Two roads to planet detection

One of the most exciting discoveries in astrophysics of the last last decade is of the sheer diversity of planetary systems. These include "hot Jupiters", giant planets so close to their host stars that they orbit once every few days; "Super-Earths", planets with sizes intermediate to those of Earth and Neptune, of which no analogs exist in our own solar system; multi-planet systems with planets smaller than Mars to larger than Jupiter; planets orbiting binary stars; free-floating planets flying through the emptiness of space without any star; even planets orbiting pulsars. Despite these remarkable discoveries, the field is still young, and there are many areas about which precious little is known. In particular, we don't know the planets orbiting Sun-like stars nearest to our own solar system, and we know very little about the compositions of extrasolar planets. This thesis provides developments in those directions, through two instrumentation projects.

The first chapter of this thesis concerns detecting planets in the Solar neighborhood using precision stellar radial velocities, also known as the Doppler technique. We present an analysis determining the most efficient way to detect planets considering factors such as spectral type, wavelengths of observation, spectrograph resolution, observing time, and instrumental sensitivity. We show that G and K dwarfs observed at 400-600 nm are the best targets for surveys complete down to a given planet mass and out to a specified orbital period. Overall we find that M dwarfs observed at 700-800 nm are the best targets for habitable-zone planets, particularly when including the effects of systematic noise floors caused by instrumental imperfections. Somewhat surprisingly, we demonstrate that a modestly sized observatory, with a dedicated observing program, is up to the task of discovering such planets.

We present just such an observatory in the second chapter, called the "MINiature Exoplanet Radial Velocity Array," or MINERVA. We describe the design, which uses a novel multi-aperture approach to increase stability and performance through lower system etendue, as well as keeping costs and time to deployment down. We present calculations of the expected planet yield, and data showing the system performance from our testing and development of the system at Caltech's campus. We also present the motivation, design, and performance of a fiber coupling system for the array, critical for efficiently and reliably bringing light from the telescopes to the spectrograph. We finish by presenting the current status of MINERVA, operational at Mt. Hopkins observatory in Arizona.

The second part of this thesis concerns a very different method of planet detection, direct imaging, which involves discovery and characterization of planets by collecting and analyzing their light. Directly analyzing planetary light is the most promising way to study their atmospheres, formation histories, and compositions. Direct imaging is extremely challenging, as it requires a high performance adaptive optics system to unblur the point-spread function of the parent star through the atmosphere, a coronagraph to suppress stellar diffraction, and image post-processing to remove non-common path "speckle" aberrations that can overwhelm any planetary companions.

To this end, we present the "Stellar Double Coronagraph," or SDC, a flexible coronagraphic platform for use with the 200" Hale telescope. It has two focal and pupil planes, allowing for a number of different observing modes, including multiple vortex phase masks in series for improved contrast and inner working angle behind the obscured aperture of the telescope. We present the motivation, design, performance, and data reduction pipeline of the instrument. In the following chapter, we present some early science results, including the first image of a companion to the star delta Andromeda, which had been previously hypothesized but never seen.

A further chapter presents a wavefront control code developed for the instrument, using the technique of "speckle nulling," which can remove optical aberrations from the system using the deformable mirror of the adaptive optics system. This code allows for improved contrast and inner working angles, and was written in a modular style so as to be portable to other high contrast imaging platforms. We present its performance on optical, near-infrared, and thermal infrared instruments on the Palomar and Keck telescopes, showing how it can improve contrasts by a factor of a few in less than ten iterations.

One of the large challenges in direct imaging is sensing and correcting the electric field in the focal plane to remove scattered light that can be much brighter than any planets. In the last chapter, we present a new method of focal-plane wavefront sensing, combining a coronagraph with a simple phase-shifting interferometer. We present its design and implementation on the Stellar Double Coronagraph, demonstrating its ability to create regions of high contrast by measuring and correcting for optical aberrations in the focal plane. Finally, we derive how it is possible to use the same hardware to distinguish companions from speckle errors using the principles of optical coherence. We present results observing the brown dwarf HD 49197b, demonstrating the ability to detect it despite it being buried in the speckle noise floor. We believe this is the first detection of a substellar companion using the coherence properties of light.

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.

