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Free-space techniques are well suited for determining material properties at high frequencies. These techniques are nondestructive and contactless. The main disadvantages of the method are the mutual coupling between the antennas and the multiple reflections between antennas and sample or other nearby objects. Both problems can be strongly reduced by a judicious use of the possibilities of the network analyzer (e.g. calibration and time-domain gating). Another important (practical) problem is the fact that the transversal dimensions of the sample must be large in order to avoid diffraction effects at the sample edges and finally the transmitted waves are not really plane as is assumed in the theoretical models. To avoid this problems use can be made of lens-antennas which compress the microwave energy. Therefore, an improved theory is presented that takes the rather spherical nature of the transmitted waves into account. In this way the distance between the antennas and sample can be seriously reduced without violating the theoretical assumptions (no plane-wave condition). As a consequence the transversal dimensions of the sample can also be reduced without the use of lens-antennas. The theory was developed for two identical pyramidal horn antennas.