  The arrival of direct electron detectors (DED) with high frame-rates in the
field of scanning transmission electron microscopy has enabled many
experimental techniques that require collection of a full diffraction pattern
at each scan position, a field which is subsumed under the name four
dimensional-scanning transmission electron microscopy (4D-STEM). DED frame
rates approaching 100 kHz require data transmission rates and data storage
capabilities that exceed commonly available computing infrastructure. Current
commercial DEDs allow the user to make compromises in pixel bit depth, detector
binning or windowing to reduce the per-frame file size and allow higher frame
rates. This change in detector specifications requires decisions to be made
before data acquisition that may reduce or lose information that could have
been advantageous during data analysis. The 4D Camera, a DED with 87 kHz
frame-rate developed at Lawrence Berkeley National Laboratory, reduces the raw
data to a linear-index encoded electron event representation (EER). Here we
show with experimental data from the 4D Camera that linear-index encoded EER
and its direct use in 4D-STEM phase contrast imaging methods enables real-time,
interactive phase-contrast from large-area 4D-STEM datasets. We detail the
computational complexity advantages of the EER and the necessary computational
steps to achieve real-time interactive ptychography and center-of-mass
differential phase contrast using commonly available hardware accelerators.
