Spatial filtering in tone reproduction and vision

This thesis is concerned with spatial filtering. What is its utility in tone reproduction? Does it exist in vision, and if so, what constraints does it impose on the nervous system?

Tone reproduction is just the art and science of taking a picture and then displaying it. The sensors available to capture an image have a greater dynamic range than the media that may be used to display it. Conventionally, spatial filtering is used to boost contrast; it ameliorates the loss of contrast that results when the sensor signal range is scaled down to fit the display range. In this thesis, a type of nonlinear spatial filtering is discussed that results in direct range reduction without range scaling. This filtering process is instantiated in a real-time image processor built using analog CMOS VLSI.

Spatial filtering must be applied with care in both artificial and natural vision systems. It is argued that the nervous system does not simply filter linearly across an image. Rather, the way that we see things implies that the nervous system filters nonlinearly. Further, many models for color vision include a high-pass filtering step in which the DC information is lost. A real-time study of filtering in color space leads to the conclusion that the nervous system is not that simple, and that it maintains DC information by referencing to white.

Space-frequency coupling, conical waves, and small-scale filamentation in water

Numerical simulations of fs laser propagation in water have been made to explain the small-scale filaments in water we have observed by a nonlinear fluorescence technique. Some analytical descriptions combined with numerical simulations show that a space-frequency coupling mainly from the interplay among self-phase modulation, dispersion and phase mismatching will reshape the laser beam into a conical wave which plays a major role of energy redistribution and can prevent laser beam from self-guiding over a long distance. An effective group velocity dispersion is introduced to explain the pulse broadening and compression in the filamentation. (c) 2005 American Institute of Physics.

Resource management of dynamic coastal environments using synoptic measures from remote sensing

In addition to providing vital ecological services, coastal areas of North Carolina provide prized areas for habitation, recreation, and commercial fisheries. However, from a management perspective, the coasts of North Carolina are highly variable and complex. In-water constituents such as nutrients, suspended sediments, and chlorophyll a concentration can vary significantly over a broad spectrum of time and space scales. Rapid growth and land-use change continue to exert pressure on coastal lands. Coastal environments are also very vulnerable to short-term (e.g., hurricanes) and long-term (e.g., sea-level rise) natural changes that can result in significant loss of life, economic loss, or changes in coastal ecosystem functioning. Hence, the dynamic nature, effects of human-induced change over time, and vulnerability of coastal areas make it difficult to effectively monitor and manage these important state and national resources using traditional data collection technologies such as discrete monitoring stations and field surveys. In general, these approaches provide only a sparse network of data over limited time and space scales and generally are expensive and labor-intensive. Products derived from spectral images obtained by remote sensing instruments provide a unique vantage point from which to examine the dynamic nature of coastal environments. A primary advantage of remote sensing is that the altitude of observation provides a large-scale synoptic view relative to traditional field measurements. Equally important, the use of remote sensing for a broad range of research and environmental applications is now common due to major advances in data availability, data transfer, and computer technologies. To facilitate the widespread use of remote sensing products in North Carolina, the UNC Coastal Studies Institute (UNC-CSI) is developing the capability to acquire, process, and analyze remotely sensed data from several remote sensing instruments. In particular, UNC-CSI is developing regional remote sensing algorithms to examine the mobilization, transport, transformation, and fate of materials between coupled terrestrial and coastal ocean systems. To illustrate this work, we present the basic principles of remote sensing of coastal waters in the context of deriving information that supports efficient and effective management of coastal resources. (PDF contains 4 pages)

The island of Kauai, Hawaii's progressive shoreline setback and coastal protection ordinance

