# Projected Pupil Plane Pattern (PPPP) with artificial Neural Networks

## TL;DR

This paper demonstrates that using an artificial neural network as a non-linear reconstructor significantly reduces laser power requirements for the Projected Pupil Plane Pattern in adaptive optics, enabling more efficient wavefront sensing.

## Contribution

It introduces a neural network-based non-linear reconstructor that lowers laser power needs for PPPP, improving efficiency over traditional linear methods.

## Key findings

- Neural network reduces laser power requirement from 1000W to 200W.
- Achieves residual wavefront error of 125-160 nm RMS at typical turbulence conditions.
- Enables wavefront sensing with a single beam profile instead of two.

## Abstract

Focus anisoplanatism is a significant measurement error when using one single laser guide star (LGS) in an Adaptive Optics (AO) system, especially for the next generation of extremely large telescopes. An alternative LGS configuration, called Projected Pupil Plane Pattern (PPPP) solves this problem by launching a collimated laser beam across the full pupil of the telescope. If using a linear, modal reconstructor, the high laser power requirement ($\sim1000\,\mbox{W}$) renders PPPP uncompetitive with Laser Tomography AO. This work discusses easing the laser power requirements by using an artificial Neural Network (NN) as a non-linear reconstructor. We find that the non-linear NN reduces the required measurement signal-to-noise ratio (SNR) significantly to reduce PPPP laser power requirements to $\sim200\,\mbox{W}$ for useful residual wavefront error (WFE). At this power level, the WFE becomes 160\,nm root mean square (RMS) and 125\,nm RMS when $r_0=0.098$\,m and $0.171$\,m respectively for turbulence profiles which are representative of conditions at the ESO Paranal observatory. In addition, it is shown that as a non-linear reconstructor, a NN can perform useful wavefront sensing using a beam-profile from one height as the input instead of the two profiles required as a minimum by the linear reconstructor.