If a microwave cavity containing an anisotropic, inhomogeneous plasma is excited with a nonresonant frequency ω, the electron density distribution inside the plasma can be obtained from a knowledge of the tangential electrical field on a surface enclosing the plasma. The main step is the derivation of an integralequation relating the tangential field to the highfrequency plasma current. An experimental setup is discussed. The obtainable precision is limited by the noise like density fluctuations in the plasma itself and is about 1% for equation image for a spatial resolution in the same order of magnitude.