*Theoretical Premises and Contemporary Optimizations of Microwave Tomography DOI: http://dx.doi.org/10.5772/intechopen.103011*

instance, as mentioned above, there is considerable debate regarding the required number of antennas. Our approach has been to configure just enough antennas for a single-plane array and then exploit mechanical motion to move the array vertically to achieve complete 3D coverage of the target—in this case the breast. We have demonstrated that 16 antennas is sufficient for the single array [52], which has kept our costs to modest levels. **Figure 3** shows the antennas mounted to a horizontal plate which is supported by opposing motors that can bring the antennas to different levels surrounding the breast to enable full volumetric coverage of the breast. Below we summarize the more significant issues for the microwave electronics.

#### *2.1.1 Large dynamic range*

In general, the dynamic range is limited on the low end by the noise floor which is defined as *N* ¼ *kTB* where k is Boltzman's constant, T is the temperature and B is the sampling bandwidth. The primary option for decreasing the noise floor is increasing the sampling time (i.e. additional averaging) which is the inverse of the bandwidth. Theoretically the noise floor could be made infinitely low if one allowed for the data acquisition to take forever. However, for practical systems, the lower end is also limited by the discretization resolution of the A/D converter. The most common way to address both is to add increased amplification in front of the receiver while also increasing the sampling time. The typical VNA is configured so that the lowest possible noise floor is roughly �100 dBm. Given that the transmit signals typically can range on the order of 1–10 mW, the maximum dynamic range is roughly 102 dB (assuming that we can realistically pick out a signal that is roughly 8 dB greater than the noise floor). In building our custom system, we have employed the Ettus B210 agile transceiver which by themselves can only see down to �110 dBm. By adding 20 dB gain, increasing the sampling time, and adding a low noise amplifier, we have simultaneously improved the overall noise figure of the system while also lowering the noise floor and boosting the signal. In this way, we are able to achieve substantially higher dynamic range capabilities in a low cost configuration. The Ettus boards cost a fraction of that of typical VNA's and are programmable using general purpose instrumentation software including Matlab (Mathworks, Natick, MA) and LabView (National Instruments, Austin, TX) [53].

#### **Figure 3.**

*Photographs of the antenna array, support structure and motors used for vertical, mechanical array motion: (a) close-up of mounting plate, (b) side view of tank, antennas and support structure, and (c) top view of the antennas in the tank.*

#### *2.1.2 Channel-to-channel isolation*

One hypothetical way to achieve a large dynamic range would be to use a 2 channel VNA coupled to a double-pole, 16 throw (DP16T) switch matrix to achieve coverage for all 16 channels. We have already discussed the challenges in achieving the dynamic range for a 2-channel system. Unfortunately, the multi-pole switch matrix introduces its own set of problems. In cases where the 2-port VNA already has a dynamic range approaching 140 dB, it is necessary for the switch matrix to have channel-to-channel isolation on the order of 140 dB. In practice it is especially difficult to achieve this and very rarely do switch manufacturers specify isolation greater than roughly 80–100 dB. There are ways to achieve this, but it generally requires substantial shielding and the addition of extra single-pole, single-throw (SPST) switches which introduces substantial insertion loss and inevitably detracts from the overall dynamic range.

Our latest concept is to exploit new software defined radio (SDR) technology as the key building block of our system [53]. In this case, we utilize the Ettus Research B210 (Austin, TX) which has two channels, each having a transmit/receive port and a dedicated receive port. Our design involves a physical separation of the boards used for transmit and receive (extra isolation), along with a set of switch/amplifier modules which add to the overall channel-to-channel isolation along with improving the dynamic range with a 20 dB gain amplifier in front of the receiver channel. One of the signals from the Transmit B210 is used as a reference signal to synchronize the transmit oscillators with those of the receive modules. **Figure 4** shows a schematic of a representative 4-channel system along with an initial prototype showing the separate transmit and receive modules along with the switch and amplifiers. This design can be readily scaled up to a full 16 channel system.

With respect to isolation, **Figure 5a** shows the shielded housings for the B210 boards. The primary feature is the ridge in the cover which lightly rests on a gold strap running across the board that physically separates the RF portion of the board from the lower frequency electronics and power supply circuitry. Tests have shown that the "one-way" leakage from these housings is on the order of 110 dB (from a nominally

#### **Figure 4.**

*(a) Schematic diagram of a 4-channel measurement system and (b) a photograph of a first prototype (a is reproduced from "Meaney PM, Hartov A, Bulumulla S, Raynolds T, Davis C, Schoenberger F, Richter S, Paulsen KD, "4-channel, vector network analyzer microwave imaging prototype based on software defined radio technology,"* Review of Scientific Instruments*, vol. 90, pp. 044708-1—044708-14, 2019," with permission of AIP Publishing [53]).*

*Theoretical Premises and Contemporary Optimizations of Microwave Tomography DOI: http://dx.doi.org/10.5772/intechopen.103011*

#### **Figure 5.**

*Photograph of the (a) shielded housings for the Ettus B210 SDR circuit boards, and (b) the shielded housing for an earlier transceiver module (b is reproduced from "Li D, Meaney PM, Raynolds T, Pendergrass SA, Fanning MW, Paulsen KD, "A parallel-detection microwave spectroscopy system for breast imaging,"* Review of Scientific Instruments*, vol. 75, pp. 2305–2313, 2004," with permission of AIP Publishing [54]).*

transmitted signal of 1 mW). While a signal of this amplitude may propagate along the outer surface of the electronics, because all of the other components of the system have comparable isolation specification, the greatest signal level that could leak back into the system would be on the order of 220 dB because of the "two-trip" attenuation in escaping the isolated board and then re-entering a companion board. **Figure 5b** shows the internal features of an earlier, custom transceiver module which included several amplifiers and switches along with a downconverting mixer. All feedthrus for the bias and control lines were coaxial low pass filters to restrict RF signals from escaping outside of the housings. Each component within the housing was sequestered to its own channelized compartment to limit internal leakage and the covers were configured with raised surfaces for tight fits of the two housing portions to further limit leakage to the outside. While somewhat cumbersome, in large quantity the housings can be fabricated at relatively low cost and have proven to be effective in limiting leakage, even to the extreme levels of 140 dBm.

#### *2.1.3 Synchronization*

Commercial VNA's are attractive because they produce measurements that guarantee built-in synchronization of the transmit and receive signals. However, as was discussed earlier and also in the subsequent sections, these network analyzers are unattractive because of their costs. There are a host of means for achieving synchronization of signals in different hardware configurations. For our SDR-based system, we exploit the phase locking of the transmit and receive oscillators with respect to a 10 MHz reference signal from their Octoclock (Ettus Research, Austin, TX). In addition, accurate and consistent triggering of the measurements is achieved via the PPS signal which is also supplied by the Octoclock. In the case with separate transmit and receive modules, we exploit the fact that the second output signal from the dedicated transmit board is synchronized to the output of the channel that feeds the antennas. This is subsequently used as a reference signal and is fed into an unused receive port of the receive channels for sampling and synchronization with the receive boards [53, 54].
