Difference Fourier syntheses in fiber diffraction

Theory applying to difference Fourier syntheses from fiber diffraction data is developed, including the calculation of expected peak heights and noise levels. The signal-to-noise ratio in fiber diffraction difference maps is much lower than in crystallography, because of the multi-dimensional nature of fiber diffraction data, but it is shown by means of examples from tobacco mosaic virus that high-order difference syntheses, for example using coefficients analogous to crystallographic 6F_obs - 5F_calc, can clearly reveal differences between an observed structure and a model. 'Omit' maps, calculated from models by omitting a region under particular scrutiny, are of limited use in fiber diffraction, but maps calculated from hybrid coefficients derived from both full and partial models have some applications.