Image Processing

In addition to real images, the power spectra (PS) are also calculated. The PS is the square of the Fourier transform of the real image. From the PS in the reciprocal space more information on the symmetry of the atomic arrangements can be obtained. Furthermore, in crystalline structures reflections appear in the PS that lie symmetrically distributed on circles around the origin. The reflections always appear as pairs under an angle of 18o° for hkl and — h — k — l. From the diameter of the circles the corresponding netplane spacings can be calculated:

Npix (total)pix Npk (radius)

Npix (total) is the total number of pixels along the quadratic frame of the PS. This is usually 128, 256, 512,... Npix(radius) is the number of pixels between the origin and the reflection in the PS. pix is the pixel size, which depends on the digitizing of the images. The PS also allows the processing of experimentally obtained images for comparison of experimental images with computer simulations. The whole procedure is normally a Fourier filtering of the images [3o—32]. Among many other aspects—such as improving the quality of experimental images—image processing by Fourier filtering allows a decrease in the influence of the background, that is, the substrate, in the images and the separation of different structures, which may overlap each other. Examples thereof will be given later.

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