Efficient, Nonlinear Phase Estimation with the Non-Modulated Pyramid Wavefront Sensor

TL;DR

This paper introduces a nonlinear estimation method using Newton's optimization for non-modulated pyramid wavefront sensors, enhancing wavefront correction accuracy in high-Strehl regimes for astronomical adaptive optics.

Contribution

It proposes a pre-computed optical model and a nonlinear estimation approach that leverages raw pixel data, improving wavefront sensing without real-time beam propagation simulations.

Findings

Nonlinear estimation outperforms linear methods at Strehl ratios above 0.3.

Using raw pixel data from surrounding pixels improves estimation accuracy.

Linear and nonlinear estimators perform similarly at low Strehl ratios due to nonlinearity dominance.

Abstract

The sensitivity of the the pyramid wavefront sensor (PyWFS) has made it a popular choice for astronomical adaptive optics (AAO) systems, and it is at its most sensitive when it is used without modulation of the input beam. In non-modulated mode, the device is highly nonlinear. Hence, all PyWFS implementations on current AAO systems employ modulation to make the device more linear. The upcoming era of 30-m class telescopes and the demand for ultra-precise wavefront control stemming from science objectives that include direct imaging of exoplanets make using the PyWFS without modulation desirable. This article argues that nonlinear estimation based on Newton's method for nonlinear optimization can be useful for mitigating the effects of nonlinearity in the non-modulated PyWFS. The proposed approach requires all optical modeling to be pre-computed, which has the advantage of avoiding real-time simulations of beam propagation. Further, the required real-time calculations are amenable to massively parallel computation. Numerical experiments simulate a currently operational PyWFS. A singular value analysis shows that the common practice of calculating two "slope" images from the four PyWFS pupil images discards critical information and is unsuitable for the non-modulated PyWFS simulated here. Instead, this article advocates estimators that use the raw pixel values not only from the four geometrical images of the pupil, but from surrounding pixels as well. The simulations indicate that nonlinear estimation can be effective when the Strehl ratio of the input beam is greater than 0.3, and the improvement relative to linear estimation tends to increase at larger Strehl ratios. At Strehl ratios less than about 0.5, the performances of both the nonlinear and linear estimators are relatively insensitive to noise, since they are dominated by nonlinearity error.