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New experimental set-ups are presented which allow multidirectional analysis of inhomogene - ous phase objects by high resolution holographic interferometry. The applicability of these arran- gements is tested in a first step. After this check of the method different kinds of plasmas are investigated. In order to obtain more sensitivity, the techniques of resonance heterodyne hologra-phic interferometry are applied. Knowing the relations between refractive index in the vicinity of a resonance line and the corresponding number density of ground state atoms this number density can be determined. 1. INTRODUCTION A fundamental problem in plasma diagnostics is the lack of sufficient symmetry of dischar-ges of technical interest. For this reason the determination of plasma parameters often turnsout difficult, assumptions like those of rotational symmetry or even a homogeneous layer are frequently not reliable. This paper demonstrates, how the methods of computerized tomographyin medicine can be adapted for optical tomography on the basis of heterodyne holographic interfe-rometry. Heterodyne holographic interferometry is used because of the small fringe shifts ocur-ring in interferometric investigations of plasmas. By an appropriate design of the optical arrange-ment a fringe system of high spatial frequency can be superimposed to the low-frequency fringesystem caused by the plasma itself. This process, known as optical heterodyning, enables the useof Fourier analysis, which is the basis for the required high resolution of the phase distortion to |