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Biniyam Tesfaye Taddese, Doctor of Philosophy, 2012 Dissertation directed by: Professor Steven M. Anlage Department of Electrical and Computer Engineering Wave-based motion sensors, such as radar and sonar, are designed to detect objects within a direct line-of-sight of the sensor. The presence of multiple reflections from surrounding objects usually confounds the sensor. As a result, surveillance of a cavity with multiple internal partitions and complicated boundary conditions generally demands use of a network of sensors, in which each sensor actively monitors a section of the cavity within its direct line-of-sight.

In the first part of the dissertation, we propose and test a new paradigm of sensing that can work in a strongly scattering environment. The sensor utilizes the time reversal invariance and spatial reciprocity properties of the wave equation, and the ray chaotic nature of most real world cavities. Specifically, classical analogs of the quantum fidelity and the Loschmidt Echo are developed with the goal of detecting small perturbations in a closed wave chaotic region. In analogy with quantum fidelity, we employ scattering fidelity techniques which work by comparing response signals of the scattering region, by means of cross correlation and mutual information of signals. The sensing techniques were compared for various perturbations induced in an acoustic resonant cavity. The acoustic signals are parametrically processed to mitigate the effect of dissipation and to vary the spatial diversity of the sensing schemes. In addition to static boundary condition perturbations at specified locations, perturbations to the medium of wave propagation are shown to be detectable, opening up various real world sensing applications in which a false negative cannot be tolerated.

As an extension of the first part of the dissertation, a sensor is developed to quantitatively measure perturbations that change the volume of a wave chaotic cavity while leaving its shape intact. The sensor was tested experimentally using a one cubic meter pseudo-integrable, microwave resonator. Volume changes that are as small as 4 parts in 105 were measured using electromagnetic waves with a wavelength of about 5cm. Therefore, the sensor is sensitive to extreme subwavelength changes of the boundaries of a cavity. Furthermore, the sensor was tested using a frequency domain approach on a numerical model of the star graph, which is a representative wave chaotic system. These results open up interesting applications such as: monitoring the spatial uniformity of the temperature of a homogeneous cavity during heating up / cooling down procedures, verifying the uniform displacement of a fluid inside a wave chaotic cavity by another fluid, etc.

The last part of the dissertation is dedicated to improving the performance of time reversal (TR) mirrors, which suffer from dissipation in wave propagation.

TR mirrors can, under ideal circumstances, precisely reconstruct a wave disturbance which happened at an earlier time, at any given later time. TR mirrors have found applications in imaging, communication, targeted energy focusing, sensing, etc. Two techniques are proposed and tested to overcome the effects of dissipation on TR mirrors. First, a tunable iterative technique is used to improve the temporal focusing of a TR mirror. A single amplification parameter is used to tune the convergence of the iteration. The tunable iterative technique was validated by tests on the experimental electromagnetic time reversal mirror, and on the star graph numerical model. Second, the technique of exponential amplification is proposed to overcome the effect of dissipation in the case of uniform loss distributions, and, to some extent, in the case of non-uniform loss distributions. A numerical model of the star graph was employed to test the applicability of this technique on realizations of the star graph with various spatial distributions of loss. The numerical results were also

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Advisory Committee:

Professor Steven M. Anlage, Chair/Advisor Professor Thomas M. Antonsen, Co-Advisor Professor Edward Ott, Co-Advisor Professor Christopher Davis Professor Rajarshi Roy ⃝ Copyright by c Biniyam Tesfaye Taddese Dedication

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I would like to acknowledge the indispensable guidance from my advisor Professor Anlage. He provided me with very much needed directions, comments, feedbacks, support, and mentorship during my Ph.D. studies. He introduced me to the exciting field of time reversal, and guided me to develop the experimental skills needed to succeed in my career. He made sure that I had access to state of the art equipment which enabled me to get productive in my research. I would never have achieved my research milestones, without his enthusiastic, timely, and unwavering support. Professor Anlage, thank you very much for your guidance.

