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A method of image reconstruction in three-dimensional (3-D) microwave tomography in a weak dielectric contrast case has been developed. By utilizing only one component of the vector electromagnetic field this method allows successful reconstruction of images of 3-D mathematical phantoms, a prototype of the 3-D microwave tomographic system capable of imaging 3-D objects has been constructed. The system operates at a frequency of 2.36 GHz and utilizes a code-division technique. With dimensions of the cylindrical working chamber z=40 cm and d=60 cm, the system allows measurement of an attenuation up to 120 dB having signal-to-noise ratio about 30 dB. The direct problem solutions for different mathematical approaches were compared with an experimentally measured field distribution inside the working chamber. The tomographic system and the reconstruction method were tested in simple experimental imaging.