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We present the results of a free-space microwave inverse scattering algorithm and experiment. The inversion algorithm is based on the Born iterative method but with a new integral equation operator that directly links the material contrasts we wish to image to S-parameter measurements of a vector network analyzer. This is done with a full-wave antenna model based on the source-scattering matrix formulation. This model allows us to absolutely calibrate an inverse scattering setup without the need for calibration targets. We describe the new operator and how it modifies the inversion algorithm, and explain how to make the algorithm and experiment consistent. We then give the results of imaging several dielectric objects and show the limits of the algorithm in experiment.