Methods for broad-stability mass analysis using a quadrupole mass filter

Abstract

A method of mass analysis comprises: generating ions from the sample; delivering the ions to a quadrupole; applying a radio frequency voltage, V, to rods of the quadrupole such that the instantaneous electrical potential of each rod is out of phase with each adjacent rod and a non-oscillatory voltage, U, across each pair of adjacent rods such that a subset of the ions having a range of mass-to-charge (m/z) ratios are selectively transmitted through the quadrupole; varying at least one of voltage U and voltage V such that the range of selectively transmitted m/z ratios is caused to vary and varying at least one additional operational parameter; acquiring a data set comprising a series of temporally-resolved images of spatial distribution patterns of transmitted ions at each combination of U, V and the at least one additional operating parameter; and mathematically deconvolving the data set to generate mass spectra.

Claims

1. A method of analyzing a sample by mass spectrometry, comprising the steps of: generating a stream of ions from the sample; delivering the ions to an inlet end of a quadrupole, the quadrupole defining a central longitudinal axis and first and second transverse axes; applying an oscillatory radio frequency (RF) voltage, V, to rods of the quadrupole such that the instantaneous electrical potential of each rod is 180-degrees out of phase with each adjacent rod and a non-oscillatory voltage, U, across each pair of adjacent rods such that a subset of the ions having a range of mass-to-charge (m/z) ratio values are selectively transmitted through the quadrupole to an outlet end of the quadrupole; varying at least one of the applied voltage U and the applied voltage V such that the range of selectively transmitted m/z ratio values is caused to vary and varying at least one additional operational parameter of the quadrupole, wherein the varying of the at least one additional operational parameter comprises varying a ratio (U/V) between the applied U and the applied V by: progressively varying both U and V in proportion to one another from a first pair of values (U.sub.1, V.sub.1) to a second pair of values (U.sub.2, V.sub.2) and in accordance with a first constant of proportionality, k.sub.1, such that U=k.sub.1V; and progressively varying both U and V in proportion to one another from a third pair of values (U.sub.3, V.sub.3) to a fourth pair of values (U.sub.4, V.sub.4) and in accordance with a second constant of proportionality, k.sub.2, such that U=k.sub.2; acquiring a data set comprising a series of temporally-resolved images of spatial distribution patterns of the selectively transmitted ions at each combination of U, V and the at least one additional operating parameter; and mathematically deconvolving the data set so as to generate a mass spectrum for each combination of U and V.

2. A method as recited in claim 1, wherein the varying of at least one additional operational parameter further comprises varying an acceleration voltage such that the ions' kinetic energy and a number of RF cycles for which the ions remain within the quadrupole is caused to vary.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The above noted and various other aspects of the present invention will become apparent from the following description which is given by way of non-limiting example only and with reference to the accompanying drawings, not drawn to scale, in which:

(2) FIG. 1 is a graphical depiction of a stability region for a quadrupole mass filter in terms of the Mathieu parameters q and a;

(3) FIG. 2 is a schematic example configuration of a triple stage mass spectrometer system;

(4) FIG. 3 is a simulated recorded image of a multiple distinct species of ions as collected at the exit aperture of a quadrupole at a particular instant in time;

(5) FIG. 4A is a schematic depiction of the simulated movement of two different ions with different masses parallel to the x-direction of a quadrupole mass filter as a function of the number of RF cycles through the quadrupole device;

(6) FIG. 4B is a schematic depiction of the simulated movement of the two different ions through the quadrupole mass filter parallel to the x-direction, as described with reference to FIG. 4A, wherein a greater axial velocity is imparted to the ions such that fewer RF cycles occur during the ions' passage through the quadrupole mass filter;

(7) FIG. 5 is an expanded graphical depiction of a portion of the stability region of FIG. 1; and

(8) FIG. 6 is a transverse cross sectional view through the quadrupole rods of a quadrupole apparatus.

