Broadband Phase Correction of FT-ICR Mass Spectra via

Aug 24, 2004 - Florida State University. ... Allied Topics, Orlando, FL 1998; p 502. (10) Beu .... by employing a previously demonstrated capacitive n...
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Anal. Chem. 2004, 76, 5756-5761

Broadband Phase Correction of FT-ICR Mass Spectra via Simultaneous Excitation and Detection Steven C. Beu,† Greg T. Blakney,‡ John P. Quinn,‡ Christopher L. Hendrickson,*,‡,§ and Alan G. Marshall‡,§

S. C. Beu Consulting, 13219 Research Boulevard, Suite I, Austin, Texas 78750, Ion Cyclotron Resonance Program, National High Magnetic Field Laboratory, Tallahassee, Florida 32310, and Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32310

In typical Fourier transform ion cyclotron resonance (FTICR) mass spectra, temporally dispersed excitation and the delay between excitation and detection result in continuous variation of signal phase with frequency in the detected time-domain ion signal. The complex frequencydomain spectrum of such a signal is a linear combination of absorption- and dispersion-mode spectral components with corresponding asymmetric peaks. For this reason, magnitude-mode spectral display is usually employed to yield a phase-independent uniform and symmetrical peak shape at the expense of spectral resolution. In this work, we implement simultaneous excitation and detection to enable Fourier deconvolution to recover absorption-mode spectra for both low- and high-field FT-ICR instruments. These spectra yield resolving power improvement factors approaching the maximum theoretical limit of 2.0, as well as reduction in frequency assignment errors relative to conventional magnitude-mode spectra. The Fourier deconvolution procedure has the additional benefit of correcting for spectral variation resulting from nonuniform power distribution over the excitation bandwidth and the potential benefit of providing useful diagnostic information for interpretation of experimental performance. Ultrahigh mass resolving power is perhaps the most celebrated of the many capabilities of Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS).1 Mass-charge ratio resolving power, (m/z)/∆(m/z)50%,2 in which ∆(m/z)50% is the mass-to-charge ratio spectral peak full width at half-maximum peak height, is equal to ion cyclotron frequency resolving power, ω/∆ω50%, which for unapodized, magnitude-mode spectra (in the limit that ions do not collide with neutrals) is approximately the number of cyclotron orbits during time-domain data acquisition.3 Mass resolving power increases linearly with increasing magnetic * To whom correspondence should be addressed. E-mail: hendrick@ magnet.fsu.edu. † S. C. Beu Consulting. ‡ National High Magnetic Field Laboratory. § Florida State University. (1) Marshall, A. G.; Hendrickson, C. L.; Jackson, G. S. Mass Spectrom. Rev. 1998, 17, 1-35. (2) Sommer, H.; Thomas, H. A.; Hipple, J. A. Phys. Rev. 1951, 82, 697-702. (3) Marshall, A. G.; Hendrickson, C. L. Rapid Commun. Mass Spectrom. 2001, 15, 232-235.

