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Drive and control electronics
The entire system can be controlled from a PC. For this purpose, a Matlab-based Graphical User Interface (GUI) has been developed. It can autonomously perform a complete data acquisition or a Phase Conjugation/DORT retransmission. There are three connections handled by Matlab’s Instrument Control Toolbox, one to the VNA (Ethernet) and two to the PIC microcontrollers (one USB cable per PIC) driving the RF components of each of the arrays (see Fig. 1.1(b)). The way these connections are set and handled in Matlab is described in §A. The VNA is remote-controlled in order to set the features of a frequency sweep (n. of frequencies, IF filter bandwidth, n. of averages), to trigger it and to read the measurement into the PC.
With reference to the PIC driving the TRM array, in Fig. 1.3(a) one can schematically see the PIC connections to the switches (SPDT’s and SP8T’s) and to attenuators and phase shifters. They were designed, together with the electronic board layout, by Marc Bianchieri- Astier during its Master 2 internship [13]. The switches are connected to the PIC through a simple buffer (not shown in the figure). In order to implement the wanted attenuation/phase
shift, the channel is addressed through three bits (1 to 8) and A/ couples controlled with the I2C protocol through two wires: one carries a clock signal, the other the data sent bit after bit (a first byte representing the address of either the attenuator or the phase shifter, followed by two bytes containing the code giving the wanted attenuation/phase shift as described in §1.8).
A communication protocol between PIC, PC and RF components has been established. It has a “server” side in Matlab and a “client” side running in the PIC (coded in a special PIC-adapted C language, cfr. §A). The PIC state machine is depicted in Fig. 1.3(b). After initialization the PIC is in the wait state; when a reset character (arbitrarily chosen and known to both Matlab and the PIC) is read, a counter i is initialized and the evaluation state is reached. Two bytes are now read, decoded (a binary to decimal conversion is needed), and sent back to the PC in the transmit to PC state for verification. This loop is repeated 17 times, 1 for the switches and 2×8 times for all the attenuators and phase shifters. Once this is done, the PIC finally goes to the I2C state: the PIC drives its outputs connected to the switches and uses the I2C protocol to communicate with attenuators and phase shifters one after the other. Notice that during the I2C communication, after writing the attenuation/phase shift code into the component, the PIC reads back the code for verification. The whole cycle approximately takes 2 seconds.
The anechoic chamber
A first anechoic chamber was built with flat absorbing panels (Fig. 1.4(a)) with dimensions 1.8×0.6×0.6 m3 (length×width×height). It was used for the initial validation of the prototype. Nevertheless, as soon as the first quantitative inverse scattering experiments were realized, the need for pyramidal panels, much more effective in absorbing electromagnetic waves under grazing angle incidences, became impellent in order to recreate free-space conditions. A second chamber with pyramidal panels has then been built (Fig. 1.4(b)), whose internal (exploitable) dimensions are 1.4×0.8×0.8 m3. This chamber is provided of a door and of aremovable panel on the TRM side, and it is completely rigidified by a 3 cmthick wood shell. Furthermore, two plexiglas supports (one of them is visible in Fig. 1.4(b)) have been realized in order to achieve a precise positioning of the array antennas. The second anechoic chamber was financed by the Institut Fresnel in Marseille; the plexiglas support was realized by the Laboratoire d’Électronique, Antennes et Télécommunications
(LEAT) in Nice-Sophia Antipolis.
VNA Calibration
The VNA calibration is an essential task for obtaining precise measurements. Since any configuration (see §1.3) necessitates both retrodiffusion and transmission measurements, the TOSM calibration type has always been used. This method, employing a Short (S), Open (O), Match (M), and Thru (T) connector set (also called standards) applied to both ports of the VNA, is one of the most complete and accurate existing calibration methods. Concerning the interface at which the calibration must be performed, a fundamental choice has to be made. In effect, calibrating the VNA means setting its phase origin at the connector where the standards are applied. Hence, especially for scattering measurements, it seems natural to calibrate the VNA at the connectors of the array antennas, since, by doing so, the data measured by the VNA would directly represent the wave propagation from the transmitting to the receiving antenna. Nonetheless, two major problems arise:
• taking for instance the reflection configuration in §1.3, assuming reciprocity, and considering that the retrodiffusion parameters Sjj |j=1,…,8 are obtained “for free” when measuring any (j, k)th, j 6= k antenna pair, there are C2 8 = 8!/2!(8−2)! = 28 different antenna couples to be tested to fill the 8×8 K matrix. This means 28 different TOSM calibrations, each of them lasting ≈ 3 minutes, which apart from the obvious “manual effort” cover a long time with respect to the VNA thermal drift issue previously mentioned.
