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The effects of attenuation on the Born inversion process for diffraction tomography are investigated. The exact forward scattered fields for a Iossy dielectric cylinder in a Iossy medium are calculated and are then used to reconstruct an image of the scattering object. As accurate image is produced only when the cylinder acts as a small perturbation on the dielectric constant of the external medium. Results indicate that even small losses have a significant effect on the resolution of the image. It is possible, however, to eliminate image distortion by matching the loss tangent of the outside medium to that within the cylinder.