Advancing the State-of-the-Art of Microwave Astronomy: Novel FPGA-Based Firmware Algorithms for the Next Generation of Observational Radio and Sub-millimeter Wave Detection

This dissertation presents a comprehensive study on the advancement of astrophysical radio, microwave, and terahertz instrumentation/simulations with three pivotal components.First, theoretical simulations of high metallicity galaxies are conducted using the supercomputing resources of Purdue University and NASA. These simulations model the evolution of a gaseous cloud akin to a nascent galaxy, incorporating variables such as kinetic energy, mass, radiation fields, magnetic fields, and turbulence. The objective is to scrutinize the spatial distribution of various isotopic elements in galaxies with unusually high metallicities and measure the effects of magnetic fields on their structural distribution. Next, I proceed with an investigation of the technology used for reading out Microwave Kinetic Inductance Detectors (MKIDs) and their dynamic range limitations tied to the current method of FPGA-based readout firmware. In response, I introduce an innovative algorithm that employs PID controllers and phase-locked loops for tracking the natural frequencies of resonator pixels, thereby eliminating the need for costly mid-observation frequency recalibrations which currently hinder the widespread use of MKID arrays. Finally, I unveil the novel Spectroscopic Lock-in Firmware (SpLiF) algorithm designed to address the pernicious low-frequency noise plaguing emergent quantum-limited detection technologies. The SpLiF algorithm harmonizes the mathematical principles of lock-in amplification with the capabilities of a Fast Fourier Transform to protect spectral information from pink noise and other low-frequency noise contributors inherent to most detection systems. The efficacy of the SpLiF algorithm is substantiated through rigorous mathematical formulation, software simulations, firmware simulations, and benchtop lab results.