Instrumental Polarization in Stellar Coronagraphy: Coherent Behavior and its Implications for Dark Hole Optimization

Stellar coronagraphs designed for high-contrast imaging of exoplanets inevitably introduce a small amount of instrumental polarization, called \emph{secondary polarization}. At the contrast levels required to detect and characterize terrestrial planets, these effects may become significant. Instrumentally induced polarization is often referred to as ``incoherent," yet this use of the term lacks rigor. This work uses Jones calculus and vector field simulations, including interactions with dielectric surfaces to show that the secondary polarization is fully coherent with the input field, but it does not interfere with it due to orthogonality. A key consequence of the coherence secondary polarization is that the process of creating a dark hole in the primary polarization tends to also significantly mitigate the intensity corresponding to the secondary polarization, called the \emph{secondary intensity}, in the dark hole region. This reduction of the secondary intensity may lead to relaxed polarization design requirements in future coronagraphs. Additionally, if the contrast is sufficient to make the secondary intensity non-negligible, modulation schemes to separate the planet from the instrumental light need to account for the modulation of the secondary intensity.