DETAILED DESCRIPTION

(9) The following description is presented to enable any person skilled in the art to make and use the invention, and is provided in the context of a particular application and its requirements. Various modifications to the described embodiments will be readily apparent to those skilled in the art and the generic principles herein may be applied to other embodiments. Thus, the present invention is not intended to be limited to the embodiments and examples shown but is to be accorded the widest possible scope in accordance with the features and principles shown and described. The particular features and advantages of the invention will become more apparent with reference to the appended FIGS. 1-3, 4A and 4B, taken in conjunction with the following description.

(10) In contrast to conventional methods of scanning a quadrupole mass filter (QMF), in which the DC and RF voltages are ramped such that a scan line passes just below the apex of the Mathieu stability region (see FIG. 1), the aforementioned U.S. Pat. No. 8,389,929 describes methods of scanning wherein the scan lines pass through wider portions of the stability region such as the scan line 1 and scan line 3 shown in FIG. 1. When operated in this fashion, the ions that are transmitted completely through the QMF at each pair of applied DC and RF voltages, U and V, will be just those ions whose masses (or mass-to-charge ratios, also denoted as m/z ratios, in the case of multiply-charged ions) are such as to place their Mathieu q and a values within the stability region and along the particular scan line being employed. For example, if a pair of DC and RF voltages, U and V, are applied in a proportion dictated by the slope of scan line 3 as illustrated in FIG. 1, then the QMF will transmit ions of a relatively wide range of masses (or mass-to-charge ratios) corresponding to the portion of scan line 3 between the scan line entry point 6 and its exit point 8. The transmitted ions will generally comprise a subset of all possible masses (or mass-to-charge ratios). As the voltages are ramped proportionately, the .sub.x values of some lighter ions whose q and a values previously resided within the stability region will increase beyond .sub.x=1 (at point 8) and such ions will no longer be transmitted. At the same time, some heavier ions whose trajectories were previously unstable will enter the stability region (at point 6) and will begin to be transmitted through the quadrupole.

(11) Accordingly, when the (a, q) values associated with an ion's mass are such that the previously unstable ion enters the stability region during a scan, the y-component of its trajectory changes from unstable to stable. Watching an ion image formed in the exit cross section progress in time, the ion cloud is elongated and undergoes wild vertical oscillations that carry it beyond the top and bottom of a collected image. Gradually, the exit cloud contracts, and the amplitude of the y-component oscillations decreases. If the cloud is sufficiently compact upon entering the quadrupole, the entire cloud remains in the image, i.e. 100% transmission efficiency, during the complete oscillation cycle when the ion is well within the stability region.

(12) Later during a scan, as the same ion's (a, q) values approach the exit of the stability region (i.e., at point 4 or point 8 or some other point along the curve corresponding to .sub.y=0), a similar effect happens, but in reverse and involving the x-component rather than the y-component. The cloud gradually elongates in the horizontal direction and the oscillations in this direction increase in magnitude until the cloud is carried across the left and right boundaries of the image. Eventually, both the oscillations and the length of the cloud increase until the transmission decreases to zero.

(13) FIG. 3 graphically illustrates such results. In particular, the vertical cloud of ions, as enclosed graphically by the ellipse 16 shown in FIG. 3, corresponds to the heavier ions entering the stability diagram, as described above, and accordingly oscillates with an amplitude that brings such heavy ions close to the denoted y-quadrupoles. The cluster of ions enclosed graphically by the ellipse 18 shown in FIG. 3 correspond to lighter ions exiting the stability region and thus cause such ions to oscillate with an amplitude that brings such lighter ions close to the denoted x-quadrupoles. Within the image lie the additional clusters of ions (shown in FIG. 3 but not specifically highlighted) that have been collected at the same time frame but which have a different exit pattern because of the differences of their a and q parameters.