Approximately two-thirds of coastal and Great Lakes states have some type of shoreline construction setback or construction control line requiring development to be a certain distance from the shoreline or other coastal feature (OCRM, 2008). Nineteen of 30 coastal states currently use erosion rates for new construction close to the shoreline. Seven states established setback distances based on expected years from the shoreline: the remainder specify a fixed setback distance (Heinz Report, 2000). Following public hearings by the County of Kauai Planning Commission and Kauai County Council, the ‘Shoreline Setback and Coastal Protection Ordinance’ was signed by the Mayor of Kauai on January 25, 2008. After a year of experience implementing this progressive, balanced shoreline setback ordinance several amendments were recently incorporated into the Ordinance (#887; Bill #2319 Draft 3). The Kauai Planning Department is presently drafting several more amendments to improve the effectiveness of the Ordinance. The intent of shoreline setbacks is to establish a buffer zone to protect shorefront development from loss due to coastal erosion - for a period of time; to provide protection from storm waves; to allow the natural dynamic cycles of erosion and accretion of beaches and dunes to occur; to maintain beach and dune habitat; and, to maintain lateral beach access and open space for the enjoyment of the natural shoreline environment. In addition, a primary goal of the Kauai setback ordinance is to avoid armoring or hardening of the shore which along eroding coasts has been documented to ultimately eliminate the fronting beach. (PDF contains 4 pages)

Topics in gravitational-wave science : macroscopic quantum mechanics and black hole physics

The theories of relativity and quantum mechanics, the two most important physics discoveries of the 20th century, not only revolutionized our understanding of the nature of space-time and the way matter exists and interacts, but also became the building blocks of what we currently know as modern physics. My thesis studies both subjects in great depths --- this intersection takes place in gravitational-wave physics.

Gravitational waves are "ripples of space-time", long predicted by general relativity. Although indirect evidence of gravitational waves has been discovered from observations of binary pulsars, direct detection of these waves is still actively being pursued. An international array of laser interferometer gravitational-wave detectors has been constructed in the past decade, and a first generation of these detectors has taken several years of data without a discovery. At this moment, these detectors are being upgraded into second-generation configurations, which will have ten times better sensitivity. Kilogram-scale test masses of these detectors, highly isolated from the environment, are probed continuously by photons. The sensitivity of such a quantum measurement can often be limited by the Heisenberg Uncertainty Principle, and during such a measurement, the test masses can be viewed as evolving through a sequence of nearly pure quantum states.

The first part of this thesis (Chapter 2) concerns how to minimize the adverse effect of thermal fluctuations on the sensitivity of advanced gravitational detectors, thereby making them closer to being quantum-limited. My colleagues and I present a detailed analysis of coating thermal noise in advanced gravitational-wave detectors, which is the dominant noise source of Advanced LIGO in the middle of the detection frequency band. We identified the two elastic loss angles, clarified the different components of the coating Brownian noise, and obtained their cross spectral densities.

The second part of this thesis (Chapters 3-7) concerns formulating experimental concepts and analyzing experimental results that demonstrate the quantum mechanical behavior of macroscopic objects - as well as developing theoretical tools for analyzing quantum measurement processes. In Chapter 3, we study the open quantum dynamics of optomechanical experiments in which a single photon strongly influences the quantum state of a mechanical object. We also explain how to engineer the mechanical oscillator's quantum state by modifying the single photon's wave function.

In Chapters 4-5, we build theoretical tools for analyzing the so-called "non-Markovian" quantum measurement processes. Chapter 4 establishes a mathematical formalism that describes the evolution of a quantum system (the plant), which is coupled to a non-Markovian bath (i.e., one with a memory) while at the same time being under continuous quantum measurement (by the probe field). This aims at providing a general framework for analyzing a large class of non-Markovian measurement processes. Chapter 5 develops a way of characterizing the non-Markovianity of a bath (i.e.,whether and to what extent the bath remembers information about the plant) by perturbing the plant and watching for changes in the its subsequent evolution. Chapter 6 re-analyzes a recent measurement of a mechanical oscillator's zero-point fluctuations, revealing nontrivial correlation between the measurement device's sensing noise and the quantum rack-action noise.

Chapter 7 describes a model in which gravity is classical and matter motions are quantized, elaborating how the quantum motions of matter are affected by the fact that gravity is classical. It offers an experimentally plausible way to test this model (hence the nature of gravity) by measuring the center-of-mass motion of a macroscopic object.

