3650 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 11, NOVEMBER 2011 A Simple Data Transformation Technique for Inverse Scattering Applications in Waveguides Ali Yapar, Emre Kılıç, Mehmet Çayören, and Funda Akleman Abstract—A new method, which can be considered as a calibra- tion technique to transform the measured raw S-parameters of a rectangular waveguide partially filled with a dielectric material into the desired reference planes, is presented. The method is based on the removal of errors arising from the multiple reflections and imperfections of the system elements such as adapters and connectors, through the T -parameter matrix representation of the system. The measured raw data are transformed into the terminal planes of the waveguide by simply calculating frequency- dependent complex coefficients. After this transformation, a quite satisfactory match is observed between the experimentally mea- sured and numerically calculated S-parameters for different types of materials and configurations. The calibrated measured data are also used in the inverse problem to determine the dielectric permittivity of the materials, and the preliminary reconstruction results are very promising. Index Terms—Calibration, dielectric-loaded waveguide, imag- ing of dielectric permittivity, S-parameters. I. I NTRODUCTION D IELECTRIC-LOADED waveguide is a typical element in microwave applications which is widely used for the mea- surement of electromagnetic properties of materials [1]–[15], filter design [16], [17], and such other purposes. The waveguide technique is very convenient for the determination of material properties, but the geometrical configuration and the position of the material play a crucial role in this technique [1], [2], [18]. Although the analysis and calculations are very simple for the materials completely filling the cross section of the waveguide, it is difficult to set up such a configuration in a high precision physically. One may overcome these difficulties by the use of partially filled materials, but this time, the analysis becomes more complicated [4], [6], [9], [10]. Another important issue is the precise measurement of S-parameters at the predetermined reference planes, in which the calibration of the measurement system becomes very vital. Therefore, in such a measurement system, additional calibration kits, such as the through-reflect- line (TRL) one, are required to remove the effects of coaxial- Manuscript received November 1, 2010; revised January 30, 2011; accepted March 8, 2011. Date of publication April 21, 2011; date of current version November 9, 2011. This work was supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under Grant 108E146. The Associate Editor coordinating the review process for this paper was Dr. Sergey Kharkovsky. A. Yapar, M. Çayören, and F. Akleman are with the Electronics and Com- munication Engineering Department, Istanbul Technical University, Istanbul 34469, Turkey (e-mail: yapara@itu.edu.tr). E. Kılıç is with Lehrstuhl für Hochfrequenztechnik, Technische Universität München, 80290 München, Germany. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2011.2135090 to-waveguide transitions and extra reflections due to the mismatching between the elements of the measurement system [6], [19]. Although the TRL calibration kits overcome these effects conveniently, new approaches are required in the lack of this kind of commercial kits particularly in relatively lower frequency bands. Consequently, the subject is still open to new contributions such as calibration-independent methods for partially filled structures [20]. Within this context, the measured (without TRL calibration) raw S-parameters of a rectangular waveguide partially filled with a dielectric material are transformed into that of the desired reference planes by a simple technique in this paper. As a matter of fact, the motivation of this study originates from a previous work of the present authors [21], where the inverse problem re- lated to the inhomogeneous materials loaded in a waveguide has been solved by an integral-equation-based method and very sat- isfactory results have been reported with simulation data. In or- der to test the inversion method given in [21] with real data, the first step is to measure the S-parameters of the system in a high precision at the reference planes corresponding to the terminals of the waveguide. To this aim, an experimental setup is con- figured here with a rectangular waveguide, and measurements are realized with partially filling materials. In the measurement procedure, only the vector network analyzer (VNA) is simply calibrated by a classical short-open-load-through (SOLT) cal- ibration instead of TRL calibration of the whole system. In order to extract the effects of the coaxial-to-waveguide transi- tions which are due to waveguide adapters and connectors, the measurements are performed for both empty and partially filled cases under dominant mode excitation. Then, an additional data transformation, which is based on the T -parameter matrix representation of the total system, is applied to the measured data in order to convert the values at the terminals of the coaxial cables into those of the reference planes, i.e., into the terminals of the waveguide. This transformation is based on removing the effects of the coaxial-to-waveguide transitions and extra reflections under the assumptions that the coaxial-to-waveguide transitions in both terminals are symmetrical and that the VSWR of these transitions is small enough. After this trans- formation, the results obtained from measurements and HFSS (3-D full-wave electromagnetic field simulation software) sim- ulations are compared, and satisfactory match is achieved for both amplitude and phase values of the S-parameters for different types of low-loss dielectric materials. Furthermore, the inversion method given in [21] is applied by convert- ing the measured S-parameters into the required field values via the aforementioned transformation. The reconstructions with calibrated data are very satisfactory for partially filling 0018-9456/$26.00 © 2011 IEEE