Fluctuations with a power spectral density depending on frequency as $1/f^\alpha$ ($0<\alpha<2$) are found in a wide class of systems. The number of systems exhibiting $1/f$ noise means it has far-reaching practical implications; it also suggests a possibly universal explanation, or at least a set of shared properties. Given this diversity, there are numerous models of $1/f$ noise. In this dissertation, I summarize my research into models based on linking the characteristic times of fluctuations of a quantity to its multiplicity of states. With this condition satisfied, I show that a quantity will undergo $1/f$ fluctuations and exhibit associated properties, such as slow dynamics, divergence of time scales, and ergodicity breaking. I propose that multiplicity-dependent characteristic times come about when a system shares a constant, maximized amount of entropy with a finite bath. This may be the case when systems are imperfectly coupled to their thermal environment and the exchange of conserved quantities is mediated through their local environment. To demonstrate the effects of multiplicity-dependent characteristic times, I present numerical simulations of two models. The first consists of non-interacting spins in $0$-field coupled to an explicit finite bath. This model has the advantage of being degenerate, so that its multiplicity alone determines the dynamics. Fluctuations of the alignment of this model will be compared to voltage fluctuations across a mesoscopic metal-insulator-metal junction. The second model consists of classical, interacting Heisenberg spins with a dynamic constraint that slows fluctuations according to the multiplicity of the system's alignment. Fluctuations in one component of the alignment will be compared to the flux noise in superconducting quantum interference devices (SQUIDs). Finally, I will compare both of these models to each other and some of the most popular models of $1/f$ noise, including those based on a superposition of exponential relaxation processes and those based on power law renewal processes.

Measurements of the response of superconducting nanowire single photon detector (SNSPD) devices to changes in various forms of input power can be used for characterization of the devices and for probing device-level physics. Two niobium nitride (NbN) superconducting nanowires developed for use as SNSPD devices are embedded as the inductive (L) component in resonant inductor/capacitor (LC) circuits coupled to a microwave transmission line. The capacitors are low loss commercial chip capacitors which limit the internal quality factor of the resonators to approximately $Qi = 170$. The resonator quality factor, approximately $Qr = 23$, is dominated by the coupling to the feedline and limits the detection bandwidth to on the order of 1MHz. In our experiments with this first generation device, we measure the response of the SNSPD devices to changes in thermal and optical power in both the time domain and the frequency domain. Additionally, we explore the non-linear response of the devices to an applied bias current. For these nanowires, we find that the band-gap energy is $\Delta_0 \approx 1.1$meV and that the density of states at the Fermi energy is $N_0 \sim 10^{10}$/eV/$\mu$m$^3$.

We present the results of experimentation with a superconducting nanowire that can be operated in two detection modes: i) as a kinetic inductance detector (KID) or ii) as a single photon detector (SPD). When operated as a KID mode in linear mode, the detectors are AC-biased with tones at their resonant frequencies of 45.85 and 91.81MHz. When operated as an SPD in Geiger mode, the resonators are DC biased through cryogenic bias tees and each photon produces a sharp voltage step followed by a ringdown signal at the resonant frequency of the detector. We show that a high AC bias in KID mode is inferior for photon counting experiments compared to operation in a DC-biased SPD mode due to the small fraction of time spent near the critical current with an AC bias. We find a photon count rate of $\Gamma_{KID} = 150~$photons/s/mA in a critically biased KID mode and a photon count rate of $\Gamma_{SPD} = 10^6~$photons/s/mA in SPD mode.

This dissertation additionally presents simulations of a DC-biased, frequency-multiplexed readout of SNSPD devices in Advanced Design System (ADS), LTspice, and Sonnet. A multiplexing factor of 100 is achievable with a total count rate of $>5$MHz. This readout could enable a 10000-pixel array for astronomy or quantum communications. Finally, we present a prototype array design based on lumped element components. An early implementation of the array is presented with 16 pixels in the frequency range of 74.9 to 161MHz. We find good agreement between simulation and experimental data in both the time domain and the frequency domain and present modifications for future versions of the array.

The Milky Way galaxy is a powerful dynamic system that is highly efficient at recycling material. Stars are born out of intergalactic gas and dust, fuse light elements into heavier elements in their cores, then upon stellar death spread material throughout the galaxy, either by diffusion of planetary nebula or by explosive events for high mass stars, and that gas must cool and condense to form stellar nurseries. Though the stellar lifecycle has been studied in detail, relatively little is known about the processes by which hot, diffuse gas ejected by dying stars cools and conglomerates in the interstellar medium (ISM). Much of this mystery arises because only recently have instruments with sufficient spatial and spectral resolution, sensitivity, and bandwidth become available in the terahertz (THz) frequency spectrum where these clouds peak in either thermal or line emission. In this dissertation, I will demonstrate technology advancement of instruments in this frequency regime with new characterization techniques, machining strategies, and scientific models of the spectral behavior of gas species targeted by these instruments.

