Peak Height Precision in Hadamard Transform Time-of-Flight Mass Spectra

Abstract

Hadamard transform (HT) time-of-flight mass spectrometry (TOFMS) is a multiplexing technique that offers high duty cycle for the mass analysis of continuous ion sources. The multiplexing advantage is maximized when spectral noise is independent of signal intensity. For conditions in which shot noise predominates, the variance in each peak is a function of the population of all measured species. We develop expressions for the performance of a HT-TOF mass spectrometer based on Poissonian statistics for the arrival times of ions at the detector. These expressions and complementary probabilistic simulations are used to estimate the magnitude of the baseline noise as a function of mass spectral features and acquisition conditions. Experiment validates the predictions that noise depends on the total number of ions in the acquired spectrum, and the achieved signal-to-noise ratio for a given species depends on its relative population. We find that for HT-TOFMS experiments encoded with an n-order binary off-on sequence that contains N ϭ 2 n Ϫ 1 elements, the peak height precision, which is the peak intensity divided by its standard deviation, is greater than that of an equivalent conventional TOF experiment by a factor of ͙ N⁄2 times the square root of the fractional abundance of the peak of interest. Thus, HT-TOFMS is superior to conventional TOF for all species whose fractional abundance F i exceeds 2/N, which for a typical N value of 2047 corresponds to [1,2] is based on the pseudorandom gating of ion packets into a time-of-flight analyzer. In its typical implementation, the technique is able to monitor continuous ion sources with a 50% duty cycle, by which we mean the sample utilization efficiency, independent of all other figures of merit. Recently, we have demonstrated that the duty cycle can be extended to 100% using patterned, twochannel detection [3]. While a conventional TOFMS experiment releases a single packet of ions and makes independent measurements of all species, an HT-TOFMS experiment releases thousands of packets and measures the intensities of species as linear sums. For a fixed acquisition time, this procedure leads to linear increases in signal intensities and a root mean square reduction in the relative magnitude of signal-independent noise. Signal-dependent noise is known to affect the achieved performance of HT-TOFMS [4], but these processes have not been carefully studied.The principles of HT-TOFMS have been presented in previous publications [1][2][3]. Briefly, a continuous, accelerated ion beam is modulated on and off the axis of detection following a binary, pseudorandom encoding sequence that is applied at MHz rates. Because the produced ion packets have nanosecond widths, and typical flight times are on the order of tens or hundreds of microseconds, thousands of ion packets drift through the flight chamber at any given moment (compared to one packet in conventional TOFMS). Ions from these packets interpenetrate one another as they fly. Consequently, the detected signal corresponds to the s...

Duty cycle and modulation efficiency of two-channel hadamard transform time-of-flight mass spectrometry

“…Figure 2a presents a schematic diagram of the HT-TOF mass spectrometer used in this work. A full description can be found elsewhere [5]. Analyte solutions were driven through 75-micron i.d.…”

“…However, Static only considers the effects from large beam size and do not take into account the dynamic behavior of the deflection. In 2C-HT-TOFMS, the dominant source of noise is the shot noise and it is evenly spread throughout the mass spectrum during the deconvolution [5]. As shown in eq 6, the variance of the ion counts in the i th acquisition bin for each channel is given by…”

“…The principles of HT-TOFMS have been presented in previous publications [1,2,5]. The most important component of the HT-TOFMS instrument is an ion modulation device, called the Bradbury-Nielson Gate (BNG) [6,7].…”

“…Under shot-noise conditions, we have shown recently [5] that the multiplexing advantage of HT-TOFMS in peak height precision (PHP) compared to what we call on-axis TOF is given by…”

“…5, this ratio normally exceeds unity and thus represents an enhancement except for ions that are a very small fraction (typically less than 0.001) of the total ion signal. We have also shown [5] that the peak height and the variance are given by…”