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An estimate of the error caused by the plane-wave approximation in free-space dielectric measurement systems

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2 Author(s)
L. E. R. Petersson ; Sch. of Electr. & Comput. Eng., Georgia Inst. of Technol., Atlanta, GA, USA ; G. S. Smith

In a free-space measurement system, the electrical constitutive parameters of a plane sheet of material are determined using incident, transmitted and reflected electromagnetic beams. The electrical parameters are almost always obtained from the measured transmission and reflection coefficients using a procedure that approximates each beam as a single plane wave whose wavefront is parallel to the surfaces of the sheet (the plane-wave approximation). A theoretical model is constructed to investigate, in a very general way, the limitations of the plane-wave approximation. The field of the incident beam is taken to be a Gaussian function at the center of the sheet and analytic expressions are obtained for the transmitted and reflected beams using the plane-wave spectrum technique. Power transmission and reflection coefficients are calculated and series expansions of these coefficients are used to determine under what conditions the plane-wave approximation applies. Graphical results are presented to show how the error associated with the plane-wave approximation depends on the various parameters for the problem: electrical size of the beam waist, electrical thickness of the sheet etc

Published in:

IEEE Transactions on Antennas and Propagation  (Volume:50 ,  Issue: 6 )