Choice of optical transformation for photonic circuit wavefront sensors

Coronagraph designs which use photonic integrated circuits have the highest theoretical throughput for off-axis signals, and therefore the highest potential exoplanet yield for future high-contrast direct imaging campaigns. Using the rejected starlight, the photonic integrated circuit may also provide simultaneous wavefront sensing, allowing for the correction of non-common-path aberrations. This work considers how a photonic circuit should be configured to maximize its sensitivity to phase aberrations. Two cases are considered: in the first, the photonic circuit is coupled directly to an electric field in a piecewise manner, while in the second, the circuit is coupled to the field via an optical mode sorter. In either case, this work constructs a unitary matrix which can be applied by a photonic circuit to produce maximum sensitivity.