  Image simulation for scanning transmission electron microscopy at atomic
resolution for samples with realistic dimensions can require very large
computation times using existing simulation algorithms. We present a new
algorithm named PRISM that combines features of the two most commonly used
algorithms, the Bloch wave and multislice methods. PRISM uses a Fourier
interpolation factor $f$ that has typical values of 4-20 for atomic resolution
simulations. We show that in many cases PRISM can provide a speedup that scales
with $f^4$ compared to multislice simulations, with a negligible loss of
accuracy. We demonstrate the usefulness of this method with large-scale
scanning transmission electron microscopy image simulations of a crystalline
nanoparticle on an amorphous carbon substrate.
