RATIONALE: Previously described methods for producing absorption mode Fourier transform ion cyclotron resonance (FTICR) mass spectra have all relied on the phase correction function being quadratic. This assumption has been found to be invalid for some instruments and spectra and so it has not been possible to produce absorption mode spectra for these cases. METHODS: The Autophaser algorithm has been adapted to allow nth order polynomial phase correction functions to be optimized. The data was collected on a modified Thermo LTQ FTICR mass spectrometer, using electrospray ionization and a novel ICR cell design (NADEL). Peak assignment and mass calibration were undertaken using the pyFTMS framework. RESULTS: An nth-order phase correction function has been used to produce an absorption mode mass spectrum of the maltene fraction of a crude oil sample which was not possible using the previous assumption that the phase correction function must be quadratic. Data processing for this spectrumin absorptionmode has shown the expected benefits in terms of increasing the number of assigned peaks and also improving the mass accuracy (i.e. confidence) of the assignments. CONCLUSIONS: It is possible to phase-correct time-domain data in FTICRMS to yield absorption mode mass spectra representation even when the data does not correspond to the theoretical quadratic phase correction function predicted by previous studies. This will allow a larger proportion of spectra to be processed in absorption mode. Copyright (C) 2015 John Wiley & Sons, Ltd.