  The discrete Fourier transform is among the most routine tools used in
high-resolution scanning / transmission electron microscopy (S/TEM). However,
when calculating a Fourier transform, periodic boundary conditions are imposed
and sharp discontinuities between the edges of an image cause a cross patterned
artifact along the reciprocal space axes. This artifact can interfere with the
analysis of reciprocal lattice peaks of an atomic resolution image. Here we
demonstrate that the recently developed Periodic Plus Smooth Decomposition
technique provides a simple, efficient method for reliable removal of artifacts
caused by edge discontinuities. In this method, edge artifacts are reduced by
subtracting a smooth background that solves Poisson's equation with boundary
conditions set by the image's edges. Unlike the traditional windowed Fourier
transforms, Periodic Plus Smooth Decomposition maintains sharp reciprocal
lattice peaks from the image's entire field of view.
