment we find that only every alternate time segment contains two peaks, one associated with the frequency component ½f.sub.0 and the other associated with the frequency component f.sub.0. Each such alternate time segment is followed by an adjacent time segment containing only one peak associated with the frequency component ½f.sub.0, as shown in FIG. 11. Thus, in order to be rid of the frequency component ½f.sub.0, one may skip or discard time segments located in the second time dimension at times t.sub.2=2T, 4T, 6T and so on (see FIG. 11) so as to provide a form of the 2D function representing only the frequency component ½f.sub.0. In a similar way it is possible to get rid of other frequency components with aliquoted frequencies (periods). In general, these are combinations of f.sub.0 and (m/n)f.sub.0 (m, n are integers, m<n), we may skip respective layers so that only f.sub.0 components are present in the signal.

(66) Averaging may be performed by combining the data associated with multiple time segments, for example by combining the data associated with the following time points along the second time dimension t.sub.2=kT, t.sub.2=(k+1)T, . . . t.sub.2=(k+N.sub.avg)T, (N.sub.avg, an integer), which each share the same point sampling point of t.sub.1 upon the first time dimension of the 2D spaces. For example, the data points for successive time segments having the same position along the t.sub.1 axis, but spaced along the t.sub.2 axis, may be summed and the result divided the result by N.sub.avg. Interpolation of values of the 2D function, F.sub.2(t.sub.1,t.sub.2), is required with respect to t.sub.1 axis. Averaging is advantageous for low intensity signals, i.e. when the signal-to-noise (S/N) ratio is small. For example, the step of segmenting the recorded signal into a number of separate time segments may include converting the 1D function, F.sub.1(t), into the 2D function, F.sub.2(t.sub.1, t.sub.2), according to the relation:

(67) $F_{\mathrm{nm}}=\frac{1}{N_{\mathrm{avg}}}\underset{j={\mathrm{mN}}_{\mathrm{avg}}}{\overset{j=\left(m+1\right)N_{\mathrm{avg}}}{.Math.}}{F}_1\left(\frac{n}{N}T+\mathrm{jT}\right)$

(68) Here, each segment in F.sub.2(t.sub.1, t.sub.2) is constructed as an average of N.sub.avg successive segments of F.sub.1(t). Possible choices of counting integers are: N=T/δt; m=1, 2, 3, . . . , M; where M=T.sub.acq(T*N.sub.avg). Of course, setting a value of N.sub.avg=1 means there is no averaging.

(69) If necessary, or desired, parts of the 2D space of the 2D function, F.sub.2(t.sub.1,t.sub.2), where no data point or measured value is available or present (i.e. where F.sub.2(t.sub.1,t.sub.2) is undefined), may be generated by interpolation between existing data points of F.sub.2(t.sub.1,t.sub.2). For example, if the signal F.sub.1(t) is not defined at some arbitrary time, t.sub.i, then its value can be interpolated using adjacent measured signal values where F.sub.1(t) is defined. For example, one may create a mesh within the segmentation interval, [0:T], and interpolate values of the signal whenever sampling points do not fall onto the mesh nodes. For example, suppose that to interpolate a value for F.sub.1(t) at an interpolation time point, t.sub.c, where no measured data value exists. If the interpolation time point falls into interval [t.sub.a; t.sub.b], where measured data values exist at both time points t.sub.a and t.sub.b, then one may use linear interpolation using the values F.sub.1(t.sub.a) and F.sub.1(t.sub.b) to generate/interpolate a value for F(t.sub.c). Other types are also possible of course.

(70) Furthermore, the method permits one to identify an instability in an electric field and/or magnetic field of said ion analyser apparatus. Such instabilities are revealed, in the second dimension of time, as a change in the position and/or duration of a periodic signal component in the first dimension of time. FIGS. 9A, 9B and 10 illustrate examples of this. For example, the method may include identifying, in the second dimension of time, a change in the position and/or duration of the periodic signal component in the first dimension of time, thereby to identify an instability in an electric field and/or magnetic field of the ion trap apparatus, 80.

(71) Referring to FIG. 9A, a waving of the “channel” formed by a periodic component within the 2D function, F.sub.2(t.sub.1,t.sub.2), when subject to the threshold, C, condition, indicates that the instantaneous frequency of this periodic component is not stable due to electrical field instability inside the ion trap, 80. This kind of analysis allows one to estimate an instability of the power supply and it is extremely sensitive compared to conventional electrical circuit measurements. In particular, the “channel” formed by the instantaneous period changes can be used to correct time axis in the first time dimension, t.sub.1, so that this period becomes stable over the second time dimension, t.sub.2, and the “channel” attains a straight path parallel to the second time dimension.

