Sensing physical fields: Inverse problems for the diffusion equation and beyond

Due to significant advances made over the last few decades in the areas of (wireless) networking, communications and microprocessor fabrication, the use of sensor networks to observe physical phenomena is rapidly becoming commonplace. Over this period, many aspects of sensor networks have been explored, yet a thorough understanding of how to analyse and process the vast amounts of sensor data collected, remains an open area of research. This work therefore, aims to provide theoretical, as well as practical, advances this area. In particular, we consider the problem of inferring certain underlying properties of the monitored phenomena, from our sensor measurements. Within mathematics, this is commonly formulated as an inverse problem; whereas in signal processing it appears as a (multidimensional) sampling and reconstruction problem. Indeed it is well known that inverse problems are notoriously ill-posed and very demanding to solve; meanwhile viewing it as the latter also presents several technical challenges. In particular, the monitored field is usually nonbandlimited, the sensor placement is typically non-regular and the space-time dimensions of the field are generally non-homogeneous. Furthermore, although sensor production is a very advanced domain, it is near impossible and/or extremely costly to design sensors with no measurement noise. These challenges therefore motivate the need for a stable, noise robust, yet simple sampling theory for the problem at hand. In our work, we narrow the gap between the domains of inverse problems and modern sampling theory, and in so doing, extend existing results by introducing a framework for solving the inverse source problems for a class of some well-known physical phenomena. Some examples include: the reconstruction of plume sources, thermal monitoring of multi-core processors and acoustic source estimation, to name a few. We assume these phenomena and their sources can be described using partial differential equation (PDE) and parametric source models, respectively. Under this assumption, we obtain a well-posed inverse problem. Initially, we consider a phenomena governed by the two-dimensional diffusion equation -- i.e. 2-D diffusion fields, and assume that we have access to its continuous field measurements. In this setup, we derive novel exact closed-form inverse formulae that solve the inverse diffusion source problem, for a class of localized and non-localized source models. In our derivation, we prove that a particular 1-D sequence of, so called, generalized measurements of the field is governed by a power-sum series, hence it can be efficiently solved using existing algebraic methods such as Prony's method. Next, we show how to obtain these generalized measurements, by using Green's second identity to combine the continuous diffusion field with a family of well-chosen sensing functions. From these new inverse formulae, we therefore develop novel noise robust centralized and distributed reconstruction methods for diffusion fields. Specifically, we extend these inverse formulae to centralized sensor networks using numerical quadrature; conversely for distributed networks, we propose a new physics-driven consensus scheme to approximate the generalized measurements through localized interactions between the sensor nodes. Finally we provide numerical results using both synthetic and real data to validate the proposed algorithms. Given the insights gained, we eventually turn to the more general problem. That is, the two- and three-dimensional inverse source problems for any linear PDE with constant coefficients. Extending the previous framework, we solve the new class of inverse problems by establishing an otherwise subtle link with modern sampling theory. We achieved this by showing that, the desired generalized measurements can be computed by taking linear weighted-sums of the sensor measurements. The advantage of this is two-fold. First, we obtain a more flexible framework that permits the use of more general sensing functions, this freedom is important for solving the 3-D problem. Second, and remarkably, we are able to analyse many more physical phenomena beyond diffusion fields. We prove that computing the proper sequence of generalized measurements for any such field, via linear sums, reduces to approximating (a family of) exponentials with translates of a particular prototype function. We show that this prototype function depends on the Green's function of the field, and then derive an explicit formula to evaluate the proper weights. Furthermore, since we now have more freedom in selecting the sensing functions, we discuss how to make the correct choice whilst emphasizing how to retrieve the unknown source parameters from the resulting (multidimensional) Prony-like systems. Based on this new theory we develop practical, noise robust, sensor network strategies for solving the inverse source problem, and then present numerical simulation results to verify the performance of our proposed schemes.Open Acces