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field,4 and higher resolving power is typically pursued at the great expense of developing higher field magnets. However, an FT-ICR mass spectral peak may be shifted, broadened, and distorted according to the strength and homogeneity of the magnetic field, the strength and accuracy of both the dc electric field used to confine the ions axially (along the magnetic field direction) and the rf electric field used to excite coherent ion cyclotron motion, and ion-ion Coulomb interactions. The computational procedures to obtain a spectrum from the acquired time-domain data can also significantly affect the achieved peak width. Of the many different approaches to extraction of frequency from the time-domain data, the most common is to multiply the N time-domain data by a weight (“window”) function, followed by “padding” by addition of N zeroes, fast Fourier transformation, and magnitude calculation to yield an apodized frequency-domain spectrum.5 Magnitude-mode display has the advantage of uniform, symmetrical spectral peak shape, at the cost of increase in spectral peak width by a factor of up to 2 relative to absorption mode. As an alternative to magnitude-mode display, spectral phase correction can recover the narrower absorption-mode peak shape (see below). Previous methods for phase correction of FT-ICR mass spectra are effective only for narrow spectral bandwidth and require user-interactive “tuning”.6-8 Here, we demonstrate that simultaneous excitation and detection9,10 enables Fourier deconvolution5 to provide broadband phase correction with no user interaction.11 The method is simple to implement and offers the additional advantage of providing an inherent correction for peak area variations resulting from excitation waveforms having nonuniform power distribution over the desired excitation bandwidth. (4) Marshall, A. G.; Comisarow, M. B.; Parisod, G. J. Chem. Phys. 1979, 71, 4434-4444. (5) Marshall, A. G.; Verdun, F. R. Fourier Transforms in NMR, Optical, and Mass Spectrometry: A User’s Handbook; Elsevier: Amsterdam, 1990. (6) Comisarow, M. B.; Marshall, A. G. Can. J. Chem. 1974, 52, 1997-1999. (7) Craig, E. C.; Santos, I.; Marshall, A. G. Rapid Commun. Mass Spectrom. 1987, 1, 33-37. (8) Vining, B. A.; Bossio, R. E.; Marshall, A. G. Anal. Chem. 1999, 71, 460467. (9) Beu, S. C. Proceedings of the 47th ASMS Conference on Mass Spectrometry & Allied Topics, Orlando, FL 1998; p 502. (10) Beu, S. C. Proceedings of the 47th ASMS Conference on Mass Spectrometry & Allied Topics, Dallas, TX 1999; CD-ROM. (11) Beu, S. C.; Hendrickson, C. L.; Quinn, J. P.; Blakney, G. T.; Marshall, A. G. Proceedings of the 51st ASMS Conference on Mass Spectrometry & Allied Topics, Montreal, PQ, Canada 2003; CD-ROM. 10.1021/ac049733i CCC: $27.50

© 2004 American Chemical Society Published on Web 08/24/2004

Figure 1. Pure absorption and dispersion spectra (a) resulting from FFT when signal phase is 0° (i.e., pure cosine) at the start of the time-domain data set and mixed-mode spectra (b) resulting from FFT when signal phase is 45° at the start of the time-domain data set. In both examples, the time-domain sinusoid was subjected to a halfHanning window prior to FFT.

In a typical FT-ICR MS experiment, excitation-induced saturation of the detection preamplifier requires that digitization of the detected ion signal be delayed until after excitation. That delay, in addition to factors such as a temporally dispersed excitation event (e.g., frequency-sweep), causes a continuous variation of phase with frequency in the time-domain data. As a result, φ (t0) will in general not be 0 or π radians for a particular frequency component and will vary with frequency. The complex frequencydomain spectrum will thus exhibit asymmetric peaks composed of varying combinations of absorption and dispersion modes. For this reason, it is typical in FT-ICR MS to display spectra in magnitude mode to yield a phase-independent symmetrical peak shape at the expense of spectral resolution (eq 2 and top peaks of Figure 1).

and the phase, φ(ωm), is represented by the arctangent of the ratio of its imaginary, Im[F(ωm)], to its real, Re[F(ωm)], components (eq 3). If all frequency components are cosines (i.e., zero initial timedomain phase, φ (t0)) the real and imaginary components of the corresponding complex frequency spectrum represent the pure absorption-, A(ω), and dispersion, D(ω), mode spectra (eqs 4 and

METHODS The goal of phase correction is to obtain a spectrum in which all frequency components exhibit pure absorption-mode peak shape. Theoretically, one could excite the time-domain signal instantaneously and begin sampling the detected signal immediately thereafter. In that limit, all of the frequency components have an initial time-domain phase of zero (cosines), and no spectral phase correction is needed (eqs 4). That situation is closely approached in Fourier transform nuclear magnetic resonance,12 in which it is possible to excite the time-domain signal in a few microseconds and begin detection less than half of one sampling interval (“dwell” time of an analog-to-digital converter)) later. Unfortunately, the much broader spectral bandwidth typical of ICR compared to NMR requires impractically high excitation amplitude for near-simultaneous excitation throughout the bandwidth; moreover, ringdown from the residual excitation signal at the detector requires more than half of one dwell period delay between excitation and detection. Fortunately, unlike FT-NMR, ICR excitation and detection are highly linear, and that linearity makes it possible to recover the desired ideal response from a nonideal experimental time-domain signal. For ion cyclotron radii less than about half of the trapped-ion cell radius, ICR excitation and detection processes are both highly linear.13 That is, the radius of the ion cyclotron orbit after excitation is a linear function of the excitation amplitude, and the amplitude of the detected image current is a linear function of the ion cyclotron radius. Under these circumstances, the detected timedomain ion signal, f (t), is simply the convolution of the applied excitation waveform, e(t), and the “ideal” response, h(t) (eq 6), to instantaneous excitation.