Relative mirror symmetry and ramifications of a formula for Gromov-Witten invariants

For a toric Del Pezzo surface S, a new instance of mirror symmetry, said relative, is introduced and developed. On the A-model, this relative mirror symmetry conjecture concerns genus 0 relative Gromov-Witten of maximal tangency of S. These correspond, on the B-model, to relative periods of the mirror to S. Furthermore, for S not necessarily toric, two conjectures for BPS state counts are related. It is proven that the integrality of BPS state counts of the total space of the canonical bundle on S implies the integrality for the relative BPS state counts of S. Finally, a prediction of homological mirror symmetry for the open complement is explored. The B-model prediction is calculated in all cases and matches the known A-model computation for the projective plane.

High fidelity probe and mitigation of mirror thermal fluctuations

Thermal noise arising from mechanical loss in high reflective dielectric coatings is a significant source of noise in precision optical measurements. In particular, Advanced LIGO, a large scale interferometer aiming to observed gravitational wave, is expected to be limited by coating thermal noise in the most sensitive region around 30–300 Hz. Various theoretical calculations for predicting coating Brownian noise have been proposed. However, due to the relatively limited knowledge of the coating material properties, an accurate approximation of the noise cannot be achieved. A testbed that can directly observed coating thermal noise close to Advanced LIGO band will serve as an indispensable tool to verify the calculations, study material properties of the coating, and estimate the detector’s performance.

This dissertation reports a setup that has sensitivity to observe wide band (10Hz to 1kHz) thermal noise from fused silica/tantala coating at room temperature from fixed-spacer Fabry–Perot cavities. Important fundamental noises and technical noises associated with the setup are discussed. The coating loss obtained from the measurement agrees with results reported in the literature. The setup serves as a testbed to study thermal noise in high reflective mirrors from different materials. One example is a heterostructure of Al_xGa_1−xAs (AlGaAs). An optimized design to minimize thermo–optic noise in the coating is proposed and discussed in this work.

Mechanics of deformable glacier beds

My focus in this thesis is to contribute to a more thorough understanding of the mechanics of ice and deformable glacier beds. Glaciers flow under their own weight through a combination of deformation within the ice column and basal slip, which involves both sliding along and deformation within the bed. Deformable beds, which are made up of unfrozen sediment, are prevalent in nature and are often the primary contributors to ice flow wherever they are found. Their granular nature imbues them with unique mechanical properties that depend on the granular structure and hydrological properties of the bed. Despite their importance for understanding glacier flow and the response of glaciers to changing climate, the mechanics of deformable glacier beds are not well understood.

Our general approach to understanding the mechanics of bed deformation and their effect on glacier flow is to acquire synoptic observations of ice surface velocities and their changes over time and to use those observations to infer the mechanical properties of the bed. We focus on areas where changes in ice flow over time are due to known environmental forcings and where the processes of interest are largely isolated from other effects. To make this approach viable, we further develop observational methods that involve the use of mapping radar systems. Chapters 2 and 5 focus largely on the development of these methods and analysis of results from ice caps in central Iceland and an ice stream in West Antarctica. In Chapter 3, we use these observations to constrain numerical ice flow models in order to study the mechanics of the bed and the ice itself. We show that the bed in an Iceland ice cap deforms plastically and we derive an original mechanistic model of ice flow over plastically deforming beds that incorporates changes in bed strength caused by meltwater flux from the surface. Expanding on this work in Chapter 4, we develop a more detailed mechanistic model for till-covered beds that helps explain the mechanisms that cause some glaciers to surge quasi-periodically. In Antarctica, we observe and analyze the mechanisms that allow ocean tidal variations to modulate ice stream flow tens of kilometers inland. We find that the ice stream margins are significantly weakened immediately upstream of the area where ice begins to float and that this weakening likely allows changes in stress over the floating ice to propagate through the ice column.

