A polar Fourier transform (PFT) method is de scribed that facilitates determination and refinement of orientations of individual biological macromolecules imaged with cryoelectron microscopy techniques, A three-dimensional density map serves as a high signal-to-noise model from which a PFT database of different views is generated and against which the PFTs of individual images are correlated, The PFT produces rotation-invariant data particularly well-suited for rapid and accurate determination of orientation parameters. The method relies on accurate knowledge of the center of symmetry and radial scale of both model and image data but is insensitive to the relative contrast and background values of these data. Density maps may be derived from a variety of sources such as computer-generated models, X-ray crystallographic structures, and three-dimensional reconstructions computed from images. The PFT technique has been particularly useful for the analysis of particles with icosahedral symmetry and could be adapted for the analysis of single particles of any symmetry for which a crude model exists or can be produced. (C) 1996 Academic Press, Inc.