Broadening of diffraction peaks from small crystal sizes, strain distributions, and instrument effects are discussed as convolutions. The convolution process is explained in detail. Fourier methods for deconvolution are derived, including practical effects of statistical noise. Methods for separating strain distributions and size distributions, based on the order of diffractions, are explained for practical work with examples. A characteristic diffraction lineshape for polycrystals with a crystal size distribution is derived, and used to highlight the effects of pair correlations on diffraction patterns. General effects of strain and size on diffraction patterns are discussed, with cautionary notes on interpretations of materials microstructures.