Improving the accuracy of convergent-beam thickness measurements

Abstract

Convergent-beam diffraction patterns taken at appropriate “two-beam” conditions allow simple, rapid determinations of a specimen's thickness, extinction length and even its anomalous absorption coefficient (1,2). We here note three points to consider when obtaining the pattern.First, in thickness measurements the ratio of the fringe spacing to the spacing between the disks is utilized; there is an underlying assumption that the two distances are on the same angular scale. This assumption is incorrect if the illumination crossover is not in the plane of the specimen and simultaneously, the diffraction lens is focused incorrectly. If the crossover is at the specimen (Fig. 1a), varying the focus of the diffraction lens (changing w) varies the distance between the disks and the sizes of features within the disks in the same way, only the magnification of the pattern is changed. Likewise, if the diffraction lens is focused correctly, on the back focal plane of the objective lens, the angular scale within the disks matches that between the disks and neither scale is affected by variations in the illumination.