(14) Both the simulated data depicted in FIG. 3 as well as the form of the voxel set data structure employed in U.S. Pat. No. 8,389,929 assume that a spatial distribution of ions is measured as the ions emerge from the outlet end of a quadrupole mass filter (QMF) during the course of a normal mass scan. The voxel sets, as previously defined, represent a snapshot of the positions of ions after being subjected to a given number of RF cycles in the quadrupole mass analyzer at a given set parameters for the device. The data deconvolution treatment, as previously described, therefore employs a model that takes into consideration the variation of the ionic m/z distribution at the outlet end in terms of the two independent spatial variables, X and Y. The prior data deconvolution treatment also employs a third independent variable, termed sub-RF variation, which requires acquisition of a series of voxel plane snapshots at various phase points within a single RF cycle.

(15) The present inventors have recognized that novel modifications to the conventional quadrupole mass filter scanning procedure can provide additional information relating to the separation of ions of different mass-to-charge ratios within a QMF device. In simulations, the inventors have noted that the ion pathways through the entire length of a QMF are significantly different for ions of differing m/z ratios. For example, curves 42 and 44 of FIG. 4A show respective calculated pathways, along the x-dimension, of two ions of different masses through a QMF as they during the ions' transit through the QMF device comprising x-rods 63 (as well as not-illustrated y-rods). The difference in mass between the two ions was set such that the difference between the q-values, q, is 0.001. The horizontal arrow in FIG. 4A indicates both the direction of the device z-axis (i.e., the axial dimension) and the direction of overall ion transport through the QMF, from an inlet end to an outlet end of the QMF. Prior data acquisition schemes, as discussed in U.S. Pat. No. 8,389,929, only consider the ion distribution at the outlet end of the quadrupole mass filter, at or near which imaging detector component 67 is located. Since a plurality of images are obtained at different RF phase values, the prior data acquisition scheme only covers a small portion of the path near the outlet end, such as region 43. However, since the x-trajectories of the ions both converge and diverge as they transit through the length of the device (FIG. 4A) these ions may or may not be well-separated in the x-direction as they exit the QMF, depending on their mass difference and the number of applied RF cycles.

(16) The present inventors have recognized that it would be desirable to not only effectively sample the ion distributions near the end of the traces 42 and 44, (FIG. 4A) as has been previously described, but to additionally effectively sample the positional variation among different-mass ions within the internal volume of the QMF, such as at the region labeled 45, so as to more-sufficiently sample the rich variety of full variability of ion trajectories and positions. The inventors have further recognized that, in order to experimentally capture the full positional variation that is exhibited by the simulations, one only needs to vary the ions axial velocity (along the z-axis) so as to change the number of RF cycles that are spent by ions inside the quadrupole. Operationally, this axial velocity variation may be accomplished by varying an axial acceleration voltage that guides ions into or through the quadrupole mass filter. Such axial acceleration voltages are often provided by ion lenses (not illustrated) positioned proximal to the inlet and outlet ends of the quadrupole mass filter and provided with respective DC electrical potentials.

(17) As an example of the effect of varying ion velocity along the z-axis, FIG. 4B illustrates the expansion of the traces 42 and 44 as the z-axis velocity is increased such that the region 45 moves to the outlet end of the detector at which point the ionic spatial distribution may be sampled by the imaging detector component 67. The sampling of region 45 (i.e., the detection of a series of ion spatial distributions by imaging detector component 67 within the range of number of RF cycles corresponding to region 45) may be performed subsequent to the sampling of region 43, after which other such regions may likewise be sampled. The sampling of a series of such regions may be performed while the applied DC and RF voltages (U and V, respectively) are essentially constant and correspond to a single point on a scan line for any particular mass-to-charge ratio, such as, for example, any of the points 2, 21, 22 or 4 (or any intervening points) on scan line 1 or any of the points 6, 25, 26, 27, 28, 29 or 8 (or any intervening points) on scan line 3 (FIG. 5). Employing such a sampling technique, each data packet (a vector) corresponding to a sampled ion abundance, or voxel set, corresponds to a four-dimensional space of independent variables, these four variables being: (1) x-position; (2) y-position; (3) number of RF cycles applied during transit through the QMF; and (4) sub-RF phase.

