Theoretical study of phase contrast images for small coherent precipitates inside a matrix

Abstract

A phase contrast image for a coherent precipitate of diameter D = 1, 2 or 5 nm has been calculated. The calculation was performed for small defocuses, where the image size is nearly equal to the precipitate size. Most of the microscope parameters were taken into account. For a large precipitate (D > 4 nm), a usual contrast was found, but for a small precipitate (D < 2 nm) the aspect of the image varies rapidly with defocus so that several contrast inversions occur in the considered defocus range (− 200 nm to + 250 nm). For 1 nm diameter precipitates the size of the objective aperture plays an important role. For this defocus range, the contrast of the precipitate against the background is no proof of the sign of the defocus.