There exists, in astronomy, many methods and techniques for observing stars. However, many of these observations treat the stars as point sources, infinitesimally small points of light. This is of course not how these objects are in reality, and is merely the limit of how they are seen from Earth. In reality, many if not all of these stars have some manner of spotted surface with ever changing features. We present here a study of these spotted stars, and how to recreate maps of their surfaces, in three unique but ultimately interconnected projects. First, we observe a sampling of Asymptotic Giant Branch (AGB) stars of various spectral types. We image these old, large, and spotted stars with the CHARA array; using the data gathered to determine their angular and physical sizes, thus helping narrow down or confirm masses and other parameters and lay the ground work for images of their surface reconstruction. With light-curve inversion (LI), we present our open source code for integrating the Alternating Direction Method of Multipliers with previous methods and a robust simulator for producing complex light-curves of spotted stars. Results are compared to other reconstructions of real data and match the other findings with great promise. Next, we discuss the Advanced Reconnaissance of Earth-orbiting Satellites (ARES) atmospheric turbulence simulator. Atmosphere effects generated with ARES match the expectations set for a wide range of turbulence, tested for D/r0 between 5 and 80, and sport the capability of simulating non-point source objects. This work endeavors to show the interconnected nature of all these topics as a study of imaging spotted stars.