Efficient calculational techniques for reflection high energy electron diff
raction (RHEED) are reported for surfaces with large periodic supercells. A
fast Fourier transform approach enables the computer time scaling of a con
ventional RHEED calculation to be reduced to n(2)log(n), where n is the num
ber of diffracted beams used in the calculation. The special technique need
ed to implement this for arbitrary incident azimuths with symmetry optimiza
tion is detailed. A Green's function method is also introduced which is par
ticularly suitable for calculations for imperfect surfaces. This combines t
he conventional approach to RHEED for dealing with substrate diffraction wi
th a Green's function treatment for an imperfect surface of supercells and
has nlog(n) time scaling. Techniques for matching the results of the conven
tional and Green's function treatments at the substrate-surface interface a
re given. In addition, numerical procedures for solving the resulting equat
ions are described and a selection of illustrative results is presented.