Astrometric detection of exoplanets in face-on orbits using vortex filters

We propose a method to detect exoplanets based on their host star's intensity centroid after it passes thru a vortex filter. Based on our calculations with planets in face-on orbits, exoplanets with relative proximity to their host stars and with low mass ratios ($m_p/m_s$) can have discernible signals that can be amplified by the topological charge $\ell$ of the vortex filter. For exoplanets that have higher mass ratios and are far from their host stars, a clear signal can also be obtained but these are not affected by the value of $\ell$ and other planet detection methods may be more suitable. We present a simple table-top optical experiment to support our calculations. Our proposed method adds to the arsenal of techniques for astrometric exoplanet detection.