I begin this work with a description of radiation pattern measurements and their use in astronomical instrument characterization. I will introduce a novel technique to measure complex (phase-sensitive) field patterns using direct detectors. I successfully demonstrate the technique with a single pixel microwave inductance detectors (MKID) experiment. I expand that work by measuring the APEX MKID (A-MKID) focal plane array of 880 pixel detectors centered at 350 GHz. In both chapters I discuss the development of an analysis pipeline to take advantage of all information provided by complex field mapping. I then discuss the design, simulation, fabrication processes, and characterization of a circular-to-rectangular waveguide transformer module integrated into a circularly symmetric feedhorn block. I conclude with a summary of this work and how to advance these technologies for future ISM studies.

The Cosmic Microwave Background (CMB) has provided precise information on the evolution of the Universe and the current cosmological paradigm. The CMB has not yet provided definitive information on the origin and strength of any primordial magnetic fields or how they affect the presence of magnetic fields observed throughout the cosmos. This work outlines an alternative method to investigating and identifying the presence of cosmic magnetic fields. This method searches for Faraday Rotation (FR) and specifically uses polarized CMB photons as back-light. I find that current generation CMB experiments may be not sensitive enough to detect FR but next generation experiments should be able to make highly significant detections. Identifying FR with the CMB will provide information on the component of magnetic fields along the line of sight of observation.

The 21cm emission from the hyperfine splitting of neutral Hydrogen in the early universe is predicted to provide precise information about the formation and evolution of cosmic structure, complementing the wealth of knowledge gained from the CMB.

21cm cosmology is a relatively new field, and precise measurements of the Epoch of Reionization (EoR) have not yet been achieved. In this work I present 2σ upper limits on the power spectrum of 21cm fluctuations (Δ²(k)) probed at the cosmological wave number k from the Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER) 64 element deployment. I find upper limits on Δ²(k) in the range 0.3 < k < 0.6 h/Mpc to be (650 mK)², (450 mK)², (390 mK)², (250 mK)², (280mK)², (250 mK)² at redshifts z = 10.87, 9.93, 8.91, 8.37, 8.13 and 7.48 respectively

Building on the power spectrum analysis, I identify a major limiting factor in detecting the 21cm power spectrum.

This work is concluded by outlining a metric to evaluate the predisposition of redshifted 21cm interferometers to foreground contamination in power spectrum estimation. This will help inform the construction of future arrays and enable high fidelity imaging and

cross-correlation analysis with other high redshift cosmic probes like the CMB and other upcoming all sky surveys. I find future

arrays with uniform (u,v) coverage and small spectral evolution of their response in the (u,v,f) cube can minimize foreground leakage while pursuing 21cm imaging.

This research compares shifts in a SuperSpec titanium nitride (TiN) kinetic inductance detector's (KID's) resonant frequency with accepted models for other KIDs. SuperSpec, which is being developed at the University of Colorado Boulder, is an on-chip spectrometer designed with a multiplexed readout with multiple KIDs that is set up for a broadband transmission of these measurements. It is useful for detecting radiation in the mm and sub mm wavelengths which is significant since absorption and reemission of photons by dust causes radiation from distant objects to reach us in infrared and far-infrared bands. In preparation for testing, our team installed stages designed previously by Paul Abers and his group into our cryostat and designed and installed other parts necessary for the cryostat to be able to test devices on the 250 mK stage. This work included the design and construction of additional parts, a new setup for the wiring in the cryostat, the assembly, testing, and installation of several stainless steel coaxial cables for the measurements through the devices, and other cryogenic and low pressure considerations. The SuperSpec KID was successfully tested on this 250 mK stage thus confirming that the new setup is functional. Our results are in agreement with existing models which suggest that the breaking of cooper pairs in the detector's superconductor which occurs in response to temperature, optical load, and readout power will decrease the resonant frequencies. A negative linear relationship in our results appears, as expected, since the parameters are varied only slightly so that a linear approximation is appropriate. We compared the rate at which the resonant frequency responded to temperature and found it to be close to the expected value.

Optical Communications are at a high point of interest by the space engineering community. After successful projects like the Lunar Laser Communications Demonstration (LLCD), NASA has become interested in augmenting their current Deep Space Network (DSN) with optical communication links. One such link is Deep Space Optical Communications (DSOC) which will be launching with the Psyche mission. To gain a full understanding of the advantages of this network, this thesis will go over the history and benefits of optical communications both on Earth and in space. This thesis will then go in depth on NASAs DSOC project through an algorithmic implementation of the communications channel.

