Technical Note pubs.acs.org/ac
Absorption Mode Fourier Transform Electrostatic Linear Ion Trap Mass Spectrometry Ryan T. Hilger,† Phillip J. Wyss,‡ Robert E. Santini,† and Scott A. McLuckey*,† †
Department of Chemistry, Purdue University, West Lafayette, Indiana 47907-2084, United States Jonathan Amy Facility for Chemical Instrumentation, Department of Chemistry, Purdue University, West Lafayette, Indiana, United States
‡
ABSTRACT: In Fourier transform mass spectrometry, it is wellknown that plotting the spectrum in absorption mode rather than magnitude mode has several advantages. However, magnitude spectra remain commonplace due to difficulties associated with determining the phase of each frequency at the onset of data acquisition, which is required for generating absorption spectra. The phasing problem for electrostatic traps is much simpler than for Fourier transform ion cyclotron resonance (FTICR) instruments, which greatly simplifies the generation of absorption spectra. Here, we present a simple method for generating absorption spectra from a Fourier transform electrostatic linear ion trap mass spectrometer. The method involves time shifting the data prior to Fourier transformation in order to synchronize the onset of data acquisition with the moment of ion acceleration into the electrostatic trap. Under these conditions, the initial phase of each frequency at the onset of data acquisition is zero. We demonstrate that absorption mode provides a 1.7-fold increase in resolution (full width at half maximum, fwhm) as well as reduced peak tailing. We also discuss methodology that may be applied to unsynchronized data in order to determine the time shift required to generate an absorption spectrum.
F
has been shown that A(ω) exhibits narrower line widths (increased resolution),2−4 as well as more accurate mass5,6 and abundance7 measurements. By manipulation of eqs 1 and 2, it can be shown that
ourier transformation is a method by which any smooth, periodic time-domain signal can be decomposed into its individual sinusoidal frequency components allowing the determination of the frequency, amplitude, and phase of each sinusoid.1 The Fourier transform includes real and imaginary parts that are linear combinations of pure absorption and dispersion spectra, Re[f ̂ (ω)] = A(ω)cos ϕ0(ω) + D(ω)sin ϕ0(ω)
(1)
Im[f ̂ (ω)] = D(ω)cos ϕ0(ω) − A(ω)sin ϕ0(ω)
(2)
A(ω) = Re[f ̂ (ω)]cos ϕ0(ω) − Im[f ̂ (ω)]sin ϕ0(ω)
The problem with determining A(ω), at least with FTICR, the oldest type of FTMS, is that ϕ0(ω), the phase of each m/z at the onset of data collection, is difficult to determine because of the frequency sweep excitation and the long time delay between excitation and the onset of detection. In FTICR, the excitation waveform normally consists of a linear frequency sweep. The ions are excited sequentially when their cyclotron frequency matches the excitation frequency. Therefore, after they are excited, ions accumulate variable amounts of phase while waiting for the excitation waveform to complete. Additionally, there is typically a delay between the end of the excitation waveform and the onset of data acquisition to prevent the sensitive detection electronics from being affected by the excitation pulse. The result is that the ions accumulate large and variable amounts of phase prior to the onset of detection. Nonetheless, information regarding certain parameters of the excitation waveform and the delay time
̂ where f(ω) is the Fourier transform of time-domain signal f(t). A(ω), D(ω), and ϕ0(ω) represent absorption, dispersion, and initial phase as functions of angular frequency ω. Instead of real and imaginary parts, Fourier transformations can be written in terms of the magnitude, M(ω), and phase, Φ(ω). M(ω) = =
(Re[f ̂ (ω)])2 + (Im[f ̂ (ω)])2
A(ω)2 + D(ω)2
(3)
⎛ Im[f ̂ (ω)] ⎞ ⎟⎟ Φ(ω) = tan−1⎜⎜ ⎝ Re[f ̂ (ω)] ⎠
(4)
In Fourier transform mass spectrometry (FTMS), M(ω) is typically plotted as the mass spectrum. However, with respect to Fourier transform ion cyclotron resonance (FTICR) MS, it © 2013 American Chemical Society
(5)
Received: June 27, 2013 Accepted: July 31, 2013 Published: July 31, 2013 8075
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Technical Note
should, in principle, allow the user to calculate ϕ0(ω). However, O’Connor and co-workers have argued8 that this method is ineffective because of small variations in ion frequency that arise from the image charge effect,9,10 space charge,11,12 and field inhomogeneities. Despite this, the FTICR community has developed many clever schemes for generating absorption mode spectra.4,6,11,13−16 However, due to the high complexity of the phasing problem, the vast majority of FTICR spectra continue to be displayed in magnitude mode. Several differences between electrostatic ion traps and FTICR instruments simplify the determination of A(ω). With instruments incorporating an electrostatic trap such as an Orbitrap or an electrostatic linear ion trap (ELIT), the ions are accelerated prior to (or during) injection rather than excited within the trap. All ions undergo rapid acceleration beginning at the same time, regardless of m/z. This situation approximates impulse excitation and therefore ϕ0(ω) = −ωΔt
acceleration, and h(t) is the unsynchronized data obtained by time shifting g(t) such that h(t) = g(t − Δt); the Fourier transform of h(t) is given by21 h(̂ ω) = g (̂ ω)e−iωΔt
Since ĝ(ω) = Mge , it follows that h(̂ ω) = Mg (ω)ei(Φg (ω) − ωΔt ) = Mh(ω)eiΦh(ω)
Φh(ω) = Φg (ω) − ωΔt
(11)
Since in the case of g(t) acquisition and acceleration are synchronized, Φg(ω) = 0 when ω is chosen to be the apex of a peak in the spectrum,4,5 so Φh(ωapex ) = −ωapex Δt
(6)
(12)
Therefore, if we take the Fourier transform of any set of timedomain data h(t) in which the data acquisition and ion acceleration are unsynchronized and graph phase (which must be unwrapped) as a function of angular frequency, where the data points are chosen to be the apexes of the peaks, the slope will be −Δt. The function h(t) may then be synchronized by subtracting Δt from the time coordinate of each data point.
