  Nanoscale strain mapping by four-dimensional scanning transmission electron
microscopy (4D-STEM) relies on determining the precise locations of
Bragg-scattered electrons in a sequence of diffraction patterns, a task which
is complicated by dynamical scattering, inelastic scattering, and shot noise.
These features hinder accurate automated computational detection and position
measurement of the diffracted disks, limiting the precision of measurements of
local deformation. Here, we investigate the use of patterned probes to improve
the precision of strain mapping. We imprint a "bullseye" pattern onto the
probe, by using a binary mask in the probe-forming aperture, to improve the
robustness of the peak finding algorithm to intensity modulations inside the
diffracted disks. We show that this imprinting leads to substantially improved
strain-mapping precision at the expense of a slight decrease in spatial
resolution. In experiments on an unstrained silicon reference sample, we
observe an improvement in strain measurement precision from 2.7% of the
reciprocal lattice vectors with standard probes to 0.3% using bullseye probes
for a thin sample, and an improvement from 4.7% to 0.8% for a thick sample. We
also use multislice simulations to explore how sample thickness and electron
dose limit the attainable accuracy and precision for 4D-STEM strain
measurements.