The most promising gravitational waves for direct detection are those emitted from highly energetic astrophysical processes, sometimes involving black holes - a type of object predicted by general relativity whose properties depend highly on the strong-field regime of the theory. Although black holes have been inferred to exist at centers of galaxies and in certain so-called X-ray binary objects, detecting gravitational waves emitted by systems containing black holes will offer a much more direct way of observing black holes, providing unprecedented details of space-time geometry in the black-holes' strong-field region.

The third part of this thesis (Chapters 8-11) studies black-hole physics in connection with gravitational-wave detection.

Chapter 8 applies black hole perturbation theory to model the dynamics of a light compact object orbiting around a massive central Schwarzschild black hole. In this chapter, we present a Hamiltonian formalism in which the low-mass object and the metric perturbations of the background spacetime are jointly evolved. Chapter 9 uses WKB techniques to analyze oscillation modes (quasi-normal modes or QNMs) of spinning black holes. We obtain analytical approximations to the spectrum of the weakly-damped QNMs, with relative error O(1/L^2), and connect these frequencies to geometrical features of spherical photon orbits in Kerr spacetime. Chapter 11 focuses mainly on near-extremal Kerr black holes, we discuss a bifurcation in their QNM spectra for certain ranges of (l,m) (the angular quantum numbers) as a/M → 1. With tools prepared in Chapter 9 and 10, in Chapter 11 we obtain an analytical approximate for the scalar Green function in Kerr spacetime.

Phase behavior of complex superprotonic solid acids

Superprotonic phase transitions and thermal behaviors of three complex solid acid systems are presented, namely Rb3H(SO4)2-RbHSO4 system, Rb3H(SeO4)2-Cs3H(SeO4)2 solid solution system, and Cs6(H2SO4)3(H1.5PO4)4. These material systems present a rich set of phase transition characteristics that set them apart from other, simpler solid acids. A.C. impedance spectroscopy, high-temperature X-ray powder diffraction, and thermal analysis, as well as other characterization techniques, were employed to investigate the phase behavior of these systems.

Rb3H(SO4)2 is an atypical member of the M3H(XO4)2 class of compounds (M = alkali metal or NH4+ and X = S or Se) in that a transition to a high-conductivity state involves disproportionation into two phases rather than a simple polymorphic transition [1]. In the present work, investigations of the Rb3H(SO4)2-RbHSO4 system have revealed the disproportionation products to be Rb2SO4 and the previously unknown compound Rb5H3(SO4)4. The new compound becomes stable at a temperature between 25 and 140 °C and is isostructural to a recently reported trigonal phase with space group P3̅m of Cs5H3(SO4)4 [2]. At 185 °C the compound undergoes an apparently polymorphic transformation with a heat of transition of 23.8 kJ/mol and a slight additional increase in conductivity.

The compounds Rb3H(SeO4)2 and Cs3H(SeO4)2, though not isomorphous at ambient temperatures, are quintessential examples of superprotonic materials. Both adopt monoclinic structures at ambient temperatures and ultimately transform to a trigonal (R3̅m) superprotonic structure at slightly elevated temperatures, 178 and 183 °C, respectively. The compounds are completely miscible above the superprotonic transition and show extensive solubility below it. Beyond a careful determination of the phase boundaries, we find a remarkable 40-fold increase in the superprotonic conductivity in intermediate compositions rich in Rb as compared to either end-member.

The compound Cs6(H2SO4)3(H1.5PO4)4 is unusual amongst solid acid compounds in that it has a complex cubic structure at ambient temperature and apparently transforms to a simpler cubic structure of the CsCl-type (isostructural with CsH2PO4) at its transition temperature of 100-120 °C [3]. Here it is found that, depending on the level of humidification, the superprotonic transition of this material is superimposed with a decomposition reaction, which involves both exsolution of (liquid) acid and loss of H2O. This reaction can be suppressed by application of sufficiently high humidity, in which case Cs6(H2SO4)3(H1.5PO4)4 undergoes a true superprotonic transition. It is proposed that, under conditions of low humidity, the decomposition/dehydration reaction transforms the compound to Cs6(H2-0.5xSO4)3(H1.5PO4)4-x, also of the CsCl structure type at the temperatures of interest, but with a smaller unit cell. With increasing temperature, the decomposition/dehydration proceeds to greater and greater extent and unit cell of the solid phase decreases. This is identified to be the source of the apparent negative thermal expansion behavior.

