Ultraviolet and optical light from stars is reddened and attenuated by interstellar dust, where different sightlines across a galaxy suffer varying amounts of extinction. Tamura et al. (2009) developed an approximate method to correct for dust extinction, dubbed the “βV method,” by comparing the observed to an empirical estimate of the intrinsic flux ratio of visible and ∼3.5 μm emission. Moving beyond that empirical approach, through extensive modeling, I calibrated the βV -method for various filters spanning the visible through near infrared wavelength range, for a wide variety of simple stellar populations (SSP) and composite stellar populations (CSP). Combining Starburst99 and BC03 models, I built spectral energy distributions of SSP and CSP for various realistic star formation histories, while taking metallicity evolution into account. I convolved various 0.44–1.65 μm filter throughput curves with each model spectral energy distribution (SED) to obtain intrinsic flux ratios, βλ,0. To validate the modeling, I analyzed spatially resolved maps for the observed V- and g-band to 3.6 μm flux ratios and the inferred dust-extinction values AV for a sample of 257 nearby galaxies. Flux ratio maps are constructed using point-spread function-matched mosaics of Sloan Digitial Sky Survey g- and r-band images and Spitzer/InfraRed Array Camera 3.6μm mosaics, with all of the pixels contaminated by foreground stars or background objects masked out. Dust-extinction maps for each galaxy were created by applying the βV -method. The typical 1σ scatter in βV around the average, both within a galaxy and in each morphological type bin, is ∼20%. Combined, these result in a ∼0.4 mag scatter in AV. βV becomes insensitive to small-scale variations in stellar populations once resolution elements subtend an area larger than 10 times that of a typical giant molecular cloud. I find noticeably redder V−3.6 μm colors in the center of star-forming galaxies and galaxies with a weak AGN. The derived intrinsic V −3.6 μm colors for each Hubble type are generally consistent with the modeling. Finally, I discuss the applicability of the βV dust-correction method to more distant galaxies, for which large samples of well-matched Hubble Space Telescope rest-frame visible and James Webb Space Telescope rest-frame ∼3.5μm images will become available in the near future.

One of the most fundamental questions in astronomy is how the Universe evolved to become the highly structured system of stars and galaxies that we see today. The answer to this question can be largely uncovered in a relatively unexplored period in the history of the Universe known as the Epoch of Reionization (EoR), where radiation from the first generation of stars and galaxies ionized the neutral hydrogen gas in the intergalactic medium. The reionization process created "bubbles" of ionized regions around radiating sources that perturbed the matter density distribution and influenced the subsequent formation of stars and galaxies. Exactly how and when reionization occurred are currently up for debate. However, by studying this transformative period we hope to unravel the underlying astrophysics that governs the formation and evolution of the first stars and galaxies.

The most promising method to study reionization is 21 cm tomography, which aims to map the 3D distribution of the neutral hydrogen gas using the 21 cm emission lines from the spin-flip transition of neutral hydrogen atoms. Several radio interferometers operating at frequencies below 200 MHz are conducting these experiments, but direct images of the observed fields are limited due to contamination from astrophysical foreground sources and other systematics, forcing current and upcoming analyses to be statistical.

In this dissertation, I studied one-point statistics of the 21 cm brightness temperature intensity fluctuations, focusing on how measurements from observations would be biased by different contaminations and instrumental systematics and how to mitigate them. I develop simulation tools to generate realistic mock 21 cm observations of the Hydrogen Epoch of Reionization Array (HERA), a new interferometer being constructed in the Karoo desert in South Africa, and perform sensitivity analysis of the telescope to one-point statistics using the mock observations. I show that HERA will be able to measure 21 cm one-point statistics with sufficient sensitivity if foreground contaminations can be sufficiently mitigated. In the presence of foreground, I develop a rolling foreground avoidance filter technique and demonstrate that it can be used to obtain noise-limited measurements with HERA. To assess these techniques on real data, I obtain measurements from the legacy data from the first season observation of the Murchison Widefield Array (MWA) and perform additional high-precision radio interferometric simulations for comparison. Through these works, I have developed new statistical tools that are complementary to the power spectrum method that is currently the central focus of the majority of analyses. In addition to confirming power spectrum detections, one-point statistics offer additional information on the distribution of the 21 cm fluctuations, which is directly linked to the astrophysics of structure formation.