Separation of electrostatic and magnetic phase shifts using a modified transport-of-intensity equation

E. Humphrey, C. Phatak, A. K. Petford-Long, M. De Graef*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We introduce a new approach for the separation of the electrostatic and magnetic components of the electron wave phase shift, based on the transport-of-intensity equation (TIE) formalism. We derive two separate TIE-like equations, one for each of the phase shift components. We use experimental results on FeCoB and Permalloy patterned islands to illustrate how the magnetic and electrostatic longitudinal derivatives can be computed. The main advantage of this new approach is the fact that the differences in the power spectra of the two phase components (electrostatic phase shifts often have significant power in the higher frequencies) can be accommodated by the selection of two different Tikhonov regularization parameters for the two phase reconstructions. The extra computational demands of the method are more than compensated by the improved phase reconstruction results.

Original languageEnglish (US)
Pages (from-to)5-12
Number of pages8
JournalUltramicroscopy
Volume139
DOIs
StatePublished - Apr 2014

Keywords

  • Lorentz transmission electron microscopy
  • Phase reconstruction
  • Transport of intensity equation

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Instrumentation

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