(18) Because the above-described novel technique of varying z-axis velocity generates a larger quantity of data than would otherwise be available, this technique requires slowing of the maximum scan rate of the quadrupole mass filter, as compared with either conventional mass scanning or with the methods discussed in U.S. Pat. No. 8,389,929, so as to capture information many times at any given scan point. Nonetheless, the mass scanning across the breadth of a scan line and the sampling of various regions at each point along the scan line (each region corresponding to a different range of number of applied RF cycles) may be performed sufficiently rapidly that the chemical composition of a material being analyzed (such as an eluate from a chromatograph) does not significantly change during the entire sequence of sampling events.

(19) The present inventors have further recognized that a second way to generate an additional dimension of data is to vary the U and V values applied to a quadrupole mass filter (and the ratio between the two applied values) such that effectively multiple scan lines are sampled as an analysis is proceeding. As one example, a first mass scan in accordance with scan line 1 may be performed, after which a second mass scan in accordance with scan line 3 may be performed. Further, at each point corresponding to application of a particular (U, V) pair (which corresponds to a single point on a scan line for any particular mass-to-charge ratio), a series of images corresponding to sub-RF increments is acquired. The entire sequence of sampling events (corresponding to all of the sub-RF image acquisitions sampled at all of the mass scan points of the two mass scans) should be performed sufficiently rapidly that the chemical composition of material being analyzed (such as an eluate from a chromatograph) does not significantly change during the entire sequence of sampling events. In alternative embodiments, the DC and RF voltages could be applied such that portions of the different scan lines are sampled in an interleaved fashion or such that sampled points alternate between the two scan lines. Employing such sampling techniques, each data packet (a vector) corresponding to a sampled ion abundance, or voxel, corresponds to a five-dimensional space of independent variables, these five variables being: (1) x-position; (2) y-position; (3) applied RF voltage, V; (4) voltage ratio (U/V) and (5) sub-RF phase.

(20) According to some embodiments, one convenient way of alternating between two scan lines would be to perform the following sequence of steps: (a) set an applied voltage, such as RF voltage V, to some desired first value, V.sub.1; (b) set the other applied voltage (in this example, DC voltage U) to a value in accordance with a first scan line (that is, set U.sub.1=V.sub.1 where is a constant of proportionality); (c) acquire data along the first scan line using the set voltages (U.sub.1, V.sub.1); (d) without changing the first applied voltage (V.sub.1), set the other applied voltage to a value in accordance with a second scan line (that is, set U.sub.2=V.sub.1 where is a second constant of proportionality); (e) acquire data along the second scan line using the set voltages (U.sub.1, V.sub.2); (f) set the first applied voltage (V) to another desired value (V.sub.2), different from the previous applied value; and, then, repeat steps (b)-(f) any desired number of times. The data acquisition steps at each pair of applied voltages, U and V, includes at least obtaining a series of images of ion spatial distributions at respective sub-RF phase values.

(21) The above description of scan line alternation may be better understood with reference to FIG. 5, which illustrates the same scan lines 1 and 3 as illustrated in FIG. 1 and a portion of the Mathieu stability field. Although the following example makes reference to just a few widely separated points along each scan line, it should be kept in mind that, in practice, there may exist a nearly continuous plurality of points at which data is acquired along each scan line. In a first step, the RF voltage, V and the DC voltage, U, are set at values U.sub.1 and V.sub.1 such that an ion having a first mass-to-charge ratio, here denoted as m.sub.h, is just on the edge of its stability region (.sub.y=0) along scan line 3 at q=0.368 (according to this example). Ions having stable trajectories and mass-to-charge ratios that are less than m.sub.1 plot at other points along scan line 3 such as at points 25, 26, 27, 28 and 29. The lightest mass (or lowest mass-to-charge ratio) m.sub.s that might be detected is such that its q and a values correspond to point 8 on scan line 3 at the opposite edge of the stability region. A series of images of ion spatial distributions (e.g., at respective sub-RF phase values) may be then obtained while the DC and RF voltages are at U.sub.1 and V.sub.1, respectively. The images will include the images of exit positions of ions having mass-to-charge ratios, m, such that m.sub.h<m<m.sub.s or, possibly, such that m.sub.hmm.sub.s.