Deep tissue fluorescence imaging with time-reversed light

Advances in optical techniques have enabled many breakthroughs in biology and medicine. However, light scattering by biological tissues remains a great obstacle, restricting the use of optical methods to thin ex vivo sections or superficial layers in vivo. In this thesis, we present two related methods that overcome the optical depth limit—digital time reversal of ultrasound encoded light (digital TRUE) and time reversal of variance-encoded light (TROVE). These two techniques share the same principle of using acousto-optic beacons for time reversal optical focusing within highly scattering media, like biological tissues. Ultrasound, unlike light, is not significantly scattered in soft biological tissues, allowing for ultrasound focusing. In addition, a fraction of the scattered optical wavefront that passes through the ultrasound focus gets frequency-shifted via the acousto-optic effect, essentially creating a virtual source of frequency-shifted light within the tissue. The scattered ultrasound-tagged wavefront can be selectively measured outside the tissue and time-reversed to converge at the location of the ultrasound focus, enabling optical focusing within deep tissues. In digital TRUE, we time reverse ultrasound-tagged light with an optoelectronic time reversal device (the digital optical phase conjugate mirror, DOPC). The use of the DOPC enables high optical gain, allowing for high intensity optical focusing and focal fluorescence imaging in thick tissues at a lateral resolution of 36 µm by 52 µm. The resolution of the TRUE approach is fundamentally limited to that of the wavelength of ultrasound. The ultrasound focus (~ tens of microns wide) usually contains hundreds to thousands of optical modes, such that the scattered wavefront measured is a linear combination of the contributions of all these optical modes. In TROVE, we make use of our ability to digitally record, analyze and manipulate the scattered wavefront to demix the contributions of these spatial modes using variance encoding. In essence, we encode each spatial mode inside the scattering sample with a unique variance, allowing us to computationally derive the time reversal wavefront that corresponds to a single optical mode. In doing so, we uncouple the system resolution from the size of the ultrasound focus, demonstrating optical focusing and imaging between highly diffusing samples at an unprecedented, speckle-scale lateral resolution of ~ 5 µm. Our methods open up the possibility of fully exploiting the prowess and versatility of biomedical optics in deep tissues.

Wnt and FGF signaling in C. elegans vulval cell lineage polarity

The interpretation of extracellular cues leading to the polarization of intracellular components and asymmetric cell divisions is a fundamental part of metazoan organogenesis. The C. elegans vulva, with its invariant cell lineage and interaction of multiple cell signaling pathways, provides an excellent model for the study of cell polarity within an organized epithelial tissue. Herein I discuss the interaction of Wnt and FGF signaling in controlling vulval cell lineage polarity with emphasis on the posterior-most cell that forms the vulva, P7.p.

The mirror symmetry of the C. elegans vulva is achieved by the opposite division orientation of the vulval precursor cells (VPCs) flanking the axis of symmetry. Opposing Wnt signals control the division patterns of the VPCs by controlling the localization of SYS-1/ β-catenin toward the direction of the Wnt gradient. Multiple Wnt signals, expressed at the axis of symmetry, promote the wild-type, anterior-facing, P7.p orientation, whereas Wnts EGL-20 and CWN-1 from the tail and posterior body wall muscle, respectively, promote the daughter cells of P7.p to face the posterior. EGL-20 acts through a member of the LDL receptor superfamily, LRP-2, along with Ror/CAM-1 and Van Gogh/VANG-1. All three transmembrane proteins control orientation through the localization of the SYS-1.

The Fibroblast Growth Factor (FGF) pathway acts in concert with LIN-17/Frizzled to regulate the localization of SYS-1. The source of the FGF ligand is the 1° VPC, P6.p, which controls the polarity of the neighboring 2° VPC, P7.p, by signaling through the sex myoblasts (SMs), activating the FGF pathway. The Wnt, cwn-1, is expressed in the posterior body wall muscle of the worm as well as the SMs, making it the only Wnt expressed on the posterior and anterior sides of P7.p at the time of the polarity decision. Both sources of cwn-1 act instructively to influence P7.p polarity in the direction of the Wnt gradient. The FGF pathway leads to the regulation of cwn-1 transcripts in the SMs. These results illustrate the first evidence of the interaction between FGF and Wnt in C. elegans development and vulval cell lineage polarity as well as highlight the promiscuous nature of Wnt signaling within C. elegans.

Optical properties of excited silicon and germanium at low temperatures

Part I of this thesis deals with 3 topics concerning the luminescence from bound multi-exciton complexes in Si. Part II presents a model for the decay of electron-hole droplets in pure and doped Ge.

Part I.

We present high resolution photoluminescence data for Si doped With Al, Ga, and In. We observe emission lines due to recombination of electron-hole pairs in bound excitons and satellite lines which have been interpreted in terms of complexes of several excitons bound to an impurity. The bound exciton luminescence in Si:Ga and Si:Al consists of three emission lines due to transitions from the ground state and two low lying excited states. In Si:Ga, we observe a second triplet of emission lines which precisely mirror the triplet due to the bound exciton. This second triplet is interpreted as due to decay of a two exciton complex into the bound exciton. The observation of the second complete triplet in Si:Ga conclusively demonstrates that more than one exciton will bind to an impurity. Similar results are found for Si:Al. The energy of the lines show that the second exciton is less tightly bound than the first in Si:Ga. Other lines are observed at lower energies. The assumption of ground state to ground-state transitions for the lower energy lines is shown to produce a complicated dependence of binding energy of the last exciton on the number of excitons in a complex. No line attributable to the decay of a two exciton complex is observed in Si:In.

