Current advancements in telescope and instrumentation technology enable us to observe planets as astrophysical objects across epochs that span Gyr of evolution, from their formation in protoplanetary disks and continued growth in debris disks to their dynamical evolution in exoplanetary systems and ultimate accretion onto white dwarfs. Measurements in each of these eras can be used to inform study in the others. Interferometry affords the highest angular resolution of any observing technique in astronomy, and the use of radio interferometry with instruments such as the Atacama Large Millimeter Array (ALMA) and the Karl G. Jansky Very Large Array (VLA) is markedly advancing the protoplanetary disk field. By further improving our methods to reconstruct high fidelity (in terms of both resolution and sensitivity) images from the interferometric observable, we can not only characterize these disks, but detect the dynamical effects of planets within them. Over a large ensemble of sources, this offers the potential to both progress disk science and connect inferences on the embedded planet population to the study of these objects in later epochs.

This thesis centers on a new imaging framework for radio interferometric observations and its specific application to detect and characterize substructures in protoplanetary disks. Chapter 1 introduces the basics of protoplanetary disk theory and observations, with a focus on the principles of radio interferometry and its application for disk science. Chapter 2 then presents Frankenstein (frank), the open source code we have developed and applied to fit sub-mm observations of disks in order to search for substructure. Chapter 3 applies frank to the high resolution (30 mas) DSHARP mm sample of 20 disks to identify new substructure in these sources and more accurately constrain known disk features. Major results include discovery of more structured inner disks (at separations within 30 au of the host star). In Chapter 4 we apply frank to the moderate resolution (120 mas) Taurus mm survey, finding that compact disks (those with radii <50 au) routinely exhibit substructure. Chapter 5 concludes by summarizing the frank algorithm and our novel scientific results with this tool, then places this evolving imaging approach in the context of future disk science.