In this paper, we
demonstrate an active 3-D millimeter wave (mmW) imaging system used for
characterization of the dielectric function of different plastic materials
and liquid solutions. The method is based on reflection spectroscopy at
frequencies between 75 and 110 GHz, denoted as W-band, and can be used to
investigate homogeneous dielectric materials such as plastics or layered
structures and liquid solutions. Precise measurement of their dielectric
properties not only allows for characterization and classification of
different fluids, but also for reliable detection and localization of small
defects such as voids or delamination within multilayer structures built from
plastic materials. The radio frequency (RF) signal generation
is based on circuits that have been designed and fabricated at the Fraunhofer
Institute for Applied Solid State Physics (IAF) using a 100 nm InGaAs mHEMT
process

The development of weight- or stability-optimized materials such as plastics
or laminates has become the basis of most modern technologies. Manufacturers
must meet highest demands in terms of quality, reliability and cost
efficiency. Consequently, there is an increasing interest in high-end product
surveillance systems that allow for non-destructive material testing at the
production stage as well as in operation. For most non-destructive testing
methods, either ultrasonics

Photograph of the mmW focusing system.

In this paper, we present a new experimental setup based on the imaging scanner and investigate the chances and challenges of non-destructive material characterization at W-band frequencies. The method is based on reflection spectroscopy and allows for measurements of the refractive indices of layered plastic samples and determination of the complex dielectric function of different liquid solutions using a Debye model.

Figure

A sketch of two exemplary DUT used for the characterization of different
materials is shown in Fig.

Block diagram of the millimeter wave imaging system used for reflectometric measurements.

Since the absorption of millimeter waves in most homogeneous plastics is
comparably small

Simulated and measured power spectra corresponding to a 20 mm thick single-layer PMP sample.

In order to investigate material dispersion in a more quantitative way, it is necessary to select narrow frequency ranges rather than the full W-band to fit the model more accurately. The following method can be used.

Fit the experimental data for the full W-band to obtain a refractive index

Define upper and lower limits for possible values of the refractive indices based on

Identify the first maximum or minimum and set a corresponding counter variable to

Select a narrow frequency range around the

In consideration of the upper and lower limits defined in step 2, fit the measured
data within the narrow range to obtain refractive indices

Slightly vary the values of

Identify the center frequency

Save data point

Select the next extremum (

Repeat steps 4 to 9 for every maximum and minimum in the spectrum.

The first two steps are mandatory for obtaining reasonable results from the
Levenberg–Marquardt algorithm when only a narrow range of measurement data
is used. In particular, there is no unique solution for multilayer DUT, and
the algorithm does not converge properly without limiting the fitting
parameters. In addition, it is useful to define a measure of inaccuracy for
the fitted model such as the following sum of squares:

In principle, the analysis of liquid samples can be performed in a similar
way. However, the assumption of negligible contribution of the complex part
of the dielectric function no longer holds for water solutions, as they are
significantly absorbing in the mmW regime

Average refractive indices of different plastics at W-band frequencies.

Table

Dispersion of different plastics measured from single discs.

By using the method described in Sect.

Multilayer samples have been investigated by building arbitrary stacks
consisting of two, three or four discs that are either 10 or 20 mm thick. An
exemplary dispersion plot corresponding to a two-layer stack is shown in
Fig.

Conductance and pH values of the different solutions.

Measurements of three- and four-layer samples have shown that, in several
configurations, the refractive indices of deeper layers are overestimated
with respect to the single-layer measurements. This behavior occurs if the
refractive indices of upper layers are larger than in lower layers.
Figure

In order to investigate whether water solutions of different physical or
chemical properties can be uniquely distinguished using reflection
spectroscopy at W-band frequencies, a set of four sample solutions based on
DI water has been prepared. By measuring their conductances and pH values,
the solutions have been characterized as shown in Table

The complex dielectric function of these solutions can be calculated using
the Debye model represented by Eq. (

However, simulations have revealed that all parameters influence the spectra
in a similar way and that

Real and imaginary parts of the dielectric function of different water solutions. Due to measurement inaccuracies, the dielectric function of the NaCl and NaOH solutions can not be uniquely distinguished.

A dielectric decrement can be attributed to the specific conductivity of the acidic solution. If this decrement is strong enough to significantly superimpose the relative increase of the dielectric function caused by its relaxation time, the above assumption no longer holds and a more detailed model must be considered to fit the measured data. Even though, to the authors' knowledge, there are no comparable measurements in the frequency range between 75 and 110 GHz, it appears likely that this is the case. However, due to the necessity of strong smoothing of the spectra, which influences both the amplitude and position of peaks, the use of more complex models is not feasible using the current experimental setup, and uncertainties in the parameters of the fitted Debye model are already significant. Hence, NaOH and NaCl solutions are not uniquely distinguishable.

We have demonstrated a reflectometric setup to measure the refractive indices and dispersion of different multilayer samples made from homogeneous plastics as well as the Debye parameters corresponding to a relaxation model describing the complex dielectric function of liquid solutions. The setup is included in a mmW imaging scanner so that the information on the dielectric behavior of different DUT can be directly used for mmW imaging.

Small defects in multilayer structures have been successfully visualized and
localized based on the data obtained by reflectometry measurements

Furthermore, the reflectances of acid and basic solutions have been investigated and compared to pure DI water. While the reflectance spectra of all the samples are clearly distinguishable with respect to statistical uncertainties, the strong parasitic interference caused by the directional coupler used in the setup leads to significant inaccuracies regarding the model parameters when the data are fitted. As a consequence, more complex models could not be investigated in more detail. In addition, samples that only differ slightly in their dielectric behavior, such as the two basic solutions that have been investigated, can not be uniquely distinguished.

The authors would like to thank the workshop of the Fraunhofer IAF for precise mechanical prototype fabrication of the parabolic mirrors used in the imaging system and the dielectric samples. Edited by: R. Lucklum Reviewed by: two anonymous referees