We present measurements of the bound exciton lifetimes for the four common acceptors in Si and for the first two bound multi-exciton complexes in Si:Ga and Si:Al. These results are shown to be in agreement with a calculation by Osbourn and Smith of Auger transition rates for acceptor bound excitons in Si. Kinetics determine the relative populations of complexes of various sizes and work functions, at temperatures which do not allow them to thermalize with respect to one another. It is shown that kinetic limitations may make it impossible to form two-exciton complexes in Si:In from a gas of free excitons.

We present direct thermodynamic measurements of the work functions of bound multi-exciton complexes in Al, B, P and Li doped Si. We find that in general the work functions are smaller than previously believed. These data remove one obstacle to the bound multi-exciton complex picture which has been the need to explain the very large apparent work functions for the larger complexes obtained by assuming that some of the observed lines are ground-state to ground-state transitions. None of the measured work functions exceed that of the electron-hole liquid.

Part II.

A new model for the decay of electron-hole-droplets in Ge is presented. The model is based on the existence of a cloud of droplets within the crystal and incorporates exciton flow among the drops in the cloud and the diffusion of excitons away from the cloud. It is able to fit the experimental luminescence decays for pure Ge at different temperatures and pump powers while retaining physically reasonable parameters for the drops. It predicts the shrinkage of the cloud at higher temperatures which has been verified by spatially and temporally resolved infrared absorption experiments. The model also accounts for the nearly exponential decay of electron-hole-droplets in lightly doped Ge at higher temperatures.

Aperiodic structures in optics and integrated optics and the transverse Bragg reflector laser

The first part of this work describes the uses of aperiodic structures in optics and integrated optics. In particular, devices are designed, fabricated, tested and analyzed which make use of a chirped grating corrugation on the surface of a dielectric waveguide. These structures can be used as input-output couplers, multiplexers and demultiplexers, and broad band filters.

Next, a theoretical analysis is made of the effects of a random statistical variation in the thicknesses of layers in a dielectric mirror on its reflectivity properties. Unlike the intentional aperiodicity introduced in the chirped gratings, the aperiodicity in the Bragg reflector mirrors is unintentional and is present to some extent in all devices made. The analysis involved in studying these problems relies heavily on the coupled mode formalism. The results are compared with computer experiments, as well as tests of actual mirrors.

The second part of this work describes a novel method for confining light in the transverse direction in an injection laser. These so-called transverse Bragg reflector lasers confine light normal to the junction plane in the active region, through reflection from an adjacent layered medium. Thus, in principle, it is possible to guide light in a dielectric layer whose index is lower than that of the surrounding material. The design, theory and testing of these diode lasers are discussed.

Acceleration Sensing, Feedback Cooling, and Nonlinear Dynamics with Nanoscale Cavity-Optomechanical Devices

Light has long been used for the precise measurement of moving bodies, but the burgeoning field of optomechanics is concerned with the interaction of light and matter in a regime where the typically weak radiation pressure force of light is able to push back on the moving object. This field began with the realization in the late 1960's that the momentum imparted by a recoiling photon on a mirror would place fundamental limits on the smallest measurable displacement of that mirror. This coupling between the frequency of light and the motion of a mechanical object does much more than simply add noise, however. It has been used to cool objects to their quantum ground state, demonstrate electromagnetically-induced-transparency, and modify the damping and spring constant of the resonator. Amazingly, these radiation pressure effects have now been demonstrated in systems ranging 18 orders of magnitude in mass (kg to fg).

In this work we will focus on three diverse experiments in three different optomechanical devices which span the fields of inertial sensors, closed-loop feedback, and nonlinear dynamics. The mechanical elements presented cover 6 orders of magnitude in mass (ng to fg), but they all employ nano-scale photonic crystals to trap light and resonantly enhance the light-matter interaction. In the first experiment we take advantage of the sub-femtometer displacement resolution of our photonic crystals to demonstrate a sensitive chip-scale optical accelerometer with a kHz-frequency mechanical resonator. This sensor has a noise density of approximately 10 micro-g/rt-Hz over a useable bandwidth of approximately 20 kHz and we demonstrate at least 50 dB of linear dynamic sensor range. We also discuss methods to further improve performance of this device by a factor of 10.

