A Rietveld method is described which extracts information on crystal structure, texture and microstructure directly from two-dimensional synchrotron diffraction images. This is advantageous over conventional texture analysis that relies on individual diffraction peaks, particularly for low-symmetry materials with many overlapping peaks and images with a poor peak-to-background ratio. The method is applied to two mineralized biological samples with hydroxylapatite fabrics: an ossified pachycephalosaurid dinosaur tendon and an Atlantic salmon scale. Both are measured using monochromatic synchrotron X-rays. The dinosaur tendon has very strongly oriented crystals with c-axes parallel to the tendon direction. The salmon scale displays a weak texture.