This thesis presents the research and development of a microwave in-strument to capture tomographic information from the inner structure ofthe biological sample. The principle of the instrument is based on theanisotropy introduced by the fibres in materials such as wood and musclesin terms of information regarding changes in the fibre structure. The in-formation is presented as images representing the state of polarization us-ing Stokes parameters, the complex polarization ratio, and the ellipticityand the linear tilt angles. The theory of wave propagation in anisotropicmedia is discussed and related to the dielectric properties of wood. Ex-periments have shown that the developed instrument can be utilized invarious applications such as localizing knots and cavities in wood andto detect mechanical contamination of meat. A second instrument hasbeen improved by introducing a new signal analysis step to estimate therelative shrinkage profile of paper. The estimator is based on trackingfrequency variations in the joint time frequency spectrum and follows thelower bound of the problem for the relevant noise levels.