In the second experiment, we used a closed-loop measurement and feedback system to damp and cool a room-temperature MHz-frequency mechanical oscillator from a phonon occupation of 6.5 million down to just 66. At the time of the experiment, this represented a world-record result for the laser cooling of a macroscopic mechanical element without the aid of cryogenic pre-cooling. Furthermore, this closed-loop damping yields a high-resolution force sensor with a practical bandwidth of 200 kHZ and the method has applications to other optomechanical sensors.

The final experiment contains results from a GHz-frequency mechanical resonator in a regime where the nonlinearity of the radiation-pressure interaction dominates the system dynamics. In this device we show self-oscillations of the mechanical element that are driven by multi-photon-phonon scattering. Control of the system allows us to initialize the mechanical oscillator into a stable high-amplitude attractor which would otherwise be inaccessible. To provide context, we begin this work by first presenting an intuitive overview of optomechanical systems and then providing an extended discussion of the principles underlying the design and fabrication of our optomechanical devices.

Multilayer Active Shell Mirrors

This thesis presents a novel active mirror technology based on carbon fiber composites and replication manufacturing processes. Multiple additional layers are implemented into the structure in order to provide the reflective layer, actuation capabilities and electrode routing. The mirror is thin, lightweight, and has large actuation capabilities. These features, along with the associated manufacturing processes, represent a significant change in design compared to traditional optics. Structural redundancy in the form of added material or support structures is replaced by thin, unsupported lightweight substrates with large actuation capabilities.

Several studies motivated by the desire to improve as-manufactured figure quality are performed. Firstly, imperfections in thin CFRP laminates and their effect on post-cure shape errors are studied. Numerical models are developed and compared to experimental measurements on flat laminates. Techniques to mitigate figure errors for thicker laminates are also identified. A method of properly integrating the reflective facesheet onto the front surface of the CFRP substrate is also presented. Finally, the effect of bonding multiple initially flat active plates to the backside of a curved CFRP substrate is studied. Figure deformations along with local surface defects are predicted and characterized experimentally. By understanding the mechanics behind these processes, significant improvements to the overall figure quality have been made.

Studies related to the actuation response of the mirror are also performed. The active properties of two materials are characterized and compared. Optimal active layer thicknesses for thin surface-parallel schemes are determined. Finite element simulations are used to make predictions on shape correction capabilities, demonstrating high correctabiliity and stroke over low-order modes. The effect of actuator saturation is studied and shown to significantly degrade shape correction performance.

The initial figure as well as actuation capabilities of a fully-integrated active mirror prototype are characterized experimentally using a Projected Hartmann test. A description of the test apparatus is presented along with two verification measurements. The apparatus is shown to accurately capture both high-amplitude low spatial-frequency figure errors as well as those at lower amplitudes but higher spatial frequencies. A closed-loop figure correction is performed, reducing figure errors by 94%.

Excitation energies and decay properties of T = 3/2 states in ^(17)O, ^(17)F and ^(21)Na

The two lowest T = 3/2 levels in ²¹Na have been studied in the ¹⁹F(³He, n), ²⁰Ne (p,p) and ²⁰Ne (p,p’) reactions, and their excitation energies, spins, parities and widths have been determined. In a separate investigation, branching ratios were measured for the isospin-nonconserving particle decays of the lowest T = 3/2 levels in ¹⁷O and ¹⁷F to the ground state and first two excited states of ¹⁶O, by studying the ¹⁵N(³He,n) ¹⁷F*(p) ¹⁶O and ¹⁸O(³He, α)¹⁷O*(n) ¹⁶O reactions.

The ¹⁹F(³He,n) ²¹Na reaction was studied at incident energies between 4.2 and 5.9 MeV using a pulsed-beam neutron-time-of-flight spectrometer. Two T = 3/2 levels were identified at excitation energies of 8.99 ± 0.05 MeV (J > ½) and 9.22 ± 0.015 MeV (J ^π = ½⁺, Γ ˂ 40 keV). The spins and parities were determined by a comparison of the measured angular distributions with the results of DWBA calculations.

