The re-emergent field of quantitative electron crystallography is described by some of its most eminent practitioners. They describe the theoretical framework for electron scattering, specimen preparation, experimental techniques for optimum data collection, the methodology of structure analysis and refinement, and a range of applications to inorganic materials (including minerals), linear polymers, small organic molecules (including those used in nonlinear optical devices), incommensurately modulated structures (including superconductors), alloys, and integral membrane proteins. The connection between electron crystallography and X-ray crystallography is clearly defined, especially in the utilisation of the latest methods for direct determination of crystallographic phases, as well as the unique role of image analysis of high-resolution electron micrographs for phase determination. Even the aspect of multiple beam dynamic diffraction (once dreaded because it was thought to preclude ab initio analysis) is considered as a beneficial aid for symmetry determination as well as the elucidation of crystallographic phases, and as a criterion for monitoring the progress of structure refinement. Whereas other texts have hitherto preferentially dealt with the analysis of electron diffraction and image data from thin organic materials, this work discusses - with considerable optimism - the prospects of looking at harder' materials, composed of heavier atoms. Audience: Could be used with profit as a graduate-level course on electron crystallography. Researchers in the area will find a statement of current progress in the field.

Maximum Entropy (ME) techniques have found widespread applicability in the reconstruction of incomplete or noisy data. These techniques have been applied in many areas of data analysis including imaging, spectroscopy, and scattering [Gull and Skilling, 1984]. The techniques have proven particularly useful in astronomy [Narayan and Nityanada, 1984]. In many of these applications the goal of the reconstruction is the detection of point objects against a noisy background. In this work we investigate the applicability of ME techniques to data sets which have strong components which are periodic in space or time. The specific interest in our laboratory is High Resolution Electron Micrographs of beam sensitive materials. However, ME techniques are of general interest for all types of data. These data mayor may not have a spatial or temporal character. Figure 1 shows an HREM image of the rigid-rod polymer poly(paraphenylene benzobisoxazole) (PBZO). The 0.55 nm spacings in the image correspond to the lateral close-packing between the extended polymer molecules. Near the center of this crystallite there is evidence for an edge dislocation. In HREM images both the frequency and position of the infonnation is important for a proper interpretation. Therefore, it is necessary to consider how image processing affects the fidelity of this information in both real and Fourier space.

The re-emergent field of quantitative electron crystallography is described by some of its most eminent practitioners. They describe the theoretical framework for electron scattering, specimen preparation, experimental techniques for optimum data collection, the methodology of structure analysis and refinement, and a range of applications to inorganic materials (including minerals), linear polymers, small organic molecules (including those used in nonlinear optical devices), incommensurately modulated structures (including superconductors), alloys, and integral membrane proteins. The connection between electron crystallography and X-ray crystallography is clearly defined, especially in the utilisation of the latest methods for direct determination of crystallographic phases, as well as the unique role of image analysis of high-resolution electron micrographs for phase determination. Even the aspect of multiple beam dynamic diffraction (once dreaded because it was thought to preclude ab initio analysis) is considered as a beneficial aid for symmetry determination as well as the elucidation of crystallographic phases, and as a criterion for monitoring the progress of structure refinement. Whereas other texts have hitherto preferentially dealt with the analysis of electron diffraction and image data from thin organic materials, this work discusses - with considerable optimism - the prospects of looking at harder' materials, composed of heavier atoms. Audience: Could be used with profit as a graduate-level course on electron crystallography. Researchers in the area will find a statement of current progress in the field.