I also would like to acknowledge my co-advisors Professor Antonsen and Professor Ott. They gave me very valuable feedback on a regular basis throughout my Ph.D. studies. They also provided me with valuable suggestions on theoretical and simulation tools that I have used to further validate and support my experimental results.

I would like to thank Zach Drikas, Dr. Matthew Frazier, Dr. Gabriele Gradoni, Dr. James Hart, Sun K. Hong, Michael Johnson, Dr. Hai Tran, and Jen-Hao Yeh, for collaborating with me in co-authoring various manuscripts, some of which are included in this dissertation. Specially, I would like to thank Professor Franco Moglie who collaborated with us, and provided us with very helpful simulation results. I would like to thank Professor Thomas H. Seligman, Dr. John Rodgers, and Professor Daniel Lathrop, for their helpful comments about my research. I would like to thank Professor Christopher Davis and Professor Rajarshi Roy for being on my dissertation

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I also would like to thank the members of our research groups, Behnood, Cihan, Creeg, David, Enrique, Harita, Laura, Mark, Ming-Jer, Nightvid, Tamin, and Tristen, for their moral support through the years.

Finally, I would like to thank my family, friends, and all the wonderful people in my life, whose list would be too long to write here; I attribute my accomplishments to all of you.

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2.1 The maximum F OML over all the parameter values tried is shown for each of the four sensing techniques detecting a perturbation at each of the six perturbation locations indicated in Fig. 2.1. In addition, the percentage of parameter values which gave a F OML that is greater than 2 is also shown............................ 52

2.2 The maximum F OML over all the windowing parameter values tried is shown for each of the four sensing techniques detecting a global perturbation with a given value of the exponential amplification parameter F. In addition, the corresponding percentage of windowing parameter values which gave a F OML that is greater than 2 is also shown.................................... 57

viii List of Figures

1.1 Outline of the dissertation. Chapter 1 introduces the background material on ray chaos, wave chaos, and time reversal. Chapter 1 introduces the extension of the Loschmidt echo and quantum fidelity to classical waves to realize practical sensors; this is the core of the dissertation. Chapter 2 formally defines the Loschmidt echo and quantum fidelity. Chapters 2 and 3 focus on the sensing problem.

Chapters 4 and 5 propose techniques to improve the performance of time reversal mirrors which extend the Loschmidt echo to classical waves. Chapter 6 provides a conclusion, and directions for future work. 12

2.1 The experiment is conducted inside a stairwell with cinderblock walls and tile floors. The locations of perturbations chosen to exemplify short, medium, and long range detection attempts, both at concealed and nonconcealed locations, with respect to the sensor, are labeled with letters A to F. The inset shows the perturbing object that is introduced at the various locations AF.................. 26

2.2 Schematic operation of a sensor based on propagation comparison.

An acoustic pulse is broadcast into the stairwell in (a) and (c). The resulting sona signals are recorded in (b) and (d). In (c) and (d), the cavity is perturbed. The sensor works by comparing the baseline and perturbed sonas through either cross correlation or mutual information. The red rectangle, which is at the bottom right corner of the schematic of the stairwell, schematically shows the speaker and microphone................................. 28 2.3 (a) The OP broadcast into the stairwell, (b) sona, (c) a baseline time reversed reconstructed pulse (BRP), (d) a perturbed time reversed reconstructed pulse (PRP). All parts show an acoustic signal (in volts) vs time................................... 33

2.4 Schematic operation of the CTRS, which is based on the extension of the LE to classical waves. A sequence of steps illustrated in (a)(d) are carried out to measure the BRP. Using the sona collected in (b), the steps illustrated in (e) and (f) are carried out to measure the PRP.

