4.5 Article

Parallel Mode Differential Phase Contrast in Transmission Electron Microscopy, I: Theory and Analysis

Journal

MICROSCOPY AND MICROANALYSIS
Volume 27, Issue 5, Pages 1113-1122

Publisher

CAMBRIDGE UNIV PRESS
DOI: 10.1017/S1431927621012551

Keywords

differential phase contrast; Fresnel; image distortion; Lorentz; transmission electron microscopy

Funding

  1. Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom [EP/M024423/1]
  2. JSPS of Japan [JP19H05826, 17H02767, 17H02923]
  3. Carnegie Trust for the Universities of Scotland
  4. Grants-in-Aid for Scientific Research [17H02767, 17H02923] Funding Source: KAKEN

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In the first part of this work, we introduce the TEM-DPC technique for quantifying phase gradients of samples with structural contrast, compared to the TIE method. The TEM-DPC technique is particularly suitable for in situ studies and complements the TIE method due to its ability to handle structural contrast.
In Part I of this diptych, we outline the parallel mode of differential phase contrast (TEM-DPC), which uses real-space distortion of Fresnel images arising from electrostatic or magnetostatic fields to quantify the phase gradient of samples with some degree of structural contrast. We present an analysis methodology and the associated software tools for the TEM-DPC method and, using them together with numerical simulations, compare the technique to the widely used method of phase recovery based on the transport-of-intensity equation (TIE), thereby highlighting the relative advantages and limitations of each. The TEM-DPC technique is particularly suitable for in situ studies of samples with significant structural contrast and, as such, complements the TIE method since structural contrast usually hinders the latter, but is an essential feature that enables the former. In Part II of this work, we apply the theory and methodology presented to the analysis of experimental data to gain insight into two-dimensional magnetic phase transitions.

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