Study of centroiding algorithms to optimize Shack-Hartmann WFS in the context of ELTs

Abstract

Along with the expected ELTs comes the diversification of Ada ptive Optics (AO) systems. Most AO are beginning to make extensive use of laser guide stars (LGS), to increase sky coverage and produce a bright beacon in order to reduce wavefront measurement errors and improve performance. However, because of the larger size of the next generation of telescopes, the elonga tion seen in a Shack-Hartmann Wavefront Sensor is larger, i.e up to 7 for a 30m telescope. With such an elongation, both photon and read noise will increase and distribution variations of sodium atoms in the sodium layer start to matter. In this paper, we conduct Shack- Hartmann simulations at the sub-aperture level made with real sodium profiles taken at Lick Observatory. We will compare focus on two methods of centroiders: the matched filt er and the correlation. We then compare results with data taken form a real bench at Uvic in the particular case of NFIRAOS AO system for TMT. The goal is to better understand the impact of such variations on the final e rror budget for the WFS. Enoise includes the CCD noise sources (readout noise and dark current), photon noise and the back- ground noise due to Rayleigh scattering of the projected laser light. ELin is due to non-linearity because of under-sampling and truncation of the LGS spot image. They have also been studied in (3) in the context of Gaussian spot. Esodium is the error due to the structure and time variability in the L GS im- ages due to variability of the sodium layer, Eresp is due to the response coe cient not equal to unity, EDi the error due to the di raction spikes in each SHWFS subaperture, and, Eatm is the error due to the atmosphere considering only speckle. We will not focus on this term in this paper. The main goal of this paper is to study the impact of the sodium variations on the wavefront measurements and compare Esodium to Enoise. The field of view of each subaperture considered in this paper will be large enough to neglect the non-linearity e ects. The geometry used here is the normal cartesian CCD. In this paper, we will only talk about the case of the central launch, leading to symmetric spots, to quantify the impact of the sodium variations on the wavefront error.