References

[1] L.A. Cowan, R.M. Morcos, N. Hatada, A. Navrotsky, S.M. Haile, Solid State Ionics 179 (2008) (9-10) 305.

[2] M. Sakashita, H. Fujihisa, K.I. Suzuki, S. Hayashi, K. Honda, Solid State Ionics 178 (2007) (21-22) 1262.

[3] C.R.I. Chisholm, Superprotonic Phase Transitions in Solid Acids: Parameters affecting the presence and stability of superprotonic transitions in the MHnXO4 family of compounds (X=S, Se, P, As; M=Li, Na, K, NH4, Rb, Cs), Materials Science, California Institute of Technology, Pasadena, California (2003).

Using space geodesy to constrain variations in seismogenic behavior on subduction megathrusts

The concept of seismogenic asperities and aseismic barriers has become a useful paradigm within which to understand the seismogenic behavior of major faults. Since asperities and barriers can be thought of as defining the potential rupture area of large megathrust earthquakes, it is thus important to identify their respective spatial extents, constrain their temporal longevity, and to develop a physical understanding for their behavior. Space geodesy is making critical contributions to the identification of slip asperities and barriers but progress in many geographical regions depends on improving the accuracy and precision of the basic measurements. This thesis begins with technical developments aimed at improving satellite radar interferometric measurements of ground deformation whereby we introduce an empirical correction algorithm for unwanted effects due to interferometric path delays that are due to spatially and temporally variable radar wave propagation speeds in the atmosphere. In chapter 2, I combine geodetic datasets with complementary spatio-temporal resolutions to improve our understanding of the spatial distribution of crustal deformation sources and their associated temporal evolution – here we use observations from Long Valley Caldera (California) as our test bed. In the third chapter I apply the tools developed in the first two chapters to analyze postseismic deformation associated with the 2010 Mw=8.8 Maule (Chile) earthquake. The result delimits patches where afterslip occurs, explores their relationship to coseismic rupture, quantifies frictional properties associated with inferred patches of afterslip, and discusses the relationship of asperities and barriers to long-term topography. The final chapter investigates interseismic deformation of the eastern Makran subduction zone by using satellite radar interferometry only, and demonstrates that with state-of-art techniques it is possible to quantify tectonic signals with small amplitude and long wavelength. Portions of the eastern Makran for which we estimate low fault coupling correspond to areas where bathymetric features on the downgoing plate are presently subducting, whereas the region of the 1945 M=8.1 earthquake appears to be more highly coupled.

Electron energy-loss spectroscopy study of polyatomic molecular systems under pyrolytic conditions

The technique of variable-angle, electron energy-loss spectroscopy has been used to study the electronic spectroscopy of the diketene molecule. The experiment was performed using incident electron beam energies of 25 eV and 50 eV, and at scattering angles between 10° and 90°. The energy-loss region from 2 eV to 11 eV was examined. One spin-forbidden transition has been observed at 4.36 eV and three others that are spin-allowed have been located at 5.89 eV, 6.88 eV and 7.84 eV. Based on the intensity variation of these transitions with impact energy and scattering angle, and through analogy with simpler molecules, the first three transitions are tentatively assigned to an n → π* transition, a π - σ* (3s) Rydberg transition and a π → π* transition.

Thermal decomposition of chlorodifluoromethane, chloroform, dichloromethane and chloromethane under flash-vacuum pyrolysis conditions (900-1100°C) was investigated by the technique of electron energy-loss spectroscopy, using the impact energy of 50 eV and a scattering angle of 10°. The pyrolytic reaction follows a hydrogen-chloride α-elimination pathway. The difluoromethylene radical was produced from chlorodifluoromethane pyrolysis at 900°C and identified by its X^1 A_1 → A^1B_1 band at 5.04 eV.

