R Henderson, JM Baldwin, KH Downing, J Lepault, F Zemlin. Structure of purple membrane from halobacterium halobium: recording, measurement and evaluation of electron micrographs at 3.5 Å resolution. Ultramicroscopy 19:147-178, 1986.
Electron micrographs of the purple membrane have been recorded using liquid nitrogen and liquid helium cooling on three cryoelectron microscopes. The best micrographs show optical diffraction spots, arising from the two-dimensional crystal, out to resolutions of around 6 Å. Large areas of several of these micrographs have been analysed using a procedure which determines the strength of the very weak high resolution Fourier components of the image of the crystal. The procedure consists of reciprocal space filtering followed by real space correlation analysis to characterise image distortions, removal of the distortions by interpolation, and finally extraction of the amplitudes and phases of the Fourier components from the distortion-corrected image of the crystal. These raw image amplitudes and phases are then used, together with previously measured amplitude and phase information, to refine the beam tilt and crystal tilt, phase origin and amount of defocus and astigmatism of the image. The phases can then be corrected for the effects of the contrast transfer function, beam tilt and phase origin. The amplitudes of all the spots which are expected to be strong from their known electron diffraction intensity are observed to be significantly above the background noise level, and the independent phases from different images, and from symmetry-related directions in the same image, show excellent agreement out to a resolution of 3.5 Å. Although only images from untilted or slightly tilted ( < 5°) crystals have been analysed using the procedure described in this paper, a simple additional step enables analysis of images at any tilt angle, providing a complete practical method for high resolution analysis of images of two-dimensional crystalline arrays.