Three-dimensional electron tomographic studies of thick specimens such as cellular organelles or supramolecular structures require accurate interpretations of transmission electron micrograph intensities. In addition to microscope lens aberrations, thick specimen imaging is complicated by additional distortions resulting from multiple elastic and inelastic scattering. Extensive analysis of the mechanism of image formation using electron energy-loss spectroscopy and imaging as well as exit wavefront reconstruction demonstrated that multiple scattering does not contribute to the coherent component of the exit wave (Han et al., 1996, 1995). Although exit wavefront restored images showed enhanced contrast and resolution, that technique, which requires the collection of more than 30 images at different focus levels, is not practical for routine data collection in 3D electron tomography, where usually over 100 projection views are required for each reconstruction, Using a 0.7-mu m-thick specimen imaged at 200 keV, the accuracy of reconstructions using small numbers of defocused images and a simple linear filter (Schiske, 1968) was assessed by comparison to the complete exit wave restoration. We demonstrate that only four optimal focus levels are required to effectively restore the coherent component (deviation 5.1%). By contrast, the optimal single image (zero defocus) shows a 25.5% deviation to the exit wave restoration. Two pairs of under-and over-defocus images should be taken: one pair at quite high defocus (>10 mu m) to differentiate the coherent (single elastic scattering) from the incoherent (multiple elastic and inelastic scattering) components, and the second pair to optimize information content at the highest desired resolution (e.g., 5 mu m for (2.5 nm)(-1) resolution). We also propose a new interpretation of the restored amplitude and phase components where the specimen mass-density is proportional to the logarithm of the amplitude component and linearly related to the phase component, This approach should greatly facilitate the collection of high resolution tomographic data from thick samples. (C) 1997 Academic Press.