Effect of the influence function of deformable mirrors on laser beam shaping.

The continuous membrane stiffness of a deformable mirror propagates the deformation of the actuators beyond their neighbors. When phase-retrieval algorithms are used to determine the desired shape of these mirrors, this cross-coupling-also known as influence function (IF)-is generally disregarded. We study this problem via simulations and bench tests for different target shapes to gain further insight into the phenomenon. Sound modeling of the IF effect is achieved as highlighted by the concurrence between the modeled and experimental results. In addition, we observe that the actuators IF is a key parameter that determines the accuracy of the output light pattern. Finally, it is shown that in some cases it is possible to achieve better shaping by modifying the input irradiance of the phase-retrieval algorithm. The results obtained from this analysis open the door to further improvements in this type of beam-shaping systems.

Beam shaping for laser-based adaptive optics in astronomy.

The availability and performance of laser-based adaptive optics (AO) systems are strongly dependent on the power and quality of the laser beam before being projected to the sky. Frequent and time-consuming alignment procedures are usually required in the laser systems with free-space optics to optimize the beam. Despite these procedures, significant distortions of the laser beam have been observed during the first two years of operation of the Gemini South multi-conjugate adaptive optics system (GeMS). A beam shaping concept with two deformable mirrors is investigated in order to provide automated optimization of the laser quality for astronomical AO. This study aims at demonstrating the correction of quasi-static aberrations of the laser, in both amplitude and phase, testing a prototype of this two-deformable mirror concept on GeMS. The paper presents the results of the preparatory study before the experimental phase. An algorithm to control amplitude and phase correction, based on phase retrieval techniques, is presented with a novel unwrapping method. Its performance is assessed via numerical simulations, using aberrations measured at GeMS as reference. The results predict effective amplitude and phase correction of the laser distortions with about 120 actuators per mirror and a separation of 1.4 m between the mirrors. The spot size is estimated to be reduced by up to 15% thanks to the correction. In terms of AO noise level, this has the same benefit as increasing the photon flux by 40%.

Computational performance comparison of wavefront reconstruction algorithms for the European Extremely Large Telescope on multi-CPU architecture.

The European Southern Observatory (ESO) is studying the next generation giant telescope, called the European Extremely Large Telescope (E-ELT). With a 42 m diameter primary mirror, it is a significant step from currently existing telescopes. Therefore, the E-ELT with its instruments poses new challenges in terms of cost and computational complexity for the control system, including its adaptive optics (AO). Since the conventional matrix-vector multiplication (MVM) method successfully used so far for AO wavefront reconstruction cannot be efficiently scaled to the size of the AO systems on the E-ELT, faster algorithms are needed. Among those recently developed wavefront reconstruction algorithms, three are studied in this paper from the point of view of design, implementation, and absolute speed on three multicore multi-CPU platforms. We focus on a single-conjugate AO system for the E-ELT. The algorithms are the MVM, the Fourier transform reconstructor (FTR), and the fractal iterative method (FRiM). This study enhances the scaling of these algorithms with an increasing number of CPUs involved in the computation. We discuss implementation strategies, depending on various CPU architecture constraints, and we present the first quantitative execution times so far at the E-ELT scale. MVM suffers from a large computational burden, making the current computing platform undersized to reach timings short enough for AO wavefront reconstruction. In our study, the FTR provides currently the fastest reconstruction. FRiM is a recently developed algorithm, and several strategies are investigated and presented here in order to implement it for real-time AO wavefront reconstruction, and to optimize its execution time. The difficulty to parallelize the algorithm in such architecture is enhanced. We also show that FRiM can provide interesting scalability using a sparse matrix approach.

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.

Comparison of minimum-norm maximum likelihood and maximum a posteriori wavefront reconstructions for large adaptive optics systems.

The performances of various estimators for wavefront sensing applications such as adaptive optics (AO) are compared. Analytical expressions for the bias and variance terms in the mean squared error (MSE) are derived for the minimum-norm maximum likelihood (MNML) and the maximum a posteriori (MAP) reconstructors. The MAP estimator is analytically demonstrated to yield an optimal trade-off that reduces the MSE, hence leading to a better Strehl ratio. The implications for AO applications are quantified thanks to simulations on 8-m- and 42-m-class telescopes. We show that the MAP estimator can achieve twice as low MSE as MNML methods do. Large AO systems can thus benefit from the high quality of MAP reconstruction in O(n) operations, thanks to the fast fractal iterative method (FrIM) algorithm (Thiébaut and Tallon, submitted to J. Opt. Soc. Am. A).