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

  • Joel R. Kimmel
  • Oh Kyu Yoon
  • Ignacio A. Zuleta
  • Oliver Trapp
  • Richard N. Zare


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=2 n −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 F i > 0.001. HT-TOF mass spectra collected at 2500 per second demonstrates the method’s capability of monitoring transient processes not possible by conventional means.


Duty Cycle Shot Noise Hadamard Transform Dark Current Noise Acquisition Pass 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Brock, A.; Rodriguez, N.; Zare R. N. Hadamard Transform Time-of-Flight Mass Spectrometry. Anal. Chem. 1998, 70, 3735–3741.CrossRefGoogle Scholar
  2. 2.
    Zare, R. N.; Fernandez, F. M.; Kimmel J. R. High-Speed Mass Spectrometry Hadamard Transform Time-of-Flight Mass Spectrometry: More Signal, More of the Time. Angew. Chem. Int. Ed. 2003, 42, 30–35.CrossRefGoogle Scholar
  3. 3.
    Trapp, O.; Kimmel, J. R.; Yoon, O. K.; Zuleta, I. A.; Fernandez, F. M.; Zare R. N. Continuous Two-Channel Time-of-flight Mass Spectrometric Detection of Electrosprayed Ions. Angew. Chem. Int. Ed. 2004, 43, 6541–6544.CrossRefGoogle Scholar
  4. 4.
    Kimmel, J. R.; Fernandez, F. M.; Zare R. N. Effects of Modulation Defects on Hadamard Transform Time-of-flight Mass Spectrometry (HT-TOFMS). J. Am. Soc. Mass. Spectrom. 2003, 14, 278–286.CrossRefGoogle Scholar
  5. 5.
    Kimmel, J. R.; Engelke, F.; Zare R. N. Novel Method for the Production of Finely Spaced Bradbury-Nielson Gates. Rev. Sci. Instrum. 2001, 72, 4354–4357.CrossRefGoogle Scholar
  6. 6.
    Harwit, M. D.; Sloane N. J. Hadamard Transform Optics; Academic Press: London, 1979, p. 58.Google Scholar
  7. 7.
    Oliver C. J. Optical Image Processing by Multiplex Coding. Appl. Opt. 1976, 15, 93–106.CrossRefGoogle Scholar
  8. 8.
    Tilotta, D. C.; Fry, R. C.; Fateley W. G. Selective Multiplex Advantage with an Electro-optic Hadamard Transform Spectrometer for Multielemental Atomic Emission. Talanta 1990, 37, 53–60.CrossRefGoogle Scholar
  9. 9.
    Tilotta D. C. Theoretical Multiplex Gain in a UV/VIS Hadamard Transform Spectrometer Utilizing a Uniformly Imperfect Encoding Mask. Talanta 1990, 37, 61–69.CrossRefGoogle Scholar
  10. 10.
    Larson, N. M.; Crosmun, R.; Talmi Y. Theoretical Comparison of Singly Multiplexed Hadamard Transform Spectrometers and Scanning Spectrometers. Appl. Opt. 1974, 13, 2662–2668.CrossRefGoogle Scholar
  11. 11.
    Fernandez, F. M.; Vadillo, J. M.; Engelke, F.; Kimmel, J. R.; Zare, R. N.; Rodriguez, N.; Wetterhall, M.; Markides K. Effect of Sequence Length, Sequence Frequency, and Data Acquisition Rate on the Performance of a Hadamard Transform Time-of-Flight Mass Spectrometer. J. Am. Soc. Mass. Spectrom. 2001, 12, 1302–1311.CrossRefGoogle Scholar
  12. 12.
    Trapp, O.; Pearce, E. W.; Kimmel, J. R.; Yoon, O. K.; Zuleta, I. A.; Zare R. N. A Soft On-Column Metal Coating Procedure for Robust Sheathless Electrospray Emitters Used in Capillary Electrophoresis/Mass Spectrometry. Electrophoresis 2005, 26, 1358–1365.CrossRefGoogle Scholar
  13. 13.
    Kimmel, J. R. Continuous, Multiplexed Time-of-Flight Mass Spectrometry of Electrosprayed Ion. Ph.D. Thesis, Stanford University, 2004, pp 18–46.Google Scholar
  14. 14.
    Lee, H.; Marshall A. G. Theoretical Maximal Precision for Mass-to-Charge Ratio, Amplitude, and Width Measurements in Ion-Counting Mass Analyzers. Anal. Chem. 2000, 72, 2256–2260.CrossRefGoogle Scholar
  15. 15.
    Wineforder, J. D.; Avni, R.; Chester, T. L.; Fitzgerald, J. J.; Hart, L. P.; Johnson, D. J.; Plankly F. W. A Comparison of Signal-to-Noise Ratios for Single Channel Methods (Sequential and Multiplex) Versus Multichannel Methods in Optical Spectroscopy. Spectrochim. Acta 1976, 31B, 1–19.CrossRefGoogle Scholar
  16. 16.
    Yoon, O. K. Power Spectral Density of Ion Current from an Electropray Ionization Source. Stanford University, Stanford, CA, unpublished work.Google Scholar
  17. 17.
    Wei, J.; Shui, W.; Zhou, F.; Lu, Y.; Chen, K.; Xu, G.; Yang P. Naturally and Externally Pulsed Electrospray. Mass Spectrom. Rev. 2002, 21, 148–162.CrossRefGoogle Scholar
  18. 18.
    Guilhaus, M.; Selby, D.; Mlynski V. Orthogonal Acceleration Time-of-Flight Mass Spectrometry. Mass Spectrom. Rev. 2000, 19, 65–107.CrossRefGoogle Scholar

Copyright information

© American Society for Mass Spectrometry 2005

Authors and Affiliations

  • Joel R. Kimmel
    • 1
  • Oh Kyu Yoon
    • 1
  • Ignacio A. Zuleta
    • 1
  • Oliver Trapp
    • 1
  • Richard N. Zare
    • 1
  1. 1.Department of ChemistryStanford UniversityStanfordUSA

Personalised recommendations