These two levels were also obsesrved as isospin-forbidden resonances in the ²⁰Ne(p,p) and ²⁰Ne(p,p’) reactions. Excitation energies were measured and spins, parities, and widths were determined from a single level dispersion theory analysis. The following results were obtained:

E_x = 8.973 ± 0.007 MeV, J ^π = 5/2 ⁺ or 3/2⁺, Γ ≤ 1.2 keV,

^Γp_o = 0.1 ± 0.05 keV; E_x = 9.217 ± 0.007 MeV, J^π = ½ ⁺,

Γ = 2.3 ± 0.5 keV, ^Γp_o = 1.1 ± 0.3 keV.

Isospin assignments were made on the basis of excitation energies, spins, parities, and widths.

Branching ratios for the isospin-nonconserving proton decays of the 11.20 MeV, T = 3/2 level in ¹⁷F were measured by the ¹⁵N(³He,n) ¹⁷ F*(p) ¹⁶O reaction to be 0.088 ± 0.016 to the ground state of ¹⁶O and 0.22 ± 0.04 to the unresolved 6.05 and 6.13 MeV levels of ¹⁶O. Branching ratios for the neutron decays of the analogous T = 3/2 level, at 11.08 MeV in ¹⁷O, were measured by the ¹⁶O(³He, α)¹⁷O*(n)¹⁶O reaction to be 0.91 ± 0.15 to the ground state of ¹⁶O and 0.05 ± 0.02 to the unresolved 6.05 and 6.13 MeV states. By comparing the ratios of reduced widths for the mirror decays, the form of the isospin impurity in the T = 3/2 levels is shown to depend on T_z.

A computer-aided investigation of motion detection units in the fly

This work deals with two related areas: processing of visual information in the central nervous system, and the application of computer systems to research in neurophysiology.

Certain classes of interneurons in the brain and optic lobes of the blowfly Calliphora phaenicia were previously shown to be sensitive to the direction of motion of visual stimuli. These units were identified by visual field, preferred direction of motion, and anatomical location from which recorded. The present work is addressed to the questions: (1) is there interaction between pairs of these units, and (2) if such relationships can be found, what is their nature. To answer these questions, it is essential to record from two or more units simultaneously, and to use more than a single recording electrode if recording points are to be chosen independently. Accordingly, such techniques were developed and are described.

One must also have practical, convenient means for analyzing the large volumes of data so obtained. It is shown that use of an appropriately designed computer system is a profitable approach to this problem. Both hardware and software requirements for a suitable system are discussed and an approach to computer-aided data analysis developed. A description is given of members of a collection of application programs developed for analysis of neuro-physiological data and operated in the environment of and with support from an appropriate computer system. In particular, techniques developed for classification of multiple units recorded on the same electrode are illustrated as are methods for convenient graphical manipulation of data via a computer-driven display.

By means of multiple electrode techniques and the computer-aided data acquisition and analysis system, the path followed by one of the motion detection units was traced from open optic lobe through the brain and into the opposite lobe. It is further shown that this unit and its mirror image in the opposite lobe have a mutually inhibitory relationship. This relationship is investigated. The existence of interaction between other pairs of units is also shown. For pairs of units responding to motion in the same direction, the relationship is of an excitatory nature; for those responding to motion in opposed directions, it is inhibitory.

Experience gained from use of the computer system is discussed and a critical review of the current system is given. The most useful features of the system were found to be the fast response, the ability to go from one analysis technique to another rapidly and conveniently, and the interactive nature of the display system. The shortcomings of the system were problems in real-time use and the programming barrier—the fact that building new analysis techniques requires a high degree of programming knowledge and skill. It is concluded that computer system of the kind discussed will play an increasingly important role in studies of the central nervous system.

I. Electronic states of heavily-doped molecular crystals--naphthalene. I. Theoretical. II. Experimental. II. Lowest singlet and triplet excited states of pyrazine

PART I

The energy spectrum of heavily-doped molecular crystals was treated in the Green’s function formulation. The mixed crystal Green’s function was obtained by averaging over all possible impurity distributions. The resulting Green’s function, which takes the form of an infinite perturbation expansion, was further approximated by a closed form suitable for numerical calculations. The density-of-states functions and optical spectra for binary mixtures of normal naphthalene and deuterated naphthalene were calculated using the pure crystal density-of-state functions. The results showed that when the trap depth is large, two separate energy bands persist, but when the trap depth is small only a single band exists. Furthermore, in the former case it was found that the intensities of the outer Davydov bands are enhanced whereas the inner bands are weakened. Comparisons with previous theoretical calculations and experimental results are also made.

