Abstract: Microwave interferometer is an efficient tool for non-intrusively diagnosis of electron density of plasma,which can be used for the measurement of plume of helicon plasma thruster. Four different numerical Abel inversion algorithms,including the discretization method,the cubic spline interpolation method,the Hankel-Fourier transform method and the Nestor-Olsen method, are used to retrieved the plume density profile that is detected by microwave interferometry for the cases with and without noise.After analysis of the effect of sampling density on the retrieval error,the smoothing and interpolating solution is proposed to mitigate the under-sampling related problem.As a summary,the procedures of the retrieval and processing are proposed.Two principle verification experiments with microwave network analyzer have been done.In the first experiment,a circular pipe is measured as a axial symmetrical target,which simulates the plume,and the retrieval results match well with the shape of the pipe.In the second experiment,spatial resolved integrated phase shifts are retrieved by Abel algorithm.The radial electron density profile within the plume is calculated.The experiments and their results verify the performance and validity of both the system design and the retrieval algorithm.