A(ω) ) Re[F(ωm)]

(4a)

f (t) ) e(t)/h(t)

D(ω) ) Im[F(ωm)]

(4b)

THEORY Fourier transformation of an N-point time-domain discrete transient, f(tn), yields a mathematically complex spectrum, F(ωm) (eq 1). The amplitude for any given frequency component is the N-1

F(ωm) )

( )

∑ f(t ) exp n

n)0

-inm N

(1)

magnitude, M(ωm), of the corresponding complex number, F(ωm), (eq 2),

M(ωm) ) x(Re[F(ωm)])2 + (Im[F(ωm)])2

(2)

φ(ωm) ) arctan(Im[F(ωm)]/Re[F(ωm)])

(3)

Figure 1a). For any other initial time-domain phase, the complex components represent linear combinationsof the absorption and dispersion modes (eqs 5), and the resulting peak shapes are asymmetrical (Figure 1b).

A(ω) ) Re[F(ω)] cosφ(t0) - Im[F(ω)] sinφ(t0) (5a) D(ω) ) Re[F(ω)] sinφ(t0) + Im[F(ω)] cosφ(t0) (5b)

(6)

From the convolution theorem,5 the Fourier transform spectra of those functions are related by

F(ω) ) E(ω)H(ω)

(7)

Thus, the spectrum, H(ω), that would result from the desired ideal response can be recovered by complex division of the spectrum, (12) Marshall, A. G. Acc. Chem. Res. 1996, 9, 307-316. (13) Grosshans, P. B.; Marshall, A. G. Int. J. Mass Spectrom. Ion Processes 1992, 115, 1-19.

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Figure 2. Real (solid line) and imaginary (dotted line) frequencydomain spectra. Fourier deconvolution-based phase correction consists of complex division of the spectrum of the time-domain ICR signal (left) by the spectrum of the time-domain excitation waveform (middle) to yield a phased broadband response spectrum (right).

F(ω), of the observed response by the spectrum, E(ω), of the excitation14 (eq 8 and Figure 2).

H(ω) ) F(ω)/E(ω)

(8)

Fourier deconvolution effectively yields phase correction over the entire excitation bandwidth, while simultaneously correcting for any spectral amplitude variation resulting from nonuniform power distribution over the excitation bandwidth. The critical requirement for implementing this process is that the detection event must incorporate the excitation interval, and the excitation and detection spectra must be temporally synchronized. In practice, this simultaneous excitation and detection (SED) is made difficult by the capacitive coupling that exists between the excitation and detection circuits. That coupling causes excitationinduced preamplifier saturation and necessitates a delay between excitation and detection. In this work, the saturation is avoided by employing a previously demonstrated capacitive nulling technique that reduces the coupled excitation signal and enables SED.9,10 In this technique, a variable capacitor is added between each excitation and detection electrode lead pair, and the resulting bridge is tuned such that the coupling of the two opposite-phase components of the differential excitation largely cancels at the preamplifier input. EXPERIMENTAL SECTION Fourier deconvolution-based phase correction was first demonstrated experimentally with a benchtop 1.0-T permanent magnet FT-ICR MS (prototype Advance Quantra, Siemens Applied Automation, Bartlesville, OK) with in-cell electron ionization and then with a home-built 9.4-T FT-ICR MS equipped with an external electrospray ionization (ESI) source.15 Both instruments were equipped with an external variable capacitor bridge between the excitation and detection leads, and the bridge was manually adjusted to minimize the detected excitation signal during SED.8,9 The goal of this nulling process is to achieve complete cancellation of the coupled excitation signal. Nulling is increasingly difficult for larger high-field instruments because of greater coupling capacitance with a large cell assembly and the required use of a higher amplitude excitation waveform. It is sufficient for the present purpose to achieve a residual coupled excitation signal (14) Marshall, A. G. Chem. Phys. Lett. 1979, 63, 515-518. (15) Senko, M. W.; Hendrickson, C. L.; Pasa-Tolic, L.; Marto, J. A.; White, F. M.; Guan, S.; Marshall, A. G. Rapid Commun. Mass Spectrom. 1996, 10, 1824-1828.

