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.

Structural and mechanistic motifs in membrane proteins: the three-dimensional modelling of rhodopsin, band 3, and the nicotinic acetylcholine receptor

Because so little is known about the structure of membrane proteins, an attempt has been made in this work to develop techniques by which to model them in three dimensions. The procedures devised rely heavily upon the availability of several sequences of a given protein. The modelling procedure is composed of two parts. The first identifies transmembrane regions within the protein sequence on the basis of hydrophobicity, β-turn potential, and the presence of certain amino acid types, specifically, proline and basic residues. The second part of the procedure arranges these transmembrane helices within the bilayer based upon the evolutionary conservation of their residues. Conserved residues are oriented toward other helices and variable residues are positioned to face the surrounding lipids. Available structural information concerning the protein's helical arrangement, including the lengths of interhelical loops, is also taken into account. Rhodopsin, band 3, and the nicotinic acetylcholine receptor have all been modelled using this methodology, and mechanisms of action could be proposed based upon the resulting structures.

Specific residues in the rhodopsin and iodopsin sequences were identified, which may regulate the proteins' wavelength selectivities. A hinge-like motion of helices M3, M4, and M5 with respect to the rest of the protein was proposed to result in the activation of transducin, the G-protein associated with rhodopsin. A similar mechanism is also proposed for signal transduction by the muscarinic acetylcholine and β-adrenergic receptors.

The nicotinic acetylcholine receptor was modelled with four trans-membrane helices per subunit and with the five homologous M2 helices forming the cation channel. Putative channel-lining residues were identified and a mechanism of channel-opening based upon the concerted, tangential rotation of the M2 helices was proposed.

Band 3, the anion exchange protein found in the erythrocyte membrane, was modelled with 14 transmembrane helices. In general the pathway of anion transport can be viewed as a channel composed of six helices that contains a single hydrophobic restriction. This hydrophobic region will not allow the passage of charged species, unless they are part of an ion-pair. An arginine residue located near this restriction is proposed to be responsible for anion transport. When ion-paired with a transportable anion it rotates across the barrier and releases the anion on the other side of the membrane. A similar process returns it to its original position. This proposed mechanism, based on the three-dimensional model, can account for the passive, electroneutral, anion exchange observed for band 3. Dianions can be transported through a similar mechanism with the additional participation of a histidine residue. Both residues are located on M10.

Measurement of the band bending and surface dipole at chemically functionalized Si(111)/vacuum interfaces

The core-level energy shifts observed using X-ray photoelectron spectroscopy (XPS) have been used to determine the band bending at Si(111) surfaces terminated with Si-Br, Si-H, and Si-CH₃ groups, respectively. The surface termination influenced the band bending, with the Si 2p_3/2 binding energy affected more by the surface chemistry than by the dopant type. The highest binding energies were measured on Si(111)-Br (whose Fermi level was positioned near the conduction band at the surface), followed by Si(111)-H, followed by Si(111)-CH₃ (whose Fermi level was positioned near mid-gap at the surface). Si(111)-CH₃ surfaces exposed to Br₂(g) yielded the lowest binding energies, with the Fermi level positioned between mid-gap and the valence band. The Fermi level position of Br₂(g)-exposed Si(111)-CH₃ was consistent with the presence of negatively charged bromine-containing ions on such surfaces. The binding energies of all of the species detected on the surface (C, O, Br) shifted with the band bending, illustrating the importance of isolating the effects of band bending when measuring chemical shifts on semiconductor surfaces. The influence of band bending was confirmed by surface photovoltage (SPV) measurements, which showed that the core levels shifted toward their flat-band values upon illumination. Where applicable, the contribution from the X-ray source to the SPV was isolated and quantified. Work functions were measured by ultraviolet photoelectron spectroscopy (UPS), allowing for calculation of the sign and magnitude of the surface dipole in such systems. The values of the surface dipoles were in good agreement with previous measurements as well as with electronegativity considerations. The binding energies of the adventitious carbon signals were affected by band bending as well as by the surface dipole. A model of band bending in which charged surface states are located exterior to the surface dipole is consistent with the XPS and UPS behavior of the chemically functionalized Si(111) surfaces investigated herein.

Microstructure control and iodine doping of bismuth telluride

On the materials scale, thermoelectric efficiency is defined by the dimensionless figure of merit zT. This value is made up of three material components in the form zT = Tα²/ρκ, where α is the Seebeck coefficient, ρ is the electrical resistivity, and κ is the total thermal conductivity. Therefore, in order to improve zT would require the reduction of κ and ρ while increasing α. However due to the inter-relation of the electrical and thermal properties of materials, typical routes to thermoelectric enhancement come in one of two forms. The first is to isolate the electronic properties and increase α without negatively affecting ρ. Techniques like electron filtering, quantum confinement, and density of states distortions have been proposed to enhance the Seebeck coefficient in thermoelectric materials. However, it has been difficult to prove the efficacy of these techniques. More recently efforts to manipulate the band degeneracy in semiconductors has been explored as a means to enhance α.