The world of micro-tools and micro-machining is still being explored, and new manufacturing processes and tools are being developed by researchers and industry leaders alike. Many of the performance metrics for ultra-small machining tools (like end mills) are still underdefined or are currently being determined. The objective of this investigation was to determine the performance and durability of the 15 micron (um) diameter micro tool manufactured by the company Performance Micro Tool (PMT). The performance of the tool was measured by the surface roughness that resulted from the micro end mill's tool path. The durability of the tool was measured by the overall linear distance cut by the end mill before complete tool failure. In total, two micro-tools were tested, and the performance and durability results were surprising and significant. The tools surpassed the initial expectations of immediate failure upon contact with the base model. The expectation of failure stemmed from the less than ideal testing conditions for the tools -- a milling machine not capable of ideal cutting parameters and imperfections in the base model manufacturing. In terms of durability, both tools survived the entire defined tool path; over 5,000 times the tool diameter, a comparable metric for industry macro tools. The performance of the end mills was spectacular, both toolpaths had average surface roughness values below 0.05um, which is lower than the industry standard for some of the highest cut quality. Ultimately, the consistent results from both tools encourages a deeper investigation into these micro-tools. The fact that both tools exceeded expectations means that an investigation of many more tools is worth the financial and time investment. A further investigation of a large number of micro-tools could yield a standardized metric for performance and durability for the 15um tools.

Balloon-borne telescopes are an economic alternative to scientists seeking to study light compared to other ground- and space-based alternatives, such as the Keck Observatory and the Hubble Space Telescope. One such balloon-borne telescope is the Balloon-borne Large Aperture Submillimeter Telescope, or simply BLAST. Arizona State University was tasked with assembling one of the primary optics plates for the telescope's next mission. This plate, detailed in the following paragraphs, is designed to detect and capture submillimeter wavelength light. This will help scientists understand the formation and early life of stars. Due to its highly sensitive nature detecting light, the optics plate had to be carefully assembled following a strict assembly and testing procedure. Initially, error tolerances for the mirrors and plate were developed using a computer model, later to be compared to measured values. The engineering decisions made throughout the process pertained to every aspect of the plate, from ensuring the compliance of the engineering drawings to the polishing of the mirrors for testing. The assembly procedure itself was verified at the conclusion using a coordinate measuring machine (CMM) to analyze whether or not the plate was within defined error tolerances mentioned above. This data was further visualized within the document to show that the assembly procedure of the BLAST optics plate was successful. The largest error margins seen were approximately one order of magnitude lower than their tolerated limits, reflecting good engineering judgement and care applied to the manufacturing process. The plate has since been shipped offsite to continue testing and the assembly team is confident it will perform well within expected parameters.

The following paper discusses the validation of the TolTEC optical design along with a progress report regarding the design of the optical mounting system. Solidworks and Zemax were used in conjunction to model the proposed optics designs. The final optical design was selected through extensive CAD modeling and testing within the Large Millimeter Telescope receiver room. The TolTEC optics can be divided into two arrays, one comprised of the warm mirrors and the second, cryogenically-operated cold mirrors. To ensure structural stability and optical performance, the mechanical design of these systems places a heavy emphasis on rigidity. This is done using a variety of design techniques that restrict motion along the necessary degrees of freedom and maximize moment of inertia while minimizing weight. Work will resume on this project in the Fall 2017 semester.

An automated test system was developed to characterize detectors for the Kilopixel Array Pathfinder Project (KAPPa). KAPPa is an astronomy instrument that detects light at terahertz wavelengths using a 16-pixel heterodyne focal plane array. Although primarily designed for the KAPPa receiver, the test system can be used with other instruments to automate tests that might be tedious and time-consuming by hand. Mechanical components of the test setup include an adjustable structure of aluminum t-slot framing that supports a rotating chopper. Driven by a stepper motor, the chopper alternates between blackbodies at room temperature and 77 K. The cold load consists of absorbing material submerged in liquid nitrogen in an open Styrofoam cooler. Scripts written in Matlab and Python control the mechanical system, interface with receiver components, and process data. To calculate the equivalent noise temperature of a receiver, the y-factor method is used. Test system operation was verified by sweeping the local oscillator frequency and power level for two room temperature Schottky diode receivers from Virginia Diodes, Inc. The test system was then integrated with the KAPPa receiver, providing a low cost, simple, adaptable means to measure noise with minimal user intervention.