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that does not exceed the dynamic range of the detection preamplifier when combined with the acquired ion signal. The residual excitation is highly reproducible and can be removed from the SED time-domain transients by background subtraction. The background transient is obtained by acquiring an SED transient in the absence of analyte ions. Although excitation and detection occur concurrently in the SED experiments, acquisition of time-domain data for the excitation waveform and detected ion signal is performed separately. This is because concurrent acquisition of both time-domain data sets would require duplicate parallel sets of acquisition circuitry and computer memory, as well as software modifications to control the simultaneous acquisitions. Simultaneous acquisition is in principle superior, because the acquired excitation data more closely represent what the analyte ions actually experience during SED; however, the obvious disadvantage is the significantly greater instrumental cost and experimental complexity. The simpler alternative approach used here is to acquire the data sets in separate experiments with identical instrument parameters and timing sequences. For both instruments, spectra of the excitation waveforms were obtained by directly coupling the excitation and detection circuits with appropriate attenuation to avoid saturation of the detection preamplifier. The coupling was accomplished as close to the cell as possible, and included the preamplifier, so that the excitation waveform was acquired with an excitation and detection signal path as similar as possible to that used during ion detection. This procedure helps to ensure that the detected excitation and ion signals are both subject to the same signal pathinduced phase shifts. Xenon spectra were acquired with the 1.0-T instrument with research grade xenon gas (Praxair, Danbury, CT) introduced to the spectrometer through a piezoelectric pulsed-valve inlet. The sample gas pulse was subjected to in-cell 70-eV electron ionization and direct-mode broadband detection (128 Kword) during SED with frequency-sweep excitation (1.0 MHz-50 kHz at 250 Hz/ µs). Electrospray mass spectra of ubiquitin were acquired with the 9.4-T instrument by previously described methods.16 Briefly, bovine ubiquitin was purchased from Sigma (St. Louis, MO) and used without further purification. A protein stock solution (100 pmol/µL) was prepared by dissolving the lyophilized sample in HPLC grade water (J. T. Baker, Philipsburg, NJ). For electrospray, an aqueous 100 µM stock solution was diluted to 1 µM in 1:1 methanol (Baker)/water with 2.5% acetic acid. Ions were externally accumulated17 in the front octopole for 0.1 s and then transferred through a quadrupole mass filter to a second (middle) octopole. This procedure was repeated three times, for a total accumulation period of 0.3 s. After accumulation, the ions were transferred from the middle octopole (modified to allow improved ejection of ions along the z-axis)18 through an octopole ion guide and captured by gated trapping in an open cylindrical cell. Simultaneous excitation (frequency sweep from 288 to 96 kHz at 5 Hz/µs) and direct-mode broadband detection yielded a 2048 Kword transient. The experimental event sequence was controlled by a MIDAS data (16) Hendrickson, C. L.; Quinn, J. P.; Emmett, M. R.; Marshall, A. G. Proceedings of the 49th ASMS Conference on Mass Spectrometry and Allied Topics, Chicago, IL, May 27-31, 2001; CD-ROM. (17) Senko, M. W.; Hendrickson, C. L.; Emmett, M. R.; Shi, S. D.-H.; Marshall, A. G. J. Am. Soc. Mass Spectrom. 1997, 8, 970-976. (18) Wilcox, B. E.; Hendrickson, C. L.; Marshall, A. G. J. Am. Soc. Mass Spectrom. 2002, 13, 1304-1312.

Figure 3. Magnitude and absorption spectra of electron-ionized xenon cations (at 1 T) derived from the same time-domain data. The absorption-mode spectrum was obtained by Fourier deconvolution.