Finally, a number of exploratory studies have been performed. The thermal decomposition of diketene was studied under flash vacuum pressures (1-10 mTorr) and temperatures ranging from 500°C to 1000°C. The complete decomposition of the diketene molecule into two ketene molecules was achieved at 900°C. The pyrolysis of trifluoromethyl iodide molecule at 1000°C produced an electron energy-loss spectrum with several iodine-atom, sharp peaks and only a small shoulder at 8.37 eV as a possible trifluoromethyl radical feature. The electron energy-loss spectrum of trichlorobromomethane at 900°C mainly showed features from bromine atom, chlorine molecule and tetrachloroethylene. Hexachloroacetone decomposed partially at 900°C, but showed well-defined features from chlorine, carbon monoxide and tetrachloroethylene molecules. Bromodichloromethane molecule was investigated at 1000°C and produced a congested, electron energy-loss spectrum with bromine-atom, hydrogen-bromide, hydrogen-chloride and tetrachloroethylene features.

Lightweight deformable mirrors for future space telescopes

This thesis presents a concept for ultra-lightweight deformable mirrors based on a thin substrate of optical surface quality coated with continuous active piezopolymer layers that provide modes of actuation and shape correction. This concept eliminates any kind of stiff backing structure for the mirror surface and exploits micro-fabrication technologies to provide a tight integration of the active materials into the mirror structure, to avoid actuator print-through effects. Proof-of-concept, 10-cm-diameter mirrors with a low areal density of about 0.5 kg/m² have been designed, built and tested to measure their shape-correction performance and verify the models used for design. The low cost manufacturing scheme uses replication techniques, and strives for minimizing residual stresses that deviate the optical figure from the master mandrel. It does not require precision tolerancing, is lightweight, and is therefore potentially scalable to larger diameters for use in large, modular space telescopes. Other potential applications for such a laminate could include ground-based mirrors for solar energy collection, adaptive optics for atmospheric turbulence, laser communications, and other shape control applications.

The immediate application for these mirrors is for the Autonomous Assembly and Reconfiguration of a Space Telescope (AAReST) mission, which is a university mission under development by Caltech, the University of Surrey, and JPL. The design concept, fabrication methodology, material behaviors and measurements, mirror modeling, mounting and control electronics design, shape control experiments, predictive performance analysis, and remaining challenges are presented herein. The experiments have validated numerical models of the mirror, and the mirror models have been used within a model of the telescope in order to predict the optical performance. A demonstration of this mirror concept, along with other new telescope technologies, is planned to take place during the AAReST mission.

Projections in a normed linear space and a generalization of the pseudo-inverse

The concept of a "projection function" in a finite-dimensional real or complex normed linear space H (the function P_M which carries every element into the closest element of a given subspace M) is set forth and examined.

If dim M = dim H - 1, then P_M is linear. If P_N is linear for all k-dimensional subspaces N, where 1 ≤ k < dim M, then P_M is linear.

The projective bound Q, defined to be the supremum of the operator norm of P_M for all subspaces, is in the range 1 ≤ Q < 2, and these limits are the best possible. For norms with Q = 1, P_M is always linear, and a characterization of those norms is given.

If H also has an inner product (defined independently of the norm), so that a dual norm can be defined, then when P_M is linear its adjoint P_M^H is the projection on (kernel P_M)^⊥ by the dual norm. The projective bounds of a norm and its dual are equal.

The notion of a pseudo-inverse F⁺ of a linear transformation F is extended to non-Euclidean norms. The distance from F to the set of linear transformations G of lower rank (in the sense of the operator norm ∥F - G∥) is c/∥F⁺∥, where c = 1 if the range of F fills its space, and 1 ≤ c < Q otherwise. The norms on both domain and range spaces have Q = 1 if and only if (F⁺)⁺ = F for every F. This condition is also sufficient to prove that we have (F⁺)^H = (F^H)⁺, where the latter pseudo-inverse is taken using dual norms.

In all results, the real and complex cases are handled in a completely parallel fashion.