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.

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For one and a half decade, software for interferometric fringe evaluation has been developed and used at Technical University Graz. Within the framework of an awarded grant to one of the authors, the Austrian Government funded activities on optical metrology in mechanical engineering. In this grant these software packages on interferometric fringe evaluation had been subsumed under Windows95/98/NT and the Unix/X-Window-System. This software is made accessible via internet to the public domain (http://optics. t'u-graz. ac. at). Its main features are phase-stepping, Fourier domain evaluation and unwrapping techniques as well as algorithms for Abel-inversion and tomographical reconstruction. Additionally, we implemented a bunch of tools for data manipulation, e.g. multiple file handling, filtering, and flexible visualization of data. Some of these features with examples from a multidirectional holographic measurement on a plasma discharge and from speckle interferometry are presented.

Multidirectional interferometric data of an inhomogeneous phase object are obtained by double exposure reflection type holography. The evaluation of the interferograms for a computerized tomographic reconstruction of the local index of refraction by the convolution method is performed with subfringe resolution. For testing purposes the phase object is made by careful modeling of a convective heat flow in air. The reconstructed refractive index field is converted into a temperature distribution and is compared with independently measured temperature values, thus providing a strict examination of the quality of the tomograms.

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