(22) After the first series of images have been obtained (at voltages U.sub.1 and V.sub.1), the DC voltage is then changed, while maintaining the RF voltage at V.sub.1, to a value, U.sub.2, in accordance with scan line 1. With this change, the a values associated with each ion increase while the q values do not change. Thus, the a value associated with the ion having mass-to-charge ratio m.sub.h changes such that this ion plots at point 23, outside the stability region. Similarly, the a value associated with the ion having mass-to-charge ratio m.sub.s changes such that this ion plots at point 31, also outside the stability region. Likewise, the a value of ions previously associated with points 25, 26, 27, 28 and 29 change such that the ions are now associated with points 24, 2, 21, 22, and 4, respectively, along scan line 1. Of these ions, only those ions having mass-to-charge values such that the ions plot at one of the points 2, 21, 22, or 4 have stable or marginally stable trajectories. Any ions (e.g., lighter ions) whose mass-to-charge values are such that they plot to the right of point 29 under the prior application of voltages U.sub.1 and V.sub.1 are no longer stable under of the application of the voltages U.sub.2 and V.sub.1. A series of images (i.e., a second series of images) of ion spatial distributions (e.g., at respective sub-RF phase values) may be then obtained while the DC and RF voltages are at U.sub.2 and V.sub.1, respectively. The images will include the images of exit positions of ions having mass-to-charge ratios between those of the ions associated with point 2 and the ions associated with point 4.

(23) After the second series of images have been obtained (at voltages U.sub.2 and V.sub.1), the RF voltage is then changed (incremented or ramped) to a new value. In this particular example the RF voltage is changed (to voltage V.sub.2) such that the q value of the ion having the mass-to-charge ratio m.sub.h changes from q=0.368 to q=0.419. The DC voltage is also changed (in this example, decreased) to a new value, U.sub.3, such that the a value of the ion having the mass-to-charge ratio m.sub.h changes such that the ion plots along scan line 3 (i.e., at point 25, at which a=0.075 in this particular example). In this new configuration (with applied voltages U.sub.3 and V.sub.2), the ion having mass-to-charge ratio m.sub.h once again possesses a stable trajectory and plots at point 25 within the stability region. Also, ions that are heavier than this ion (ions that plot between point 6 and point 25) enter the stability region for the first time. Ions whose mass-to-charge values are such that they previously plotted at point 2 on scan line 1 plot at point 27 on scan line 3. A series of images (i.e., a third series of images) of ion spatial distributions (e.g., at respective sub-RF phase values) may be then obtained while the DC and RF voltages are at U.sub.3 and V.sub.2, respectively. The images will include the images of exit positions of ions having mass-to-charge ratios between those of the ions associated with point 6 and the ions associated with point 8.

(24) The sequence of steps comprising acquiring data with U and V set in accordance with a first scan line, changing only one of the voltages such that the new U/V ratio is in accordance with a second scan line, acquiring a second set of data at the new voltage settings and then changing both voltage settings such that the U/V ratio is once again in accordance with a first scan line may be repeated any number of times. After each such sequence of steps, some ions that previously had stable trajectories will no longer have stable trajectories, some ions whose trajectories were previously unstable will have stable trajectories and, possibly, some ions whose trajectories were stable may remain stable. Although this method of alternating scan lines has been described, in this example, as including steps of only incrementing V and steps of both incrementing and decrementing U, alternative embodiments may include steps of incrementing only U and of both incrementing and decrementing V.

