Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

DoITPoMS Teaching & Learning Packages Diffraction and Imaging Applications of the theory of optical diffraction and imaging

# Applications of the theory of optical diffraction and imaging

The principles of optical diffraction and image formation are equally valid for other waves: for example, neutrons, electron beams and X-rays. The similarity in the diffraction behaviour means that the theory presented here is applicable to them as well.

The symmetry of a diffraction pattern can reveal useful information on the symmetry of the mask. This is exploited in the electron diffraction of crystals, where the pattern can reveal the nature of the crystallographic symmetry, e.g. the periodicity of the structure; the distribution of atoms in the unit cell; and the shape of the crystal. X-ray diffraction patterns are used to measure spacing between layers or rows of atoms, and to determine crystal orientations and structures.

Electron diffraction patterns are two-dimensional sections of the reciprocal lattice of the diffracting crystal. X-ray diffraction patterns are simply 3-dimensional extensions of Fraunhofer diffraction. With X-rays, the crystal only diffracts in a few directions.

The nature of diffraction from a single slit allows macro-scale measurements to be used to calculate micro-scale dimensions. This has important implications - for example, allowing microscopes resolve to very fine scale (nanometre scale).

In optics, the basic shape of the mask is preserved in the bright field image, and some fine detail is lost. In electron diffraction, the contrast of the bright field image is due entirely to thickness and density variations in the sample. A convex glass lens is typically used to focus laser light, but magnetic fields are required to focus electron beams. By selecting individual diffraction spots, dark field images can be used in electron microscopy to distinguish phases (such as characterising two phase intergrowths in crystals).

Multi-beam images (composed of various spots, and known as 'high resolution images') are commonly used to study dislocations. Dark field imaging can be used to highlight the dislocation lines, and by tilting the electron beam, the Burgers vector can be determined. These techniques are common in Transmission Electron Microscopy.