Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Learning Atom Probe Tomography time-of-flight peaks for mass-to-charge ratio spectrometry



Kevin J. Coakley, Norman A. Sanford


In laser-assisted atom probe tomography, an important goal is to reconstruct the mass-to-charge ratio, (m/z), spectrum due to various ion species. In general, the probability mass function (pmf) associated with the time-of- flight (TOF) spectrum produced by each ion species is unknown and varies from species-to-species. Moreover, measuring pmfs for distinct ion species in calibration experiments is not practical. Here, we present a mixture model method to determine TOF pmfs that can vary from peak-to-peak. In this approach, we determine weights of candidate pmfs with a maximum likelihood method. In a proof-of-principle study, we apply our method to a TOF spectrum acquired from a silicon sample and determine intensity estimates of singly charged isotopes of silicon.


Atom Probe Tomography, Cross-validation, Expectation Maximization algorithm, Machine learning, Maximum likelihood, Mixture model, Silicon isotopes


Coakley, K. and Sanford, N. (2022), Learning Atom Probe Tomography time-of-flight peaks for mass-to-charge ratio spectrometry, Ultramicroscopy, [online],, (Accessed September 21, 2023)
Created April 2, 2022, Updated November 29, 2022