The other route to thermoelectric enhancement is through minimizing the thermal conductivity, κ. More specifically, thermal conductivity can be broken into two parts, an electronic and lattice term, κ_e and κ_l respectively. From a functional materials standpoint, the reduction in lattice thermal conductivity should have a minimal effect on the electronic properties. Most routes incorporate techniques that focus on the reduction of the lattice thermal conductivity. The components that make up κ_l (κ_l = 1/3Cνl) are the heat capacity (C), phonon group velocity (ν), and phonon mean free path (l). Since the difficulty is extreme in altering the heat capacity and group velocity, the phonon mean free path is most often the source of reduction.

Past routes to decreasing the phonon mean free path has been by alloying and grain size reduction. However, in these techniques the electron mobility is often negatively affected because in alloying any perturbation to the periodic potential can cause additional adverse carrier scattering. Grain size reduction has been another successful route to enhancing zT because of the significant difference in electron and phonon mean free paths. However, grain size reduction is erratic in anisotropic materials due to the orientation dependent transport properties. However, microstructure formation in both equilibrium and nonequilibrium processing routines can be used to effectively reduce the phonon mean free path as a route to enhance the figure of merit.

This work starts with a discussion of several different deliberate microstructure varieties. Control of the morphology and finally structure size and spacing is discussed at length. Since the material example used throughout this thesis is anisotropic a short primer on zone melting is presented as an effective route to growing homogeneous and oriented polycrystalline material. The resulting microstructure formation and control is presented specifically in the case of In₂Te₃-Bi₂Te₃ composites and the transport properties pertinent to thermoelectric materials is presented. Finally, the transport and discussion of iodine doped Bi₂Te₃ is presented as a re-evaluation of the literature data and what is known today.

Band structure and transport properties of simple cubic tellurium-base alloys

The electrical transport properties and lattice spacings of simple cubic Te-Au, Te-Au-Fe, and Te-Au-Mn alloys, prepared by rapid quenching from the liquid state, hove been measured and correlated with a proposed bond structure. The variations of superconducting transition temperature, absolute thermoelectric power, and lattice spacing with Te concentration all showed related anomalies in the binary Te-Au alloys. The unusual behavior of these properties has been interpreted by using nearly free electron theory to predict the effect of the second Brillouin zone boundary on the area of the Fermi surface, and the electronic density of states. The behavior of the superconducting transition temperature and the lattice parameter as Fe and Mn ore added further supports the proposed interpretation as well as providing information on the existence of localized magnetic states in the ternary alloys. In addition, it was found that a very distinct bond structure effect on the transition temperatures of the Te-Au-Fe alloys could be identified.

Band Engineering in Thermoelectric Materials Using Optical, Electronic, and Ab-Initio Computed Properties

Thermoelectric materials have demanded a significant amount of attention for their ability to convert waste heat directly to electricity with no moving parts. A resurgence in thermoelectrics research has led to significant enhancements in the thermoelectric figure of merit, zT, even for materials that were already well studied. This thesis approaches thermoelectric zT optimization by developing a detailed understanding of the electronic structure using a combination of electronic/thermoelectric properties, optical properties, and ab-initio computed electronic band structures. This is accomplished by applying these techniques to three important classes of thermoelectric materials: IV-VI materials (the lead chalcogenides), Half-Heusler’s (XNiSn where X=Zr, Ti, Hf), and CoSb₃ skutterudites.

In the IV-VI materials (PbTe, PbSe, PbS) I present a shifting temperature-dependent optical absorption edge which correlates well to the computed ab-initio molecular dynamics result. Contrary to prior literature that suggests convergence of the primary and secondary bands at 400 K, I suggest a higher convergence temperature of 700, 900, and 1000 K for PbTe, PbSe, and PbS, respectively. This finding can help guide electronic properties modelling by providing a concrete value for the band gap and valence band offset as a function of temperature.

Another important thermoelectric material, ZrNiSn (half-Heusler), is analyzed for both its optical and electronic properties; transport properties indicate a largely different band gap depending on whether the material is doped n-type or p-type. By measuring and reporting the optical band gap value of 0.13 eV, I resolve the discrepancy in the gap calculated from electronic properties (maximum Seebeck and resistivity) by correlating these estimates to the electron-to-hole weighted mobility ratio, A, in narrow gap materials (A is found to be approximately 5.0 in ZrNiSn).

I also show that CoSb₃ contains multiple conduction bands that contribute to the thermoelectric properties. These bands are also observed to shift towards each other with temperature, eventually reaching effective convergence for T>500 K. This implies that the electronic structure in CoSb₃ is critically important (and possibly engineerable) with regards to its high thermoelectric figure of merit.

