Rotationally shearing interferometer for exoplanet detection: mathematical derivation, theory, and simulation

This paper presents a comprehensive mathematical derivation and simulation for the application of a rotationally shearing interferometer (RSI) in the detection of exoplanets. The study focuses on the interaction between wavefronts from a distant star and its orbiting planet, exploring the generation and manipulation of interferometric patterns. Key optical elements, such as Dove prisms and Risley prisms, are analyzed for their role in isolating the planet's signal by introducing phase shifts and rotations. A rigorous mathematical model is developed to describe these wavefront interactions, phase modulations, and spatial frequency shifts. The theoretical framework provided serves as the foundation for understanding signal processing within the RSI and facilitating future experimental validation. The simulation results demonstrate the potential of RSI in exoplanet detection by effectively distinguishing planetary signals from stellar noise through precise phase and spatial frequency manipulation.