Figure 4. Mass scale expansion for 132Xe (at 1 T) in the spectrum of Figure 3, illustrating the resolving power advantage of absorptionmode relative to magnitude-mode spectra.

acquisition system.19 Time-domain data for both the xenon and ubiquitin samples were initially subjected to background subtraction to remove any residual excitation signal evident during SED. All time-domain data were then subjected to half-Hanning apodization7 (for which the time-domain weighting is unity at the beginning and gradually reduces to near zero at the end of the time-domain data, rather than unity at the center and gradually reducing to near zero at both the beginning and end of the timedomain data as in full apodization) and a single zero-fill prior to applying the fast Fourier transform and deconvolution procedure. Frequency-to-m/z conversion was performed with a two-term calibration equation.20,21 RESULTS AND DISCUSSION Fourier Deconvolution. Proposed theoretically in 1979,14 the feasibility of Fourier deconvolution-based phase correction was first demonstrated experimentally for electron ionization FT-ICR mass spectra of xenon acquired with the 1.0-T instrument. In Figures 3 and 4, an uncorrected magnitude-mode xenon spectrum is compared with a corresponding phase-corrected absorptionmode spectrum obtained from the same time-domain data. The phase-corrected absorption-mode spectrum exhibits an enhancement in resolving power, m/∆m50%, in which ∆m50% is peak full width at half-maximum height, by a factor of 1.7 relative to the magnitude spectrum. That result is consistent with the theoretical prediction of resolving power enhancement ranging from 1.4 to 2.0 depending on system pressure and collision dynamics.8,22 The value of 1.7 corresponds to a pressure-limited Langevin collision model in which ion/induced-dipole interactions dominate, as expected for low-mass ions undergoing the relatively low velocity collisions prevailing at 1.0 T in a small ICR cell. We subsequently demonstrated Fourier deconvolution-based phase correction for ESI FT-ICR mass spectra of ubiquitin obtained with the 9.4-T FT-ICR MS instrument. Figures 5 and 6 compare (19) Senko, M. W.; Canterbury, J. D.; Guan, S.; Marshall, A. G. Rapid Commun. Mass Spectrom. 1996, 10, 1839-1844. (20) Ledford, E. B., Jr.; Rempel, D. L.; Gross, M. L. Anal. Chem. 1984, 56, 27442748. (21) Shi, S. D.-H.; Drader, J. J.; Freitas, M. A.; Hendrickson, C. L.; Marshall, A. G. Int. J. Mass Spectrom. 2000, 195/196, 591-598. (22) Guan, S.; Li, G.-Z.; Marshall, A. G. Int. J. Mass Spectrom. Ion Processes 1998, 167/168, 185-194.

Figure 5. Magnitude and absorption spectra of electrospray-ionized ubiquitin, [M + 10H]10+ (at 9.4 T), derived from the same time-domain data. The absorption-mode spectrum was obtained by Fourier deconvolution.

Figure 6. Mass scale expansion for the most abundant peak in the ubiquitin [M + 10H]10+ spectrum (at 9.4 T) of Figure 5, illustrating the resolving power advantage of absorption-mode relative to magnitude-mode spectra.

an uncorrected magnitude-mode spectrum with a phase-corrected absorption-mode spectrum obtained from the same time-domain data. The phase-corrected absorption-mode spectrum exhibits an enhancement in resolving power by a factor of 1.8 relative to the magnitude spectrum. This factor approaches the theoretical maximum of 2.0 for an undamped time-domain signal.4 A detection interval long enough to allow significant signal damping would Analytical Chemistry, Vol. 76, No. 19, October 1, 2004

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Figure 7. Mass assignment errors for magnitude (9) and absorption (b) mode display for the isotopic distribution of ubiquitin 10+ charge state (Figure 5).

