Astronomical Wavefront Sensing with Partially Coherent Beacons

Abstract

Astronomical adaptive optics (AO) systems and wavefront sensors (WFS) have advanced significantly over the past three decades. However, WFS development has typically focused on coherent or incoherent sources. This work seeks to extend the design and optimization of astronomical WFS to partially spatially coherent sources, such as laser beacons with AO correction, to reduce the beacon size below the limit imposed by atmospheric turbulence. This work develops a theoretical foundation for partially coherent wavefront sensing using Hopkins' formula, leading to a discrete approximation of the Fisher information matrix for a generic class of astronomical WFSs. The derivation provides insight into the degradation in WFS sensitivity due to partial coherence and suggests an approach for mitigating the deleterious effects by limiting interference to include only coherent point pairs in the pupil. The derived numerical approximation also leads to a new technique for simulating partially coherence sources and linear WFSs using the coherent impulse response (CIR) of the WFS and the complex coherence factor of the source, evaluated at the entrance pupil. Because this new simulation approach more directly accounts for the effects of spatial coherence on the detector output, arbitrarily large source sizes can be quickly and accurately modeled. Insights gained by the theoretical work suggest two novel methods for optimizing WFS sensitivity with partially coherent sources: pupil segmentation (PS) and impulse response engineering (IRE). The former method takes the form of a hybrid WFS which pairs pupil subdivision with a high-sensitivity coherent wavefront sensing method to measure the wavefront over each subaperture. The latter method modifies the CIR of the WFS to match the coherence area of the source. Simulation results, using both the new CIR and more traditional Fresnel propagation methods, indicate a significant decrease in the photon-noise gain with each approach. The efficacy of the PS approach is demonstrated using a novel hybrid Shack-Hartmann pyramid WFS setup, while the IRE approach was explored using modifications to a Zernike WFS. The simulation results were further confirmed using a novel software-defined WFS installed on a bench top AO system and used to directly measure the sensitivity of various WFS configurations with an extended beacon simulating a partially coherent source. The bench-level results showed good agreement with the simulation results confirming the validity of the proposed optimization methods for increasing WFS sensitivity with a partially coherent source.