The EWPC transform enables lattice structure measurement at sub-pm precision and sub-nm resolution that is robust to small sample mistilts and random = ,Ī classical method used to characterize the strain in modern semiconductor devices is nanobeam diffraction (NBD) in the transmission electron microscope. With tracking the inter-atomic spacing peaks in EWPC patterns, strain mapping is demonstrated for two practical applications: mapping of ferroelectric domains in epitaxially strained PbTiO 3 films and mapping of strain profiles in arbitrarily oriented core-shell Pt-Co nanoparticle fuel-cell catalysts. We describe a simple analytical model for interpretation of these patterns that cleanly decouples lattice information from the intensity variations in NBED patterns caused by tilt and thickness. The EWPC transforms NBED patterns into real-space patterns with sharp peaks corresponding to inter-atomic spacings.

Here we present an approach to address these challenges using a transform, called the exit wave power cepstrum (EWPC), inspired by cepstral analysis in audio signal processing. Robust data processing techniques are needed to provide accurate and precise measurements for complex samples and non-ideal conditions.

However, intensity variations caused by dynamical diffraction and sample mistilts can hinder the measurement of diffracted disk centers as necessary for quantification. Scanning nanobeam electron diffraction (NBED) with fast pixelated detectors is a valuable technique for rapid, spatially resolved mapping of lattice structure over a wide range of length scales.

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