Recently the increasing use of microwaves for industrial testing procedures is being generated by the strong need of accurate NDT techniques of permittivity measurement at microwaves. The simultaneousness of each layer dielectric constant and thickness d estimation is the peculiar feature of dielectric sandwich NDT because the process of structure manufacturing and material property forming take place at the same time. The necessity of testing parameter set simultaneously demands the application of multi frequency methods.

METHOD DESCRIPTION

Special microwave units under computer control were used to measure of structure reflection. The units operate at the frequency ranges 17.4-25 and 26-37.5 GHz.

The impossibility to obtain simple general analytic relations between interesting parameters and directly measuring values, i. e. values of reflection coefficient (RC) on set of frequencies, is the cause of complexity of the simultaneous estimation of the parameters of every layer. Instead of solving inverse problem directly, parameter vector p is found as a vector minimizing the functional (objective function):

(1)

where R( _i ) is RC values measured at the set of frequencies, F(p, _i ) is the output of model under _i and p, is discrete correlation function. The minimization of (1) and maximization of r are equivalent Thus this approach is similar to correlation methods of targets discrimination.

The initial guesses for optimisation procedure were obtained by well-known means of spectral analysis: discrete Fourier transform (FT), Prony (PM) and pencil-of-function methods (POFM)[1]. Experience shows that choosing initial guesses with help of FT provides more stable results than the POFM in the case of high level of noise. If two time-domain peaks were overlapping and forming single peak, the next approach was used. After FT and estimation of single peak parameters the model data with estimated parameters are subtracted from time-domain signal. Parameters of two maximum peaks of residue are used as initial guesses of optimization procedure. If amplitudes of latter peaks are lower than noise level the decision of presence of only single peak are taken.

The consideration of expression (1) minimization as correlation discrimination allows layer parameters to determine through use of other methods of target discrimination. K-pulse method has been elaborated recently [2]. The inversion of RC in frequency domain transforms zeroes into poles. In this case these artificial poles produce resonances with high Q -factor and discrimination can be performed sensitively. The most sensitive discrimination measure was determinated as

EXPERIMENTAL RESULTS AND CONCLUSION

Real experiments for set of structures were carried out. Measurement data in frequency domain for single-layer structure of ceramics ST-10 with average thickness equal 5.6 mm and two-layered structure fibreglass-rubber with layer thicknesses equal 31.1 and 28.8. mm were used. PM for ceramics ST-10 with the model order from 5 to 10 has given the values of and d equal from 13.87 to 8.45 and from 9.09 to 4.9 mm correspondingly. Minimization method of objective function for all using initial guesses has given the values of and d equal 8.52 and 6.54 mm correspondingly. The parameter estimation of the two-layered structure were 3.76 and 2.3 and 32.1 mm and 29.6mm correspondingly. Using K-pulse conception suggested has provided the next estimates: =8.55 and d=5.6 mm. For single-layer plexiglass with real thickness 4.0 mm estimates were =2.5 and d=3.95 mm. Thus Rayleigh limit was exceeded approximately 2.8 times.

The application of the presented methods is shown to posses a good perspective for the increase of accuracy of the estimation of the dielectric sandwich parameters especially when measurement frequency bandwidth is not wide enough, thus microwave NDT method can be improved. The approach developed uses only general properties of waves, thus it can be applied for processing results of probing not only microwaves but waves of another nature as acoustic waves and so on. REFERENCE

1. Z. A. Maricevic, T. K. Sarkar, Y. Hua, A. R. Djordjevic, ``Time-domain measurements with the Hewlett-Packard network analyzer HP 8510 using the matrix pencil method", IEEE Trans. On Microwave Theory and Techniqus, Vol. 39, No. 3, pp. 538-547, 1991
2. F. Y. S. Fok and D. L. Moffatt, ``The K-pulse and E-pulse, " IEEE Trans. On Antennas and Propagation, Vol. 35, No. 11, pp. 1325-1326, 1987.