Design of antenna-coupled lumped-element titanium nitride KIDs for long-wavelength multi-band continuum imaging

Many applications in cosmology and astrophysics at millimeter wavelengths including CMB polarization, studies of galaxy clusters using the Sunyaev-Zeldovich effect (SZE), and studies of star formation at high redshift and in our local universe and our galaxy, require large-format arrays of millimeter-wave detectors. Feedhorn and phased-array antenna architectures for receiving mm-wave light present numerous advantages for control of systematics, for simultaneous coverage of both polarizations and/or multiple spectral bands, and for preserving the coherent nature of the incoming light. This enables the application of many traditional "RF" structures such as hybrids, switches, and lumped-element or microstrip band-defining filters.

Simultaneously, kinetic inductance detectors (KIDs) using high-resistivity materials like titanium nitride are an attractive sensor option for large-format arrays because they are highly multiplexable and because they can have sensitivities reaching the condition of background-limited detection. A KID is a LC resonator. Its inductance includes the geometric inductance and kinetic inductance of the inductor in the superconducting phase. A photon absorbed by the superconductor breaks a Cooper pair into normal-state electrons and perturbs its kinetic inductance, rendering it a detector of light. The responsivity of KID is given by the fractional frequency shift of the LC resonator per unit optical power.

However, coupling these types of optical reception elements to KIDs is a challenge because of the impedance mismatch between the microstrip transmission line exiting these architectures and the high resistivity of titanium nitride. Mitigating direct absorption of light through free space coupling to the inductor of KID is another challenge. We present a detailed titanium nitride KID design that addresses these challenges. The KID inductor is capacitively coupled to the microstrip in such a way as to form a lossy termination without creating an impedance mismatch. A parallel plate capacitor design mitigates direct absorption, uses hydrogenated amorphous silicon, and yields acceptable noise. We show that the optimized design can yield expected sensitivities very close to the fundamental limit for a long wavelength imager (LWCam) that covers six spectral bands from 90 to 400 GHz for SZE studies.

Excess phase (frequency) noise has been observed in KID and is very likely caused by two-level systems (TLS) in dielectric materials. The TLS hypothesis is supported by the measured dependence of the noise on resonator internal power and temperature. However, there is still a lack of a unified microscopic theory which can quantitatively model the properties of the TLS noise. In this thesis we derive the noise power spectral density due to the coupling of TLS with phonon bath based on an existing model and compare the theoretical predictions about power and temperature dependences with experimental data. We discuss the limitation of such a model and propose the direction for future study.

Filtering N.M.R. spectra

Methods of filtering an n.m.r. spectrum which can improve the resolution by as much as a factor of ten are examined. They include linear filters based upon an information theory approach and non-linear filters based upon a statistical approach. The appropriate filter is determined by the nature of the problem. Once programmed on a digital computer they are both simple to use.

These filters are applied to some examples from ¹³C and ¹⁵N n.m.r. spectra.

The oculomotor system: (1) Vertical-horizontal interaction and signal recognition, (2) Time delays and power spectra

In the first section of this thesis, two-dimensional properties of the human eye movement control system were studied. The vertical - horizontal interaction was investigated by using a two-dimensional target motion consisting of a sinusoid in one of the directions vertical or horizontal, and low-pass filtered Gaussian random motion of variable bandwidth (and hence information content) in the orthogonal direction. It was found that the random motion reduced the efficiency of the sinusoidal tracking. However, the sinusoidal tracking was only slightly dependent on the bandwidth of the random motion. Thus the system should be thought of as consisting of two independent channels with a small amount of mutual cross-talk.

These target motions were then rotated to discover whether or not the system is capable of recognizing the two-component nature of the target motion. That is, the sinusoid was presented along an oblique line (neither vertical nor horizontal) with the random motion orthogonal to it. The system did not simply track the vertical and horizontal components of motion, but rotated its frame of reference so that its two tracking channels coincided with the directions of the two target motion components. This recognition occurred even when the two orthogonal motions were both random, but with different bandwidths.

In the second section, time delays, prediction and power spectra were examined. Time delays were calculated in response to various periodic signals, various bandwidths of narrow-band Gaussian random motions and sinusoids. It was demonstrated that prediction occurred only when the target motion was periodic, and only if the harmonic content was such that the signal was sufficiently narrow-band. It appears as if general periodic motions are split into predictive and non-predictive components.

For unpredictable motions, the relationship between the time delay and the average speed of the retinal image was linear. Based on this I proposed a model explaining the time delays for both random and periodic motions. My experiments did not prove that the system is sampled data, or that it is continuous. However, the model can be interpreted as representative of a sample data system whose sample interval is a function of the target motion.

It was shown that increasing the bandwidth of the low-pass filtered Gaussian random motion resulted in an increase of the eye movement bandwidth. Some properties of the eyeball-muscle dynamics and the extraocular muscle "active state tension" were derived.