Mitigation of truncation effects in elongated Shack-Hartmann laser guide star wavefront sensor images.

Laser guide star Shack-Hartmann wavefront sensor images on extremely large telescopes (ELT) will be significantly elongated due to the off-axis projection of the laser relative to the subapertures. The finite number of pixels of the wavefront sensor detector means the most elongated images will be truncated, introducing errors in the centroid measurements. In this paper, we propose appending to the truncated wavefront sensor image the most likely missing tails from a high-resolution nontruncated reference image, which can be calculated from all of the low-resolution images. We show, via numerical simulation, that we can improve the centroid estimate for the most elongated subapertures on an ELT in the presence of read and photon noise.

Laser guide star wavefront sensing for ground-layer adaptive optics on extremely large telescopes.

We propose ground-layer adaptive optics (GLAO) to improve the seeing on the 42 m European Extremely Large Telescope. Shack-Hartmann wavefront sensors (WFSs) with laser guide stars (LGSs) will experience significant spot elongation due to off-axis observation. This spot elongation influences the design of the laser launch location, laser power, WFS detector, and centroiding algorithm for LGS GLAO on an extremely large telescope. We show, using end-to-end numerical simulations, that with a noise-weighted matrix-vector-multiply reconstructor, the performance in terms of 50% ensquared energy (EE) of the side and central launch of the lasers is equivalent, the matched filter and weighted center of gravity centroiding algorithms are the most promising, and approximately 10×10 undersampled pixels are optimal. Significant improvement in the 50% EE can be observed with a few tens of photons/subaperture/frame, and no significant gain is seen by adding more than 200 photons/subaperture/frame. The LGS GLAO is not particularly sensitive to the sodium profile present in the mesosphere nor to a short-timescale (less than 100 s) evolution of the sodium profile. The performance of LGS GLAO is, however, sensitive to the atmospheric turbulence profile.

Optimal reconstruction for closed-loop ground-layer adaptive optics with elongated spots.

The design of the laser-guide-star-based adaptive optics (AO) systems for the Extremely Large Telescopes requires careful study of the issue of elongated spots produced on Shack-Hartmann wavefront sensors. The importance of a correct modeling of the nonuniformity and correlations of the noise induced by this elongation has already been demonstrated for wavefront reconstruction. We report here on the first (to our knowledge) end-to-end simulations of closed-loop ground-layer AO with laser guide stars with such an improved noise model. The results are compared with the level of performance predicted by a classical noise model for the reconstruction. The performance is studied in terms of ensquared energy and confirms that, thanks to the improved noise model, central or side launching of the lasers does not affect the performance with respect to the laser guide stars' flux. These two launching schemes also perform similarly whatever the atmospheric turbulence strength.

Improving the performance of a pyramid wavefront sensor with modal sensitivity compensation.

We describe a solution to increase the performance of a pyramid wavefront sensor (P-WFS) under bad seeing conditions. We show that most of the issues involve a reduced sensitivity that depends on the magnitude of the high frequency atmospheric distortions. We demonstrate in end-to-end closed loop adaptive optics simulations that with a modal sensitivity compensation method a high-order system with a nonmodulated P-WFS is robust in conditions with the Fried parameter r 0 at 0.5 microm in the range of 0.05-0.10 m. We also show that the method makes it possible to use a modal predictive control system to reach a total performance improvement of 0.06-0.45 in Strehl ratio at 1.6 microm. Especially at r 0=0.05 m the gain is dramatic.

Comparison between a model-based and a conventional pyramid sensor reconstructor.

A model of a non-modulated pyramid wavefront sensor (P-WFS) based on Fourier optics has been presented. Linearizations of the model represented as Jacobian matrices are used to improve the P-WFS phase estimates. It has been shown in simulations that a linear approximation of the P-WFS is sufficient in closed-loop adaptive optics. Also a method to compute model-based synthetic P-WFS command matrices is shown, and its performance is compared to the conventional calibration. It was observed that in poor visibility the new calibration is better than the conventional.

Analysis of modes and behavior of a multiconjugate adaptive optics system.

We study the so-called three-dimensional mapping of turbulence, a method solving the cone effect (or focus anisoplanatism) by using multiple laser guide stars (LGSs). This method also permits a widening of the corrected field of view much beyond the isoplanatic field. Multiple deformable mirrors, conjugated to planes at chosen altitudes among the turbulent layers, are used to correct in real time the wave fronts measured from the LGSs. We construct an interaction matrix describing the multiconjugate adaptive optics system and analyze the eigenmodes of the system. We show that the global tilt mode is singular because it cannot be localized in altitude, so that it must be corrected only once at any altitude. Furthermore, when the tilt from the LGS cannot be measured, the singularity of the global tilt yields the delocalization of particular forms of defocus and astigmatism. This imposes the use of a single natural guide star located anywhere in the corrected field to measure these modes. We show as an example that the cone effect can be corrected with a Strehl of 0.8 with four LGSs (tilt ignored) on an 8-m telescope in the visible when a single laser star provides a Strehl of 0.1. The maximum field of view of 100 arc sec in diameter can be reconstructed with an on-axis Strehl ratio of 30%. We also show that the measurement of the height of the layers can be done with current techniques and that additional layers, not accounted for, do not significantly degrade the performance in the configuration that we model.

Adaptive optics with four laser guide stars: correction of the cone effect in large telescopes.

We study the performance of an adaptive optics (AO) system with four laser guide stars (LGSs) and a natural guide star (NGS). The residual cone effect with four LGSs is obtained by a numerical simulation. This method allows the adaptive optics system to be extended toward the visible part of the spectrum without tomographic reconstruction of three-dimensional atmospheric perturbations, resolving the cone effect in the visible. Diffraction-limited images are obtained with 17-arc ms precision in median atmospheric conditions at wavelengths longer than 600 nm. The gain achievable with such a system operated on an existing AO system is studied. For comparison, performance in terms of achievable Strehl ratio is also computed for a reasonable system composed of a 40 x 40 Shack-Hartmann wave-front sensor optimized for the I band. Typical errors of a NGS wave front are computed by use of analytical formulas. With the NGS errors and the cone effect, the Strehl ratio can reach 0.45 at 1.25 microm under good-seeing conditions with the Nasmyth Adaptive Optics System (NAOS; a 14 x 14 subpupil wave-front sensor) at the Very Large Telescope and 0.8 with a 40 x 40 Shack-Hartmann wave-front sensor.