(7)
Here, tacquire is the time at which data acquisition is initiated and taccel is the time at which ions commence acceleration. Under these conditions, the simplest way of obtaining A(ω) is to start collecting data at the same instant at which the ions begin accelerating. Under these circumstances, ϕ0(ω) = 0 and A(ω) = Re[f ̂ (ω)] = M(ω)cos Φ(ω)
(10)
where the subscripts h and g are used to differentiate between the two functions. It follows from eq 10 that
where Δt = taccel − tacquire
(9)
iΦg
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EXPERIMENTAL SECTION Materials. The cesium iodide sample was prepared by dissolving the analyte to a concentration of 9 mM in a solvent consisting of 49.5% H2O, 49.5% methanol, and 1% acetic acid. Cesium iodide was purchased from Sigma-Aldrich (St. Louis, MO). Methanol and glacial acetic acid were purchased from Mallinckrodt (Phillipsburg, NJ). Water was purified with a water purifier (D8961, Barnstead, Dubuque, IA) prior to use. Mass Spectrometry. The mass spectrometer (depicted in Figure 1) has been described previously22 and is based on the design of Benner23 as well as that of Dahan and co-workers.24 Briefly, sample solution is loaded into a pulled glass capillary placed in front of the sampling orifice. An electrospray is created by applying high voltage to a platinum wire in contact
(8)
This method has been used to obtain absorption spectra from Orbitrap mass spectrometers,17−19 and it is the method used herein. Synchronization of acceleration and data collection need not be done with hardware. Rather, the time coordinates of the points making up the time-domain data can simply be shifted by the appropriate value during data processing prior to Fourier transformation. Typically, a trigger event is used to initiate data acquisition and assign the t = 0 point in the time-domain data. The goal of the time shifting is to make the t = 0 point coincide with the moment of acceleration, even if no data are actually being acquired at this point in time. This procedure of shifting the time origin has been used for many years by the NMR community to correct frequency dependent phase shifts resulting from the finite length of the excitation pulse and the turn-on time of the receiver electronics.20 In practice, ion acceleration is often triggered by the same hardware that triggers data acquisition, and the relationship between these two events is known to, and perhaps even adjustable by, the user. It is tempting to believe that hardware synchronization will trivialize the acquisition of absorption mode data; however, convoluting factors such as propagation delays, rise/fall times, and electronic phase shifts make hardware synchronization nontrivial. Even if hardware synchronization is achieved “by eyeball”, small variations in taccel can arise because of changes to the acceleration potentials or even the number of ions accumulated prior to acceleration. Although manual resynchronization is always possible, it would be useful to have a method for calculating the appropriate time shift from data acquired with an unsynchronized system. Such a method is presented below. Let us define two functions: g(t) will be the time-domain data acquired when data acquisition is synchronized with ion
Figure 1. Schematic diagram depicting the ion path of the mass spectrometer (not to scale). 8076
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Figure 2. (a) Spectrum of CsI clusters obtained using eq 8 when synchronization of data collection with ion acceleration is attempted using hardware. Pure absorption peaks are not observed due to a linear dependence of ϕ0(ω) on ω from imperfect synchronization. (b) Spectrum obtained after synchronization by applying a small time shift (2.4 μs) to the time-domain data prior to Fourier transformation. Pure absorption peaks are observed across the entire mass range with the exception of the peak at 358 m/z, which is a harmonic.
Figure 3. Expanded views of several peaks in Figure 2b demonstrating the improvement in peak shape that results when spectra are plotted in absorption mode. Resolution improves by an average factor of 1.7, and abundance sensitivity is improved as a result of reduced tailing.
with the solution.25 The ions are transported to a quadrupole linear ion trap (QLIT) where they are accumulated before being pulsed into the ELIT. Here, the ions oscillate between two reflectrons, and their image charge signal is generated using a central pickup electrode. The ion frequencies vary from approximately 100−300 kHz for a mass range of 300−1800 Th (1 Th = 1 Da/e). The signal is amplified and shaped before being digitized at a rate of 10 MHz. The acquisition time is sufficient to allow the signal to decay into the noise. The onset
of data acquisition is timed to coincide with the release of the ions from the QLIT using a pulse and delay generator (model 575, Berkeley Nucleonics, San Rafael, CA), although this is insufficient to generate absorption spectra as discussed above and demonstrated below. Signal Processing. The time-domain signal is processed using a program written in LabVIEW 11.0 (National Instruments, Austin, TX). The program provides the means for time shifting (as described above), zero filling, and exponential 8077
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apodization. The program then Fourier transforms the data to generate M(ω) and Φ(ω). Equation 8 may then be used to generate an absorption spectrum, providing that ion acceleration and data acquisition are properly synchronized. The spectra presented are frequency domain averages of 25 individual spectra.
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necessary to maintain pure absorption peaks across the entire mass range. However, it is desirable to have a method of determining Δt that does not involve intervention from the user. As discussed in the introduction, a plot of unwrapped phase Φ versus ω for any unsynchronized spectrum will have a slope of −Δt provided that the chosen values of ω correspond to the apexes of peaks (ω = ωapex). The values of ωapex can be determined from a magnitude spectrum. The requirement for the phase to be unwrapped poses a problem since, under most circumstances, fast Fourier transform (FFT) algorithms only provide accurate values for phase when it is wrapped (confined to values between −π and π). This is because, computationally, any value for phase behaves the same when it has had any integer multiple of 2π (so-called full revolutions) either added to or subtracted from it. This makes the unwrapping problem very difficult when phase shifts across the spectrum include many full revolutions, as is the case with FTICR.6,8,11 However, after our attempted hardware synchronization, the remaining phase shifts are small, ranging from 1.2 rad at 1800 m/z to 4.7 rad at 300 m/z. Thus, for many ions, there are no full revolutions, and light ions might have a phase shift including at most a few full revolutions. With this knowledge in hand, the unwrapping problem is vastly simplified. Figure 4 was
RESULTS AND DISCUSSION
Figure 2 illustrates the effect of proper synchronization on the spectra obtained using eq 8. Figure 2a was obtained after attempting to synchronize data acquisition with ion acceleration using the pulse and delay generator as described in the Experimental Section. Unfortunately, pure absorption peaks are not obtained, as is evident from the negative peaks and zero crossings. It is apparent from Figure 2a that ϕ0(ω) not only is nonzero but also varies with ω (the b1 peak is approximately 90 degrees out of phase with the b5 peak). This is expected, since in the event of improper synchronization, ϕ0(ω) should be linear with ω. Figure 2b was obtained by applying a small time shift (Δt = 2.4 μs) to the time-domain data prior to Fourier transformation; the spectrum exhibits pure absorption peaks across the entire mass range. The one exception is the poorly phased peak at 358 m/z. This peak does not phase properly because it is the second harmonic of the b5 peak. It has been previously noted that artifacts and harmonics are easily distinguished in absorption spectra because they do not phase.7,16 It should be noted that the spectra in Figure 2 were obtained after zero filling the time-domain data to triple its original length and using exponential apodization to reduce spectral leakage. Figure 3 shows expanded views of several peaks from Figure 2b overlaid with their corresponding magnitude mode peaks. The resolution (R) values are calculated on the basis of the full width at half-maximum. In absorption mode, the resolution is improved by an average factor of 1.7 relative to magnitude mode. This is consistent with results from the FTICR community4,6,7,14,15 and with theory3,4 that predicts an improvement by a factor of between 1.40 and 2 for unapodized FTICR spectra depending on the collision regime. The absorption mode peaks in Figure 3 also show reduced tailing compared to magnitude mode, which is also consistent with theory3 and experiments4,7,14,15 from the FTICR community. Reduced tailing results in an improvement in the abundance sensitivity: the ratio of the signal recorded at a specified m/z value to the signal arising from the same species recorded at a neighboring m/z value.26 Having demonstrated the advantages of absorption spectra, we will turn our attention to the matter of determining Δt, the value by which to time shift the data in order to obtain absorption spectra by means of eq 8. As discussed above, we typically (attempt to) initiate data acquisition at the moment the ions are released from the QLIT. However, as demonstrated in Figure 2, this does not result in perfect synchronization. We hypothesize that this is a result of propagation delays and time constants in the circuitry that result in an unpredictable but consistent time difference between the two events. However, we can be reasonably confident that Δt will be small (on the order of microseconds), so it is trivial to manually vary Δt until an absorption spectrum is obtained. We have observed that, once known, Δt is relatively stable unless large changes are made to the number of injected ions. Occasionally, small (