The CTRS works by comparing the baseline and perturbed pulses collected................................... 35 2.5 (a) A typical measured exponentially decaying sona signal, (b) exponentially amplified sona with F = 1, (c) exponentially amplified sona with F = 2 after rectangular windowing between times tST ART and tST OP.................................... 41 ix

2.6 Contour plots of the lower bound on the FOM (F OML ) as a function of start time (tST ART ) and stop time (tST OP ) parameters of the rectangular time windowing function applied to the sona. The plots show detection attempts at perturbation location A (indicated in Fig.

1) using F = 0. (a) F OML for CTRS1, (b) F OML for CTRS2, (c) F OML for SCC, (d) F OML for SMI................... 46

2.7 Contour plots of the lower bound on the FOM (F OML ) as a function of start time (tST ART ) and stop time (tST OP ) parameters of the rectangular windowing function applied to the sona. (a) Long range detection at location F, indicated in Fig. 1, using CTRS1 with F = 0, (b) long range detection at location F using CTRS1 with F = 1, (c) long range detection at location F using CTRS1 with F = 2...... 48

2.8 Contour plots of the lower bound on the FOM (F OML ) as a function of tST ART and tST OP parameters of the rectangular windowing function applied to the sona. In all plots, an exponential amplification of F = 1 is applied to the sona. The three plots shown here show detection attempts at different locations of perturbations illustrated in Fig. 1. (a) short range detection at location A, (b) medium range detection at location C, (c) long range detection at location E..... 51

2.9 Indicator values of perturbation for CTRS1, ICT RS1, vs measurement number (approximately 18s elapse between each measurement).

Halfway in the displayed time interval, a mechanical fan is briefly activated in the stairwell perturbing the medium of wave propagation.

Each of the plots correspond to cases in which the sona is exponentially amplified by different F values. In all cases, the sonas are windowed with tST ART = 0s and tST OP = 0.3s: (a) F = 0, (b) F = 1, and (c) F = 2................................ 55

2.10 The lower bound on the FOM (F OML ) vs the exponential amplification parameter F for detection of global perturbation using CTRS1, CTRS2, and SCC. The CTRS based techniques work best when F is close to 2, and SCC works best when F is close to 1.......... 58

2.11 A plot of peak-to-peak amplitude (PPA) of the reconstructed pulse amplitude in volts versus the standard deviation of the Gaussian phase noise distribution in radians. Gaussian distributed random numbers with zero mean and a standard deviation, which is systematically varied between 0 and π, are added to the phase of the Fourier transform of the sona signal. This effectively scales the reconstructed pulse by a Gaussian function of the standard deviation of the underlying phase noise.............................. 61

2.12 Long term drift in the PPA in volts of the reconstructed time reversed pulse in the stairwell. The PPA exhibits a drift as the reverberant cavity and air medium go through thermally-induced changes in time. 63 x

2.13 The effect of a volume preserving perturbation on the reconstructed time reversed (TR) pulse. The TR pulses (a) before (P P A = 1.11V ) and (b) after (P P A = 0.92V ) perturbation have a normalized correlation of 93%, but the PPA drops by 17%. The perturbation is done by rotating a rectangular box (30cmx60cmx80cm) by ninety degrees inside the reverberant cavity (stairwell)................. 65

2.14 SF of sonas before and after a perturbation as a function of time.

The SF plotted here is averaged over 25 realizations. The width of the time window over which the ISCC and hence the SF is computed is 0.1s. The six SF curves are labeled A through F; the labels correspond to the locations of the perturbations illustrated in Fig. 1. For example, the slowest decaying SF curve comes from sonas measured before and after perturbing the cavity at location F in Fig. 1. The rates of fidelity decay are generally indicative of the relative distance of the perturbations from the sensor................... 67

3.1 Schematic illustrating Volume Changing & Shape Preserving (VCSP) perturbations. (a) Sona is collected from a baseline cavity of volume V1. (b) Sona is collected from a perturbed cavity of volume V2. (c) Pulse exciting the resonances of the baseline system. (d) The same pulse exciting the perturbed resonances of the perturbed system... 76

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