Zernike mode sorting with vortex Fourier filters

Spatial mode sorting has become a prominent optical processing modality due to its capability of saturating fundamental limits to several sensing tasks, including wavefront sensing, exoplanet detection, and superresolution imaging. Yet despite these potential sensitivity 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). Because most imaging and sensing systems are circularly symmetric, an arguably more prudent strategy is to instead demultiplex modes that are natural to circular optics, namely the Zernike polynomials. To realize this goal, we propose a mode sorting architecture that relies on a cascade of vortex-phase Fourier filters and Mach-Zehnder interferometers. When these filters' vortex charges are appropriately chosen, we show that it is possible to assemble a series of vortex-phase Fourier filters that can isolate the various Zernike modes losslessly and without crosstalk. Our idea is demonstrated via applications to phase estimation and exoplanet imaging, where we propose an optical system that saturates the quantum sensitivity limits to both tasks. We therefore anticipate that this work will be of practical value for the high-contrast imaging of extrasolar planets, enhancing both wavefront control and coronagraph performance.