Computation of a three dimensional image of a periodic specimen from a single view of an oblique section

Abstract

We describe here a method for computing a three dimensional map of a periodic specimen from a single electron micrograph of an obliquely cut section. Neighbouring areas of such an image display successively the contents of the unit cell of the structure. The reconstruction procedure can be considered in two steps. The first step involves restacking of successive areas to produce an image akin to that produced by serial section reconstruction. The resolution normal to the section would, at this stage, be limited by the thickness of the section, since the micrograph represents a projection of the density in the section. However, because of the periodic nature of the specimen, the image contains redundant information, which can be used in an attempt to deconvolute the section thickness and thus produce improved resolution normal to the section. The computation can be carried out directly with the densities or more conveniently, particularly for three dimensional crystals, by using Fourier transforms. The approach, which is most powerful when the section is thin, is insensitive to the collapse of the section caused by electron irradiation. Striated muscle provides particularly suitable specimens for such analysis and we present, as examples, computed maps of the M-band of fish muscle and of insect flight muscle in rigor.