PART II

The energy states and optical spectra of heavily-doped mixed crystals are investigated. Studies are made for the following binary systems: (1) naphthalene-h₈ and d₈, (2) naphthalene--h₈ and αd₄, and (3) naphthalene--h₈ and βd₁, corresponding to strong, medium and weak perturbations. In addition to ordinary absorption spectra at 4˚K, band-to-band transitions at both 4˚K and 77˚K are also analyzed with emphasis on their relations to cooperative excitation and overall density-of-states functions for mixed crystals. It is found that the theoretical calculations presented in a previous paper agree generally with experiments except for cluster states observed in system (1) at lower guest concentrations. These features are discussed semi-quantitatively. As to the intermolecular interaction parameters, it is found that experimental results compare favorably with calculations based on experimental density-of-states functions but not with those based on octopole interactions or charge-transfer interactions. Previous experimental results of Sheka and the theoretical model of Broude and Rashba are also compared with present investigations.

PART III

The phosphorescence, fluorescence and absorption spectra of pyrazine-h₄ and d₄ have been obtained at 4˚K in a benzene matrix. For comparison, those of the isotopically mixed crystal pyrazine-h₄ in d₄ were also taken. All these spectra show extremely sharp and well-resolved lines and reveal detailed vibronic structure.

The analysis of the weak fluorescence spectrum resolves the long-disputed question of whether one or two transitions are involved in the near-ultraviolet absorption of pyrazine. The “mirror-image relationship” between absorption and emission shows that the lowest singlet state is an allowed transition, properly designated as ¹B_3u ← ¹A_1g. The forbidden component ¹B_2g, predicted by both “exciton” and MO theories to be below the allowed component, must lie higher. Its exact location still remains uncertain.

The phosphorescence spectrum when compared with the excitation phosphorescence spectra, indicates that the lowest triplet state is also symmetry allowed, showing a strong 0-0 band and a “mirror-image relationship” between absorption and emission. In accordance with previous work, the triplet state is designated as ³B_3u.

The vibronic structure of the phosphorescence spectrum is very complicated. Previous work on the analysis of this spectrum all concluded that a long progression of v_6a exists. Under the high resolution attainable in our work, the supposed v_6a progression proves to have a composite triplet structure, starting from the second member of the progression. Not only is the v_9a hydrogen-bending mode present as shown by the appearance of the C-D bending mode in the d₄ spectrum, but a band of 1207 cm^-1 in the pyrazine in benzene system and 1231 cm^-1 in the mixed crystal system is also observed. This band is assigned as 2v_6b and of a_1g symmetry. Its anonymously strong intensity in the phosphorescence spectrum is interpreted as due to the Fermi resonance with the 2v_6a and v_9a band.

To help resolve the present controversy over the crystal phosphorescence spectrum of pyrazine, detailed vibrational analyses of the emission spectra were made. The fluorescence spectrum has essentially the same vibronic structure as the phosphorescence spectrum.

An Optically recombined laser interferometer for gravitational wave detection

Kilometer scale interferometers for the detection of gravitational waves are currently under construction by the LIGO (Laser Interferometer Gravitational-wave Observatory) and VIRGO projects. These interferometers will consist of two Fabry-Perot cavities illuminated by a laser beam which is split in half by a beam splitter. A recycling mirror between the laser and the beam splitter will reflect the light returning from the beam splitter towards the laser back into the interferometer. The positions of the optical components in these interferometers must be controlled to a small fraction of a wavelength of the laser light. Schemes to extract signals necessary to control these optical components have been developed and demonstrated on the tabletop. In the large scale gravitational wave detectors the optical components must be suspended from vibration isolation platforms to achieve the necessary isolation from seismic motion. These suspended components present a new class of problems in controlling the interferometer, but also provide more exacting test of interferometer signal and noise models.

This thesis discusses the first operation of a suspended-mass Fabry-Perot-Michelson interferometer, in which signals carried by the optically recombined beams are used to detect and control all important mirror displacements. This interferometer uses an optical configuration and signal extraction scheme that is planned for the full scale LIGO interferometers with the simplification of the removal of the recycling mirror. A theoretical analysis of the performance that is expected from such an interferometer is presented and the experimental results are shown to be in generally good agreement.