(72) To achieve this, the signal processor unit maybe configured to determine a function G(t.sub.2) which reflects non-linear path indicated in FIG. 9A. The function G(t.sub.2) is a line following centre of the “channel” (or, alternatively, the position of the transient signal peak maximum) within the 2D function. The value of G(t.sub.2) at a given time in the second dimension, t.sub.2, is simply equal to the value of t.sub.1 corresponding to the projection of the non-linear path upon the first time dimension. Thus, G(t.sub.2) can be obtained by reading position, t.sub.1, of the centre of the “channel” within the 2D function, as shown in FIG. 9A, or the position, t.sub.1, of a peak in the 2D function if the threshold condition, C, is not being applied, in each time segment of the stack defining the 2D function.

(73) The instantaneous period T(t) can be determined via G(t.sub.2) using formula:
T(t)=T′×(dG(t.sub.2)/dt.sub.2+1),
where T′ is the period used to generate the 2D function, F.sub.2(t.sub.1,t.sub.2). The derivative, (dG(t.sub.2)/dt.sub.2), can be calculated either analytically or numerically.

(74) Next, the time axis or the time domain signal is corrected according to the following formula:
δt.sub.i=δt×T′/T(t.sub.i)
which defines the current time-step (sampling step, δt.sub.i), where the counting integer, i, runs from 0 (zero) to the number of sampling points N in the 1D time-domain signal, F.sub.1(t). The normal sampling step, δt is corrected at each step of signal correction procedure. This will form a new, non-uniform time mesh t.sub.new. Subsequently the 1D time-domain signal, F.sub.1(t.sub.new), may be interpolated, using these non-uniform time mesh points, onto a uniform time mesh again, for further use and analysis as desired. The quantity δt is the sampling interval described above with reference to FIG. 4. Effectively, this last operation shrinks/stretches time axis in the first dime dimension, t.sub.1, so that the instantaneous time period, T, increases/reduces as appropriate, i.e. the time axis becomes non-uniform. T(t) may be interpolated or fitted with an analytical function in order to get individual T(t.sub.i) values, if required. Sometimes it is preferable to smooth the T(t) function before this time axis correction is performed. Interpolation, fitting and smoothing can be performed on the G(t) function alternatively.

(75) An example of the 2D function, F.sub.2(t.sub.1,t.sub.2), when subject to the threshold condition, C, is shown in FIG. 9A. The G(t) function approximated by an analytical expression is shown by a dashed curve. The same data after correction is shown in FIG. 9B. The G(t) function used for this correction is shown by white curve, 60. This correction is especially useful when instability of the trapping field is caused by gate electrode pulse at the beginning of transient. Absorption mode (A-mode) of Fourier Transformation is substantially deteriorated in this case and cannot be used for mass spectra representation, because each peak will be inevitably accompanied by confusing side peaks. The correction method described above solves this problem for any frequency component. FIG. 10 shows an example of a Fourier Transform peak generated in A-mode of the signal presented in FIG. 9A. The A-mode Fourier Transform frequency peak generated from the un-corrected data is shown together with the A-mode Fourier Transform frequency peak generated from the corrected signal.

(76) The method is especially efficient for non-harmonic signals which bear transient pulses having pulse widths/durations (cf. the interval of time, Δt.sub.1) smaller compared to period of oscillations of a frequency component. Apart from its high resolution power, the method permits the dynamics of frequency components to be seen and analysed. Dynamics of the signal behaviour provided by the 2D function is useful for single ion analysis used in charge detection FTMS. Using the appropriate degree of averaging of time segments within the 2D function one can see single ion events including collision events occur during transient and resulting in collisional fragmentation. Furthermore, the fate of the ion can be seen, for example ion fragment and the change in ion kinetic energy even when this changes a little so that its frequency of oscillation changes only a little, or changes so much that the ion is subsequently unable to sustain oscillatory motion in the ion trap. It is important to detect these events as they will influence a Fourier Transform peak amplitude which might be used to gather statistics on single ion events to build an isotopic mass spectrum, and to determine a charge state of an ion.

(77) For events in which frequency is changed only a little after collisional fragmentation, it is possible to gain information of what mass of the fragment is and it is possible to correct the instantaneous frequency so that it gives proper contribution into single ion event statistics.

EXAMPLE

(78) As a brief example, applied to CDMS, once the correct period, T.sub.i of the periodic component has been identified within the image-charge/current signal generated by the oscillatory motion of an ion, as described above, one may then determine the charge on the ion as follows.

(79) One may define a lifetime (LT) of an ion as a duration of time when the frequency of the periodic signal component associated with the ion is substantially constant. For example, a “channel” feature presented in the 2D function, F.sub.2(t.sub.1, t.sub.2), is present and linear (cf. FIG. 7B). One may average all of the data across all of the segments (i.e. the data summed and averaged over the second time dimension, t.sub.2) that exist within this LT interval. This produces a single 1D curve, S(t.sub.1), in the first time dimension, t.sub.1, alone since the second time dimension has been collapsed by the averaging process. This curve will represent an averaged time-domain peak induced by a single ion, e.g. a multiply-charged ion. The apex height/amplitude of a peak feature formed by the periodic component, gives the amount of charge on this ion.

