Blind deconvolution of time-of-flight mass spectra from atom probe tomography

A major source of uncertainty in compositional measurements in atom probe tomography stems from the uncertainties of assigning peaks or parts of peaks in the mass spectrum to their correct identities. In particular, peak overlap is a limiting factor, whereas an ideal mass spectrum would have peaks at their correct positions with zero broadening. Here, we report a method to deconvolute the experimental mass spectrum into such an ideal spectrum and a system function describing the peak broadening introduced by the field evaporation and detection of each ion. By making the assumption of a linear and time-invariant behavior, a system of equations is derived that describes the peak shape and peak intensities. The model is fitted to the observed spectrum by minimizing the squared residuals, regularized by the maximum entropy method. For synthetic data perfectly obeying the assumptions, the method recovered peak intensities to within ±0.33 at%. The application of this model to experimental APT data is exemplified with Fe-Cr data. Knowledge of the peak shape opens up several new possibilities, not just for better overall compositional determination, but, e.g., for the estimation of errors of ranging due to peak overlap or peak separation constrained by isotope abundances.