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A new method is described for analysing variations in structure from high resolution electron microscope images. In Fourier theory, the image of a perfect crystal can be considered as the sum of sinusoidal lattice fringes having constant amplitude and phase given by the corresponding Fourier component. Imperfections are introduced by allowing these Fourier components to be a function of position, thus combining real space and reciprocal space information. It is shown how images can be obtained of the local value of the amplitude and phase of each major image periodicity. The amplitude and phase images are interpreted in terms of image detail and structural variations. Relationships are derived between the phase images and displacement fields due to a distortion of the lattice fringes and variations in the local reciprocal lattice vector. The meaning of the amplitude and phase images is illustrated by the analysis of experimental images of antiphase boundaries. Quantitative analysis of experimental images of carbon nanotubes is carried out using amplitude images and of strained metal multilayers using phase images.

Analysis of Variations in Structure from High Resolution Electron Microscope Images by Combining Real Space and Fourier Space Information