Abstract
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.
Highlights
The submicron scale characterization of electro- and magnetostatic fields supported by materials has been critical to fundamental research into materials and to the development of data storage and other novel devices
Within transmission electron microscopy (TEM), several Lorentz parallel beam imaging modes have been developed over the decades and many are in regular use today, including holography (Gabor, 1949; Fukuhara et al, 1983), smallangle electron scattering (Goringe & Jakubovics, 1967; Togawa, 2013), Foucault (Marton, 1948; Nakajima et al, 2016), and Fresnel (Cohen, 1967; Chapman, 1984)
We have outlined a methodology for quantitative phase recovery from Fresnel imaging in a standard TEM that has origins dating back half a century, but that has since gone largely unused in electron microscopy
Summary
The submicron scale characterization of electro- and magnetostatic fields supported by materials has been critical to fundamental research into materials and to the development of data storage and other novel devices. To elucidate the relevant features, advantages and limitations of the TEM-DPC method and to compare it against the TIE one, we perform standard numerical image calculations, incorporating parallel illumination from a 200 kV source, defocus, and sample induced phase changes (DeGraef, 2001) for two illustrative cases: a sinusoidal phase object and a simple model of a magnetic domain wall We use the former to demonstrate linearity of the two methods and how intensity changes at large defocus limit the TEM-DPC method, while the latter is used to show how the dominant signal moves from intensity to deflection with increasing structural contrast. Even with high dynamic range imaging, the TEM-DPC method may be much more efficient and practical to use for this type of data
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