An optical method for the analysis of periodicities in electron micrographs, and some observations on the mechanism of negative staining.

The intensity distribution is investigated experimentally using an optical diffractometer, and the positions of the axial minima on either side of the geometrical focus are measured. The results are compared with the predicted theoretical distributions in various planes perpendicular to the optical axis.

Attempt to Investigate Experimentally the Intensity Distribution near the Focus in the Error-Free Diffraction Patterns of Circular and Annular Apertures

The change in phase that occurs in the degree of coherence is investigated by a method involving two-beam interference with partially coherent light. Examples are given to illustrate the phase change, and a comparison made with the theoretical predictions.

Illustration of the phase change in two-beam interference with partially coherent light

The analogy between the diffraction of light by a set of holes, and the diffraction of X -rays by a set of atoms can be exploited in solving many different types of X -ray diffraction problem . A special instrument has been built to obtain diffraction patterns rapidly, making possible several different approaches to the determination of crystal structures. Of particular importance is that involving the ‘optical transform’ of a molecular representation. Consideration of the optical transform, which is closely related to the Fourier transform, can, for simple space groups, lead directly to the crystal structure. For more complicated space groups, optical transforms of molecules in different orientations have to be combined, and some rules governing their combination are given. The discussion includes several examples of structures which have been determined by optical-transform methods. These methods require the presentation of the X -ray data in the form of a weighted reciprocal lattice, from which information can often be obtained directly. For several new structures such information as the separation of two similarly oriented molecules, or the orientation of hexagonal arrangements of atoms, has been deduced by considering the weighted reciprocal lattice alone. In some cases this led to the complete structure; in others it was a valuable supplement to the optical transform method. Despite the lack of quantitative accuracy, optical methods can be of use in refining approximate structures by ordinary Fourier methods. Examples are given of the deter­mination of the relative phase angles of the reflexions of both centrosymmetric and non-centrosymmetric structures. The relationships between optical methods and more conventional methods of structure determination are discussed.

The application of the principles of physical optics to crystal-structure determination

SUMMARY

Methods of analysing electron micrographs are reviewed, with special reference to the needs of the practising electron microscopist. It is concluded that a simplified optical diffractometer and a projection ‘Periodograph’ can be particularly helpful, especially in biological investigations, to which extensive reference is made in the bibliography.

Instrumental aspects of image analysis in the electron microscope

The methods described involve the observation of the diffraction patterns of holes punched in thin card to represent atomic arrangements. Details are given of the instrument that is used to observe these patterns and also of the pantograph-punch that is used to prepare the cards. Several examples of diffraction patterns are given; some illustrate the performance of the instrument with lenses of various optical qualities and others illustrate the use of the instrument in the teaching of physical optics.

https://iopscience.iop.org/article/10.1088/0950-7671/30/4/301/pdf

C A Taylor

Papers

Apparatus used in the development of optical-diffraction methods for the solution of problems in X-ray analysis