(80) A predetermined calibration curve may be used which relates a measured apex height/amplitude with ion charge. The apex height/amplitude may be determined by determining the maximal value of the 1D curve, S(t.sub.1), or may be more accurately determined e.g. fitting the 1D curve, S(t.sub.1), or at least the part of that curve containing the peak feature, to a Gaussian curve, a parabolic curve, or via an RC circuit signal fitting.

(81) Alternatively, one may generate a 1D function, S(t), as an integrated or ‘accumulated’ signal in which discrete values of the 1D function F.sub.1(t), at sampling time points t.sub.i, are each multiplied by the value of a pre-determined periodic function at the same respective sampling time points t.sub.i. The resulting products are then summed. This maybe embodied as a scalar product, F.sub.1(t).Math.G(t), of two vectors, F.sub.1(t) and G(t), as follows:

(82) $\mathrm{Where},\begin{array}{c}S\left(t\right)=\underset{t_i=0}{\overset{t}{.Math.}}{F}_1\left(t_i\right)G\left(t_i\right)\\ F_1\left(t\right)={\left[F_1\left(t_0\right),F_1\left(t_1\right),\mathrm{.Math.},F_1\left(t_i\right),\mathrm{.Math.},F_1\left(t\right)\right]}^T\\ G\left(t\right)={\left[G\left(t_0\right),G\left(t_1\right),\mathrm{.Math.},G\left(t_i\right),\mathrm{.Math.},G\left(t\right)\right]}^T\end{array}$

(83) Here, G(t.sub.i) is the pre-determined periodic function with period of T, this being the period of the periodic component that has been identified within the image-charge/current signal generated by the oscillatory motion of an ion, as described above. The result is a function S(t) which is defined over the whole data acquisition time interval: t=[0;T.sub.acq]. If the period, T, of the periodic component (signal frequency, f=1/T) remains constant, then the magnitude of the function, S(t), grows linearly with time (t) with a substantially constant rate of change (i.e. underlying ‘slope’ of rise). However, if the period of the periodic component changes (i.e. T.fwdarw.T*≠T), then the rate of change (i.e. ‘slope’ of rise) of the magnitude of the function, S(t), also changes. This change in period occurs when the ion(s) responsible for generating the image-charge/current signal generated by the oscillatory motion, escapes from stable oscillatory motion. This growth and change in S(t) is schematically shown in FIG. 13A. Gaussian basis functions, as examples of G(t.sub.i), are schematically shown in FIG. 13B. These Gaussian basis functions collectively define the pre-determined periodic function in the sense that the Gaussian function repeats with a period of T. If the periodic function, G(t.sub.i), comprises sinusoidal basis functions (e.g. ˜‘sin’ or ˜‘cos’ function, or exponential basis functions, ˜exp(−i2π.Math.t/T)), then it is not necessary to select an appropriate phase of the function—any phase is appropriate. However, for other forms of the periodic function, G(t.sub.i), (e.g. non-sinusoidal, such as Gaussian basis functions or delta-function basis functions) one may preferably select an appropriate phase of the periodicity within G(t.sub.i), for improved results. This phase preferably corresponds to the phase of the periodic components within their intervals [0;T]. In other words, the phase may preferably correspond to a time, 0≤t′≤T, within the very first segment [0;T], when an ion produces the very first signal pulse on the pick-up detector. As an example, if t′=T/3 then the phase of the periodic function, G(t.sub.i), may be selected so that the first Gaussian function, or delta function etc., is centred at the time t′=T/3 with all subsequent Gaussian function, or delta function etc., following at regular, periodic time intervals, T.

(84) It is found that the rate of change of the magnitude of the function, S(t), (i.e. the slope of the growth of S(t)) within the data acquisition time interval: t=[0:T.sub.acq], is proportional to the charge, z, of the ion:

(85) $\frac{\mathrm{dS}\left(t\right)}{\mathrm{dt}}=\mathrm{az}+b$

(86) Here, the terms ‘a’ and ‘b’ are constants, predetermined calibration values. The charge, z, of the ion may be determined according to this equation.

REFERENCES

(87) A number of publications are cited above in order to more fully describe and disclose the invention and the state of the art to which the invention pertains. Full citations for these references are provided below. The entirety of each of these references is incorporated herein. WO02/103747 (A1) (Zajfman et al.) U.S. Pat. No. 7,964,842 (B2) (Köster et al.) WO2012/116765 (A1) (Ding et al) “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. “A Simulation Study of the Planar Electrostatic Ion Trap Mass Analyzer”: by Li Ding, Ranjan Badheka, Zhengtao Ding, and Hiroaki Nakanishi; J. Am. Soc. Mass Spectrom. 2013, 24, 3, 356-364. WO2016/1083074A1 (Rusinov, et al.)