yield a lower resolution enhancement factor, ultimately approaching a value near 1.4 as previously shown for high-mass ions colliding with low-mass neutrals (i.e., pressure-limited hard-sphere collision dynamics).8,22 It is well known that overlap of closely spaced peaks in magnitude-mode spectra can result in systematic errors in the assignment of peak frequencies,23-26 because the magnitude calculation is inherently nonlinear (eq 2). Thus, magnitude spectra are not additive. The magnitude of the error depends on the degree of peak overlap, the relative magnitudes of the overlapped peaks, the choice of windowing function, and the signal damping rate,24,25 as well as the relative phase of the overlapping peaks.23-26 Although appropriate manipulation of these factors can reduce frequency (and therefore, mass) assignment error, the underlying cause of the error may be avoided25 by employing absorptionmode spectral display as shown in Figure 7, in which the errors in mass assignment for the individual peaks in the isotopic distribution of ubiquitin 10+ charge state ions are compared for magnitude- and absorption-mode spectra. Phasing Artifacts and Their Remediation. The phasecorrected spectra of both xenon and ubiquitin exhibit evidence of peak “fronting”. This asymmetry is also present in the uncorrected magnitude spectra; however, the broader base of the unphased peaks largely obscures it. In both cases, the asymmetry may be caused by frequency drift27 occurring early in the timedomain transients, perhaps due to evolution of ion cloud geometry and concomitant space charge effects immediately following excitation. Another possibility is that the fronting is related to the detected near-resonance ion motion that occurs during SED as the excitation waveform sweeps through the ion cyclotron resonance frequency (investigation of this effect is underway). That the fronting is associated with the early part of the timedomain data is evident from its disappearance when full, rather than half, apodization is employed; however, full apodization will result in significant negative side lobes in the absorption-mode spectra8 and is therefore not compatible with optimal phasing. (23) Lee, J. P.; Comisarow, M. B. J. Magn. Reson. 1987, 72, 139-142. (24) Lee, J. P.; Chow, K. H.; Comisarow, M. B. Anal. Chem. 1988, 60, 22122218. (25) Chow, K. H.; Comisarow, M. B. Int. J. Mass Spectrom. Ion Processes 1989, 89, 187-203. (26) Tolmachev, A. V.; Masselon, C. D.; Anderson, G. A.; Udseth, H. R.; Smith, R. D. J. Am. Soc. Mass Spectrom. 2002, 13, 387-401. (27) Guan, S.; Wahl, M. C.; Marshall, A. G. Anal. Chem. 1993, 65, 3647-3653.

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Two factors that have little or no effect on magnitude-mode spectra but can cause significant distortion of the absorption-mode spectra are the delay between excitation and detection and failure to accurately digitize the first few points of the time-domain signal, both of which can cause baseline oscillation or “roll”.7 SED-based Fourier deconvolution avoids both of these error sources by eliminating the delay between excitation and detection and by obviating distortion from the initial points of the time-domain data. Starting signal digitization just prior to the start of the excitation gives the digitizer time to stabilize before acquisition of critical data points. Additional Noise Sources and Their Remediation. Fourier deconvolution introduces additional noise because the sources of noise in the excitation spectrum and the uncorrected sample spectrum are not correlated. For uncorrelated noise, complex division will result in an overall increase in noise amplitude in the phased spectrum.5 Although that noise may compromise phasing results for those peaks with amplitudes comparable to the noise, it is not a significant problem for higher amplitude peaks. The larger peaks may exhibit some susceptibility to phasing noise near the baseline, usually evidenced by small positive or negative amplitude spikes on either side of the peak. As can be seen in Figure 1, the dispersion spectrum has large positive and negative amplitudes on either side of the centroid frequency, whereas the absorption spectrum has near-zero amplitude in these areas. A relatively small phase error in this region of the excitation spectrum causes a significant portion of the complex magnitude to be “phased” into the absorption component (rather than the dispersion component). The complex division is in effect incorrectly distributing the magnitude between the two components (i.e., there is “leakage” from the dispersion spectrum into the absorption spectrum). Conversely, a similar phase error near the center of the peak (where the absorption component is large and the dispersion small) causes a much smaller change in the absorption component amplitude. The overall effect is an enhancement of the effects of errors on either side of the phased peak, and this may result in associated positive or negative spikes in region. The susceptibility to noise-related artifacts in the phasing process may be reduced by conventional signal averaging. Because the excitation spectrum does not have to be reacquired for each sample spectrum, an extensively signal-averaged excitation spectrum may be stored and reused for phasing of any sample spectrum acquired with the same relevant experimental parameters. The noise content of the excitation spectrum can be further minimized by terminating acquisition of the time-domain data immediately following conclusion of the excitation waveform output and then zero-filling to match the duration of sample timedomain data. The duration of the excitation is typically much shorter than the data acquisition period for the resulting ICR signal, and employing the same observation time for the excitation as is used for the sample would result in the undesirable acquisition of additional noise in the case of the excitation data. Finally, the effects of noise may also be remedied to some extent by employing concurrent acquisition of the excitation waveform and ion signal as discussed above. The careful implementation of concurrent acquisition could yield significant noise