ACOUSTO-OPTIC IMAGING IN DIFFUSE MEDIA USING PULSED ULTRASOUND AND THE PHOTOREFRACTIVE EFFECT

Acousto-optic imaging (AOI) in optically diffuse media is a hybrid imaging modality in which a focused ultrasound beam is used to locally phase modulate light inside of turbid media. The modulated optical field carries with it information about the optical properties in the region where the light and sound interact. The motivation for the development of AOI systems is to measure optical properties at large depths within biological tissue with high spatial resolution. A photorefractive crystal (PRC) based interferometry system is developed for the detection of phase modulated light in AOI applications. Two-wave mixing in the PRC creates a reference beam that is wavefront matched to the modulated optical field collected from the specimen. The phase modulation is converted to an intensity modulation at the optical detector when these two fields interfere. The interferometer has a high optical etendue, making it well suited for AOI where the scattered light levels are typically low. A theoretical model for the detection of acoustically induced phase modulation in turbid media using PRC based interferometry is detailed. An AOI system, using a single element focused ultrasound transducer to pump the AO interaction and the PRC based detection system, is fabricated and tested on tissue mimicking phantoms. It is found that the system has sufficient sensitivity to detect broadband AO signals generated using pulsed ultrasound, allowing for AOI at low time averaged ultrasound output levels. The spatial resolution of the AO imaging system is studied as a function of the ultrasound pulse parameters. A theoretical model of light propagation in turbid media is used to explore the dependence of the AO response on the experimental geometry, light collection aperture, and target optical properties. Finally, a multimodal imaging system combining pulsed AOI and conventional B- mode ultrasound imaging is developed. B-mode ultrasound and AO images of targets embedded in both highly diffuse phantoms and biological tissue ex vivo are obtained, and millimeter resolution is demonstrated in three dimensions. The AO images are intrinsically co-registered with the B-mode ultrasound images. The results suggest that AOI can be used to supplement conventional B-mode ultrasound imaging with optical information.Center for Subsurface and Imaging Systems via NSF ERC award number EEC-9986821

From RF-Microsystem Technology to RF-Nanotechnology

The RF microsystem technology is believed to introduce a paradigm switch in the wireless revolution. Although only few companies are to date doing successful business with RF-MEMS, and on a case-by-case basis, important issues need yet to be addressed in order to maximize yield and performance stability and hence, outperform alternative competitive technologies (e.g. ferroelectric, SoS, SOI,…). Namely the behavior instability associated to: 1) internal stresses of the free standing thin layers (metal and/or dielectric) and 2) the mechanical contact degradation, be it ohmic or capacitive, which may occur due to low forces, on small areas, and while handling severe current densities.The investigation and understanding of these complex scenario, has been the core of theoretical and experimental investigations carried out in the framework of the research activity that will be presented here. The reported results encompass activities which go from coupled physics (multiphysics) modeling, to the development of experimental platforms intended to tackles the underlying physics of failure. Several original findings on RF-MEMS reliability in particular with respect to the major failure mechanisms such as dielectric charging, metal contact degradation and thermal induced phenomena have been obtained. The original use of advanced experimental setup (surface scanning microscopy, light interferometer profilometry) has allowed the definition of innovative methodology capable to isolate and separately tackle the different degradation phenomena under arbitrary working conditions. This has finally permitted on the one hand to shed some light on possible optimization (e.g. packaging) conditions, and on the other to explore the limits of microsystem technology down to the nanoscale. At nanoscale indeed many phenomena take place and can be exploited to either enhance conventional functionalities and performances (e.g. miniaturization, speed or frequency) or introduce new ones (e.g. ballistic transport). At nanoscale, moreover, many phenomena exhibit their most interesting properties in the RF spectrum (e.g. micromechanical resonances). Owing to the fact that today’s minimum manufacturable features have sizes comparable with the fundamental technological limits (e.g. surface roughness, metal grain size, …), the next generation of smart systems requires a switching paradigm on how new miniaturized components are conceived and fabricated. In fact endowed by superior electrical and mechanical performances, novel nanostructured materials (e.g. carbon based, as carbon nanotube (CNT) and graphene) may provide an answer to this endeavor. Extensively studied in the DC and in the optical range, the studies engaged in LAAS have been among the first to target microwave and millimiterwave transport properties in carbon-based material paving the way toward RF nanodevices. Preliminary modeling study performed on original test structures have highlighted the possibility to implement novel functionalities such as the coupling between the electromagnetic (RF) and microelectromechanical energy in vibrating CNT (toward the nanoradio) or the high speed detection based on ballistic transport in graphene three-terminal junction (TTJ). At the same time these study have contributed to identify the several challenges still laying ahead such as the development of adequate design and modeling tools (ballistic/diffusive, multiphysics and large scale factor) and practical implementation issues such as the effects of material quality and graphene-metal contact on the electrical transport. These subjects are the focus of presently on-going and future research activities and may represent a cornerstone of future wireless applications from microwave up to the THz range

A Multidisciplinary Analysis of Frequency Domain Metal Detectors for Humanitarian Demining

This thesis details an analysis of metal detectors (low frequency electromagnetic induction devices) with emphasis on Frequency Domain (FD) systems and the operational conditions of interest to humanitarian demining. After an initial look at humanitarian demining and a review of their basic principles we turn our attention to electromagnetic induction modelling and to analytical solutions to some basic FD direct (forward) problems. The second half of the thesis focuses then on the analysis of an extensive amount of experimental data. The possibility of target classification is first discussed on a qualitative basis, then quantitatively. Finally, we discuss shape and size determination via near field imaging

Liberated pixels : alternative narratives for lighting future cities

Thesis (Ph. D.)--Massachusetts Institute of Technology, School of Architecture and Planning, Program in Media Arts and Sciences, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 165-171).Lighting and illuminated displays shape our relations to urban environments and to one another at night and increasingly during the day by transforming what Kevin Lynch referred to as the "image of the city" (1964). Today, the wide-spread availability of LEDs (light-emitting diodes) in combination with embedded, miniaturized computation offers different ways of designing ambient infrastructures. In this dissertation, I explore these alternatives by exploiting the programmable and responsive capabilities of LED-based, low-resolution systems. In short, I examine the alternative aesthetic and communications opportunities afforded by a new generation of lighting and display technologies in the city. I investigate the origins of lighting and displays to illustrate how they have evolved through a complex interleaving of the social and the material. This grounding leads me to develop three design explorations that focus on programmability, addressability, responsiveness, mobility and ad-hoc control. The first of these explorations, Urban Pixels, presents a wireless network of individual, autonomous physical pixels that can be deployed on any surface in the city. The second, Light Bodies, reconnects with the history of lights-on-people like lanterns that travel through the city with their users. The third, Augmented-reality (AR) Street Light, provides a layer of programmability for existing infrastructural networks. Together the historical perspective and design interventions lead to a framework of what I call "liberated pixels", a new generation of lighting and display technologies. Liberated pixels can be placed flexibly within any context and recruited in different situations for aesthetic and ambient information purposes. This vision captures the contingent and emergent nature of "sociomaterial assemblages" (Suchman 2007) to chart holistic technical, aesthetic, and social directions for future infrastructures of "imageability" (Lynch 1964) in the city.by Susanne SeitingerPh.D

Technology 2004, Vol. 2

Proceedings from symposia of the Technology 2004 Conference, November 8-10, 1994, Washington, DC. Volume 2 features papers on computers and software, virtual reality simulation, environmental technology, video and imaging, medical technology and life sciences, robotics and artificial intelligence, and electronics

Determinants of leaf water use efficiency in the C4 crop sorghum bicolor

Intrinsic water use efficiency (iWUE) is an important leaf trait that can influence crop productivity. This PhD project aimed to identify leaf morphological and functional traits that correlate with high iWUE in a key C4 crop. In the first two experimental chapters, a small number (6-10) Sorghum bicolor genotypes were grown under different growth temperatures (Chapter 2) or under changing diurnal light conditions (Chapter 3), and leaf gas exchange was correlated with leaf anatomy and stomatal kinetic responses. In the third experimental chapter (Chapter 4), a large number (89) of Sorghum genotypes with different aquaporin alleles were grown under wet and dry conditions. All experiments were carried out in potted plants grown either in the glasshouse (Chapters 2 and 4) or growth cabinets (Chapter 3). In chapter 2, the importance of leaf width in determining stomatal conductance and iWUE was elucidated. Narrow leaves were generally thinner, with smaller guard, mesophyll and bundle sheath cells and airspace compartments. This compact arrangement likely allowed for more efficient gas exchange and thermoregulation under high temperatures. In chapter 3, the regulation of morning and midday iWUE was correlated to morning and midday stomatal conductance, while afternoon conductance had little effect on afternoon iWUE as well as integrated diurnal iWUE. Tight control on the stomatal aperture was the key factor in reducing conductance and increase diurnal iWUE, not strictly stomatal structural features. High diurnal iWUE was associated with speedy stomatal closure and water conservation under photosynthetically unfavourable conditions. In chapter 4, the onset of water stress in a large set of genotypes revealed the changing relationship between stomatal conductance and carbon assimilation, exposing the differential contributions of both components to iWUE under different conditions. The extent of genetic variation in gas exchange and hydraulic traits was assessed. In chapter 5, I discuss those different findings and attempt to integrate them via exploring how carbon assimilation and stomatal conductance vary under different conditions and explaining the impact of vapour pressure deficit in determining anatomical control on stomatal conductance. The findings of this thesis are put into the context of global change and the need for improved agricultural productivity. Suggestions are made on the possible agronomic impact of traits found beneficial in this thesis, their possible trade-offs, and how these findings can be taken further in future research