·Table of Contents ·Methods and Instrumentation | Holographic Approach to Multifrequency Microwave Methods of Dielectric Material NDEOleg O. Drobakhin,Dniepropetrovsk State University, 13 Nauchnaya Str., Dniepropetrovsk, 49050 Ukraine Contact |
Use of a vector analyzer such as six-port one is traditional way of complex reflection and transmission coefficient measurements [3]. But apparatus realization requires some precise microwave components and the set of standard loads for calibration procedure. For the purpose of obtaining the time-domain signal, an ordinary scalar reflectometer with an additional reference reflection (comparison reflectometer) can be applied. The idea of time-domain signal synthesis without direct phase measurements is very attractive and provides simple apparatus realization. It was shown previously [4] that if distance between the reference discontinuity and DS was provided more value than DS electric thickness, one could obtain a part of result of transformation in time domain coinciding with the time-domain signal calculated by Fourier transform of the complex reflection coefficient. This approach is similar to ordinary Fourier holography and the condition for time intervals is analogous to Leith and Upatnieks one for angles. This idea was applied to measure reflection characteristics of DS in free space using reflection from a waveguide open end as the reference signal. A typical distance between antenna and DS was 10 cm.
Increasing the distance requires using a horn instead the open end of waveguide. The latter has gain 6-7 dB. Horn's gain is approximately 20-25 dB. But the horn has two discontinuities with reflection coefficients R_{1}exp(jwt_{1}) and R_{2}exp(jwt_{2}). Both of them play role of reference reflections. At frequencies that are more than 100 GHz waveguide junctions can not be realized so thoroughly as in 17-37 GHz frequency range thus they can play the role of additional reference reflections. This fact requires consideration of the situation with a few reference signals. This situation has not similar one in the traditional Fourier holography.
which is square of modulus of sum of the N reflections in the horn and waveguides and DS reflection. After subtracting results of measurements under conditions of radiation into the space without DS
(2) |
coinciding with spectrum of horn's autocorrelation function, expression (1) is transformed to
Inverse Fourier transform of A(w) contains autocorrelation function r_{A}(t)=F^{-1}{|R(w)|^{2}}(F^{-1}{ } - inverse Fourier transform) and set of cross-correlation functions r_{i}(t)=F^{-1}{R_{i}^{*}R(w)exp(-jwt_{i})} which appear at positive time and r_{i}(t)=F^{-1 }{R_{i}R^{*}(w)exp(+jwt_{i})} which are observed at negative time.
Cross-correlation functions r_{i}(t) are not overlapping with autocorrelation function r_{A}(t) if t_{i} are greater than time t of propagation in DS. The condition of non-overlapping r_{i}(t) and r_{k}(t) is | t_{i}-t_{k} | > t. Thus the length of the horn must be longer than DS electrical thickness. The technique of impulse DS characteristic calculation on base of scalar measurements at many frequencies is similar to holographic approach. If any R_{i} has uniform frequency characteristics, any cross-correlation functions r_{i}(t) coincides in form with time-domain response of DS. If R_{k} is dominant then only r_{k }(t) can be used and situation can be simplified. Thus the conditions for time intervals must be satisfied only for reference discontinuity R_{k} . If R_{i }is uniform, r_{i}(t) is the time-domain response of DS. But for a horn, R_{i }is not uniform. A method of combination of modulus of autocorrelation function spectrum and phase of spectrum of cross-correlation function with reference signal is used for overcoming this shortage.
Measurements are multifrequency ones. The time-domain signal was calculated by means of inverse discrete Fourier transform. The procedure includes time-gating. The form of time-gate was chosen as Batterworth band-pass filter for extracting a cross-correlation function and Batterworth low frequency filter for extracting the autocorrelation function. A transformation of time-domain signal after time-gating to frequency domain by means of a direct discrete Fourier transform gives complex RC as function of frequency. Normalization is reached by dividing the frequency data by ones for metallic plate disposed at the same distance as the DS. Similar to filtering, time-gating distorts boundaries of frequency band. Time-gating is a linear operation thus it can not separate completely informative and spurious parts of time-domain signals. This fact induces additional components of error. This approach is not appropriate for frequency property of reference reflection is not optimal thus the error of modulus reconstructed from cross-correlation function is rather large.
Analysis of (3) shows that combination of time-gating and inverse Fourier transform can extract k|R(w)|^{2}. After square rooting modulus of RC is obtained. Phase information is taken from the inverse Fourier transforms of the cross-correlation function. This approach is appropriate if frequency property of reference reflection is not optimal. Another appropriate situation is one if autocorrelation is greater than any cross-correlation functions. But under real conditions all spurious reflections form their proper autocorrelation functions. Spectra of all these functions have identical support thus informative autocorrelation function is corrupted. Practical significance of this approach lies in situation then additional signals are absent or rather low.
For satisfaction of the time interval condition the third horn with aperture sizes and length equal to 81.25×87.65 mm and 201 mm was investigated. The horn was made with the same angle expansion so reflection coefficients in the throats were approximately equal. The third one has the wall thickness 1mm. Reflection coefficient in the throats at 18-19 24-25 GHz were ~0.05 and ~0.025 for the second horn, and ~0.04 and 0.02 for the third one respectively. Reflection coefficient of aperture were 0.03, 0.015 and 0.015, 0.007 respectively. The advantages of the longer horn were confirmed experimentally for the three-layered DS. The horns allow to carry out measurements of two samples of foams at distance in 50 cm from the aperture plane. But the longer horn requires more high level of technology, it has larger zone of radiation and its length is the part of distance between reference reflection and DS.
The approach was experimentally checked for a glassplastic-rubber structure. Thickness of both layers and dielectric constants were estimated with quite high accuracy. The estimates were e_{1} = 4,35, e_{2} = 2,75, tgd_{1} = 0,008, tgd_{2}=0,014, d_{1} = 29,5 d_{2} = 28,5mm. Experimental and model data are presented. Modulus and phase of reflection coefficient against frequency are showed in fig. 1, 2. Synthesized signal against space coordinate is displayed in fig. 3. The peak 1 is reflection from frontier interface of structure, the peak 2 is the reflection of interior interface, and the peak 3 is reflection from the rear interface. The dotted line is used for model data with estimated parameters which values are presented. The solid line is used for experimental data. The modulus was calculated using autocorrelation function. The phase was calculated using cross-correlation function. Real average thickness obtained by direct means of geometrical measurements were 31,1 and 28,8 mm.
Fig 1: |
Fig 2: |
Fig 3: |
Experiments were carried out also in range 126.6 - 145.4 GHz with step 200 MHz. The error of frequency setting up was ±1.5%, i. e. ~ 2 GHz. An ordinary scalar waveguide reflectometer with two directional couplers was used. The size of rectangular waveguide cross-section was 1.6 × 0.8 mm. Voltmeters have served as power-meters. The horn had sizes: length was 50 mm, aperture sizes were 21 × 26 mm. The width of peak at 3 dB level is 12.8 mm, i.e. ~ 45 ps. The time-domain signal for plexiglass layer with thickness 39 mm was synthesized. Estimates of effective e^{'} and tg d were 2.95 and 0.037. But restriction of this frequency range is high level of dielectric losses. An attempt of foams measurements was failure. It was noted that reassembling measuring sometimes caused a swap of dominant reference reflections. For instance sometimes reflection in the connection of the waveguide section and the horn was dominant.
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