correlation between the excitation and sample spectra and thus minimize any increase in noise resulting from the phasing process. It may also be beneficial to use an excitation spectrum derived from FFT of the input to the transmitter plates or excitation amplifier, or a purely digital (theoretical) waveform. Other Aspects of Absorption-Mode versus MagnitudeMode Spectra. An N/2-point magnitude-mode spectrum has x2 higher signal-to-noise ratio than the corresponding N/2-point absorption-mode spectrum obtained from the same N-point timedomain data, because Fourier transformation of the original N-point time-domain data distributes information equally between the N/2-point absorption and N/2-point dispersion data. However, Fourier transformation of a 2N data set produced by padding (zerofilling) the original time-domain data with an additional N zeroes generates N-point absorption and N-point dispersion spectra, each of which contains all of the available information.28 Thus, the mass measurement precision of an N/2-point magnitude spectrum (without zero-filling) is the same as that for an N-point absorption spectrum from once zero-filled time-domain data. For well-isolated peaks, magnitude-mode display requires only half as much data storage, for the same mass precision. What then is the net advantage of phased (absorption-mode) display? Basically, the narrower peak width (especially near the peak base) of absorption-mode display becomes important when there is significant overlap between closely spaced peaks, for two reasons. First, the “wings” of the dispersion-mode spectrum extend much farther than those of absorption mode, so that magnitude-mode peaks must be much farther apart for the same degree of overlap as absorption-mode peaks. Second, the magnitude-mode calculation is inherently nonlinear. Thus, the resultant absorption-mode spectrum of two overlapped resonances is simply their sum, whereas the dispersion-mode components of two overlapped resonances will partly cancel when added, leading to asymmetrical “cusps” between adjacent magnitude-mode peaks (somewhat evident in Figure 5), and incorrect peak positions (as noted above) and incorrect relative abundances based on magnitude-mode peak heights. Another difference between magnitude-mode and absorptionmode spectra is their noise distribution. Magnitude-mode noise is necessarily positive, whereas absorption-mode noise is Gaussian-

distributed about zero amplitude. As a result, magnitude-mode noise is described by a Rayleigh distribution, not a Gaussian distribution.5

(28) Bartholdi, E.; Ernst, R. R. J. Magn. Reson. 1973, 11, 9-19.

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CONCLUSION Although the primary goal of phasing is to enhance the resolving power of FT-ICR mass spectra, an important aspect of the phasing process is that it can reveal imperfection in experimental data that would otherwise be obscured by conventional data treatment and display. In an ideal experiment, the excitation and detection processes are linear, there is no change is cyclotron frequency during the detection period, the signal phase is determined solely by the excitation phase, and noise is insignificant. To the extent that the experimental results deviate therefrom, phasing will reveal deviations from pure absorption-mode peak shape. Although not aesthetically pleasing, the information that is revealed may be of significant diagnostic value. For example, a marked asymmetry in absorption-mode peak shape may indicate the peak is aliased or that it has no causal connection to the excitation (i.e., a noise peak). More subtle distortions may indicate a loss of phase correlation between the excitation and the resulting ion motion, and the shape of the asymmetry may correspond to particular experimental imperfections (e.g., space charge effects, nonlinearity, etc.). In addition to developing experimental improvement in the phasing process, future work will be focused on identifying those experimental parameters that have the most significant effect on phase correlation between the excitation and the resulting ion motion. Phase correction may then be developed as a tool for diagnostics and experimental optimization, in addition to its primary use as a means of providing enhanced resolving power. ACKNOWLEDGMENT This work was supported by the NSF National High Field FTICR Facility (CHE-99-09502), Florida State University, and the National High Magnetic Field Laboratory in Tallahassee, FL. Access to the prototype Quantra FT-ICR MS provided by Siemens Applied Automation is gratefully acknowledged. Received for review February 16, 2004. Accepted July 12, 2004.

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