  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. However, intensity variations
caused by dynamical diffraction and sample mistilts can hinder the measurement
of diffracted disk centers as necessary for quantification. Robust data
processing techniques are needed to provide accurate and precise measurements
for complex samples and non-ideal conditions. 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. The EWPC
transforms NBED patterns into real-space patterns with sharp peaks
corresponding to inter-atomic spacings. 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. By
tracking the inter-atomic spacing peaks in EWPC patterns, strain mapping is
demonstrated for two practical applications: mapping of ferroelectric domains
in epitaxially strained PbTiO3 films and mapping of strain profiles in
arbitrarily oriented core-shell Pt-Co nanoparticle fuel-cell catalysts. The
EWPC transform enables lattice structure measurement at sub-pm precision and
sub-nm resolution that is robust to small sample mistilts and random
orientations.
