A new numerical solution of Abel-type integral equations is presented which is based on the principle of Fourier-analysis. The unknown radial distribution is expanded in a series of cosine-functions. the amplitudes of which are calculated by least-squares-fitting of the Abel-transformed series to the measured data. Advantages and applications of the new method are discussed, followed by a short comparison with methods, commonly used for Abel-inversion.

A recently devised new method for numerical Abel inversion is compared with four other commonly used methods. One of them, the convolution method, is employed in computer tomography for reconstructing asymmetrical objects. It is investigated whether this method can be adapted for the case of radial symmetry.As a first approach the comparison is performed by computer simulation. Special attention is given to the propagation of errors according to their origin. The result is a recipe for minimizing errors and for choosing the optimal method for reconstruction.The second step is a comparison of experimentally obtained radial profiles with functions resulting from Abel inversion of measured side-on data. Thus it is shown that the concept developed by computer simulation can be applied in practice.

The authors present an interferometric method for the investigation of phase objects which employs a Mach-Zehnder arrangement with objects being located outside. It functions as a differential interferometer with the practical advantage that the sensitivity and the carrier fringe system can be chosen arbitrarily and independently. The computerized evaluation is well adapted to the experimental set-up, which helps to achieve high accuracy of the results. For the case of radially symmetrical objects a numerical method is presented for calculating the refractive index distribution from data measured with the above mentioned type of differential interferometer. The results of a demonstration experiment are shown and further applications of this differential interferometer are discussed.

The principles of resonance interferometry are described with regard to two applications: High accuracy particle density determination within plasmas and interferometrical determination of spectral line profiles. The usability of this technique is investigated numerically, and physical limits are given for the regions in which resonance interferometry may be employed successfully. The discussion and the results are helt general for making it possible to decide whether or not to apply this method for an actual problem. An example (an object being longitudinally homogeneous with respect to the direction of light: end-on observation) shows how to use the presented results for calculating the detection limits of the method for a given object geometry.