By J. Frank, M. Radermacher (auth.), James K. Koehler Ph. D. (eds.)

This quantity is a continuation of 2 previous books on complex electron microscope innovations. the aim of this sequence has been to supply in intensity analyses of tools that are thought of to be on the innovative of electron microscopic study strategies with functions within the organic sciences. The project of the current quantity continues to be that of a resource e-book for the examine practitioner or complicated scholar, specially one already good versed in uncomplicated electron optical tools. it isn't intended to supply in troductory fabric, nor can this modest quantity desire to hide the full spectrum of complex expertise now on hand in electron microscopy. some time past decade, desktops have discovered their approach into many examine laboratories due to the large raise in computing strength and stor age to be had at a modest rate. The ultrastructural zone has additionally benefited from this enlargement in a few methods with the intention to be illustrated during this quantity. 1/2 the contributions talk about applied sciences that both at once or in some way make vast use of computing device methods.

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A) Single-tilt projection: the tilt azimuth is kept constant and the absolute tilt angle is varied. (b) Conical-tilt projection: the absolute tilt angle is kept constant and the tilt azimuth is varied. (RADERMACHER 1980) 1980; RADERMACHER 1980). As in the case of single-axis tilting, a weighting function can be calculated for conical geometry which takes into account the share of sampling points in Fourier space contributing to the various spatial frequency ranges. In order to introduce the weighting function, we must first define the coordinate system: in the untilted position, the specimen lies in the x-y plane fixed to the electron microscope.

10) is by use of a priori information, which is done both in the maximum entropy method and in the "inexact" reconstruction method. However, for these methods, the resolution attainable is mathematically difficult to determine. 4 The Point Spread Function and the Effect of Angular Limitations ± In the electron microscope, the restriction of the tilt range to 60° poses an additional problem for the data analysis. (Only recently, tilt angles close to 90° have been achieved with special tilt holders (CHALCROFT 1984).

The great simplification of the reconstruction problem introduced by the single-axis tilting geometry therefore lies in the reduction of dimensionality, which implies that the 3-D reconstruction can be sequentially processed with a minimum requirement for computer memory, and that selected slices can be computed separately. However, as we will show below (Sect. 5), single-axis tilting is not always the most efficient method of data collection if part of the angular range is missing, as is the case in the electron microscope.