Zernike Mode Sorting with Vortex Phase Filters: Perfect Coronagraphs and Ideal Wavefront Sensors

Spatial mode sorting has come to prominence as an optical processing modality capable of saturating fundamental limits to numerous sensing tasks including wavefront sensing, coronagraphy, and superresolution imaging. But despite their promising theoretical advantages, contemporary mode sorters often feature large crosstalk, high loss, or sort modes that are poorly adapted to conventional imaging systems (e.g., Hermite- and Laguerre-Gauss). Here, we introduce an alternative architecture that sorts spatial modes natural to circularly symmetric apertures: Zernike polynomials. Using conventional optics hardware and even-order vortex phase plates, we show how to assemble a series of vortex phase filters that can in principle separate the various Zernike polynomials losslessly and without crosstalk. This idea is demonstrated via application to wavefront sensing and coronagraphy, where we propose an optical system that saturates the quantum sensitivity limits to both tasks. We expect our work to prove useful for high-contrast imaging of extrasolar planets, improving both wavefront control and coronagraph performance.