Assessing phase reconstruction accuracy for different nonlinear curvature wavefront sensor configurations

The nonlinear curvature wavefront sensor (nlCWFS) offers improved sensitivity for adaptive optics (AO) systems compared to existing wavefront sensors, such as the Shack-Hartmann. The nominal nlCWFS design uses a series of imaging planes offset from the pupil along the optical propagation axis as inputs to a numerically-iterative reconstruction algorithm. Research into the nlCWFS has assumed that the device uses four measurement planes configured symmetrically around the optical system pupil. This assumption is not strictly required. In this paper, we perform the first systematic exploration of the location, number, and spatial sampling of measurement planes for the nlCWFS. Our numerical simulations show that the original, symmetric four-plane configuration produces the most consistently accurate results in the shortest time over a broad range of seeing conditions. We find that the inner measurement planes should be situated past the Talbot distance corresponding to a spatial period of $r_0$. The outer planes should be large enough to fully capture field intensity and be situated beyond a distance corresponding to a Fresnel-number-scaled equivalent of $Z\approx50$ km for a $D=0.5$ m pupil with $\lambda=532$ nm. The minimum spatial sampling required for diffraction-limited performance is 4-5 pixels per $r_0$ as defined in the pupil plane. We find that neither three-plane nor five-plane configurations offer significant improvements compared to the original design. These results can impact future implementations of the nlCWFS by informing sensor design.