• as shown in Tab. 1.3, up to 25 dB path loss exist for a tranmission measurement involving the TRM array. Such a loss must be subtracted from the VNA dynamic range during calibration and greatly affects the precision of the calibration factors calculated. The result is then an imprecise calibration giving imprecise measurements. Due to the last item, then, not even an 8-port VNA would solve the issue, despite its capability of calibrating all 8 ports simultaneously. The solution found consists in calibrating the VNA at its own test ports, and in retrieving the wave propagation part of the measurement by using the transfer matrix formalism as explained next.
Extraction of the propagating medium through the use of the transfer matrices
Among the configurations in §1.3, the example of a reflection configuration involving the TRM array, i.e., Sjk (j 6= k, j, k ≤ 8), is used here. Fig. 1.10 shows that the VNA actually measures the cascade of three 2-port networks, the kth MUX path, the propagating medium, and the jth A/ path. The overall measurement is the S-parameters matrix S, whereas the sub-network matrices are, respectively, SMUX k , Sair, and SA/ j .
Table of contents :
Introduction
Notation
1 Microwave imaging prototype
1.1 State of the art
1.1.1 Time domain implementation
1.1.2 Stepped-frequency implementation
1.1.3 Time Reversal through dispersive optical fibers
1.2 Prototype description
1.2.1 RF section
1.2.2 Drive and control electronics
1.2.3 The anechoic chamber
1.3 Measurement configurations
1.3.1 Reflection
1.3.2 Transmission
1.3.3 Full
1.4 Dynamic range
1.4.1 VNA output power
1.4.2 VNA Noise floor
1.4.3 Thermal drift
1.5 VNA Calibration
1.5.1 Extraction of the propagating medium through the use of the transfer matrices
1.6 Signal processing for scattering measurements
1.6.1 Differential measurements for antenna direct coupling reduction
1.6.2 FFT window and time-gating
1.6.3 Drift correction
1.6.3.1 Implementation of the algorithm
1.7 Experimental characterization of the antennas
1.7.1 Far-field, uncoupled antenna
1.7.2 Arrayed antennas
1.7.2.1 Time-domain characterization
1.8 Experimental beamforming
2 Detection/localization with Time Reversal-based methods
2.1 Time Reversal theoretical background
2.2 Active source case
2.2.1 Time Reversal experiments
2.2.1.1 Details of measurements
2.2.1.2 Experimental results and discussion
2.3 Scattering case
2.3.1 Kirchhoff migration
2.3.1.1 Conclusions
2.3.2 Time Reversal
2.3.3 DORT
2.3.3.1 Extended target in near-field
2.3.3.2 Time-domain extension
2.3.3.3 Time-domain singular vectors
2.3.3.4 Different Tx and Rx arrays
2.3.3.5 Multiple targets case
2.3.3.6 Acquisition of the K matrix
2.3.3.7 Conclusions
2.3.4 TR-MUSIC
2.3.4.1 Time-domain extension
2.3.4.2 Arrival time regularization
2.3.4.3 Conclusions
2.3.5 An experimental case study: the Through-The-Wall measurement campaign
3 Quantitative inverse scattering
3.1 Problem formulation
3.1.1 Non-linearity and ill-posedness
3.2 Overview of inversion methods
3.3 M2GM inversion algorithm
3.3.1 Multi-view multi-frequency inversion
3.3.2 Line search and stop criterion
3.3.3 Initial estimate
3.4 Available information and Ewald’s circle
3.5 Experimental inversion: the calibration issue
3.5.1 2D incident field and Green function models
3.5.1.1 Phase center correction
3.5.1.2 Elevation radiation pattern correction
3.6 Experimental results
3.6.1 Data preparation
3.6.2 Direct problem: validation of the calibration procedure
3.6.3 SNR definition
3.6.4 Inverse problem
3.6.4.1 Frequency weighting
3.6.4.2 Reflection configuration
3.6.4.3 Transmission configuration
3.6.4.4 Full configuration
3.6.5 Conclusions
4 Inversion in cluttered media exploiting the DORT method
4.1 The DORT cost function FDORT
4.1.1 TX beamforming
4.1.2 RX beamforming
4.1.3 About the computational burden
4.2 Regularized cost function
4.3 Numerical experiments
4.3.1 Noiseless inversion: TX vs. RX beamforming
4.3.2 Influence of the spatial scale of clutter
4.3.3 Influence of the line size
Conclusion and perspectives
References
