Pure absorption-mode spectra from Bayesian maximum entropy analysis of ion cyclotron resonance time-domain signals

Fourier transform ion cyclotron resonance (FT/ICR) mass spectra are normally reported in the (phase-independent) magnitude-mode format. In principle, the absorption-mode format offers spectral resolution enhanced by a factor ranging from square root of 3 to 2 over the corresponding magnitude-mode spectrum obtained by discrete FT of the same unapodized time-domain data. However, an absorption-mode display is generally unsuitable in practice because of the auxiliary spectral peaks (Gibbs oscillations) resulting from the relatively long time delay between excitation and detection. Although the resulting large phase variation (up to 100 pi rad or more across the Nyquist spectral bandwidth) can be corrected exactly for a continuous time-domain signal, phase correction of a discrete time-domain signal results in Gibbs oscillations even for a perfectly phased absorption-mode spectrum. In this paper, we show that a Bayesian "maximum-entropy" analysis of simulated and experimental ion cyclotron resonance time-domain noisy signals can recover a precisely phased absorption-mode frequency-domain spectrum that is devoid of Gibbs oscillations, is less sensitive to noise, and offers improved mass accuracy over that obtained from a conventional magnitude-mode discrete fast Fourier transform (FFT) spectrum.