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Moiré interference effects have been observed in the electron diffraction patterns from crystals of lanthanum oxide iodide (LaOI). Optical transform methods were used to assist in the characterization of these patterns. The rotational misalignment of the overlapping pairs of thin crystals viewed in projection down [001] was found to take widely varying values. The higher values of the misalignment angle were found to occur close to the special values of tan-1(1), tan-1(1/2), tan-1(2/3) etc. Patterns in which three different crystal orientations are overlapped have also been observed.