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Using the Huygens-Fresnel principle the expressions for the intensity and the phase in Fresnel diffraction phenomena have been derived. The cases of spherical, cylindrical and plane scalar waves incident upon the plane diffraction screen have been investigated. The diffraction screen may consist of any number of parallel strips of different transmissivities and different phase shifts, the width of the individual strips being large compared with the wavelength. As special cases of the general formulae, the intensity and phase distributions in the diffraction patterns for the following forms of the diffraction screen have been calculated: opaque and partially transparent half-plane, slit, strip and double slit. By means of the derived expressions, the validity of Babinet's principle for Fresnel diffraction phenomena of this type has been verified.

S‐layers are now considered a common cell wall structure in Bacteria and Archaea as well as in some algae. Morphological and chemical studies have revealed that S‐layers consist of crystalline arrays of protein or glycoprotein subunits forming oblique, square or hexagonal lattices on the cell surface. Electron microscopy and computer image enhancement techniques have been applied to obtain structural information down to the nanometer range. This chapter deals with the wide distribution of S‐layers among cyanobacteria, and their morphological and chemical characterization, and the potential of high resolution electron microscopic studies applied to the cell envelope of Pyrodictium. The occurrence of S‐layers in cyanobacteria was investigated by cryomethods and ultrathin sectioning. These investigations indicate that the ultrastructure of S‐layers may be exploited as an auxiliary taxonomic criterion in the classification of cyanobacteria. Pyrodictium is the first organism which has shown an optimum growth temperature above 100°C. The highly irregularly shaped, flagellated cells are interconnected by extracellular tubules. The three‐dimensional structure of this network was visualized with high resolution scanning electron microscopy while the fine structure of the cell wall architecture was studied in detail with various electron microscopic techniques. Both contributions demonstrate that the investigation of the fine structure of S‐layers is fundamental for establishing structure‐function relationships for these two‐dimensional crystalline arrays.

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