Nonlinear techniques for few-mode wavefront sensors

TL;DR

This paper introduces nonlinear wavefront sensing techniques for few-mode sensors, including model-based and polynomial methods, with demonstrations and applications to sensor analysis and polychromatic extensions.

Contribution

It presents novel nonlinear calibration and modeling approaches for few-mode wavefront sensors, expanding beyond traditional linear methods.

Findings

Nonlinear techniques improve wavefront reconstruction accuracy.

Model-based methods enable direct phase-to-intensity mapping.

Numerical continuation aids in understanding sensor nonlinearity.

Abstract

We present several nonlinear wavefront sensing techniques for few-mode sensors, all of which are empirically calibrated and agnostic to the choice of wavefront sensor. The first class of techniques involves a straightforward extension of the linear phase retrieval scheme to higher order; the resulting Taylor polynomial can then be solved using the method of successive approximations, though we discuss alternate methods such as homotopy continuation. In the second class of techniques, a model of the WFS intensity response is created using radial basis function interpolation. We consider both forward models, which map phase to intensity and can be solved with nonlinear least-squares methods such as the Levenberg-Marquardt algorithm, as well as backwards models which directly map intensity to phase and do not require a solver. We provide demonstrations for both types of techniques in simulation using a quad-cell sensor and a photonic lantern wavefront sensor as examples. Next, we demonstrate how the nonlinearity of an arbitrary sensor may studied using the method of numerical continuation, and apply this technique both to the quad-cell sensor and a photonic lantern sensor. Finally, we briefly consider the extension of nonlinear techniques to polychromatic sensors.