Centroiding and Extraction of Tip/Tilt Information from Nonlinear Curvature Wavefront Sensor Measurements

TL;DR

This paper investigates methods to directly extract tip/tilt information from nonlinear curvature wavefront sensor images, demonstrating that outer measurement planes provide more accurate data, with potential for real-time adaptive optics correction.

Contribution

It introduces and compares tip/tilt extraction techniques from nlCWFS measurements, highlighting the effectiveness of linear models and the importance of measurement plane selection.

Findings

Outer measurement planes yield more accurate tip/tilt data.

Finite field of view biases tip/tilt retrieval from outer planes.

Linear models can quickly and accurately estimate tip/tilt modes.

Abstract

The nonlinear curvature wavefront sensor (nlCWFS) uses multiple (typically four) out-of-focus images to reconstruct the phase and amplitude of a propagating light beam. Because these images are located between the pupil and focal planes, they contain tip/tilt information. Rather than using a separate sensor to measure image locations, it would be beneficial to extract tip/tilt information directly and routinely as part of the reconstruction process. In the presence of atmospheric turbulence, recovering precise centroid offsets for each out-of-focus image becomes a dynamic process as image structure is altered by changing aberrations. We examine several tip/tilt extraction methods and compare their precision and accuracy using numerical simulations. We find that the nlCWFS outer measurement planes confer more accurate and reliable tip/tilt information than the inner measurement planes, due to their larger geometric lever arm. However, in practice, finite field of view (detector region of interest) effects bias tip/tilt retrieval when using the outer planes due to diffraction. Using knowledge of the $z$-distance to each plane, we find that applying a best-fit linear model to multiple image centroid locations can offer fast and accurate tip/tilt mode retrieval. For the most demanding applications, a non-linear tip/tilt extraction method that self-consistently uses the speckle field may need to be developed.