  We use a near-field scanning microwave microscope to simultaneously image the
dielectric constant, loss tangent, and topography in a PbTiO_3 crystal. By this
method, we study the effects of the local dielectric constant and loss tangent
in the geometry of periodic domains on the measured resonant frequency, and
quality factor. We also carry out theoretical calculations and the results
agree well with the experimental data and reveal the anisotropic nature of
dielectric constant.