(25) The oscillation frequencies of any ion species that remain stable during the process of changing applied DC and RF voltages from those in accordance with the first to the second scan line (or vice versa) will significantly change from one data acquisition step to the subsequent data acquisition step. These frequency changes occur because the process of alternating between scan lines changes both the .sub.x and .sub.y values associated with the new applied voltage conditions. For example, an ion whose mass causes it to plot at point 26 under the described applied voltage conditions that correspond to scan line 3 will plot at point 2 under application of the described voltage conditions in accordance with scan line 1. The same ion will plot at point 27 upon returning the applied voltage conditions to those in accordance with scan line 3 in the fashion described. The first change causes .sub.y to decrease from 0.27 to near zero and .sub.x to increase from 0.59 to 0.66. The second change causes .sub.y to increase back to 0.35 and .sub.x to further increase from 0.66 to 0.69.

(26) Further, each change from a first scan line to a different scan line causes those ions that remain stable both before and after the change to be mixed with an assemblage of ions that is different from the assemblage of ions with which they were mixed before the change. In the example shown in FIG. 5, each change from scan line 3 to scan line 1 causes ions to be lost from the assemblage in both low and high mass-to-charge regions but each change from scan line 1 to scan line 3 causes low mass-to-charge ions to be lost from the assemblage while new high mass-to-charge ions are added to the assemblage. Using the Mathieu stability diagram, it is possible to accurately predict the range of masses to be expected at any point on either scan line as well the expected x and y oscillation frequencies. This information can be used to predict model curves which may be used in the deconvolution procedures (described elsewhere in this document) that are applied to the acquired data so as to determine abundances of ions at each mass-to-charge ratio.

(27) Both of these methods (i.e., the method of varying the number of RF cycles during ion transit and the method of varying the scan line in a, q space by varying applied DC and RF voltages according to a prescribed pattern) would be somewhat limited by the velocity of ions through the quadrupole device, but it is anticipated that both variable RF cycles and a varied U, V space could be modulated on the order of 10 kHz to achieve effective results. Either or both of these novel techniques could be employed as an additional scan mode that might be chosen for the purpose of higher resolution scans where maximum information per point was desired over scan speed.

(28) Moreover, the two above-described novel data acquisition methods (i.e., the method of varying the number of RF cycles during ion transit and the method of varying the scan line in a, q space by varying applied DC and RF voltages according to a prescribed pattern) could be used in combination. That is, a single mass analysis could employ both varying total RF cycles (equivalent to varying ion velocity along the z-axis as described above) and varying scan lines. As but one example, a first mass scan in accordance with scan line 1 may be performed, after which a second mass scan in accordance with scan line 3 may be performed. Further, at each point corresponding to application of a particular (U, V) pair (which corresponds to a single point on a scan line for any particular mass-to-charge ratio), the ion z-axis velocity is caused to vary such that the total number of RF cycles experienced by ions during transit through the device assumes a certain number of values. Still further, for each assumed value of total number of RF cycles at each (U, V) pair, a series of images corresponding to respective sub-RF phase increments is acquired. Employing such combined sampling techniques, each data packet (vector) corresponding to a sampled ion abundance, or voxel, corresponds to a six-dimensional space of independent variables, these six variables being: (1) x-position; (2) y-position; (3) applied RF voltage, V; (4) voltage ratio (U/V); (5) number of RF cycles applied during transit through the QMF; and (6) sub-RF phase.

(29) Once data has been acquired as described above, a deconvolution process is performed. The deconvolution process is a numerical transformation of the image data acquired from a specific mass spectrometric analyzer (e.g., a quadrupole) and a detector. The deconvolution process is employed to essentially extract signal intensity corresponding to each ion in the proximity of interfering signals from other ions. In the present instance, the instrument response to a mono-isotopic species can be described as a stacked series of two dimensional images, and that these images appear in sets that may be grouped into a multidimensional data packet described herein as a voxel set.

