Abstract: In this dissertation we review the author's work in experimental astrophysics including several cryogenic infrared instruments built at the University of Florida Department of Astronomy, and applications to two science cases. Exploratory science and instrumentation go hand-in-hand. New measurements require new instruments, and new instruments require domain-specific knowledge in order to be effective. Our work focuses on instruments that will revolutionize the science that can be done both in our local Solar neighborhood and at the Galactic Center (GC) using novel instrumentation techniques and tools such as slicers, 3D printers, and bolt-and-go design. These instruments include one-off prototype technology demonstrators, visitor-class, and facility-class instruments for one of the largest telescopes on Earth: the Gran Telescopio Canarias (GTC). The first science case examines the Crab Nebula Pulsar Wind Nebula, in which we attempt to make the first (to date) quantified velocity measurements. Our second science case looks toward the center of the Milky Way Galaxy, and walks through our attempt to build up an astronomical extinction map. At the GC, extinction due to scattering and absorption by dust and gas is severe enough that less than 1 in 10 trillion visible-wavelength photons make it to our telescopes. Even at longer wavelengths in the near-infrared less than 1 in 100 photons propagate through the dust and gas. Our extinction map uses a Bayesian approach and surface brightness photometry using both ground- and space-based observations to estimate both the absolute amount of extinction and the extinction law, which is tied to the physical properties of the dust (such as size and composition). We present extinction maps and de-reddened color-color diagrams of ground-based photometry, useful for target selection for X-Ray binary infrared counterparts and other population studies. We find that there is no variation spatially of the extinction law at the GC. Dissertation Discovery Company and University of Florida are dedicated to making scholarly works more discoverable and accessible throughout the world. This dissertation, "Science-Driven Instrumentation" by Richard Constantine Stelter, was obtained from University of Florida and is being sold with permission from the author. A digital copy of this work may also be found in the university's institutional repository, IR@UF. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation.