Laser guide stars for extremely large telescopes: efficient Shack-Hartmann wavefront sensor design using the weighted centre-of-gravity algorithm

Abstract

Over the last few years increasing consideration has been given to the study of laser guide stars (LGS) for the measurement of the disturbance introduced by the atmosphere in optical and near‐infrared (near‐IR) astronomical observations from the ground. A possible method for the generation of a LGS is the excitation of the sodium layer in the upper atmosphere at approximately 90 km of altitude. Since the sodium layer is approximately 10 km thick, the artificial reference source looks elongated, especially when observed from the edge of a large aperture. The spot elongation strongly limits the performance of the most common wavefront sensors. The centroiding accuracy in a Shack–Hartmann wavefront sensor, for instance, decreases proportionally to the elongation (in a photon noise dominated regime). To compensate for this effect, a straightforward solution is to increase the laser power, i.e. to increase the number of detected photons per subaperture. The scope of the work presented in this paper is twofold: an analysis of the performance of the weighted centre of gravity algorithm for centroiding with elongated spots and the determination of the required number of photons to achieve a certain average wavefront error over the telescope aperture.

Shack-Hartmann tomographic wavefront reconstruction using LGS: analysis of spot elongation and fratricide effect

“…A laser guide star is not only at a finite distance leading to cone effect, but also extended over the whole thickness of the sodium layer. A Shack-Hartmann WFS (SH WFS) looking at a LGS is confronted to spot elongation leading to specific slope noise [1] with possibly anisoplanatism [2,5]. Systems using multiple LGS beams with CW lasers are also affected by fratricide effect.…”

“…In this paper, we explore the interactions between the spot elongation and fratricide effects, with analytical tomographic modal wavefront reconstruction techniques to eventually define a preferred launching scheme. This is a generalization of the noise propagation of the work presented in [1] to a multi-LGS constellation sensed through a multi-layer turbulence profile supplementing the work done in [3]. We envisage the impact of these effects in terms of SH WFS accuracy and related performance on central direction in the scientific field of view (FoV) for MAORY/ATLAS/EAGLE projects [6][7][8].…”

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

“…The threshold value for the normal Thresholding is 10% of the maximum [8] and the threshold for the peak finder in the correlation method is 1% at high SNR and 60% at low SNR. Another useful algorithm not described in this paper is the weighted centroid [9], [3], [10]. The next step is to reconstruct the wavefront using a Fourier Transform reconstructor [11].…”

Advanced Methods for Improving the Efficiency of a Shack Hartmann Wavefront Sensor

“…A single subaperture spot pattern is simulated by convolving the vertical sodium layer density profile (length proportional to the elongation length defined in Eqn. 13 with atmosphere like phase screen (Schreiber et al, 2009). The simulated phase screen includes the effect of the round trip that the laser has undertaken and the phase screens can be easily simulated based on a Fourier technique (Harding et al, 1999).…”

“…The result from the simulation of an elongated spot pattern (no atmosphere) with the launch point matching with the center of the telescope aperture is shown in Fig 6. Another problem along with the non uniform elongation is the temporal variability of the vertical sodium density profile (Davis et al, 2006). Hence, an advanced image processing tool is necessary for accurate detection of the centroid position in the case of LGS based Shack Hartmann sensor (Schreiber et al, 2009;Thomas et al, 2008).…”