(30) The aforementioned U.S. Pat. No. 8,389,929 describes data collection in terms of three-dimensional voxel sets where the three dimensions of x, y and sub-RF phase comprise the independent variables that define a voxel set. The data analysis treatment, as described in that patent, is a representative example of a general deconvolution procedure for illustration purposes. A more-advanced mathematical analysis of mass spectral deconvolution that is applicable to the present application is provided in co-pending U.S. patent application Ser. No. 14/263,947 in the names of inventors Smith et. al. which was filed Apr. 28, 2014 and which is entitled Method for Determining a Spectrum from Time-Varying Data and which is incorporated herein by reference in its entirety. The analysis in co-pending U.S. patent application Ser. No. 14/263,947 describes the generation of an objective function from the mass spectral data, where the objective function can include a noise vector that modifies the mass spectral data so as to provide a solution that is constrained to be non-negative. Both of the above-noted mathematical treatments are general in the sense that each mathematical formulation applies to any number of dimensions of independent variables.

(31) Although the instrument response is not completely uniform across the entire mass range of the system, it is constant within any locality. Therefore, there are one or more model instrument response vectors that can describe the system's response across the entire mass range. Acquired data comprises convolved instrument responses. The mathematical process of the present invention thus deconvolves the acquired data (i.e., images) to produce an accurate list of observed mass positions and intensities.

(32) To construct the mass spectrum for the present invention, it is beneficial to specify, for each m/z value, the signal, the time series of ion images that can be produced by a single species of ions with that m/z value. One approach, as described in U.S. Pat. No. 8,389,929, is to construct a reference signal, offline as a calibration step, by observing a test sample and then to express a family of reference signals, indexed by m/z value, in terms of the canonical reference signal. A set of reference signals comprises a set of reference basis functions for purposes of deconvolution. Each reference basis function corresponds to the data expected to be acquired for an ion having a given value for a parameter (such as m/z).

(33) Accordingly, the deconvolution process is beneficially applied to data acquired from a mass analyzer that often comprises a quadrupole device, which as known to those of ordinary skill in the art, has a low ion density. Because of the low ion density, the resultant ion-ion interactions are negligibly small in the device, effectively enabling each ion trajectory to be essentially independent. Moreover, because the ion current in an operating quadrupole is linear, the signal that results from a mixture of ions passing through the quadrupole is essentially equal to (N) overlapping sum of the signals produced by each ion passing through the quadrupole as received onto, for example, a detector array, as described above.

(34) The result of the deconvolution process is the expression of an observed signal as a linear combination of a mixture of reference signals. In this case, the observed signal is the time series of acquired images of ions exiting the quadrupole. The reference signals are the contributions to the observed signal from ions with different m/z values. The coefficients in the linear combination correspond to a mass spectrum. The reference signal is a series of images that are generated either experimentally or synthetically, where each image represents the spatial distribution of exiting ions of a single species produced by a particular state of the fields applied to the quadrupole. Thereafter, spatial and temporal raw data of an abundance of one or more ion species from an exit channel of said quadrupole is acquired. The deconvolution solves for the abundances of one or more ion species and generally includes: the number of distinct ion species and, for each species, accurate estimates of its relative abundance and mass-to-charge ratio.

(35) The discussion included in this application is intended to serve as a basic description. Although the present invention has been described in accordance with the various embodiments shown and described, one of ordinary skill in the art will readily recognize that there could be variations to the embodiments or combinations of features in the various illustrated embodiments and those variations or combinations of features would be within the spirit and scope of the present invention. The reader should thus be aware that the specific discussion may not explicitly describe all embodiments possible; many alternatives are implicit. Accordingly, many modifications may be made by one of ordinary skill in the art without departing from the scope and essence of the invention. Neither the description nor the terminology is intended to limit the scope of the inventionthe invention is defined only by the claims. Any patents, patent applications or other publications mentioned herein are hereby explicitly incorporated herein by reference in their respective entirety.